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Wednesday, January 23, 2013

Common Core leading districts to adopt unproved math programs and failed approaches

By Laurie H. Rogers
Many of America’s public schools have incorporated “student-centered learning” models into their math programs. An adoption committee in Spokane appears poised to recommend the adoption of yet another version of a “student-centered” program for Grades 3-8 mathematics.

It’s critically important that American citizens know what that term means. Aspects of the Common Core State Standards initiatives are leading many districts to adopt new curricular materials that have “student-centered learning” as a centerpiece.

In Spokane Public Schools, student-centered learning (also known as “inquiry-based” learning or “discovery-based” learning or “standards-based” learning) has been the driver of curriculum adoptions for nearly 20 years. This approach has not produced graduates with strong skills in mathematics. Spokane now suffers from a dearth of math skills in most of its younger citizens.

Nor is Spokane alone with this problem. Student-centered learning has largely replaced direct instruction in the public-school classroom. It was pushed on the country beginning in the 1980s by the National Council of Teachers of Mathematics, the federal government, colleges of education, and various corporations and foundations. Despite its abject failure to produce well-educated students, student-centered learning is coming back around, again pushed by the NCTM, colleges of education, the federal government and various corporations and foundations.

Despite the lack of supporting research for the approach, trillions of taxpayer dollars were spent on implementing it across the nation. Despite its grim results, trillions more will be spent on it via the Common Core initiatives. But what is student-centered learning, and why do people in public education still love it?

Student-centered learning is designed to “engage” students in discussion, debate, critical thinking, exploration and group work, all supposedly to gain “deeper conceptual understanding” and the ability to apply concepts to “real world” situations. New teachers receive instruction in student-centered learning in colleges of education, and their instruction in the approach (i.e. their indoctrination) continues non-stop at state and district levels.

The popularity of student-centered learning in the education community rests on: a) constant indoctrination, b) ego, c) money, and d) the ability to hide weak outcomes from the public.

Ask yourself this: How does one actually quantify “exploration,” “deeper conceptual understanding” and “application to real world situations”? How do we test for that? We can’t, really, which helps explain why math test scores can soar even as actual math skills deteriorate.

With student-centered learning, teachers are not to be a “sage on the stage” – they are to be a “guide on the side.” Students are to innovate and create, come up with their own methods, develop their own understanding, work in groups, talk problems out, teach each other, and depend on their classmates for help before asking the teacher. Student-centered learning is supposed to be a challenge for teachers, whereas direct instruction is considered to be too easy (basically handing information over to students on a silver platter).

Ask yourself this: How much learning can be done in a class with 28 students of different abilities and backgrounds, all talking; a teacher who guides but doesn’t teach; and classmates who must teach each other things they don’t understand? How do students get help with this approach at home? What happens to students who don't have a textbook, don't have proper guidance, and don't have any help at home? Direct instruction does make learning easier; that’s a positive for it, not a negative. Learning can be efficient and easy. How is it better to purposefully make children struggle, fail and doubt themselves?

But adult egos can be stroked by the enormous challenge of making student-centered learning work, even as it utterly fails the children.

In student-centered learning, student discussion and debate precedes (and often replaces) teacher instruction. “Deeper conceptual understanding” is supposed to precede the learning of skills. But placing application before the learning puts the “why” before the “how,” thus asking students to apply something they don’t know how to do. How does that make sense?

In student-centered learning, it’s thought to be bad practice to instruct, answer student questions, provide a template for the students, teach efficient processes, insist on proper structure or correct answers, or have students practice a skill to mastery. It’s OK for a class to take all day “exploring” because exploration supposedly promotes learning, whereas efficient instruction is supposedly counterproductive. Children are supposed to “muddle” along, get it wrong and depend on classmates for advice and guidance. Struggling is seen as critical to learning. Getting correct answers in an efficient manner is seen as unhelpful.

Ask yourself this: How can “efficient” instruction be counterproductive? Math is a tool, used to get a job done. Correct answers are critical, and efficiency is prized in the workforce. Quick, correct solutions reflect a depth of understanding that slow, incorrect solutions do not. Students do not enjoy struggling and getting things wrong. For children, struggle and failure are motivation killers.

The focus of a student-centered classroom is on supposed “real-world application.” (My experience with “real-world application” is that it’s typically a very adult world rather than a child world, and that now, it’s also a political world with a heavily partisan focus.)

Ask yourself this: How does it help children to be enmeshed in an adult world of worries, prevented from learning enough academics, and basted in a politically partisan outlook? (It doesn’t help them, but it suits adults who want a certain kind of voter when the students turn 18.)

All of this is at the expense of learning sufficient skills in mathematics.

Here is one example of an adult perspective of student-centered learning. We can only guess whether students would enjoy this lesson or learn from it. The article is called “Messy monk mathematics: An NCTM-standards-inspired class session.” It’s dedicated to Stephen I. Brown, who is said to be “an inspiration for inquiry-based teaching and learning.” The author, Larry Copes, has a doctorate in mathematics education (not in mathematics). His doctoral work was on the ways math instruction can “encourage intellectual, ethical, and identity development.”

After reading Copes’ article, did you say: “Wow! I love the method! The students were so engaged!” Or, did you say: “What a waste of time! The ‘lesson’ was obviously designed to stroke the teacher’s ego and not to provide students with the math concept.”

I see the teacher in that anecdote as egotistic, holding knowledge over the students’ head, refusing to give it to them, making them jump for it over and over. It seems selfish. The students didn’t appear to ever understand the concept. What’s the point of tossing in the name of a Theorem (the Intermediate Value Theorem) without ever explaining it? Although the students wrote down the name, they didn’t pursue it, and the anecdote ended without a resolution or proof that they learned anything. I wonder if the teacher cared whether they learned the Theorem, or if his little game and his complete focus on himself were what mattered to him.

My daughter read Copes’ article, and she wrote (as if the author were speaking): “I am an individual afflicted with an extraordinary amount of hubris, which has affected my research.”

My daughter is funny, but it does seem impossible to bridge these gaps in perception:
  • Proponents of the “student-centered” approach see themselves as hard workers, suffering with opponents who are stuck in the 18th century. The “deeper conceptual understanding” that they believe they foster in students seems more important to them than building math skills that consistently lead to correct answers.
  • Proponents of direct instruction see the students’ weakening self-image and poor skills, and we view the student-centered approach as limiting and even unkind. Math skills and correct answers are the point of math instruction, and we don’t believe students can have “deeper conceptual understanding” if they lack procedural skills.
Proponents of student-centered learning like to call their approach “best practices,” “research-based,” “evidence-based,” and so on, but no one has ever provided verifiable, replicable proof that student-centered learning works better than direct instruction as a method for teaching math. There is actually a wealth of solid evidence to indicate the contrary.

Unfortunately, the pushing of the Common Core on states has encouraged many districts to pursue “student-centered learning” models all over again, as if they were required to do so. Some folks are already making pots of money off the Common Core and the new, unproved materials that are supposedly aligned with the Common Core. But student-centered learning hasn’t worked for the children in the last 30 years, and it won’t work in the next 30.

Nevertheless, the stated mission of Spokane’s adoption committee is to “deeply” align to the Common Core. (Not to choose a curriculum that will – oh, I don’t know – lead students to college or career readiness?) In supporting their stated mission, committee members asserted that the Common Core was vetted by “experts,” so they believe the initiatives will produce internationally competitive graduates. They provided no data, no proof, no solid research or studies for their belief. And they can’t because there aren’t any. The Common Core initiatives are an obscenely expensive, nation-wide pilot of unproved products.

Welcome to public education: Another day, another experiment on our children, except that this time, there is strong evidence that this experiment – a rehashing of the last experiment – will again fail. Try telling that to education and political leaders. No one seems to see the evidence. When you tell leaders about it or show it to them, no one seems to care. Meanwhile, many of those leaders get tutoring or outside help for their own children. (FYI: I have never seen a professional tutor use the “student-centered” method to teach math to any child.)

The Spokane adoption committee’s mission of “deep” alignment to the Common Core has caused them to choose to pilot – you guessed it – several sets of new (and unproved) materials that are distinctly more “student-centered” in their approach, heavy on words and discovery, and light on actual math.

Kicked to the bottom of their preferences were proved and rigorous programs favored by homeschooling parents and tutors, including Saxon Mathematics and Singapore Math. Saxon got my own daughter almost all of the way through Algebra II by the end of 8th grade, most of that without a calculator. When I asked my email list and various online contacts for their preferences, the majority picked Saxon over every other math program, and by a wide margin.

But a member of the Spokane adoption committee – a district employee – told me the Saxon representative called Saxon “parochial” and that the publisher initially refused to send Saxon to Spokane because it was unlikely to be adopted. (“Parochial” means provincial, narrow-minded, or “limited in range or scope.”) Do you believe the Saxon rep would call his product narrow-minded and limited in scope? Saxon is efficient, thorough, clear and concise. If there is a stronger K-8 math program out there, I don’t know of it. Naturally, the Spokane adoption committee does not want Saxon.

One of the programs the committee did choose to pilot is Connected Mathematics, a curriculum already being used in Spokane, one of the worst programs on the planet, excoriated for decades by mathematicians from border to border and from coast to coast. The district employee assured me the committee is hiding nothing from the public, but the committee didn’t mention to the public that it is again piloting Connected Mathematics. They don’t seem to see its failure. They love its focus on student-centered learning. The devastation it wreaks on math skills appears to matter naught to them.

There is one more community meeting for this adoption committee, on Tuesday, Jan. 29, at Sacajawea Middle School in Spokane. Whether you can attend or not, please take a moment to fill out the district survey – either the short version or the long version. Tell the Spokane superintendent what you want in a math program. If we want Spokane teachers to ever be allowed to actually teach mathematics to the children, we’re going to have to say so.

I know district administrators and board directors have not been good about listening to community wishes on math, and that it seems pointless to talk to them. But for the good of the children, please try. Perhaps this time, someone will listen.

Please note: The information in this post is copyrighted. The proper citation is:
Rogers, L. (January 2013). "Common Core leading districts to adopt unproved math programs and failed approaches." Retrieved (date) from the Betrayed Web site: 


Barry Garelick said...

Excellent article. As I've said elsewhere, Common Core math standards lend themselves to be interpreted as requiring the student-centered inquiry-based pedagogy you write about. There is a pedagogical bias inherent in the CC stds. They do not HAVE to be interpreted in this manner, however. The content standards can be met without the progressive education focus.

Jenny Siler said...

Hi Laurie, I just found your blog via the Parents Against Everyday Math facebook page. Thanks so much for all your hard work and for a giving a voice to so many of us who are fed up and frustrated. My daughter in is the 4th grade in Portland Maine. I have just applied to be on the district's curriculum committee. I will definitely be using your blog as a reference.

Paul M. Rutherford, PhD said...

I have been a mathemtics, physics, and engineering educator for 30 years, and that was after 11 years as naval aircraft maintenance/engineering duty officer. I earned my mechanical/aerospace engineering degree prior to my commissioning as a navy officer. I am a product of 'direct instruction' throughout my pre-college years. When I arrived in an engineering degree program, I struggled. Why? I was chalk full of facts, and equations. I graduated top in my high school class of 645 students. I was NEVER taught how to think on my own. I was simply told to do physics and mathematics problems, "This way." I NEVER had the opportunity to 'discover', to inquire, as-it-were. Theodore von Karman, the father of modern aeronautics, quoted in Richard Rhodes, "The Making of the Atomic Bomb", "we never had to memorize equations, and facts. We were allowed to explore. What better training for a scientist!" If this country IS to produce scientists, mathematicians, engineers, doctors, etc. we MUST provide opportunities for our students to explore, to get frustrated, granted with a caring and content expert teacher close-at-hand. I provide my students with many and varied activities to learn the concepts of physics, and upwards of 95% of them go on to earn their engineering degrees and subsequently become professional engineers. Now granted, I balance 'inquiry' with 'direct' instruction. Anyone who thinks at is all one or the other is a fool. When I was a nanvy officer, I was witness to so many of my young sailors lacking in basic mathematics and science when they were undergoing training to maintain some of the most advanced aircraft on the planet. Much time was spent 're-learning' what 'direct' instruction failed to teach because that was the sole method back in their high schools. In closing, there must be a balance between both pedagogies. "A mind is not merely a vessel to be fillled, but rather a fire to be kindled." ~Plutarch

An Army Aviator said...

To Paul Rutherford:

You’re an aerospace engineer. Presumably, you understand aerodynamics. Your students have to learn the concept of Rho before they can apply it in a lift-drag-total aerodynamic force construct. They can’t inquire their way to Rho. They can’t discover lift and drag and resultant total aerodynamic force without the tools that someone must “directly” teach to them.

chen zhao said...

Laurie, I found Where's the Math org and your blog today. Thanks so much and I have been furious with how math is taught at public schools ever since my son moved from a private school to Bellevue's gifted program as a 3rd grader. Bellevue uses Math Expressions. Perhaps better than Everyday Math but I still found errors and misleading questions to confuse kids.

To Paul, you have an interesting point, but my counter point is that the teachers at the schools (especially at elementary level) are NOT ready to teach math in the way that you suggested. Because they do not have advanced degrees in math and science (they don't even specialize - they teach all subjects). They need a more structure curriculum to hand the kids the most basic tools first. And then perhaps at high school level, the kids will be ready to explore with more specialized teachers. Not at K-5. So I agree with the Army Aviator.

I almost got my PhD in math in US and was educated in China K-12. I always say that to be a math and science major coming out the US K-12 system, one must be a genius and natural math person because the education system does nothing to help. So Paul, you must be one of the natural math/science persons. I am naturally more of an artist, but I was so much better in math than most of my peers in US college (because my K-12 was in China) that I majored in math. I know a lot of math/engineering professional from China or India may not be the best "natural" math persons, but the right system can produce engineers more effectively. I am pretty sure that if I had my K-12 in US, I would be an artist, not a data scientist. (I am not arguing which way is better, but as far as the problem is about producing more students who are competent in math, a more structured and systematic approach is more effective at a macro level.

Dawn Llewellyn said...

This has happened in Fairfield, CT with a secondary math curriculum CPM. CPM is a student centered inquiry based pedagogy that has been implemented in our Algebra 1 classes under the guise of Common Core. The sell by administrators was that it best aligned with the mathematics practices. However after months of research and advice from professors and experts in the mathematics, parents found out that the Common Core does not dictate curriculum or instructional model. Our administrators are pure constructivists who are pushing their own pedagogy. The CPM textbook was never approved by the board. CT State Statute10-229 states that any change of a textbook needs two- thirds vote by the board members. Shortly after this statute was presented to Central office,administrators and board members started to change their stories- now the book was a "piloted" textbook not an instructional model.- pilots don't need approval in our district just periodic reports to board- which never even happened. Parents filed with the State Department of Education and this is where we stand as of today -

Parents want to set guidelines and policies for future pilots. With the Common Core at the back door, we can only see more of these implementations happening in the future. Our administrators are not required to provide the parent of the Algebra 1 students with a statistical analysis of the study. There were no benchmarks or metrics in their so called pilot. They used every Algebra I student in the district- no control and comparison groups. They only used "testimonies" to tell parents in May that "feedback" about the program has influenced their decision not to use CPM next year. Our children were basically used as lab rats in an experiment... even lab rats have an official statistical report at the end of their experiment. Dawn Llewellyn-Fairfield Math Advocates

thanh pham said...

Hello everyone,
I'm doing a research about CPM math curriculum.
Anyone have information about the curriculum or any state, school districts drop it, please contact me at PHAMTHANH472@YAHOO.COM
Thank you!

Scott Smith said...

Outstanding blog. For all concerned, there is a concerted effort by WA OSPI to promote "open source" 'curriculum' like Math Vision Project (MVP) - a PURE 'Discovery' scheme with ZERO math content and also EngageNY.

This is promoted as "deeply aligned" and "free". At our district, the intent is to replace Holt with MVP. Not "Free" - parents and tutors have to put in a lot of time to get the kids up to speed. Kids without resourcing at home will - and are - failing.

If anyone has information on MVP, please send to