GREATER THAN OR EQUAL TO?: Debate continues on the merits of teaching equation solving, geometry proofs and other old-school approaches in math education versus reform methods, which stress visual representations and real-world applications.
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Over the past 20 years educators have fought over the best way to teach numbers to kids. Advocates of traditional math tout the practice of algorithms and teacher-centered learning, whereas reform-math proponents focus on underlying concepts and student inquiry. In the face of continued declining scores in the U.S., these so-called math wars have heated up recently with the circulation of petitions, the release of contested curriculum guidelines and, in one case, the filing of a lawsuit. At stake is the ability of American high school graduates to perform everyday math tasks and compete in a global economy.
The war began in 1989, when the National Council of Teachers of Mathematics (NCTM) released a set of standards that reshaped a generation of instruction. Instead of having students memorize formulas and compute problems such as adding fractions, advocates of reform math encouraged students to develop their own visual representations of math concepts and use calculators to solve numerical tasks.
In recent years a détente between the two camps formed, one that emphasized a middle ground. But if there is a truce, it is an uneasy one—new volleys from both sides continue to appear. Last October, for example, the NCTM released yet another document, “Focus in High School Mathematics: Reasoning and Sense Making,” which calls for a new approach revolving around applications. “Our 15-year-olds cannot use math to address simple real-life situations,” explains Gary Martin, a professor of math education at Auburn University and chair of the committee that wrote the document. Martin says that the new guidelines teach students how to “apply mathematical reasoning in a variety of contexts” instead of simply “carrying out procedures in a rote way.” He cited as an example a problem that asks students to compare the relative fuel-efficiency gains in two pairs of vehicles. The answer varies depending on whether one considers relative fuel efficiency or the total number of gallons of gasoline saved.
Although many educators have praised the report, critics say the document’s vague approach to mathematical analysis is reminiscent of the NCTM’s 1989 guidelines. “The sense is that all reasoning students attempt is valuable and should be celebrated,” says Stanford University mathematician Jim Milgram, who prefers a more traditional approach. “The trouble with this approach is that it is exactly status quo; we seem to have a mindset that, ‘Gee, Johnny reasoned’; it doesn’t matter that his actual reasoning is flawed.”
Vern Williams, a math teacher in Falls Church, Va., who has participated in several national math panels, says the high school guidelines downplay the link between reasoning and traditional procedures such as factoring polynomials. “Some of the most elegant math problems are deemed useless because they don’t involve real-world applications,” he says. Williams adds that many courses in geometry, “the one high school class that demands formal reasoning,” have already been “gutted” and are no longer proof-based. Instead students use algebraic tools to analyze geometric shapes, build three-dimensional models, and solve actual construction and design problems.
For his part, Martin says the document was not intended to define specific content; rather it shows how reasoning and sense making can be incorporated throughout the curriculum. But detractors of reform math do not seem to be ready to agree. In one notable example, a group of parents and educators in Seattle have filed a brief appealing the school board’s decision last May to adopt the Discovering Mathematics series, a reform-math high school text that uses student investigations as a means of discovering math principles—such as using toothpick models to derive recursive sequences. Citing declining test scores after a three-year pilot of the text, the suit claims the Discovering series is associated with a widening achievement gap between white students and minority and low-income students.*
*Erratum (2/25/10): The Discovering Mathematics series was not part of a three-year test pilot as mentioned in the story. The text should have read: "Citing declining test scores after a three-year pilot of a similar text, the suit claims that reform math is associated with a widening achievement gap between white and minority low-income students."
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115 Comments
Add CommentIf our students perform so poorly compared to those of other countries, why don't we see how math is taught there? No mention of this in this article or most others on the problems of US education.
Reply | Report Abuse | Link to thisStop arguing. Get unentrenched. Look around the world. See what's working. Do that.
Reply | Report Abuse | Link to thisMath is taught with too many moving parts. Program the basics into calculators and concentrate on fewer problem types. Get kids past lower math and higher math will make it worthwhile.
Reply | Report Abuse | Link to thisSad but true. I was at a fast food drive thru when the computers were down. They had to make change the old fashioned way. But the girl could not figure out how much change to give me. She seemed lost as she tried to calculate the difference between what I gave her and what the food cost. She had to call in the manger, who took way to long to compute the change (eventually she found a hand-held calculator).
Reply | Report Abuse | Link to thisApparently even simple arithmetic is no longer well taught, learned and/or retained. Reliance on machines to "teach math" is only good if one has a machine when it is needed. My daughter had these classes where the calculator was required. The problem was that after smaking the keyboard a few times, she could come up with an obviously non-sensical answer. She would just write it down and move on. I asked her one time how she could multiple two numbers that each were less than one and come up with an answer that was greater than ten. The blank stare said it all (fyi - she failed to enter the decimal points correctly).
Want to terrify a teen-ager? Ask them to multiply 12 times 12. Is the answer immediate or not? Forget adding simple fractions. And we expect these kids to learn algebra and higher mathematics?
Are kids today less proficient even in arithmetic than in the past? Surely we can tell if these newer teaching methods are getting better results or not. As for me, I think my daughter did better in arithmetic in elementry school. After middle and high school, she seems to have "lost" the ability to easily do the arithmetic she learned earlier in life. I blame the calculator.
I think the use of calculators should not be introduced until students MASTER doing it by hand and in their heads. Students should be using calculators until they reach calculus! I've tutored a number of students and I am appalled when a step requires one to multiply 6*3 or add -3+1 and the student reaches for their calculator! I will soon be a math teacher and I will not be having calculators in my class. Just like RDH said, if you don't know what your answer should look like, how do you even know that your calculator is giving you the correct answer. I often mistype a problem into the calculator but I can usually notice a mistake when my answer doesn't make sense. A calculator should be a tool but not a crutch!
Reply | Report Abuse | Link to thisI think the use of calculators should not be introduced until students MASTER doing it by hand and in their heads. Students should be using calculators until they reach calculus! I've tutored a number of students and I am appalled when a step requires one to multiply 6*3 or add -3+1 and the student reaches for their calculator! I will soon be a math teacher and I will not be having calculators in my class. Just like RDH said, if you don't know what your answer should look like, how do you even know that your calculator is giving you the correct answer. I often mistype a problem into the calculator but I can usually notice a mistake when my answer doesn't make sense. A calculator should be a tool but not a crutch!
Reply | Report Abuse | Link to thisi meant to say students SHOULDN'T use calculators until calculus
Reply | Report Abuse | Link to thisI am not good at math. It's most likely because I was not taught the basic facts to apply. Use both ideas. They are both useful in different ways.
Reply | Report Abuse | Link to thisIt is a mistake to downplay or remove the emphasis on mastering basic maths concepts, such as being able to add, subtract, multiple and divide without the use of electronic aids, by trying to redirect attention to learning logic and reasoning. The latter must be based on and supported by the former.
Reply | Report Abuse | Link to thisIncorrect: "Citing declining test scores after a three-year pilot of the text," I know as I submitted much of the data on which Judge Spector found: "based upon a review of the entire administrative record, that there is insufficient evidence for any reasonable Board member to approve the selection of the Discovering series.”
Reply | Report Abuse | Link to thisThe three year inquiry based pilot used a different Key Press product. IMP : Interactive Math Program. This was a school based project at two schools funded by the NSF. These schools got additional resources through the University of Washington, which included lots of professional development for teachers and collaborative planning. Typical of so many NSF reform math based efforts to push the reform math materials (development cost of around $100 million and likely way over that amount implement and push) the results were underwhelming. At Cleveland High School with about a 5% white population the scores of Black students on the 10th grade math WASL test changed for the worse as over 70% of that population scored at the lowest level, level 1, far below basic. In Spring 2009, Limited English students' scores went to zero passing.
It should be noted that the Superintendent, Dr. Maria Goodloe-Johnson, who is on the board of "The Broad" foundation, was pushing IMP for adoption in Spring 2008. For 2009 she pushed and got "Discovering" it has more numbers than IMP.
Oddly "Discovering" believes that in Algebra students can learn to solve two simultaneous equations written in two variables by both substitution and elimination in one lesson with little practice.
The State of Washington's OSPI pushed reform math for at least a decade. Seattle and Bellevue Central Administration both were on the Band wagon .. the teachers not so much .. but true believers in "reform" gained favor.
A factor in the Spector decision were continually widening Math Achievement Gaps over the decade of reform math use. This was not happening in Reading and Writing.
The SPS responded in court that "Discovering" was not an inquiry program but a "Balanced" Program. The Judge noticed that all the texts had "Discovering" in the title and on page four the publisher claimed this was an investigative approach to mathematics. She also noticed that every lesson began with an investigation. Attorney Keith Scully pointed all this out to Judge Spector.
You can find out more at:
http://mathunderground.blogspot.com/
and download documents at
http://seattlemathgroup.blogspot.com/
Donations needed as we are still $7000 in the whole.
I think some of us are missing the point. Using or not a calculator isn't the point. Its being able to construct the model that represent the situation and then how you solve it is almost secondary. Take the AP Calculus exam, half is with and half is without calculator. Kids report back the the half with is always more challenging. If kids just memorize techniques, they'll never success in creating the model. Once the model is in hand, heck, the TI89 or Mathametica can solve it for you.
Reply | Report Abuse | Link to thisLet's see. 80% of classrooms in America use traditional approaches to mathematics and approximately 20% use reform inquiry approaches. But we should believe that ALL of the troubles of America's students should be blamed on reform approaches. Seems like Dempsey needs a math lesson herself.
Reply | Report Abuse | Link to thisI hated arithmetic in grade school and did poorly. I dreaded and the endless rote practice of homework problems until I finally learned to estimate arithmetic answers from my dad, just before high school.
Reply | Report Abuse | Link to thisEstimating helped me developed a sense of proportion, add from the left and think in compliments of 10. I also finally memorized (and pictured) my multiplication tables. That, in turn, helped me do very well in math from algebra through calculus and now lets me calculate on the fly in my head while I read. If I can't estimate it, I don't think I really understand it.
I wonder if estimating skills would provide a bridge between the "Real Math" and "Discovery" camps that would address both side's concerns?
Hermit
Dear DrM,
Reply | Report Abuse | Link to thisYou need a better data source. That 80% - 20% is Not applicable to the situation being discussed.
Not in our state of Washington. At the elementary level over 90% of children were taught using reform materials in 2007. That is being reversed at bit currently as Terry Bergeson lost her re-election bit for a fourth term as SPI. WA state legislature funded new math standards and after Bergeson's extremely high bidder the Dana Center (bid was three times higher than nearest of the other bidders) failed to deliver a satisfactory product, WA legislature turned the job over to Strategic Teaching to get a fairly decent product.
This year several districts are abandoning the old OSPI math direction and following the new WA state math standards and most districts are choosing better instructional materials and making their curriculum the new state math standards.
67% of WA districts were using Connected Math Project at grades 6, 7, 8. For high school Core-Plus was the most popular series.
As stated over 90% reform at elementary school with around 33% TERC/Investigations and 33% Everday Math.
Seattle switched from TERC to EDM in 2007.
To improve a system requires the intelligent application of relevant data . -- W. Edwards Deming
When did you get that 80% - 20% stat? perhaps 1987
Wash. Constitution Article IX:
"It is the paramount duty of the state to make ample provision for the education of all children residing within its borders, without distinction or preference on account of race, color, caste, or sex. "
Many years of TERC produced large math achievement gaps. From large gaps EDM produced rising achievement gaps for all subgroups of educationally disadvantaged learners in its first two years of use.
Seattle and Bellevue have huge problems when Article IX enters a "reform math" adoption proposal.
Dear Hermit,
Reply | Report Abuse | Link to thisThis article presents this as a situation of: "if not reform, then traditional." I am not at all happy with traditional. I used a blend of materials and approaches in my career. I've really liked a lot of things coming out of the Math Learning Center in Oregon. In Seattle and Bellevue we have seen a big thrust for following the EDM pacing guide in Seattle and previously the TERC pacing guide in Bellevue. It seems that Central Admin thinks we are making widgets not realizing the variability in the persons we are teaching.
I would like to see decent textbooks that students can learn from ... with sufficient examples and practice. We need to have an internationally competitive math program. This does not mean a monolithic uniform approach. I've taught on Reservations, in Orchard country, inner city, private high schools, etc. in 17 different locations in 4 states. Teachers need to be given the flexibility to teach students. Currently Seattle has a bloated Central Office that becomes more bloated and autocratic by the year. Research Manual High School in Denver, for an antidote listen to Principal Rob Stein here:
http://www.youtube.com/watch?v=09T2wGF5uHs
Seattle School Board President Michael DeBell makes a lot of sense:
http://www.youtube.com/watch?v=6ywxLqte6lc
I know this has been mentioned, but I can't help thinking that we should just look at what the high-performing nations are doing in their math classes. If those methods are based on systems too different from our own to possibly implement, then we should do the scientific thing and experiment. Get several districts for each of the possible methods, control for variables such as rich versus poor (shouldn't be too hard on a multi-district scale), and just run it for 5 years and see who wins. Implement the most successful program everywhere, and if problems emerge, run another test.
Reply | Report Abuse | Link to thisThanks Linda for giving us a forum for a discussion with global implications even in the next generation. Having taught at all levels and been a life coach for parents with special needs children this debate is a side issue. Studies prove that while our academic confidence soars only the elite know how far behind the"less civilized world" the masses in public schools have become. I taught myself to read before I was 5 years old, and my children have IQ's that seem to be off the charts. My 28 year old son's being 147 and my 5 year old daughter's who I won't test. And in teaching so many others and studying my own, the fundamentals are what have empowered the known world who are then qualified to compete for the next generation of global thought leaders. Thankfully those of us who run our businesses from home, are miles ahead of the public education pack. As more parents exit or never enter their children into these mind camps we'll stand a chance of keeping our edge on the world stage.
Reply | Report Abuse | Link to thisBelieve well!
Adelaide Zindler
http://www.HomeOfficeMommy.com
Coming soon!
Thanks Linda for giving us a forum for a discussion with global implications even in the next generation. Having taught at all levels and been a life coach for parents with special needs children this debate is a side issue. Studies prove that while our academic confidence soars only the elite know how far behind the"less civilized world" the masses in public schools have become. I taught myself to read before I was 5 years old, and my children have IQ's that seem to be off the charts. My 28 year old son's being 147 and my 5 year old daughter's who I won't test. And in teaching so many others and studying my own, the fundamentals are what have empowered the known world who are then qualified to compete for the next generation of global thought leaders. Thankfully those of us who run our businesses from home, are miles ahead of the public education pack. As more parents exit or never enter their children into these mind camps we'll stand a chance of keeping our edge on the world stage.
Reply | Report Abuse | Link to thisBelieve well!
Adelaide Zindler
http://www.HomeOfficeMommy.com
Coming soon!
The math wars are over. Students need both arithmetic skills and a conceptual understanding. In order to get both of these students need to practice math with the US algorithms until they are fluent with the procedure. With this practice teachers can break down th ealgorithm to explain how and why it works. And, then students can apply it to actual problems.
Reply | Report Abuse | Link to thisThe problem with inquiry-based programs is that they are designed to only develop a conceptual understanding. The spiral nature and lack of practice with efficient strategies (such as th eUS algorithm) leaves out the other half of the equation to develop students proficient in math.
Please review the work of the National Math Advisory Panel and the NCTM Focal Points. Even the NCTM realized its 1989 approach was not working and published its Focal Points.
Johny's reasoning is flawed ! How dare you !. Nothing Johny does can be flawed because he is himself ! If he wants to poke his / your eyes out then that is the result of his "reasoning". There can be no such thing as "flawed" or "correct". Maybe he wanted to drive off the road into a tree. Who are we to say ?
Reply | Report Abuse | Link to thisMoney usually gets a pretty consistent "maths" result, it has been observed down tha ages. I heard of a famous mathematician and teacher - Wittgenstein ? - who was sacked from his job teaching maths, for teaching of matters other than money. It was a while back.
I used to wonder what the purpose of the "Abacus" was at school. Maybe this is becoming self-evident. A good one that - "self-evident". Isn't that similar to "Axiomatic". But it's all a bit old-fashioned. We have much better ideas ! And a growth industry - powered by environmental destruction - to sort-out the mess.
Definition of terms ! Just what is "math" supposed to mean.
Reply | Report Abuse | Link to thisI'm a student - never seen any of this - what is it about !!?
I really know that you are totally correct. The "4 functions" stem from "self-evident truth" - and definition. If we cannot see that self-evidence" - the number of beads on an Abacus wire is constant, for example - than we really need special care. I believe that much "teaching technique" serves only to mystify and make mumbo-jumbo "algorithms" of what should be an understandable process. But then I'm just the cleaner.
Reply | Report Abuse | Link to thisNo ammount of "teacher training" will compensate for a clear understanding in the head of the teacher. And if the teacher themself sees Mathematics, as "math" as more mumbo-jumbo, then that is what the kids get imparted to them, and naturally wish to forget a.s.a.p.
Dempsey claims that: " At the elementary level over 90% of children were taught using reform materials in 2007." Where is the proof of this statement? I bet she cannot provide any data to back up such a ridiculous claim.
Reply | Report Abuse | Link to thisMoreover, reform textbooks may believe in inquiry approaches but teachers are the ones that make pedagogical decisions. Most teachers do not subscribe or are trained in inquiry approaches and no matter the textbook they use, most teachers use traditional drill and kill in classrooms especially in high schools. Dempsey's rhetoric is not matched by the reality of what occurs in classrooms.
I absolutely agree that students must master basic math IN THEIR HEAD with NO CALCULATORS. They should be aware of them, how they work, andbe ready to transition them and be comfortable with them, but every child in america needs to know the multiplication table to 12 and do it WITHOUT THOUGHT, INSTANTLY in their heads. No fingers, toes, gimmicks, waiting - just an instant answer hardwired into their brain.
Reply | Report Abuse | Link to thisI am also an elementary teacher, and I LOVE TECHNOLOGY, but these kids have to be able to do basic math on their own.
Also, MATH IS NOT ABOUT EFFORT; math is absolute and universal. There is a write answer, and many wrong ones. Ultra-liberal people who want to reward effort and variety will doom this country.
Dempsey's data is so flawed. Estimates of the market share of NSF-funded textbooks range from 10-20 percent of students and teachers at the secondary level and from 20-30 percent at the elementary level (Education-Market) http://www.educationmarketresearch.com/
Reply | Report Abuse | Link to thisThus I ask again for how can 100% of the America's math troubles be blamed on reformed curricula when, in reality, the overwhelming majority of students use traditional methods? Dempsey needs to do a little more math HW.
DrM:
Reply | Report Abuse | Link to thisI don't have nationwide numbers, but I believe 20-30% is extremely low. I live in Northern Virginia and I know that Fairfax, Prince William, Stafford and Arlington all use Math Investigations or Everyday Math in their counties. Looking up the data from the VA State Dept. of Education, those 4 counties account for 107K of 466K Grades 1-5 children (23%).
I also know that Loudoun (23K) has been slowly expanding its use of Math Investigations and believe VA Beach (27K) uses reform math, but I'm not sure if it's Everyday Math or Math Investigations.
Thus without checking any of the other 100+ school districts in Virginia, 23% definitely use reform math. Another 5% (Loudoun) have some exposure to it and another 6% (VA Beach) likely use it, but I can't find a reference right now.
I would hope that many other parts of the nation bring the numbers down into the 20-30% range, but here in VA, I'd expect 80% is more likely than 20%.
For more background on the math wars, see http://educationnext.org/anamazeingapproachtomath/
Reply | Report Abuse | Link to thisI think if we want to get this resolved, we need to look at what we are trying to achieve. If we want cash register attendants who can add and subtract quickly when the power goes out, then by all means teach memorization of basic math operations. But if we want engineers and scientists, then is would be a waste of time.
Reply | Report Abuse | Link to thisI have had a very successful career in physics and elec engineering, but always had trouble memorizing the times tables. To this day I still have to work it out sometimes rather than remember it. Rote memorization has always been hard for me. But this has not been a problem in my career at all. But what has been continuously helpful is understanding the basics of what addition, subtraction, etc operations are doing. So for the ones headed for technical careers, this is the sort of education we need to be stressing more.
TTLG - what a great post. It is so nice to hear that a person with real experience in physics and EE claims that understanding is so crucial and that rote memorization is not the only key to success in STEM careers.
Reply | Report Abuse | Link to thisOne principal flaw with this article is that the people quoted were primarily professors of mathematics. As a group, professors know their subjects very well, but unfortunately few know much if anything about how educating a mind works.
Reply | Report Abuse | Link to thisSo very true docwright912!
Reply | Report Abuse | Link to thisMathematicians are by far some of the worst teachers in the world. Ask any undergraduate student at any major University and they will confirm that. Mathematicians have no formal education training and have little to no contact nor interest in K-12 schools.
But the traditionalists would argue that anyone can teach especially using direct instruction.
In WA state there is a file that is generally available that lists all of the math programs used at each school district throughout the state. The data is easily available but not reproducible in a short comment except in summary. Fuss all you want, but the data isn't actually debatable. In 2006 when I had access to the data, nearly 100% of Delaware used reform math. It is well known that EDM has over a 20% share of the market all by itself.
Reply | Report Abuse | Link to thisIndeed, for mathematician, read 13th grade teacher, and, yes, they are not qualified to teach 12th grade. However, they know what math students must know when they come to them if they are going to get through the 13th grade. It does not matter if they know "about how educating a mind works" in K-12. K-12 can either produce, or the kids can take remedial math.
Reply | Report Abuse | Link to thisI have great respect for mathemeticians and their knowledge of their field. My comment is that they are not qualified to assess educational stratgies. The issue is far more complex than a direct correlation with the data to which you allude. Remember, university math profs see a very low percentage of the students who graduate from high school. It is not a case of teaching "grade 13". By the way, my PhD is in education.
Reply | Report Abuse | Link to thisAs a mathematician, I don't care how K-12 teachers teach math. What I care about is that students know content when they get to college. 80% of high school graduates go on to college and many of them have to take math (here in MD any student at a state supported college has to take a math course for credit). There are a bit over 2 million freshmen each year and in the fall of 2007 there were 2,228,000 students signed up for math classes in colleges. This is not "a very low percentage". I repeat. K-12 can get them ready for college or they can take remedial math in college. I do not suggest that K-12 teachers listen to college math teachers about how to teach, but they MUST listen to us about what to teach or their students will end up in remedial courses. The "math wars" are not about "how" to teach, they are about "what" to teach. I have reviewed a number of reform math programs and I've only seen one that had the required content, and when I saw it, I said it. The problem, in general, is the missing content.
Reply | Report Abuse | Link to thisIf I were to critique the math education that I was presented with it would be on the basis of it's complete lack of context, both external and internal. It was only much later, when I was presented with the Feynman lectures in algebra did I see the true beauty and elegance of simple algebra.
Reply | Report Abuse | Link to thisWhen I graduated high school for example, I could certainly manipulate complex numbers, knew trigonometry, could factor, graph, divide polynomials, etc. and do it well. But the fundamental concept of number was not there. I always had some suspicion that there were some mysterious cases where complex numbers didn't work, or weren't allowed for example, and that I was learning by example rather than by understanding what I was doing.
And I must add, that I had a particularly good mathematical education.
One lecture by Feynman clarified everything. And for that I salute him.
There is a reason why some of the dumbest people on earth grok algebra. In my opinion their ability to overgeneralize and the rote following of simplistic rules assists them.
From K8 though 13, at the start of the year start with Feynman.
I'm sure there were complex problems that depended on your understanding of many different concepts of math, as well as mastery of specific procedures. Saying that your experience in high school math was the rote following of simplistic rules is at best a mischaracterization and at worst a lie. The fact that you were good at math prepared you for later courses in college. That is the intent and goal of K-12 math. The abstract aspect of algebra that you say Feynman lectured about is, I assume, the axiomatic approach that encompasses groups, rings, and fields. I had that in my junior year in college. It was eye opening, but I certainly didn't feel that my prior experience in high school was a waste of time.
Reply | Report Abuse | Link to thiswsw states that data is readily available but supplies nothing. He/she also claims that data that he cant produce is not debatable. Market research clearly shows that across America no more than 20 to 30% of classrooms use reform programs. This is fact and can be proven at http://www.educationmarketresearch.com/ (they will charge you a fee for the data). I would assume that Dempsey would want the data to prove her case. No matter how much one wants to blame reform math for all of our woes, their numbers do not add up. More than 2/3 of our kids in America learn from traditional programs in traditional classrooms with traditional methods but reform math is to blame? Maybe Dempsey and Garelick could use some remedial math?
Reply | Report Abuse | Link to thisTTLG, as a fellow practicing engineer (EE w/ 10 years in research & a total of 24 years in IT), We are standing at the crossroads in American education where we need two different types of teachers in math, and two diffierent types of math courses _each_year_ through junior high and high school.
Reply | Report Abuse | Link to thisOne course should teach rote methods ("mathematical mechanics i/ii/iii/iv"?) while the other should teach theoretical methods and applications ("mathematical theory i/ii/iii/iv"?). Making the school day 50 minutes longer to accomodate this change would be more than worthwhile. Ensure that both classes are taught at grade level, and that the teachers of both are CAPABLE of teaching the material (as was an issue in my personal experience). Let's lose the labels algebra/geometry/algebra II/trigonometry. They can be used for historical reference, but part of the problem is a lack of flow. When analytic geometry and calculus are taught, there is no separation between algebra and geometry. They are two required foundational fields to build upon to then learn college-level mathematics.
A problem with even "gifted" high school students is that, currently, they are only as good at solving the problems as they are at programming their calculators. They need to understand the theory of WHAT they are being asked to solve, and to be able to correctly set up the problem so that they know WHAT to program into a calculator. The type of calculator should also be "graduated" - non-graphing scientific calculators for students until they graduate high school - basically for trig functions and quick arithmetic.
In college, use of programmable graphing calculators should be mandated. There should be a freshman orientation to the calculators by the math departments or math societies on campus, so that the students can learn the power of the tools, while not having to ask the professor how to use the calculator in class, consuming valuable class time. Furthermore, both colleges and high schools should be using mathematical software to program (or demonstrate, at the grade appropriate) mathematical models, showing real-world applications, as well as examples of problems and their solutions.
EM and DrM,
Reply | Report Abuse | Link to thisInterested in discussion or just attacking?
You need to go to November 2008 and click on curricula adoption and usage at the following link:
http://soundmath.wetpaint.com/page/Washington+Math+History
The rude Dr. M said:
Dempsey's data is so flawed. Estimates of the market share of NSF-funded textbooks range from 10-20 percent of students and teachers at the secondary level and from 20-30 percent at the elementary level (Education-Market) http://www.educationmarketresearch.com/
Thus I ask again for how can 100% of the America's math troubles be blamed on reformed curricula when, in reality, the overwhelming majority of students use traditional methods? Dempsey needs to do a little more math HW.
Seattle, Washington is where the hearing took place.
Read the School District Mathematics Curricula Adoption
and Usage Report to the Legislature November 2008.
I stand by the data I reported.
EM said:
"Moreover, reform textbooks may believe in inquiry approaches but teachers are the ones that make pedagogical decisions. Most teachers do not subscribe or are trained in inquiry approaches and no matter the textbook they use, most teachers use traditional drill and kill in classrooms especially in high schools. Dempsey's rhetoric is not matched by the reality of what occurs in classrooms."
Not in Mike Riley's Bellevue schools with TERC/Investigations, Connected math Project, Core-Plus and the district mandated pacing plan.
========================
Or are you going for that argument that "Reform Math" has just not been properly implemented ... thus we need more NSF grants for professional development?
==================
Ivaylo Ivanov states:
(comment #2)
The high school math curriculum in the Bellevue School District is garbage. A year ago, my parents divorced, and as a result I had to move to a town on the outskirts of Houston. The math curriculum here is just that: math. Actual math that the rest of the world does. Needless to say, I was not prepared to do this type of math, having attended Newport, which is supposedly one of the best high schools in the country.
The school district needs to implement a curriculum that teaches its students math, and not one that provides students with extra opportunities for socializing during these "group investigations" that the students are so used to doing.
Have some Bellevue data here:
http://mathunderground.blogspot.com/2010/02/richard-lesh-phd-has-opinion.html
go here:
http://www.keypress.com/x24956.xml
some of the poorly informed
Dear Dr.M and EM,
Reply | Report Abuse | Link to thisI am a male please use the pronoun him. Note the "Jr."
In regard to "Discovering" series:
I looked at Bethel, WA district, which uses EDM – Connected – Discovering just as Seattle is doing this year. Bethel adopted EDM the same year as Seattle both have used Everyday Math for 2.5 school years. Bethel has used the Discovering Series for 3.5 years. There are shocking similarities in the Discovering results from Bethel that parallel the inadequacies of IMP 2007-2009 at Cleveland over the same three years. Bethel’s level 1 numbers were declining until Discovering was adopted and then began rising. Here are Bethel’s Level 1 absolute numbers for the three years before and then three years after:
Bethel’s Level 1 absolute numbers (far below basic)
2004 : 2005 : 2006 ::-:: 2007 : 2008 : 2009
525 478 361 :-: 470 501 : 555
Cleveland HS w/ IMP Black students at level 1 by %
2005 : 2006 ::-:: 2007 : 2008 : 2009
67.0% : 59.5% ::: 74.6% : 83.4% : 74.7%
To improve a system requires the intelligent application of relevant data. I've been try to get the SPS to do just that for over 3 years. SPS ignorantly adopted "Discovering" on May 6, 2009. When SPS ignores three hundred pages of relevant materials that is ignorance. On May 20th Marty and I gave a 6 minute testimony as a tag team telling them how we had reached an extreme level of frustration and were going to pursue legal action.
Reply | Report Abuse | Link to thisNow we need to pay legal bills.
See the T-Shirt:
http://mathunderground.blogspot.com/2010/02/t-shirt-arbitrary-capricious-in-seattle.html
"Arbitrary and Capricious" in Seattle.
In discussing or attacking? Dempsey is pure attack and has no interest in discussion. Read her blog and you will see nothing but attacks and vicious ones directed at specific people. It is clear that she cannot repudiate the nationwide data that shows only 20 to 30% of students in America use reform programs. While this may be higher in some areas (maybe Washington state and/or Delaware), it is much lower in others (California for one). Thus the question for Dempsey and Garelick remains on the table: How can such smart people like you two blame 100% of America's math troubles on reform approaches that are used in a minority of America's classrooms? I think this case is closed.
Reply | Report Abuse | Link to thisSee Jo Boaler - STANFORD UNIVERSITY MATHEMATICS TEACHING AND LEARNING STUDY: Initial Report – A Comparison of IMP1 and Algebra 1 at Greendale School.
Reply | Report Abuse | Link to thishttp://tinyurl.com/ydch9s5
"As a group, professors know their subjects very well, but unfortunately few know much if anything about how educating a mind works." If we're talking about the actual cognitive science behind math learning, neither do most k12 teacher or most math methods education professors. Egregiously absent from these NSF-funded, so-called "scientifically based" Reform Math programs is actual peer-reviewed research from cognitive science-as discussed, for example, by cognitive scientists like Dan Willingham and Stanislas Dehaene.
Reply | Report Abuse | Link to thisKatharine Beals
http://katharinebeals.com/
"As a group, professors know their subjects very well, but unfortunately few know much if anything about how educating a mind works." If we're talking about the actual cognitive science behind math learning, neither do most k12 teachers, most math methods education professors, and most Reform Math curriculum developers. Egregiously absent from these NSF-funded, so-called "scientifically based" Reform Math programs and pedagogies is actual peer-reviewed research from cognitive science-as discussed, for example, by cognitive scientists like Dan Willingham and Stanislas Dehaene.
Reply | Report Abuse | Link to thisKatharine Beals
http://katharinebeals.com/
DrM,
Reply | Report Abuse | Link to thisPlease read my responses more thoroughly. I am Mr. Dempsey and the pronouns needed are those of the male gender.
(ex: "he" or "him" not "she" or "her").
You state: "How can such smart people like you two blame 100% of America's math troubles on reform approaches that are used in a minority of America's classrooms?"
#1.. Excellent straw-man argument construction but the article and my responses say nothing about blaming 100% of America's problems. I won't be playing on that field at this time.
#2.. Stick with the article and facts at hand. My data sources are perfect for the argument at hand. Let us stick to the trial in Seattle or the Math situation in Washington State as that is where the data is focused that you requested ( really you said did not exist). Now that the data is before you, use it. I've been using it extensively over the last four years trying to understand why Seattle would be opting to continue a decade of failure. That is why McLaren et al. v. Seattle was filed. We want it stopped and we also wish to understand: Why this is continuing.
As usual the answers are multiple. I would be happy to explain about NSF money that has sponsored and continues to sponsor much of what has occurred; but there is so much more.
Let me know if you wish to:
#1.. discuss the trial,
#2.. Seattle's current or former Math Program Managers and relevant data from WA State.
#3.. The data from reform math using districts either those with or without pacing plans.
#4.. or some other Washington State math related issue.
In the meantime others might like to learn something about what underlies this controversy inside the brain (as suggested by others earlier).
I suggest reading:
An Evolutionarily Informed Education Science
by David C. Geary
Department of Psychological Sciences
University of Missouri at Columbia
Columbia, MO
and
"Why minimally guided instruction does not work"
by Kirchner (Netherlands), Clark (USA) and John Sweller, an Australian educational psychologist who is best known for formulating an influential theory of cognitive load.
I am an electrical engineer. It is a fact that most numerical calculations today are done by computers. Even "simple" transactions like withdrawing money from your bank account involve calculating the compound interest since your last deposit/withdrawal - this is so complex that no-one would do it on paper.
Reply | Report Abuse | Link to thisIn my opinion, there are some quite different goals that that have traditionally been fulfilled by mathematics curriculum:
- Rote learning of facts: Sometimes this is necessary in life, but it is much easier if you can see the patterns behind the facts. I would still encourage kids to learn the alphabet (no pattern), and addition/multiplication tables (deep patterns in 0, 1, composite/prime, commutivity, inverses, etc which go to make up the essence of groups & fields at university level)
- The ability to see if an answer is "sensible": Achieved by trying a few problems to get a "feel" for correct answers - this includes change in the supermarket or withdrawing money from an ATM. For young kids this can be done with counters, but the best way to try a wide range of scenarios is with a computer. The best way to quickly visualise a wide range of scenarios is with graphics.
- Ability to understand & follow an algorithm/algorism: This is best done by executing algorithms on a computer. In a specialised high-school class on computer architecture you could study binary arithmetic and the algorithms for binary addition, multiplication and division (which are much simpler than their decimal equivalents); decimal algorithms don't belong in primary school.
- Practice formulating problems in a way they can be solved: Logical thinking to look at what information is present, what is the issue, and how to combine the information at hand to resolve the problem. For numerical problems, this produces a sequence of mathematical steps that compute the solution. This sequence of steps should be able to be written as a "once-off" algorithm in a computer. (Of course, once you have coded the algorithm, you can easily use it to explore, and get a gut feel for similar problems.)
(Continued goals of the maths curriculum...)
Reply | Report Abuse | Link to this- The ability to analyse, find faults and correct problems: Humans are not good at solving problems or executing and coding algorithms (or even pressing buttons on calculators). Humans need a well-developed sense of "oops!" - the ability to check what they have done from several viewpoints, check against "known" results, and retrace their logic to find the fault. This is best done while debugging their own algorithms on a computer. We need to get away from the modern idea that "any idea is a valid idea", while not inhibiting creativity & insight.
- Sorting out the Engineers and Scientists from the History & English majors: I would argue that all of the above skills are required by all groups. The ones who excel at it and enjoy it would go on to be the Scientists & Engineers.
- The ability to get the "exactly right" answer to an arithmetic problem: I would de-emphasise this as a goal. Once you understand algorithms & debugging, you could work it out if you needed to. As an increasing amount of our data is coming in electronic form (eg barcode/RFID tag instead of a human-readable price tag), the ability to keep your supermarket running in a blackout is becoming a distant dream. Keep a calculator handy.
- The ability to predict trends in real life: Humans are good at predicting linear growth, even parabolic functions (catching a ball). However, the real challenges today come from exponential growth (eg Moore's Law & growing consumption despite finite resources) and exponential decline (eg the cost of genome sequencing & fish populations) and the chaotic results these often entail. These exponential functions are too complex for paper-calculation, and yet I believe that intuitive understanding of these concepts is required in primary school. I think the best way to give these ideas is to use computer simulations such as predator/prey relationships (as a graphic game). The reason they like linear algebra in university - it's good at solving the simple problems, but somewhat limited in real-life situations.
THE MATH MYTH
Reply | Report Abuse | Link to thisThe math myth is the myth that the future of the American economy is dependent upon the masses having higher mathematics skills. This myth goes back to at least Sputnik, when the Russians were going to surpass us because they were better in math and science. It returned in the late 80's when the Germans and Japanese were going to surpass us because they were better in math and science. It's occurring again now because the Indians and Chinese are better than us in math and science. I find it difficult to find anyone who uses more than Excel and eighth grade level mathematics. In the summer of 2007 I taught an advanced geometry course and had two students in the class who had been engineers and one who had been an actuary. They claimed never to have used anything beyond Excel and eighth grade level mathematics; never a trig function or even a log or exponential function! I have since confirmed that most engineers and actuaries don't use anything more than Excel and eighth grade level mathematics. There is in fact a deskilling going on in our economy, where even the ability to make change is about to disappear as an important skill.
Vivek Wadhwa has described how there's no shortage of scientists and engineers ( see:
http://www.businessweek.com/print/smallbiz/content/oct2007/sb20071025_827398.htm
I've been concerned with what skills those who are working as scientists and engineers actually use. I find that the vast majority of scientists, engineers and actuaries only use Excel and eighth grade level mathematics. This suggests that most jobs that currently require advanced technical degrees are using that requirement simply as a filter. In particular, I'm working on documenting the following:
Math Myth Conjecture: If one restricts one's attention to the hardest cases, namely, graduates of top engineering schools such as MIT, RPI, Cal. Tech., Georgia Tech., etc., then the percent of such individuals holding engineering as opposed to management, financial or other positions, and using more than Excel and eighth grade level mathematics (arithmetic, a little bit of algebra, statistics, and programming) is less than 25% and possibly less than 10%.
This is a conjecture that desperately needs resolving with solid statistics and in-depth interviews. If it holds up, the educational implications should be revolutionary.
While we are suggesting reading, I suggest you read Jo Boaler's What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject at http://tinyurl.com/ykyd648 (Just $11 in paperback).
Reply | Report Abuse | Link to thisDr. Boaler won an award from the Marie Curie foundation, giving her the post of Marie Curie professor, a the University of Sussex, England. She has also held a faculty position at Stanford where you suffered from personal attacks from Milgram.
I await the data from Washington state (please post anywhere you please) clearly displaying the percentage of districts (or students) taught by reformed texts. I have yet to see you post it clearly and transparently. The national data cannot be disputed (20 to 30% market share for reform texts).
While we are suggesting reading, I suggest you read Jo Boaler's What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject at http://tinyurl.com/ykyd648 (Just $11 in paperback).
Reply | Report Abuse | Link to thisDr. Boaler won an award from the Marie Curie foundation, giving her the post of Marie Curie professor, a the University of Sussex, England. She has also held a faculty position at Stanford where you suffered from personal attacks from Milgram.
I await the data from Washington state (please post anywhere you please) clearly displaying the percentage of districts (or students) taught by reformed texts. I have yet to see you post it clearly and transparently. The national data cannot be disputed (20 to 30% market share for reform texts).
Geez, this is getting boring. I poked around on my computer until I found the file and put it on my website at:
Reply | Report Abuse | Link to thishttp://www.math.jhu.edu/~wsw/ED/PSESDDistrictMathMaterialsFINAL.xls. Okay, now it is your turn. Please produce the data you have, and don't tell us that it will cost us money to see it. That wouldn't be fair. This is a breakdown of all the school districts in WA and what math program they use.
Evan_S, you make reasonable assumptions, but lack awareness of what is going on in education today. I'm looking at all the states' K-12 math standards and it is rare for them to suggest memorizing the single digit number facts (something you suggest should still be done) or teach the standard algorithms for arithmetic. In fact, the elementary math program with the biggest market share in the country, EDM, does not do the standard algorithm for multiplication, for example. Where is the background in algorithms you want, if they won't even teach the "starter" algorithms in elementary school?
Reply | Report Abuse | Link to thisAs long as you want folks to read Boaler, they should also read an analysis of one of her major works:
Reply | Report Abuse | Link to thishttp://www.math.jhu.edu/~wsw/ED/boaler.pdf
I've posted the WA state data and look forward to you posting the national data. I've wanted to see it for a long time, but not been willing to cough up the money. You apparently have done so since you claim "the national data cannot be disputed." This is certainly true if you don't produce.
Dr Wilson - I presume?
Reply | Report Abuse | Link to thisWow - didn't realize such an esteemed mathematician was posting here. Great respect for you. Some call you the most dangerous math professor in America (and that's a compliment). I will post the national numbers for you as soon as I find a way to legally do it. I doubt you will trust this, but here are the numbers for grades 3-5 nationally.
Everyday Math 15.5% share
Scott Foresman 15.1% share
Houghton Mifflin 11% share
Saxon 8.7% share
All others 49.7 % (you can only draw the conclusion that no other texts has a large enough share to be noted).
I realize you have no reason to trust this data. I will work on getting it to you through an intermediary.
As for your Washington data, it needs to be analyzed further. A quick analysis shows CMP in high school in many places. We both know that doesn't make sense as CMP is grades 6-8. Can you explain that? I also see limited use of HS reform texts such as IMP and Core.
Most interesting national data. Only a little surprising. A few years back we had it on good authority that Everyday Math was at 20%, but they might have just been bragging. I'm surprised that TERC Investigations didn't make the cut, but they seem to crash and burn with the same frequency they are taken on and that must keep their numbers lower than expected since they seem to be everywhere. Please let me know when/if you analyze the WA data. It is interesting but suffers from little things like the one you pointed out: CMP is not a high school program, what are they really using? Is the national data you are quoting the most recent? I will wear your quote (danger!) with pride. Thanks for the data.
Reply | Report Abuse | Link to thisBridges 21,264 2.1%
Reply | Report Abuse | Link to thisCMP/Prentice Hall 210,867 20.7%
EM 187,417 18.4%
Growing 47,065 4.6%
Harcourt 8,475 0.8%
Houghton Mifflin 9,970 1.0%
Investigations 291,941 28.7%
Saxon 4,027 0.4%
SF/AW 48,305 4.7%
SRA 2,431 0.2%
Trailblazers 93,656 9.2%
Other/Blank 92,359 9.1%
Total 1,017,777 100.0%
From the elementary textbook data you provided, there are several interesting findings:
Everyday Math has 18% market share which is right about the national average.
Investigations has nearly 29% which is way above the national average. Why does Investigations have such a strong presence in Washington State? Are districts using Investigations as their only source or are they using it in conjunction with SF/AW (as the publisher is pushing a joint usage plan).
EM, Invest, & Trailblazers equal approximately 56% of the market in Washington. This is a heavy reformed presence.
But the data has validity questions as 21% of the data states that CMP/Prentice Hall is used in the elementary grades and this obviously is false.
Will analyze the middle and high school data later but a quick glance show a significant decline in the reformed texts especially in high school.
Dr. M,
Reply | Report Abuse | Link to thisThanks so much, I was wondering why the WWC picked TERC/Investigations over Everyday. In the current longitudinal study of TERC, SF-AW, Saxon, Math Expressions.
Interesting that TERC/Investigations is the market leader by a long way in this group of Four and is currently in 4th place out of 4 after grade 1 results were tabulated.
In answer to the request for data from Seattle here it is:
Reply | Report Abuse | Link to thishttp://soundmath.wetpaint.com/page/Results
Hopefully everyone as in all now has a clear picture as to why the Seattle Math Group went to court.
Donate $$$$ here:
http://seattlemathgroup.blogspot.com/
Heads up for a T-Shirt here:
http://mathunderground.blogspot.com/2010/02/t-shirt-arbitrary-capricious-in-seattle.html
These results are based on data supplied by Dr. Wilson, who is one of the most respected mathematicians in the country. Even so at least 20% of the data is not valid (list CMP as an elementary text) and another 10% of the data has no textbook at all listed. Drawing conclusions with such data is unsound at best. Moreover, the data is only from Washington state and does NOT reflect the national averages which I posted previously. Investigations does not even make a showing in the national data as their market share is so small.
Reply | Report Abuse | Link to thisDr. M,
Reply | Report Abuse | Link to thisThanks for setting me straight that TERC/Investigations is only a blip nationally. Our Former SPI Dr. Bergeson and the UW probably led WA into TERC as it was judged among the most aligned with the State WASL test by OSPI.
Next question for you. In the current ongoing longitudinal study at the WWC why is TERC in there instead of EDM. It was some kind of competitive selection process did Everyday not want to play?
Keep in mind that the data for WA is not "my" data, but it comes from OSPI, the super's office. I just passed the file on. The uneven distribution of math programs is easy to believe. MD has a bunch of counties, as does Virginia, that use TERC Investigations. Neighbors talk to each other. TERC Investigations could have a 7 or 8% market share and not show up on the national data given here since that is smaller than the smallest individual program listed. 7% market share equals more money than I can even imagine.
Reply | Report Abuse | Link to thisI have been impressed with the work of Seymour Papert et al on programming for young children. Teaching kids to control a drawing robot ("turtle") introduces a kinesthetic component to learning, and introduces the robotic world of the future.
Reply | Report Abuse | Link to thisCreating algorithms for squares, triangles, houses, circles, birds and towns is a powerful introduction to the idea of building on what you have already done, not throwing it out and starting again. The turtle graphics translates well to graphics on a screen.
I would get kids to generate their own multiplication tables (and compare to the teacher's one). Finding the numbers that are "missing" introduces primes; I would use the Sieve of Eratosthenes as a numerical algorithm.
I would introduce cellular automata, as these createinteresting patterns, and leads into some basic real- world simulations like predator/prey dynamics.
[...by the way, as mentioned by others, I also do most of my engineering programming in EXCEL, because it is good at manipulating data (translating it, applying algorithms), finding patterns (analysing, exploring) and presenting graphs of the results (a picture is worth a thousand words). To achieve these results I do apply findings from university-level physics, algebra, statistics, as well as simulating aspects of the real world when it gets too complex for analytic techniques. I also sometimes use the built-in programming language...]
While this article is well-written and provides various viewpoints, it contains an important error regarding the Seattle case:
Reply | Report Abuse | Link to thisThe three-year pilot referred to in the article did NOT include any materials from the Discovering Mathematics textbook series. The plaintiffs relied on data from other curricula to make their claims, not on any data regarding Discovering Mathematics.
In addition, Discovering Mathematics had not been used in the Seattle School District when the lawsuit was filed. The plaintiffs reacted to the choice of materials and not the results from the high-school classrooms.
Seattle’s textbook selection process chose Discovering Mathematics after exhaustive review by administrators, educators, curriculum and instruction department staff, parents, school board members, and mathematicians.
The Discovering Mathematics curriculum incorporates multiple teaching methods. You get the best of both worlds by learning not just “how” to do something, but also “why” you’re doing it.
The program is comprehensive with extensive resources for not only the classroom but also for parents and students to practice from home.
The Discovering Mathematics series teaches high school Algebra, Advanced Algebra, and Geometry. It is currently in use in all 50 states. Books from the Discovering Series are used abroad by the U.S. Department of Defense for its high schools, as well as by the schools in the US Virgin Islands, American International Schools, and have been translated for schools in Asia.
Thank you for allowing me to set the record straight. For more facts, please go to http://www.keypress.com/seattle.
Karen Coe
President & CEO, Key Curriculum Press
Publisher of Discovering Mathematics
There is a lot of misunderstand of the research referred to as the Achievement Effects of Four Early Elementary School Math Curricula which includes TERC, Math Expressions, Saxon, and SF/AW.
Reply | Report Abuse | Link to thisFirst and foremost, a competitive process was used to select four curricula.
The process for selecting the curricula began with the study team inviting developers and publishers of early elementary school math curricula to submit a proposal to include their curricula in the evaluation.
A panel of outside experts in math and math instruction then reviewed the submissions and recommended to IES curricula suitable for the study. The goal of the review process was to identify widely used curricula that draw on different instructional approaches and that hold promise for improving student math achievement.
I do not know who the outside experts were (maybe Dr. Wilson does?). And I do not know if Everyday Math applied to be part of the study (but I assume they did).
I hope when quoting the research, the background as stated above is included.
Constructivism, the ideology that one commits to memory better when one discovers a concept himself, is an ideology that permeates all schools of ed. Noone can argue that such learning does result in memory, but, surely, it is not the only way students learn. In fact, for grade school students a great deal of foundational landscape must be taught for students to acquire the skills to discover. And, much research casts great doubt on the merit of inquiry-based learning.
Reply | Report Abuse | Link to thisEd schools prey on students destined to become teachers. They indoctrinate these students into believing that inquiry-based learning is the key to education.
Rather than pointing the finger at textbook market shares, afterall these companies are just following the education dollars, and the indoctrinated teachers, the focus needs to be placed on schools of education and their myopic philosophies.
It's simple, I don't recall "math wars" when we were all learning math the traditional way. We learned our math facts. Now that fuzzy math has de-emphasized math facts, parents are outraged.
Reply | Report Abuse | Link to thisI've tutored students in math. Fuzzy math is a disaster. Yes, the gifted can handle it, but this is no way a child should learn math. They end up hating it and feeling stupid. We purposely avoided fuzzy math schools !
Fuzzy math is a disaster. I don't recall math wars when I was a kid learning math the traditional way. Now that we have fuzzy math where kids aren't required to master basic math facts, we have math wars.
Reply | Report Abuse | Link to thisWe purposely avoided fuzzy math schools. After tutoring kids in math, I could see it was a disaster. They hate math and think they're dumb.
Between the ages of 11 and 13, my mathematical ability (Elementary Maths in this case) was average at best. When I was 14, I chose to do primarily science subjects and added Additional Maths (comprising Calculus and Applied Maths basics) to my schedule. To my surprise, I found myself scoring very high marks in Additional Maths assignments, class tests and end-of-term exams, compared to average marks in Elementary Maths (Algebra, Trigonometry, Geometry etc.) My Add Maths and Elem Maths teachers were actually husband and wife.
Reply | Report Abuse | Link to thisMy decision to apply the learning processes proposed by my Add Maths teacher to my Elem Maths studies was a hit. I just went from being average to very good in Elem Maths almost overnight.
It demonstrates how teaching methods (and they differ a lot) determine a person's level of understanding of a given subject. A solution would be to adopt universally perfect teaching methods. However, we don't live in a perfect world.
I don't need to read the whole article to realize there are maddening, well-intentioned idiots that haven't done any research to support their premises.
Reply | Report Abuse | Link to thisI grew up in the 60s and 70s with the "new math". Sometime in college, I remember learning about base arithmetic in 7th grade. Why was I taught something completely useless that I forgot until I got to college and was completely retaught?
Enough with the warm, fuzzy teaching methods. Teach the students the formulas they need and how to use them. Teach them the theoretical underpinnings afterward, when they can appreciate them.
A lay person can be forgiven for using the "I saw this clerk who couldn't subtract" argument aganst newer ways of teaching math. For an educated person to do so is either sad or reprehensible.
Reply | Report Abuse | Link to thisSeiing that someone can't subtract is easy. But few of us can spot an inability to solve real problems Few spot blind following of formulas when the answer obtained is absurd. One of my teachers fifty years ago had to deal with students on tests coming up with probabilities that were greater than one.
Using the can't subtract argument against reform teaching mehtods is like arguing that small insects only come out in daytime because we don't see them at night.
Hermit,
Reply | Report Abuse | Link to thisI was a teacher in high school math classrooms for 17 years and I agree with you that estimation doesn't get the attention that it should. A first step would be to teach elementary school teachers how to estimate. They really don't know.
Gustafson
How critical is it that a typical American know how to use algebra? I'll argue that only one in ten need to. That said, I believe that nine in ten need to know the basic operations for positive rational numbers, and when and how to use them, including elementary probability theory.
Reply | Report Abuse | Link to thisAs a retired high school math teacher, we don't do that very well. We don't because of one-size-fits-all education. Special education recognizes that, but we need to find ways to individualize education for general education students. Gifted students can learn rational number arithmetic by age eleven, but children grow up differently. Our current system seems to humiliate children who aren't gifted and they give up.
We need to make various alternatives available, and put parents, rather than school administrators, in charge of a child's education.
Gustafson
This already proves what we already knew. Fat = stupid, since the US has the most fat people it makes sense they have poor performance in school.
Reply | Report Abuse | Link to thisExercise doesn't only train the body it also keeps the mind in shape.
It is amazing that Scientific American would not do fact-checking on their Seattle reference. The fact is that until the new adoption, the Discovering Math series has never been used in Seattle and was never piloted in Seattle. However it is used successfully and without incident in a number of surrounding districts. Mass tries to blur the facts and give the impression that the Discovering series has been used in Seattle, but this is just not factual. The lawsuit was full of bogus facts and linkages like this. Bad science. Bad law.
Reply | Report Abuse | Link to thisWhenever you took math, there were plenty of studies (e.g. A Nation at Risk) saying math in the US was in trouble because our students were such low achievers, especially in the 80s when Back to Basics was in vogue, but really since the 50s with Sputnik. And those math students from the 80s are now parents. Hmm.
Reply | Report Abuse | Link to thisDear Dr.M,
Reply | Report Abuse | Link to thisI was thinking since Everyday Math is one of the most widely used elementary math instructional materials in America that odds were they did not apply. It sure would be nice to know if they did submit why they were not taken.
EDM has been less than spectacular in Seattle over its 2.5 years.
My Response to President and CEO Karen COE
Reply | Report Abuse | Link to thiscan be found in the Bethel School District 18,000 students
and using "Discovering" for three years. Located 50 miles from Seattle. There are a number of things that Ms. Coe is mistaken about in her response to set things straight. I hope the following link will clarify a few of the points that need clarification in President Coe's comment.
http://mathunderground.blogspot.com/2010/02/big-response-to-key-press.html
Kleinbottle,
Reply | Report Abuse | Link to thisYou said: "The lawsuit was full of bogus facts and linkages like this."
The press did a poor job of reporting. Please name one fact on which the lawsuit was based that you consider bogus. Perhaps you can name several since is was full of bogus facts.
Please tell me which document you are referring to when you cite these bogus facts.
It was most clear at trial that the use of an NSF supported "inquiry" math program which produced a WASL math pass rate of 0 for Limited English Students. There was no reference to "Discovering" as being the text. In fact when Judge Spector asked the SPS attorney if the board was aware that Limited English Speaking Students has seen sharp declines in pass rates with the use of inquiry math, her response included that the program in question was not Discovering and that Discovering is not an inquiry program. It is a balanced program. Plaintiffs attorney Keith Scully responded that on page 4 of each book could be found the publishers statement that this was an investigative approach to mathematics. He then went on to demonstrate that lesson after lesson always began with an investigation.
Check the two .pdf files below for what happened at Bethel.
file #1 of 3 pages
http://www.box.net/shared/d1bos1fnep
file #2 of 8 pages
http://www.box.net/shared/r3x41z4tih
I await your next bogus facts.
Would you like to support us by getting a T-Shirt?
http://mathunderground.blogspot.com/2010/02/t-shirt-arbitrary-capricious-in-seattle.html
Thanks for your interest in the case,
Dan
#6. Minimally guided instruction failed to produce improvement in the expensive PD3 school-based three-year projects at Cleveland and Garfield as measured by grade 10 WASL test data. In addition each school had the Base Rate of Limited English Speaking Students drop to 0% at Garfield in 2008 and 0% at Cleveland in 2009. In addition the percent of the Black Student population at Clevelnad testing at level 1 far below standard (the lowest WASL rating) rose to above 70% of the population. Garfield is the Academic AP magnet school for Seattle and its results were less shocking than Cleveland’s results.
Reply | Report Abuse | Link to this#7. In speaking with the curriculum director at the 2,000 student South Whidbey School District, which is mentioned on your Seattle web-page and which began using “Discovering” in SY 2009-2010, I learned the following: (a) South Whidbey went whole hog reform as OSPI pushed it: Trailblazers, Connected Math Project, and Core-Plus. (b)Although WASL pass rates were good for High School it was apparent that far too many students were unprepared for collegiate level mathematics. (c) A change was definitely needed. (d) In looking at the available H.S. texts and keeping in mind that students were coming from the current k-8 program it was felt that going to Holt or Prentice-Hall would be difficult and “Discovering” was selected. (e) At k-8 SWSD has now moved away from reform by adopting books with increased explicit instruction at the k-8 level.
#8. KCP has this on the Seattle web-page: “Discovering Mathematics was chosen in Seattle because the School Board could see the potential to serve a diverse student population and improve mathematical achievement across the district.” That statement is pure fiction. There is nothing to that effect in evidence. It is particularly apparent that the Seattle School District’s thrust for minimally guided instruction has served educationally disadvantaged learners poorly. Specifically, which directors saw this “potential to serve” and how did they see it? You seem to be reporting on the statements of staff opinion not the school board members. The school board president in an extended explanation voiced the exact opposite view of the one you present in explaining his view of the “Discovering” materials on 4-22-2009. Take a You Tube look at Director DeBell here:
http://www.youtube.com/watch?v=6ywxLqte6lc
If your intent is to set the record straight please do so with evidence not "Hearsay".
Education is an immature profession because far too many decisions are not based on evidence.
Dear KCP President Karen Coe,
Reply | Report Abuse | Link to thisIn response to your attempt to set things straight in a comment on a Scientific American article posted:
Karen Coe at 06:10 PM on 02/22/10, several things are not set straight. I would encourage you to investigate the following:
#1. The selected committee members were blind scored on a five-question application and rubric.
This application was extremely slanted toward inquiry-based learning. Thus most of the adopting committee members selected were prone to select “inquiry” type materials. This is in the court records.
#2. At no time was it stated that “Discovering” was used previously in Seattle Schools. The product that was used at Cleveland and Garfield high schools that performed poorly, in spite of a major input of NSF resources and UW guidance unavailable to other schools, was a different Key Curriculum Press product “IMP”.
#3. In your list of “Discovering” using districts you neglected to list the Bethel School District, which has used “Discovering longer than most school districts listed (three-years), which is larger than many listed districts (18,000 students).
WASL Math Performance for Black students dropped below the state average for Black students for the first time in Years.
Performance for Hispanic Students dropped precipitously.
Watch the scores of 6 subgroup of students decline on the graphs here:
http://www.box.net/shared/r3x41z4tih
#4. You made the statement that the objection to “Discovering” was not based upon classroom use. This is incorrect it was based upon results from the classroom and in addition to classroom empirical data my experience of teaching two Discovering Algebra classes for one school year.
#5. The achievement gaps have grown significantly for the major subgroups of disadvantaged learners over the last 15 years in Seattle especially at grades k-5 as measured by 4th grade math WASL test data. The push for "reform math" correlates with this decline. Causation I guess is undetermined in your view. Others have investigated more thoroughly and suspect "reform math" causation is likely.
I appreciate SciAm bringing attention to the issues which prompted our lawsuit in Seattle, which was subsequently decided in favor of the plaintiffs, of which I am one.
Reply | Report Abuse | Link to thisFor further information, including copies of our declaration, briefs, the decision, and a transcript of the hearing, readers may go to https://seattlemathgroup.blogspot.com/
Correction to the Erratum (2/24/10): "Citing declining test scores in Cleveland after a three-year pilot of a similar text, the suit claims that reform math is associated with a widening achievement gap between white and minority low-income students." Should be: "....test scores at Seattle Public Schools' Cleveland and Garfield High Schools after a three-year pilot...."
Reply | Report Abuse | Link to thisAs an algebra teacher I saw several areas that students should have mastered before being placed in an algebra class. The first is knowing multiplication and division facts. Fractions stops many students, and understanding the various relationships between numbers is a third weakness. My 4th grade grandson has always liked math until this year. He has been given the opportunity to reason and explain his answers, but now he is being asked to memorize his facts. As Vygostsky said, the students need the psychological tools of the culture - in this case being able to do some basic math. But he also said that children must be guided in their reasoning so as not to draw wrong conclusions. We need BOTH kinds of instruction. As some other readers wrote, let's see what is working.
Reply | Report Abuse | Link to thisSee what one of the world's foremost researchers in the field of learning and cognition, Dr. Paul Kirschner, of the Netherlands writes to Issaquah Superintendent Dr. Steve Rasmussen about the failures of inquiry based instruction. Issaquah S.D., east of Seattle, like Bellevue S. D. is seriously considering adoption of KCP's "Discovering" Math Series.
Reply | Report Abuse | Link to thishttp://soundmath.wetpaint.com/page/Washington+Local+District+Adoptions
Be sure and Check out the colorful charts at the bottom of this page to see how well served the non-white and low income students were served by the reform math k-12 combination of TERC/ Investigations, Connected Math Project, and Core-Plus.
http://soundmath.wetpaint.com/page/Bellevue
When a school adopts the Discovering series, parents are expected to purchase a $100+ calculator for the experience. If your family cannot afford one, at our school your student can borrow one from the library - they have 6 of them for over 800 students. Is there any studies linking success of this series to calculator ownership/accessibility?
Reply | Report Abuse | Link to thisMathematics score in PISA 2006
Reply | Report Abuse | Link to thisOECD & Partners
Finland 548
Korea 547
Hong Kong-China 547
Netherlands 531 ------ Kirschner is from here where they use evidence and intelligently apply relevant data on decision making.
Switzerland 530
Canada 527
Macao-China 525
Liechtenstein 525
Japan 523
New Zealand 522
Belgium 520
Australia 520
Denmark 513
Czech Republic 510
Iceland 506
Austria 505
Germany 504
Sweden 502
Ireland 501
France 496
United Kingdom 495
Poland 495
Slovak Republic 492
Hungary 491
Luxembourg 490
Norway 490
Latvia 486
Spain 480
Russian Federation 476
United States 474 ----- Key Curriculum Press sells products in this nation way down here in this chart
Portugal 466
Italy 462
Greece 459
Uruguay 427
Turkey 424
Thailand 417
Indonesia 391
Brazil 370
Tunisia 365
The Netherlands, as pointed out, scores very high on PISA. But what isn't pointed out is that the country's curriculum is based on Realistic Mathematics Education. RME believes that mathematics must be connected to reality, stay close to childrens experience and be relevant to society, in order to be of human value.
Reply | Report Abuse | Link to thisInstead of seeing mathematics as ready-made knowledge to be transmitted, it stressed the idea of mathematics as a human activity. Mathematics lessons should give students the guided opportunity to re-invent mathematics by doing it. This means that in mathematics education, the focal point should not be on mathematics as a closed system, but on the activity, on the process of mathematization (Freudenthal, 1968).
Isnt that everything that most traditionalists like Dempsey oppose?
Read more about the Netherlands math curriculum and philosophy at: http://subs.emis.de/journals/ZDM/zdm054a4.pdf
DrM,
Reply | Report Abuse | Link to thisDefine traditionalist.
I think you may have made an unwarranted assumption.
It probably was unwarranted. I should allow you to define yourselves. Please do. But it doesn't change my point that the Netherlands math curriculum is based on RME.
Reply | Report Abuse | Link to thisDr. M,
Reply | Report Abuse | Link to thisAgain please:
Define traditionalist.
Dr. M,
Reply | Report Abuse | Link to thisIn regard to your request for Dempsey & McLaren to define themselves. For the purposes of this discussion we can do a reasonable job in 6 minutes:
Seattle excluded all evidence provided by the public in making the decision to adopt "Discovering" for HS math on May 6, 2009
This was a virtual replay of May 30, 2007 when directors decided to trust their hired professionals instead of using evidence in adopting Everyday Math.
The six minutes is our response to the SPS board on May 20th to their decision to adopt "Discovering" on May 6th.
Let this play past the 4 second intro. Then move the slider to find us from minute 22:15 to minute 28:30
SPS Board meeting video of May 20, 2009 part I:
http://www.seattlechannel.org/videos/video.asp?ID=4538
Now please define traditionalist.
Thanks,
Dan
jimnmy37 – “I grew up in the 60s and 70s with the 'new math'. Sometime in college, I remember learning about base arithmetic in 7th grade. Why was I taught something completely useless that I forgot until I got to college and was completely retaught?”
Reply | Report Abuse | Link to this“Enough with the warm, fuzzy teaching methods. Teach the students the formulas they need and how to use them. Teach them the theoretical underpinnings afterward, when they can appreciate them.”
I appreciate your experiences with new math but mine were nearly polar opposite. I grew up in the 1960s traveling up and down the railroad line every year or so, continuously experiencing new school environments, often being expected to repeat past lessons. I could never see the point in memorizing formulas that had no real purpose for me and practicing pointless problems, and failed miserably.
I do remember something called SMSG from Yale Press in the early 1960s. I do recall learning base number arithmetic and graph theory. Unlike you I did not attend college, but I did pass my high school equivalency exam in Viet Nam. Afterwards I took a short course in computer programming and began a 30+ year career in information systems, retiring having spent many years as Technical Fellow, IT Systems Planning. I did publish one paper: “Modeling Large Scale IMS Transaction Processing Systems Using Commercial Queueing Model Software” that was well received, but had more critical issues to address to spend much time on relatively academic pursuits.
You see, I never did memorize the formulas considered necessary by most of my math teachers but, understanding the crucial concepts at work in a given situation, was able to determine the formulas necessary to solve actual critical problems.
I suspect that both theoretical and applied mathematics education are beneficial to students, and that each is more appropriate for different types of students. While I appreciate that for you it may have been a waste of time, if I hadn’t been exposed to a little math theory fairly early in my education, I suspect I’d have had much different professional experiences.
Come to think of it, I still need some help from a capable mathematician - please refer to the comment/essay: "Dark Matter as Gravitational Estimation Error" posted with the article at:
Reply | Report Abuse | Link to thishttp://www.scientificamerican.com/article.cfm?id=dark-matter-cdms
The Erratum still contains three factual errors.
Reply | Report Abuse | Link to thisI am a mathematician at the University of Washington and am the Principle Investigator of the professional development and research project that is alluded to as the "pilot" in this quotation, and which has been the subject of additional untrue assertions by parties in this matter.
(1) There was no pilot of textbooks, similar or otherwise. There was a project that included as one of many parts the use of new textbooks but cannot be considered a pilot of textbooks.
(2) The textbooks used in this project are not similar to the Discovering Math series.
(3) The results of the project overall improved math outcomes with minority and low-income students, not the reverse.
Supporting information for the first of these three statements follows (no space for the others).
(1) The nature of the project
This was primarily a professional development project that involved working with teachers in Seattle high schools. The participating schools included Garfield High School (GHS) and Cleveland High School (CHS), both of which are named in the lawsuit. The focus and goals of the project were on opening up the practice of teaching so that teachers would work together on math teaching in a more collaborative way.
Briefly, here are some of the principle components of the project:
(a) a monthly "video club" in which teachers from all three schools came together to observe and discuss videos taken in the classroom of one of the participating teachers (b) intensive teacher professional development directed toward the classroom (c) creating course teams of teachers with an extra hour per day for planning together (d) attending a national summer institute in mathematics (e) use of new textbooks with training in the use of these books.
In addition, at GHS only, students in the University of Washingtons Secondary Math Methods course came once a week to observe classes and then discuss what they observed with teachers.
I list these parts to make clear that in this project there at least six important variables. In fact in terms of time and effort, the important points in the list are much more (b) and (c), then (a) and (e). Thus it would be a serious scientific error to attribute any outcome, good or bad, to any one of these variables alone, especially without any deep investigation. In particular, given all the changes in classroom practice taking place that had nothing to do with textbooks, it would be invalid to attribute test scores to textbooks.
James King, University of Washington
I think people are mixing too many areas of study into a single subject called "Math." For the Scientific American crowd we need to be more discerning.
Reply | Report Abuse | Link to thisArithmetic is not fundamentally a Mathematical issue and is better labeled as Calculation. Spending a great deal of time teaching youth (or society at large) arithmetic could be considered wasteful as the computers/calculators (when they are running) easily beat the average person hands down. Why fight it? Do students need some calculation, of course, but the example of the clerk who cant make change is old and uninformative.
I think the greater question, is why do we teach Math in schools at all? Unlike music or Spanish it typically is a required course nationwide. It is to an attempt to make the majority of people minor mathematicians who can regurgitate Geometry Theorems or other formal math constructs? I think it is more designed to help people think, to help people know what numbers to put into the calculator in the first place.
Chasing international test scores may not be worth it. What is the focus of the tests and does the math focus apply to vast majority of the population who are not professional mathematicians? If we are going to have a debate on Math in society, we need to better define why math is an important subject for all. People who say, I am bad at math because I didnt keep all of the facts straight, may have more mathematical (thinking) skill that previously thought. People who water math down to a single right answer miss maths great history in addressing societies leading questions, problems which require thinking; not the rigid application of theorems developed in the past to solve yesterdays troubles.
This continues my comments on the 3 ways the corrected article is reporting allegations that are incorrect.
Reply | Report Abuse | Link to thisThe new textbook series used in this project was the Interactive Math Program (IMP). The choice of IMP was the teachers’ choice, not one imposed by the project leadership. One reason for choosing this series over others was that IMP was already used in a high school in north Seattle.
These books are structured very differently from traditional math textbooks. The whole year is organized around about five modules, each of which is devoted to an important mathematical idea. The modules do not expound the math as explicitly as most textbooks but lead students through a sequence of mathematical experiences that build up to the mathematical conclusion at the end. Since IMP is organized as very differently from traditional math textbooks, a teacher teaching from it must be willing to make major changes in his or her teaching practice.
The Discovering Math books look like what most of us expect to see in a math book. While they do use investigation and inquiry to introduce or motivate new ideas, they also contain plenty of clearly labeled information and lots of both challenging problems and practice exercises organized in a traditional way. The Discovering books are organized into chapters in the way that most math books are organized. Even books that advertise themselves as “traditional” now usually include investigations of some kind.
Are the IMP books "similar" to the Discovering Math books? No they are not. The Discovering Mathematics series is closer to traditional mathematics texts than it is to IMP. The IMP books, whether one likes them or dislikes them, are an intentionally novel approach to integrated mathematics that grew out of an NSF project. The Discovering books are an algebra-geometry-algebra series that that grew out of classroom experience and traditional publishing practices and are structured in a traditional way.
I am quite familiar with these books. I have been teaching math for over forty years and have seen a lot of textbooks. In my strong opinion the word “similar” does not apply here as it has been used.
This concludes my comments on errors in the claims made about the Seattle lawsuit.
Reply | Report Abuse | Link to this(3) What were the outcomes for minority and low-income students?
While the project was asking many questions and observing many things, Ill limit my remarks to the publicly available measure of WASL test scores cited in the lawsuit and the news coverage.
For high school, the WASL test is given in the tenth grade. Scores can be found on the web at http://reportcard.ospi.k12.wa.us/ and can be broken out by district, school and by various student groups, especially those tracked by No Child Left Behind. Note that state scores went down after 2007 after some policy changes.
Did this project produce successful student outcomes? The experience was different in each school.
Garfield High School had the fullest and longest participation in all facets of the project.
The smaller Cleveland High School initially had some challenges and instability that prevented it from as full participation until recently.
Intensive teacher professional development for our project began in spring 2005. IMP was introduced in ninth grade math classes in autumn 2005, so most of these students took the WASL as tenth graders in 2007. Thus, one can look for impact in the scores for the four years 2006-9.
The scores at GHS went up, not down. The state named Garfield a School of Distinction in 2007 for its improved math and reading scores. The scores for black students more than doubled over the average for the previous four years; low-income students had similar results.
One score that the lawsuit highlighted is that one year there were 0% limited-English-proficiency students who passed clearly an undesirable outcome. This score raises questions, but the answers are not clear because the science scores were also 0% (for two years). In 2009 the math scores bounced back to 16.7%, the highest value in the decade, presumably with the same textbook in use a fact that is never mentioned in the reporting of the lawsuit.
The scores at CHS are mixed, starting from low levels. Overall math scores are up. Some group scores have improved (black and low-income students) but others have not.
No one is satisfied with these scores, but overall there is improvement, not the reverse, so no grounds for the assertions in the lawsuit. And of course the results are not relevant to the adoption of the Discovering Math series at all, since they are not the result of a pilot and the textbook was not similar.
As a casual reader I only got the sense that the article was addressing a philosophical debate among educators, although there was brief mention of a lawsuit. Examining recent comments of apparently those involved leads to a somewhat different conclusion.
Reply | Report Abuse | Link to thisI doubt this can be of any help to those of you who have been at the mercy of legal proceedings, especially those involving statistical analyses, but from the little I could determine I’ll offer an observation of an innocent bystander.
It seems most reasonable that, if the primary issue is the poor test performance of students who have limited comprehension of the English language and are taught in the English language, the fact that those students belong to minority racial groups most likely has little causal bearing on the outcome of their test scores. Language difficulty would be the most likely causal factor of the low test scores. Just a casual independent analysis offered in the slim hope that it could help in some way. Good luck to all.
Both types of math are essential. Students need to be able to add, subtract, multiply and divide rational numbers as well as understanding estimating to ensure that solutions make sense. Calculators are great for visualizing the effects of graphing functions but the algorithm needs to be taught as well. Math classes should contain a balance of both, ensuring conceptual understanding and use of algorithms. This debate has been around for over 25 years and will go on forever in the same way English teachers debate sight-reading and phonics. As math teachers we need to teach students to use the calculator effectively and using it to add and subtract two or three number is not effective but using it to add 100 numbers together is effective. As I tell my students the calculator is a tool much like a skill saw and it is only as smart as its' operator.
Reply | Report Abuse | Link to thisI believe that most of the argumentation in the 'Math Wars' occurs primarily because of mis-understanding or non-understanding by each side of the reasoning of the other sides - and this sorry state of affairs is, I think, reflected here as well.
Reply | Report Abuse | Link to thisSuch fruitless argumentation can be very significantly reduced through clearer understanding of the relationship(s) between 'elements' of the discussion to other elements of the discussion. In the conventional 'prose mode' discussion it is very difficult indeed (perhaps even impossible) to make clear the relationship(s) between different elements of the discussion.
The late John N. Warfield in his investigations of complex systems developed practical tools to enable such relationships to be made clear to all sides involved. In fact, we followers of Warfield claim that it was Warfield's contributions that created 'systems science' out of 'general systems theory'. Information about Warfield's contributions are described at http://www.jnwarfield.com and at the "John N. Warfield Collection" held at the library of George Mason University, Fairfax, VA, USA - check out: http://ead.lib.virginia.edu/vivaead/published/gmu/vifgm00008.tp
Based on Warfield's contributions to systems science, there has developed a uniquely powerful aid to problem solving and decision making that I call the 'One Page Management System' (OPMS), which enables users to develop effective Action Planning for any identified 'Mission' from their own current ideas. The OPMS approach ensures that mistaken/ weak ideas are improved, strengthened or weeded out through the human mind's inherent ability for self-correction.
I believe that much of the fruitless argumentation in these 'Math Wars' could be easily avoided - and the discussion could be taken to the level of actually developing effective 'math education systems', which is an urgent need in the US (and, in fact, everywhere). I do not yet have empirical evidence to support this claim - but I do have the case of a (freshman) college student using the OPMS approach to successfully accomplish the following Mission: "To understand all topics of my math syllabus thoroughly and thereby to improve my results in my math exams". His success could be measured by the fact that right through his school career he had never gotten above 45% in a math exam or test - and within 6 months of him starting to use the OPMS on this Mission he was consistently scoring above 75% in his math test, exams and quizzes. All needed information provided on request.
Reference my earlier posting, I request the SciAm editors to take a look at this recommended approach, with a view to checking out how the 'One Page Management System' (OPMS) approach could enable and enhance wider public understanding of complex issues of science and society.
Reply | Report Abuse | Link to thisThanks,
GSC
I am a former secondary Math/Science Instructor who is still dismayed by the mish-mash curriculum touted by the federal government and the states. Twenty years ago, the claim was that the United States was not producing good scientists and engineers. We had to overhaul the education system to keep up with the rest of the world.
Reply | Report Abuse | Link to thisMyth 1:
We were behind academically. (We were not, we had fallen behind behaviorally.)
I went through my teacher education program being infected with memes of the banality of rote learning. Blooms taxonomy ruled. We were to program all children from an early age with the virtues of analysis and synthesis, the pinnacles of Bloom.
My time as a teacher in the Peace Corps, taught me differently. I learned a new respect for the memory/recall method. It was the maligned foundation, the battered scaffolding for the western worlds analysis and synthesis. The cry from the already educated was, They can always look up the facts and formulas. So we gave students calculators at too early an age. Calculators are addictive drugs that give false confidence of understanding to too many who have not mastered the abstract concepts of numbers and operations. (Research now shows the value of kinesthetic manipulation to the long term integration of memory. Writing by hand is kinesthetic!) But doesnt, the machine always give the correct answer? How can a person sense to check their input if they do not have a developed inner sense of how numbers change size when operated on?
Myth 2:
We can always look it up. (We cannot if we have not mastered enough of the facts of communication and knowledge within a field of study to have a sense of where to turn for the information. Do you want your surgeon to have to look it up during the surgery? We need to have a certain amount of ready-to-access information stored in our own personal data bank (brain) to efficiently perform mental tasks.)
Then there are the now beleaguered theories of Piaget. All student teachers must study them. But, the concepts first camp has assailed these ideas as scientifically invalid due to the limited scope of Piagets study group, his children. My experience has shown that most people start their understanding of a new idea from the concrete formative stage, even those who are trained to be flexible thinkers. Young children are great sponges of information input and output. Even the first computers had to give back information as it was input before they could be programmed to apply concepts to use it.
Myth 3:
Children can be programmed to conceptualize abstract ideas before knowing the underlying knowledge on which the concepts are based. (There are always exceptions to any statement. This one included. How many conceptually bright people do you know that were considered brilliant at an early age? Maybe their sponge factor operated more quickly than other children, allowing them to make the leaps sooner.
We know from experience that the more often a person practices a task or concept, the more efficient they tend to become at it. Of course, the practice must be monitored to ensure correct application of the principles involved. Mastering comprehension of numbers, operations, formulas, etc. relies on repeated practice. Current integrated math instruction provides too much too fast for the majority of students. It is what I call A.D.D. instruction. This brings up the concept of short term memory integration into long term memory storage. According to educational theory each person has five plus or minus two short term memory cells in which to place information destined for long term storage. If more information comes in before the transition is accomplished, prior input is lost. This causes the sequence of the input information to be disrupted resulting in confusion, frustration, and lack of motivation to continue. (It can also result in an excessive need for guidance in problem solving from the teacher.)
Myth 4:
Integrated Maths reliance on review questions every session to reinforce prior learning is an improvement over former traditional learning spending multiple mastery sessions on the topic. (We have imprinted into our culture that young children are unable to focus for longer periods of time. Current research is now showing that our brains wire or re-wire themselves as they are influenced to by their environment. One full year of substitute teaching in elementary schools showed me how we program brains to be attention deficit. Magically in middle school, students are now supposed to shift their attention spans from 15-20 minutes to 40-90 minutes. They are programmed to be A.D.D. Being able to nimbly move from concept to concept still requires strong foundations that, for most individuals, require repeated, focused efforts. Before we can skip back and forth over the stones in a stream we need to make sure they are firmly set.
Learning is a time based endeavor. Any job requires repetition at a task in order to improve. The old school of math instruction, the process thinking of Algebra, logic of Geometry, and combined processes in Trigonometry, helped to develop a focused mind. The challenge should have been to tweak the system to provide more real world examples not to totally turn the cart upside down.
It is touted by pundits and politicians that a strong educational system is the true foundation of our economy and culture. We have turned a first class educational system into a poverty stricken child in the past twenty years.
Is it any wonder why the United States has fallen so far so fast?
Docwright912, I keep hearing that: "Mathematicians know math but don't know how to teach it to children."
Reply | Report Abuse | Link to thisWhere is your proof for this statement? I have more proof for the statement that many decision-makers in public education appear to be completely clueless about how children learn. This is evidenced by the weak math skills across the nation. You have nothing to support your statement, but we'll keep hearing it, I'm sure, because it's a neat and tidy way to dismiss all pertinent evidence from reliable sources. Your argument is basically this: "I don't have to listen to these professionals because they don't know anything about teaching." It's a stereotype that is based on nothing. You should be ashamed to present this as if it's any kind of solid argument.
What does it matter if reformers know how to teach better if they aren't teaching the content? The content is what matters. It's all that matters. But I take issue with the idea that reformers automatically know how to teach math betters than mathematicians do. That hasn't been my experience at all. I would sooner have students take math from a mathematician any day over having them take it from a reformer.
By any proper measure, evidenced by data, statistics, research and feedback from parents and students -- a steady diet of reform math and constructivist teaching styles leaves students starving for mathematics.
Open up your mind and look around you. It's all there for you to see.
jhgv
Reply | Report Abuse | Link to thisThe article provides illustration of the fact that, on complex issues such as these, the argument only goes 'round and 'round the mulberry bush, it seems forever.
Reply | Report Abuse | Link to thisIt would not be really difficult to develop a truly workable Action Plan to ensure that the math 'teaching-&-learning system' functions effectively as it should.
The late John N. Warfield, in his seminal contributions to 'systems science' developed powerful modeling tools that enable all stakeholders in any issue to put forth their sound ideas AND ensure that those good ideas are properly reflected in the Action Plan that develops through effective discussion on the issue. Effective discussion would actually involve the clear articulation of the relationships perceived by stakeholders between the 'elements' (ideas) put forth. Information about Warfield's contributions to systems science is available at http://www.jnwarfield.com and from the "John N. Warfield Collection" held at the library of George Mason University - check out: http://u2.gmu.edu:8080/handle/1920/3059
The Action Plan would necessarily have to take in ideas from every section of stakeholders: teachers; students; parents; administrators; mathematicians; business people and community leaders (and politicians as well!) - and each of these groups would provide ideas that they truly know about.
-- Teachers, for example, would know how to teach a specific subject (or would develop effective means of teaching the subject);
-- Students would know what is wrong with the current teaching (and, to a considerable extent) what should be done to ensure that what is taught would capture their interest;
-- Parents obviously have a sizable stake in the whole system, and they should definitely provide their inputs;
-- Mathematicians would be the best people to tell us of just what is needed to be taught to ensure that the school math is effective in relationship to the needs of the world;
-- Likewise the administrators; community leaders and politicians, etc., would provide their specialized inputs.
The modeling tools and the whole discussion process that Warfield developed could ensure that the discussions do not go off-track into futile argumentation which is the fate of most discussions on complex societal issues.
A powerful generic aid to problem solving and decision making, the 'One Page Management System' (OPMS) enables the sophisticated systems tools that Warfield developed to be used for any Mission with the greatest of ease.
Sciam could usefully consider carrying some articles in detail...
I cannot believe what I've just read. This is back to the 1960s again; God help the poor kids who have to be "recovered" from this disaster!
Reply | Report Abuse | Link to thisMost of this debate misses the point - did anyone actually look at classroom practice to see if the resources were actually used as they were intended in those classrooms. As someone who for the past 20 years has been involved in teacher learning of effective instructional practices in math, I can state that the resource will be used in the way the teacher chooses to. The so called "reform" methods, (actually the problem solving approach that has driven Japan and other nations success in helping student make connections between the traditional operations and their application) are only used by teachers who have either been taught with these methods or who have had extensive opportunities to come to an understanding of pedagogical content knowledge (see Deborah Ball's work at Michigan) - the understanding that I need to know the math conceptually and the methods to have students achieve it. Contrary to popular belief PhD's do not use traditional computations methods. When 70 professional mathematicians were given basic computation questions they only used traditional algorithms 5% of the time. The rest of the time they used what are now being called mental math strategies. They even fought over which of these methods had universal applicability - often changing their mind when they discovered algorithms that were unknown to them before. For instance if I were to be given this subtractions 2013-1988: the most efficient method is to add 12 (the difference between 1988 and 2000) and 13 to get 25. Much quicker and easier than going through all the "borrowing". Rote learning children will never do this but "mathematical reasoners" will. If I want to "learn" my multiplication tables the most important thing to understand is the commutative property, because now I only need to learn "half" of the whole multiplication tables because if I know 7x8, I know 8x7 if I think using this pattern. Add this to the research in the last decade or so on the importance of assessment for learning: the ability of the teacher to adapt the instruction and give specific detailed feedback as critical. (e.g good is useless feedback, just as right or wrong is useless feedback unless the reason why is is correct or incorrect is examined). The actual classroom observations make it clear that most teachers are not effective at feedback or adjusting - therefore it doesn't matter what resource you provide - teachers will just each as they have been taught unless they develop the pedagogical content knowledge to adjust to the students learning need
Reply | Report Abuse | Link to thisMost of this debate misses the point - did anyone actually look at classroom practice to see if the resources were actually used as they were intended in those classrooms. As someone who for the past 20 years has been involved in teacher learning of effective instructional practices in math, I can state that the resource will be used in the way the teacher chooses to. The so called "reform" methods, (actually the problem solving approach that has driven Japan and other nations success in helping student make connections between the traditional operations and their application) are only used by teachers who have either been taught with these methods or who have had extensive opportunities to come to an understanding of pedagogical content knowledge (see Deborah Ball's work at Michigan) - the understanding that I need to know the math conceptually and the methods to have students achieve it. Contrary to popular belief PhD's do not use traditional computations methods. When 70 professional mathematicians were given basic computation questions they only used traditional algorithms 5% of the time. The rest of the time they used what are now being called mental math strategies. They even fought over which of these methods had universal applicability - often changing their mind when they discovered algorithms that were unknown to them before. For instance if I were to be given this subtractions 2013-1988: the most efficient method is to add 12 (the difference between 1988 and 2000) and 13 to get 25. Much quicker and easier than going through all the "borrowing". Rote learning children will never do this but "mathematical reasoners" will. If I want to "learn" my multiplication tables the most important thing to understand is the commutative property, because now I only need to learn "half" of the whole multiplication tables because if I know 7x8, I know 8x7 if I think using this pattern. Add this to the research in the last decade or so on the importance of assessment for learning: the ability of the teacher to adapt the instruction and give specific detailed feedback as critical. (e.g good is useless feedback, just as right or wrong is useless feedback unless the reason why is is correct or incorrect is examined). The actual classroom observations make it clear that most teachers are not effective at feedback or adjusting - therefore it doesn't matter what resource you provide - teachers will just each as they have been taught unless they develop the pedagogical content knowledge to adjust to the students learning need
Reply | Report Abuse | Link to thisMost of this debate misses the point - did anyone actually look at classroom practice to see if the resources were actually used as they were intended in those classrooms. As someone who for the past 20 years has been involved in teacher learning of effective instructional practices in math, I can state that the resource will be used in the way the teacher chooses to. The so called "reform" methods, (actually the problem solving approach that has driven Japan and other nations success in helping student make connections between the traditional operations and their application) are only used by teachers who have either been taught with these methods or who have had extensive opportunities to come to an understanding of pedagogical content knowledge (see Deborah Ball's work at Michigan) - the understanding that I need to know the math conceptually and the methods to have students achieve it. Contrary to popular belief PhD's do not use traditional computations methods. When 70 professional mathematicians were given basic computation questions they only used traditional algorithms 5% of the time. The rest of the time they used what are now being called mental math strategies. They even fought over which of these methods had universal applicability - often changing their mind when they discovered algorithms that were unknown to them before. For instance if I were to be given this subtractions 2013-1988: the most efficient method is to add 12 (the difference between 1988 and 2000) and 13 to get 25. Much quicker and easier than going through all the "borrowing". Rote learning children will never do this but "mathematical reasoners" will. If I want to "learn" my multiplication tables the most important thing to understand is the commutative property, because now I only need to learn "half" of the whole multiplication tables because if I know 7x8, I know 8x7 if I think using this pattern. Add this to the research in the last decade or so on the importance of assessment for learning: the ability of the teacher to adapt the instruction and give specific detailed feedback as critical. (e.g good is useless feedback, just as right or wrong is useless feedback unless the reason why is is correct or incorrect is examined). The actual classroom observations make it clear that most teachers are not effective at feedback or adjusting - therefore it doesn't matter what resource you provide - teachers will just each as they have been taught unless they develop the pedagogical content knowledge to adjust to the students learning need
Reply | Report Abuse | Link to thisMathematicsGuy raises the question:
Reply | Report Abuse | Link to this"Did anyone actually look at classroom practice to see if the resources were actually used as they were intended in those classrooms?"
We now have results from State testing after the first year of Discovering use in Seattle. (issued 8/31/20100)
The SPS spent $800,000 on texts and $400,000 on professional development in year one. Additionally the District employs 111.5 academic coaches for teachers at a cost of $10.5 million.
Cleveland and Rainier Beach received additional funding the last three years through the Southeast Education Initiative. Cleveland, Garfield, and Rainier Beach also received additional funds and extra planning time in math through an NSF grant and University of Washington help.
If this is not enough help to get the teachers to be able to make "Discovering" work, then what more needs to be done and who is going to pay for it?
The results for Black Students are even worse than before.
Check it out here:
http://mathunderground.blogspot.com/2010/09/test-results-in-math-and-seattle-needed.html
"Discovering" is the piece that completes the k-12 vertically aligned instructional materials that the Superintendent desired. Everyday math, Connect Math Project 2, Discovering.
Results for Everyday math remain lackluster. Yet Schmitz Park school with a waiver after two years of Singapore Math produced the highest 5th grade math scores in the entire District surpassing even the "Accelerated Program Schools".
It remains incredibly puzzling as to why what works is rejected in favor of what might work if we can provide teachers enough training. Clearly the vast expenditures were not enough training in Seattle to make "Discovering" work in Southeast Seattle.
Note: Class longitudinal cohort scores reveal that when the 7th("07) and 8th("08) average is compared with the 10th grade scores in 2010 ...
White students went from 72.35% passing to 67.8%
Black students went from 24.2% to 12.4%
White students scored at 94% of middle school average
Black students scored at 51% of middle school average
The results for English Language Learners were equally bad:
http://mathunderground.blogspot.com/2010/09/ospi-testing-seattle-has-no-idea-what.html
Perhaps Dr. James King would care to respond this data.
Reply | Report Abuse | Link to thisSpring 2010 Washington State OSPI HSPE math results. The first year for results from Seattle's $1.2 million expenditure. $800,000 for books and $400,000 for professional development.
10th grade Black Pass rates over three years. 2008, 2009, 2010
State of Washington 22.2 : 20.9 : 19.0 (-1.9)
Seattle Schools 16.0 : 16.3 : 12.5 (- 3.8)
Cleveland HS 6.3 : 12.7 : 5.7 (-7.0)
Garfield (the academic magnet) 22.5 : 29.8 : 16.7 (-13.1)
Rainier Beach (with UW COE Math Education Project support)
21.6 : 15.6 : 3.9 (-11.7)
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10th grade Limited English Student Pass rates over three years. 2008, 2009, 2010
State of Washington 12.7 : 8.1 : 9.3 (+1.2)
Seattle Schools 19.5 : 11.2 : 7.0 (-4.2)
Cleveland HS 4.8 : 0.0 : 3.3 (+3.3)
Garfield (the academic magnet) 0.0 : 16.7 : 0.0 (-16.7)
Rainier Beach (with UW COE Math Education Project support the last 2 years) had too small a population for results.
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This case is in Appeals Court on March 8, 2011 as the Superintendent supports this text book selection. Apparently Dr. Maria Goodloe-Johnson wishes to go to court rather than appropriately serve the district's students.
So, I never got why people never really got the kid's opinions for things like this. Kind of like with <a href="http://www.adoptionchoices.org/unplanned/unplannedpregnancy.html">adoption in denver</a>. The kids should have the biggest say in their lives.
Reply | Report Abuse | Link to thisSo, I never got why people never really got the kid's opinions for things like this. Kind of like with <a href="http://www.adoptionchoices.org/unplanned/unplannedpregnancy.html">adoption in denver</a>. The kids should have the biggest say in their lives.
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