Credit: Alison Yin for EdSource

The California State Department of Education has released a new draft of its curriculum framework for K-12 mathematics. While it is notably improved regarding opportunities for advanced work, the document is still woefully laden with dogma about politics and about how to teach math.

The framework promotes only the progressive-education approach to teaching math, calling it “student-led” instruction, “active learning,” “active inquiry,” and “collaborative” instruction. But evidence from the 1950s through recent times shows that this way of teaching math is ineffective. That evidence comes from scrutinizing carefully designed studies featuring randomized control and what are called quasi-experiments, which approximate the effect of a randomized assignment of students to different groups. Quasi-experiments look at cases, for example, where two adjoining districts with similar populations or two adjoining similar schools adopt different policies. Both sorts of studies are much stronger evidence than the case studies that progressive educators rely on.

In the spring 2012 issue of American Educator, the magazine of the American Federation of Teachers, top educational psychologists Richard E. Clark, Paul A. Kirschner and John Sweller summarized “decades of research” that “clearly demonstrates” that for almost all students, “direct, explicit instruction” is “more effective” than inquiry-based progressive education in math.

Clark, Kirschner and Sweller conclude that after “a half century” of progressive educators advocating inquiry-based teaching of math, “no body of sound research” can be found that supports using that approach with “anyone other than the most expert students.” Evidence from the best studies, they emphasize, “almost uniformly” supports “full and explicit” instruction rather than an inquiry-based approach. Yet when explicit, direct instruction is discussed in the proposed math curriculum (chapters 3 and 6), it is deprecated.

To be more specific, the framework uses the term “struggle” (or “struggling”) over 75 times, typically in phrases such as, “Students learn best when they are actively engaged in questioning, struggling, problem solving, reasoning, communicating, making connections, and explaining,” or “Teachers should also underscore the importance and value of times of struggle.” While the former is a mouthful and includes essentially everything and the kitchen sink—with a notable exception of “practice”— the latter is a direct pitch for “struggle.” It is as if the authors were guided by Mao Zedong’s old exhortation, “Dare to Struggle, Dare to Win.”

Is it true that student struggle is such a critical component of learning that it should be singled out and treated as primary? The framework offers a variety of cherry-picked citations supporting this idea. Yet, it carefully avoids mentioning that research warns against excessive struggle as time-wasting and discouraging, often leaving students with incorrect understanding. In the absence of such cautions, teachers are likely to walk away convinced that the more they let their students struggle—and struggle is common with the inquiry-based pedagogy promoted by the framework—the more they will learn. This is like saying a child should be tossed in the water rather than taught to swim.

This illustrates two related major flaws that underlie this draft framework: what does “research-based” mean, and the quality of its citations.

State-adopted education programs and recommendations are supposed to be “research-based.” This does not just mean an article or two in a peer-reviewed journal. It means there is a consensus or strong evidence of effectiveness in the published research. If no strong evidence exists, a practice should not be broadly recommended. If there is no consensus, both pro and con evidence should be cited. An example of that can be seen in the Institute of Education Sciences Practice Guides, which identify practices as having strong, medium or weak evidence.

None of this is indicated for “struggle,” or the framework’s push for “inquiry learning” over explicit instruction that is effectively unmentioned in the framework, or its ignoring of highly effective engagement with worked-out problems, or the framework’s lack of any recommendations regarding the proven effective spaced (or distributed) practice — the use of homework and quizzes intentionally spread over a period of weeks after learning a topic, to maximize retention. The focus on inquiry learning, which relies heavily on students’ struggles, has been discouraged by strong research. Distributed practice and use of worked-out examples are supported here and here, yet are ignored in the framework. Instead, the framework offers us “trauma induced pedagogy,” teachers who are considered exemplary for promoting “sociopolitical consciousness,” taking a “justice-oriented perspective,” and embedding “environmental or social justice” in the math work given to children. This is not even a weakly research-based pedagogical framework — this is an ideological manifesto.

In fact, poor and selective research citations undermine much of this framework’s recommendations. Dozens of citations refer to unpublished works on the website of Jo Boaler, one of the framework’s authors. More than five dozen citations of her published works exist in the framework, far more than anyone else’s, yet only a single one of her references was published in one of the top 100 influential education journals. Her 2008 study, cited seven times in the framework, had its accuracy and methodology called into serious question in an analysis by two California math professors and a statistician.

If the framework writers had wanted solid evidence, they would have relied on the final report and subgroup reports of the 2008 federal National Mathematics Advisory Panel. They would have made even more use of the federal Institute of Education Sciences practice guides, which are designed for teachers and curriculum writers. Instead, the framework’s writers pretend this high-quality evidence doesn’t even exist.

•••

Ze’ev Wurman is a research fellow at the Independent Institute, chief software architect with MonolithIC 3D, and former senior policy adviser with the Office of Planning, Evaluation and Policy Development at the U.S. Department of Education.

Williamson M. Evers is a senior fellow and director of the Center on Educational Excellence at the Independent Institute in Oakland, California. He is a former assistant secretary for planning, evaluation and policy development at the U.S. Department of Education.

The opinions in this commentary are those of the authors. If you would like to submit a commentary, please review our guidelines and contact us.

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  1. Tom B. Carvey 3 months ago3 months ago

    I am a middle school teacher and wholeheartedly agree with the contents of this article. Enough of the politics! Our students deserve to be taught math explicitly.

  2. Peggy 3 months ago3 months ago

    I accidentally hit "post comment'. What I wanted to say is that direct instruction seems to work well as the primary means of transferring information. We also reserve time for students to work through problems on the board, with assistance from their peers if they hit a snag. Finally, I give them puzzles to work on outside of class, and I try to make them somewhat challenging but not ridiculously difficult. This seems to inspire … Read More

    I accidentally hit “post comment’. What I wanted to say is that direct instruction seems to work well as the primary means of transferring information. We also reserve time for students to work through problems on the board, with assistance from their peers if they hit a snag. Finally, I give them puzzles to work on outside of class, and I try to make them somewhat challenging but not ridiculously difficult. This seems to inspire friendly competition and engagement with the material, without being a time burden. I find the students’ attitudes toward math seem to improve over the duration of a course.

  3. Norm Budman 4 months ago4 months ago

    I have been tutoring math at the fourth and fifth-grade level for fourteen years in Oakland public schools. The vast number of students come to the fourth grade not knowing the multiplication facts/tables despite being introduced to those in the second/third grade. There is simply not the rigor required in the third grade for repetition and practice required to learn/memorize them and students are behind from that time forward. I agree wholeheartedly with the notion … Read More

    I have been tutoring math at the fourth and fifth-grade level for fourteen years in Oakland public schools. The vast number of students come to the fourth grade not knowing the multiplication facts/tables despite being introduced to those in the second/third grade. There is simply not the rigor required in the third grade for repetition and practice required to learn/memorize them and students are behind from that time forward.

    I agree wholeheartedly with the notion of repetition in the early years to learn math and master the proscribed steps/rules in multiplication, division, and what follows. “Struggle” should be left for later years when requiring application of basic arithmetic to problems solving for unknowns. To not require mastery of the basics prior to needing them on a daily basis for algebra is setting up students to fail.

    So-called “old school” repetition while learning the basics allows quick-learning students to move ahead soon and gives those needing more time the opportunity to be successful. I guess I am just an “old-school” tutor.

    Replies

    • Matthew Hoy 3 months ago3 months ago

      I’ve taught math as a long-term sub for several years. Sadly, I’ve found that many high school age students still don’t have their multipcation tables memorized. It blows my mind when I ask students what 3×7 is and they reach for the calculator app on their phones.

  4. Chester 4 months ago4 months ago

    Math teacher for many years here. Glad to see this debate is alive and kicking. Both sides are right and both sides are wrong. "Struggle" instruction is by far the best, but implementing it in a real classroom is basically impossible. "Direct" instruction, while it allows students to pass carefully setup tests, leaves them with little more than a disconnected mishmash of memorized rules. So take your pick. Some students do learn math (from … Read More

    Math teacher for many years here. Glad to see this debate is alive and kicking. Both sides are right and both sides are wrong. “Struggle” instruction is by far the best, but implementing it in a real classroom is basically impossible. “Direct” instruction, while it allows students to pass carefully setup tests, leaves them with little more than a disconnected mishmash of memorized rules. So take your pick.

    Some students do learn math (from either instructional approach), but they are the few who have the innate ability figure it out on their own. What we need are new ways to teach math progressively, and as long as this debate is active, educators and others will be open to find such ways.

    Replies

    • Zeev Wurman 4 months ago4 months ago

      Actually struggle is not the best. It may work well if the basics are already inculcated but experiments show that students that acquired knowledge through "struggle" do not have any better ability to transfer that knowledge to other problems than those who learned it through explicit instruction. Furthermore, struggle can leave students with misconceptions acquired during lengthy struggle that a brief summary at the end by the teacher will be insufficient to correct. Not to mention … Read More

      Actually struggle is not the best. It may work well if the basics are already inculcated but experiments show that students that acquired knowledge through “struggle” do not have any better ability to transfer that knowledge to other problems than those who learned it through explicit instruction.

      Furthermore, struggle can leave students with misconceptions acquired during lengthy struggle that a brief summary at the end by the teacher will be insufficient to correct. Not to mention the excessive instruction time struggle takes, and the distaste/resentment it fosters towards the subject in many students.

  5. Susan W. Morrison 4 months ago4 months ago

    **sigh** What goes around comes around in educational fad cycles. We went through a period in the '90s when math and language instruction was all touchy feely – accuracy was less important than how you "feel" about your work. Learning times tables? Nah. The students can just use calculators. Never mind that learning math facts trains the brain to see numerical relationships. So it looks like we're at it again in the crazy stuff. Math is all … Read More

    **sigh**
    What goes around comes around in educational fad cycles. We went through a period in the ’90s when math and language instruction was all touchy feely – accuracy was less important than how you “feel” about your work. Learning times tables? Nah. The students can just use calculators. Never mind that learning math facts trains the brain to see numerical relationships.

    So it looks like we’re at it again in the crazy stuff.

    Math is all about numerical relationships. These are fun to discover and fun to practice.

    Struggle? Wow. Maybe we should just give the kids the car keys and let them struggle to learn to drive.

    Oh, but wait …..

    Replies

    • Chester 4 months ago4 months ago

      "Struggle" means "making it your own." It's fitting something new into the right place(s) in your existing intellectual framework. It's usually not obvious (unless you're a genius) where something new will fit in, and that's what the struggle is. Direct instruction, on the other hand, is like painting a wall. It's relatively easy to do, but then you just have this surface thing that doesn't meld in with your prior knowledge. It … Read More

      “Struggle” means “making it your own.” It’s fitting something new into the right place(s) in your existing intellectual framework. It’s usually not obvious (unless you’re a genius) where something new will fit in, and that’s what the struggle is.

      Direct instruction, on the other hand, is like painting a wall. It’s relatively easy to do, but then you just have this surface thing that doesn’t meld in with your prior knowledge. It should be noted that it takes self-confidence and general “hope” for struggle instruction to work. I had some students who were lacking in those qualities, and they hated my method of teaching. Usually I could win them over, but it would be tough going at first. But after they would “get it” and become okay with not immediately knowing the answer, it was a wonderful change to witness. It is an empowering thing you helped them attain.

  6. MICHAEL WILLIAM COMER 4 months ago4 months ago

    If the research indicates that the 'inquiry approach' for math instruction is ineffective when compared to 'explicit instruction', then does the same logic apply to science instruction? The new science standards (including NGSS) seem to expect students to 'discover' the essence of core science concepts through observing phenomena and creating their own questions to investigate without a focus on learning the fundamental concepts from guided investigations, targeted readings, and explicit real world examples. Would … Read More

    If the research indicates that the ‘inquiry approach’ for math instruction is ineffective when compared to ‘explicit instruction’, then does the same logic apply to science instruction? The new science standards (including NGSS) seem to expect students to ‘discover’ the essence of core science concepts through observing phenomena and creating their own questions to investigate without a focus on learning the fundamental concepts from guided investigations, targeted readings, and explicit real world examples. Would seem that the same learning approach in math would be relevant to science since the students are the same.

    Replies

  7. MB 4 months ago4 months ago

    I wish we could have a discussion about the frameworks without the politics. Direct instruction is in fact supported by research (see Marzano). Teachers are often surprised that they can use direct instruction as opposed to the other inquiry based methods (which can also be effective).

    Direct instruction does not mean “drill and kill.” Students especially with limited prior knowledge of a content matter can benefit from direct instruction. This either/or debate is hurting students in the long run.

  8. Jim 4 months ago4 months ago

    Great article! Thank you.

  9. stephanie erickson 4 months ago4 months ago

    Progressive agenda. LOL.

    Replies

    • SFUSD Teacher 4 months ago4 months ago

      I actually wish they would stop using the phrase “Progressive Agenda,” because the casual reader thinks they’re referring to progressive politics, like Bernie Sanders. Progressive Education is actually the name of a style of learning that dates back to John Dewey, and if you take the time to read about it, you’ll see that it’s deeply problematic.

  10. Bill delucchi 4 months ago4 months ago

    The authors work for conservative think tanks. They want to go back to “unscrewing” heads and pouring in facts. Backwards pedagogy in my opinion.

    Replies

    • SFUSD Teacher 4 months ago4 months ago

      Did you read the article? Do you understand what valid research is? I'm 100% liberal, anti-racist, pro-LGBTQIA+, and pro-union. The great thing about math is that it's the "great equalizer," as my hero Jaime Escalante said, and it doesn't lie if done properly. All these authors have done is to state facts. The fact that you dismiss their argument because they work for "conservative" think tanks is precisely what they're talking about. I might not … Read More

      Did you read the article? Do you understand what valid research is? I’m 100% liberal, anti-racist, pro-LGBTQIA+, and pro-union. The great thing about math is that it’s the “great equalizer,” as my hero Jaime Escalante said, and it doesn’t lie if done properly. All these authors have done is to state facts. The fact that you dismiss their argument because they work for “conservative” think tanks is precisely what they’re talking about. I might not like their politics, but their analysis is spot on.

  11. JudiAU 4 months ago4 months ago

    Thank you for excellent and fact based summary.

  12. Maya K 4 months ago4 months ago

    I find it fascinating that all mentions of the grand success that was San Francisco was removed from the second draft as if it never existed at all. 4% failed 8th grade Algebra the 2013/14 year, the last year it was offered. 100 students out of 2359. Not the 40% claimed. If it wasn't for CPRA laws (public data requests) I think the first draft would have passed and the state would be facing … Read More

    I find it fascinating that all mentions of the grand success that was San Francisco was removed from the second draft as if it never existed at all. 4% failed 8th grade Algebra the 2013/14 year, the last year it was offered. 100 students out of 2359. Not the 40% claimed. If it wasn’t for CPRA laws (public data requests) I think the first draft would have passed and the state would be facing SF’s disastrous 7 years. CPRA data: https://drive.google.com/drive/folders/1Ia-NG2dogL1MS-JKkVQEtoG-gmEJKiDC

    I think the state should start from scratch and bring in diverse STEM professors who see what the high schools are sending them and work from there.