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couple of years ago the so-called “Reading Wars” were in the spotlight as schools started passing laws to prohibit the “three cueing” method or to mandate that teachers teach phonics in class. Three cueing was based on the idea of whole word reading and essentially taught children to guess words based on pictures and context clues. Among the foundational ideas informing this method are that children will enjoy reading more if they are not drilling phonics and also that reading is as natural as speaking and that if children simply have enough books around them, they will learn to read. Sight words became the preferred method of reading, with the idea that even though English writing is phonetic and not symbol and character based like Chinese, for example, that children should read words by memorizing how they look. The curriculums that used these methods such as the Fountas and Pinnell and Lucy Calkins’s Readers Workshop were both very popular and very lucrative. However, reading scores plummeted as these curriculums became widespread. States that have pulled up their reading scores dramatically are the ones that passed laws against three cuing and several schools even in very poor areas who simply never got on board with the three cuing and sight words trend and kept their “old fashioned” phonics curriculums had reading scores better than some of the schools in wealthier areas.
Get ready for the same thing to go down with math. Much like phonics vs. sight words debate, the controversy surrounding the Science of Math comes down to whether it’s better for students to learn with teacher led, step-by-step direct instruction and drilling math facts, or if student led inquiry and discovery based learning based around concepts is better (Barshay, 2023). The Discovery Led Learning model posits that children learn better when they are given concepts to work with and then allowed to engage in “productive struggle” to figure out how to solve a challenging problem on their own. It posits that having a growth mindset (“I can’t do it now, but I will be able to do it eventually”) will help them do this, but these ideas are not proven to be helpful at all (Henebery, 2022). (And now it’s making sense why my oldest was coming home from 6th grade talking about “growth mindset” and why so much classroom decor I see is focused on telling students that if they can’t do it now they will be able to later. This theory is so engrained in teaching that it’s in the classroom decorations!) A Discovery Based teaching model holds that teachers should give students examples and let them make observations about the concept they are learning. The idea is that students will build independence and self efficacy because they will know that they did it by themselves. Graphic organizers are especially recommended for this type of teaching (Chiapetta, 2023). (It’s all coming together now. Here’s the origin of all the trendy graphic organizers and Foldables!) Productive struggle seems to be an integral part of Discovery Led Math. Since the teacher isn’t supposed to actually teach anything, the student has to figure things out.
Another thing that is being pushed by the CMF is to avoid tracking children into below average, average and above average levels out of a fear that children in lower tracks will become self-fulfilling prophecies of underachieving because they don’t see themselves as being good at math and also to have students take less advanced math in middle and high school There’s an emphasis on group projects, no tests and real world applications (Galchen, 2022). There is also a distaste for drilling and rote memorization, fearing that memorizing concepts means that children won’t actually understand math, and that will simply be parroting back facts. Discovery Based math also has no timed assessments because they create anxiety (Parker, 2015). There is a desire among the Discovery Based Math camp to have children develop a “positive mathematics identity” as an outcome of math teaching. (I think this means that they think of themselves as “math people” or as a person who loves math.) Another goal of mathematics education is the rather nebulous objective of having children use math as an expression of creativity and humanity. A rather odd argument from the discovery camp is that explicit teaching of mathematics is a “pedagogy of poverty”. They state that it was the standard in urban schools and that in predominantly Black and Hispanic classrooms there is less inquiry based and more teacher based instruction. It seems that because direct and explicit teaching is used in minority and urban schools it’s somehow equated with being less effective. Another argument they have against direct teaching is that rote learning and explicit instruction will have children simply mimicking the teacher without understanding the concepts. There’s also a concern that children won’t find math fun and that it should be appealing (NCSM, 2025). The Discovery Math camp uses words like “passion”, “creativity”, “expression”, and “humanity” to describe their goals for student outcomes in math. Those are conveniently not quantifiable. While math can be a passion or a creative pursuit, it can’t unless students understand how to actually do math.
Jo Boaler, a mathematics teaching professor at Harvard, has been a vocal proponent of many of these ideas. Much like Lucy Caulkins and Fountas and Pinnell with their extremely lucrative whole language based reading curriculums, she’s now coming under fire for her promotion of Discovery Based math and the large consulting fees she charges to schools to implement her ideas. She’s one of the chief architects of the 2023 CFM (Galchen, 2022). Lately a lot of attention has been focused on the 2023 California Math Framework, but the problem of most kids being unable to do math was there before the Science of Reading started in 2020 and it’s been a concern in other countries. A key paper about mathematics teaching myths came from Australia. And the source I cited from Stanford about Jo Boaler and Discovery Based Mathematics was from 2015. The Discovery Based Mathematics camp is digging in their heels as the Science of Math gets traction and defending their claims as seen in the NCSM paper, but the proof is in the pudding. Math scores and competence in the US, but particularly in California are down. American 15 year olds rank 37th of 79 industrialized countries in math. California is frequently in the lowest quartile for US math achievement (Galchen, 2022).
The interesting thing is that whether it’s reading or math, the same underlying principle seems to be at play with these discredited— but popular— methods: Children already have all the skills/knowledge/capability to do the reading or math, the teacher just needs to let them discover the reading or math. In this model, a teacher is like a gardener. The plant already knows how to grow and will grow on its own, the gardener just needs to set the right conditions for the growth to happen. It’s a very appealing idea. It’s not harsh or strict and it seems to be very nurturing and it aims to promote independence. It reminds me of a quote in Tom Wolfe’s Bonfire of the Vanities: “When the Movement was going strong one of the things we tried to do on campuses was to break down the wall of formality between faculty and students, because it was nothing but an instrument of control.” The irony is that it’s also very similar to an educational idea that every teacher I have seen roundly criticizes: unschooling. In unschooling, the idea is that the child leads the learning and the child learns through every day experiences, more or less. Though there are some nuances and differences, both philosophies take the stance that the child doesn’t need an adult to teach them and that learning is more enjoyable when it isn’t being directed. But while teachers deride unschooling, they promote a similar form of it, as long as it is in the classroom. This “child led” form of teaching seems to have informed teacher training as well. Most math teaching degrees in Australia didn’t teach teachers how to actually teach students (Henebery, 2022). The Science of Reading podcast discussed many times how elementary school teaching degrees haven’t been teaching teachers anything about how to teach reading. But this approach to teacher training is probably informed by the idea that teachers shouldn’t actually teach students. They are merely there to support students’ discovery. The teacher led classroom has been viewed as an “instrument of control” and the idea was that breaking down that barrier by getting away from direct instruction would lead to happier schools and better performing students. But it’s been the opposite.
There seems to be some contempt for the Science of Math because it seems to follow the pattern of the Science of Reading movement. There’s a backlash against current practices and philosophies which focus on being child-led, being unscientific and they take aim at women who have heavily promoted and profited from these practices and philosophies. I don’t think this is a matter of the Science of Math movement creating a problem just to get attention for their ideas and copying the Science of Reading. I think it’s a reflection of how educational policy and practice gets accepted. These ideas sound good and have popular promoters who promise solutions and that takes precedence over actual evidence and research.
The fact is that American education has been in a crisis for decades and it needs to change. But I think everyone knows that now, even if they don’t want to admit it. In my experience though, direct instruction doesn’t lead to students feeling oppressed or controlled or bored. Breaking down the steps and showing them how to do math opens it up for them. The light bulb moments happen and they get excited when they crack the code. I was subbing in a mild to moderate SPED class one day and I had a group of girls who needed to work on long division. They were alternating problems and as we went over each one step by step, they started to get it. One girl started getting really good at it and then she wanted to do the next problem, but the girl next to her said that was hers and she couldn’t have another one. As our session wound down, the first girl said her class was probably doing something boring and she wanted to stay and do more math. And I found myself uttering the words I never in my life thought I would say, “I know math is fun, but I still have to send you back to class now.” Math can be fun, but not when it’s shrouded in mystery and they are left to fend for themselves. It’s magical when kids are given the tools and information and the practice they need to get good at it.
Sources
Barshay, J. (2023 May 8). Proof Points: How a debate over the science of math could reignite the math wars. Hechinger Report https://hechingerreport.org/proof-points-how-a-debate-over-the-science-of-math-could-reignite-the-math-wars/
Chiapetta, E. (2023 August 21). Teaching Math Through Discovery. Edutopia https://www.edutopia.org/article/discovering-mathematical-truths-middle-high-school/
Galchen, R. (2022 September 8). California Students Are Struggling in Math. Will Reforms Make the Problem Worse? The New Yorker. https://www.newyorker.com/science/elements/california-students-are-struggling-in-math-will-reforms-make-the-problem-worse
Henebery, B. (2022 August 11). Harmful myths undermining maths teaching – new report. The Educator Australia. https://www.theeducatoronline.com/k12/news/harmful-myths-undermining-maths-teaching--new-report/280786
National Council of (2025). Strengthening Research Informed Decision Making for Mathematics Education: A Position Statement from NCSM. https://www.mathedleadership.org/wp-content/uploads/2025/12/Position-Paper-2025-Strengthening-Research-informed-Decision-REV12-25.pdf
Parker, C.B. (2015 December 17). Cultivating a growth mindset in mathematics. Stanford Graduate School of Education: News and Media. https://ed.stanford.edu/news/cultivating-growth-mindset-math
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