Ze'ev Wurman worked over 30 years in the high tech industry, most recently as the Chief Software Architect with Monolithic 3D, a semiconductor start-up in the Silicon Valley. He has a long involvement with mathematics standards and assessment in California and served on the 1997 Mathematics Framework Committee and on the STAR Mathematics Assessment Review Panel since its inception in 1998. He was a member of the 2010 California Academic Content Standards Commission that evaluated the suitability of Common Core’s standards for California. He was a member of the Teaching Mathematics Advisory Panel to the California Commission on Teacher Credentialing. Between 2007 and 2009 Wurman served as a Senior Policy Adviser to the Assistant Secretary for Planning, Evaluation, and Policy Development in the U.S. Department of Education. Wurman has B.Sc. and M.Sc. degrees in Electrical Engineering from the Technion, Israel Institute of Technology.
Mr. Ze'ev Wurman and I are members of the American Math Forum (AMF). We are thankful for the opportunity AMF has provided in making this Q & A session possible.
Questions & Answers
1) As an evaluator of Math Standards in CA, are you satisfied that Reform Math (TERC, EDM, etc.) is sufficiently rigorous in preparing students for Middle School, High School, and College without need for tutoring, supplemental or remedial courses, and other crutches?
ZW: I also have served on statewide textbook adoptions in California and that, perhaps, is my best source of experience to answer this question. Simply put, it is very difficult to quickly reject a textbook series -- publishers are aware that they are first and foremost being evaluated against content standards. Consequently, they will try and put at least *something* that is relevant to every standard in their textbook and then point to it. It takes a lot of effort and experience to wade through the ocean of material publishers supply and come with supported and persuasive answers to the following *cardinal* questions:
a) Does it (i.e., the textbook series) include the overwhelming majority of the content as outlined in content standards?
b) Does it treat the content at appropriate depth as implied by the content standards?
c) Does it treat the content in essentially a pedagogically-sound manner? In other words, is it presented in a cohesive and logical way, does it bring topics to a closure, and does it promote fluency and mastery with basic skills?
Then there are secondary -- however important -- questions about the quality and quantity of practice, support for ELLs, differentiation, technology support, etc. But if the cardinal questions are not answered in the positive, no amount of excellence in the secondary areas can compensate for the essential deficiencies.
Based on this, the answer to your question is that TERC fails on all of them. It has large holes in content as is clear to anyone who bothers to carefully analyze it vis-à-vis almost any state standards. Depth of treatment is reasonable for a handful of topics but large holes in content immediately imply there cannot be deep treatment of much of the expected content. Finally, TERC fails immediately on closure and fluency aspects as it -- quite explicitly -- doesn't expect any. There can be a disagreement whether it treats the content in logical and cohesive manner -- some will assert it does, others will point out that perforce it cannot be cohesive if it omits large chunks of relevant content.
The case for EDM is somewhat different. It does cover much more content and it probably addresses the full standards of some states, although not of the better-ranked ones (as graded, for example, on the Fordham review). Its depth of coverage varies quite widely across topics but is generally acceptable. But if fails hard on pedagogy. The topic progression is quite incoherent and units jump from one topic to another without much rhyme or reason. Topics are rarely brought to closure as the program always expects that some fraction of students will not "get it" and that the topic will anyway be revisited the following year (or semester). Finally, the program has an aversion to developing fluency and mastery, against all we know from research in cognitive psychology.
I don't believe anyone going through these two programs without significant supplementation, either in-class or outside (home, tutoring) can be ready for an authentic Algebra 1 program in either middle or high school. For me, that implies anything beyond Algebra 1 too, whether geometry, trig, or precalc.
a) Does it (i.e., the textbook series) include the overwhelming majority of the content as outlined in content standards?
b) Does it treat the content at appropriate depth as implied by the content standards?
c) Does it treat the content in essentially a pedagogically-sound manner? In other words, is it presented in a cohesive and logical way, does it bring topics to a closure, and does it promote fluency and mastery with basic skills?
Then there are secondary -- however important -- questions about the quality and quantity of practice, support for ELLs, differentiation, technology support, etc. But if the cardinal questions are not answered in the positive, no amount of excellence in the secondary areas can compensate for the essential deficiencies.
Based on this, the answer to your question is that TERC fails on all of them. It has large holes in content as is clear to anyone who bothers to carefully analyze it vis-à-vis almost any state standards. Depth of treatment is reasonable for a handful of topics but large holes in content immediately imply there cannot be deep treatment of much of the expected content. Finally, TERC fails immediately on closure and fluency aspects as it -- quite explicitly -- doesn't expect any. There can be a disagreement whether it treats the content in logical and cohesive manner -- some will assert it does, others will point out that perforce it cannot be cohesive if it omits large chunks of relevant content.
The case for EDM is somewhat different. It does cover much more content and it probably addresses the full standards of some states, although not of the better-ranked ones (as graded, for example, on the Fordham review). Its depth of coverage varies quite widely across topics but is generally acceptable. But if fails hard on pedagogy. The topic progression is quite incoherent and units jump from one topic to another without much rhyme or reason. Topics are rarely brought to closure as the program always expects that some fraction of students will not "get it" and that the topic will anyway be revisited the following year (or semester). Finally, the program has an aversion to developing fluency and mastery, against all we know from research in cognitive psychology.
I don't believe anyone going through these two programs without significant supplementation, either in-class or outside (home, tutoring) can be ready for an authentic Algebra 1 program in either middle or high school. For me, that implies anything beyond Algebra 1 too, whether geometry, trig, or precalc.
2) Same question as above for Traditional / Singapore Math?
ZW: "Traditional" is open to interpretations and can mean many books. Singapore math (Primary Math series, not the Math in Focus!) easily qualifies on the three cardinal questions. Saxon qualifies easily on (a) and (c) and quite well on (b), although there can be some argument about the depth of coverage of a few topics. Still, Saxon covers most topics in sufficient depth even if many teachers are frequently distracted by its explicitly didactic presentation and don't notice its considerable depth.
3) If you had to rate EDM vs. Singapore Math in achieving real math proficiency, what would be your ranking on 1-10 scale (10 being best) for each program?
ZW: Proficiency is hard to define. I would use the preparation for an authentic Algebra 1 course (Nat'l Advisory Math Panel definition) instead.
TERC = 2,
EDM = 4,
Saxon = 7 or 8,
Singapore (Primary Math) = 10.
Clearly, supplementation may change the results for the less effective programs.
4) The body of cognitive research seems to show, according to NAMP, that learning is more in-depth and longer-lasting if the curriculum seeks to achieve “mastery” at the level of instruction before moving on, and reinforced through distributed practice over subsequent weeks (as the Asians practice it) rather than through distributed instruction over years with incremental progress each year until full mastery is achieved. Where does EDM fit in this framework?
ZW: I would say that through a spiraling such as practiced by EDM there will be almost always a group of kids that will not master the content, simply because teachers are not expected to have the whole group taught to mastery and there always is the promise of "the next time." Consequently, the weaker kids tend to be left behind, while the stronger are getting bored for what seems to them an endless repetition. Eventually the teacher needs to move on and the weaker kids are left with knowledge and skills gaps. Further, as the key content is taught multiple times during K-6 span, there is not enough time to teach less cardinal content, which is anyway barely touched on in the program and tends to get skipped when time runs out. Finally, mastery is simply not stressed by Everyday Math.
5) What would be your best recommendation for parents in Elementary/Middle School wishing to ensure math proficiency for their children?
ZW: - Don't assume the schools, or the teachers, understand the issues around math and science education well, particularly in elementary grades. Most elementary teachers have little background in, or understanding of, math and science.
- Use publicly available assessments such as here to get a better sense how you child is doing. Don’t wait -- take action if the results indicate a problem.
- Don't turn off your common sense at the school's door and assume school knows best.
- Use publicly available assessments such as here to get a better sense how you child is doing. Don’t wait -- take action if the results indicate a problem.
- Don't turn off your common sense at the school's door and assume school knows best.
6) Do you think Parents/Educators/Mathematicians would be well advised to reject Everyday Math if they had the opportunity to do so?
ZW: It is a rare mathematician or scientist who had his children exposed to Everyday Math and didn't rise up against it. That is how California HOLD and Mathematically Correct came to be, with the support of much of Stanford's math faculty. That is how NYC HOLD came to be with the support of much of the Courant Institute faculty. Unfortunately, schools of education are mostly staffed with education theorists rather than mathematicians, scientists, historians, or simply with truly well-educated people.
7) How can EDM survive and thrive when it continuously flouts the scientific research/evidence and the protests of so many experts and parents? It’s got to be more than because the Ed. Schools are obtuse, no?
ZW: Many reasons; I will only touch on a few:
- It is not as if prior teaching was perfect -- it had some problems too. It's just that the cure was worse than the disease.
- University of Chicago pedigree helped, and NSF's imprimatur in 1999 helped even more.
- Ed. school defocus from knowledge and skills made many teachers rationalize their absence in their students.
- Constant drumming to mistrust and ignore the results of testing, particularly objective multiple-choice testing. An interesting pact between teacher unions interested in protecting teachers' jobs and Ed schools interested in protecting their own careers.
- Any time international evidence is brought up, many rush to excuse it with "different culture," "less social inequity" (as if) "tutoring and cramming," and similar.
- Very few well done curriculum studies were actually done. They are very hard to do well. EDM, because of its academic pedigree, has the most studies around except that almost none of them (1 out of 72) are worth anything. Others have even less formal research. EDM keeps touting those worthless studies. I think I mentioned one of the few (only one???) good studies finding for Saxon and actually a rather new reform program (Math Expressions) and against TERC and another "traditional" (not really, but never mind) programs. Did you hear anyone speaking about them?
- University of Chicago pedigree helped, and NSF's imprimatur in 1999 helped even more.
- Ed. school defocus from knowledge and skills made many teachers rationalize their absence in their students.
- Constant drumming to mistrust and ignore the results of testing, particularly objective multiple-choice testing. An interesting pact between teacher unions interested in protecting teachers' jobs and Ed schools interested in protecting their own careers.
- Any time international evidence is brought up, many rush to excuse it with "different culture," "less social inequity" (as if) "tutoring and cramming," and similar.
- Very few well done curriculum studies were actually done. They are very hard to do well. EDM, because of its academic pedigree, has the most studies around except that almost none of them (1 out of 72) are worth anything. Others have even less formal research. EDM keeps touting those worthless studies. I think I mentioned one of the few (only one???) good studies finding for Saxon and actually a rather new reform program (Math Expressions) and against TERC and another "traditional" (not really, but never mind) programs. Did you hear anyone speaking about them?
Real World Impacts
8) As an end-user of graduates, is the math proficiency of students graduating from US-based high schools or colleges at the same level as those of foreign institutions?
ZW: I live in the Silicon Valley and that's my point of reference. Simply put, in many conference rooms around the valley you will find only a few, if any, U.S. born engineers. And most of those would be second generation immigrants or guys over 50. Look at the names of a recent Intel (ex Westinghouse) Talent Search semi-finalists here and compare it with the one of 2001-2 here. Better yet, check the names of the finalists over the last 20-30 years here.
9) Can you directly attribute these differences to the Reform Math wave of the last 20 years?
ZW: No. Not directly. First, the changes have been pitched for already more than 20 years -- perhaps 25-30 is a better number. More importantly, this is not only about mathematics. Shifting away from the focus on content knowledge toward a focus on process has been occurring also in teaching of literacy, history, and the sciences. Hirsch's Cultural Literacy speaking against this trend was published already in mid 1980s. However, I am absolutely convinced that “textbooks” like TERC of Everyday Mathematics contributed strongly to the acceptance of this shift in teaching mathematics.
10) How is your company or Silicon Valley adjusting to this downward trend in math proficiency in US vs. World?
ZW: By hiring the best we can get. We apply for many H1 visas (smile). And when we can't hire here, we hire them elsewhere. Silicon Valley's overseas engineering (not just manufacturing!) operations exploded over the recent decade and a half. Many (most?) Silicon Valley companies run large engineering shops in India, China, Singapore, Russia, Armenia, Romania, and many other places. With internet and telecommunication it becomes easier every year.
11) In your view, is the US losing economic competitiveness in areas requiring strong math computational skills?
ZW: Hard to say. So far we can still hire a lot of world's best talent through H1 visas. We are also lucky that our universities still draw the world's brightest to come here to study, and many stick around, at least for a time. At the same time many more are now going back to their homelands as opportunities across the world grow too.
The more immediate problem is that our own students, particularly from disadvantaged backgrounds, have little chance to compete with them and climb the social ladder, as they tend to exit our K-12 schools ill-prepared for college and the job market. The more affluent get help and tutoring when parents finally catch on. Most still may never be able to compete in engineering and science with immigrants, but they can compete with their less advantaged peers.
The more immediate problem is that our own students, particularly from disadvantaged backgrounds, have little chance to compete with them and climb the social ladder, as they tend to exit our K-12 schools ill-prepared for college and the job market. The more affluent get help and tutoring when parents finally catch on. Most still may never be able to compete in engineering and science with immigrants, but they can compete with their less advantaged peers.
Great start to a blog here Can I ask who you'll be interviewing next?
ReplyDelete