Stanford math education professor Jo Boaler spends a lot of time worrying about how math education in the United States traumatizes kids. Recently, a colleague’s 7-year-old came home from school and announced he didn’t like math anymore. His mom asked why and he said, “math is too much answering and not enough learning.”

This story demonstrates how clearly kids understand that unlike their other courses, math is a performative subject, where their job is to come up with answers quickly. Boaler says that if this approach doesn’t change, the U.S. will always have weak math education.

“There’s a widespread myth that some people are math people and some people are not,” Boaler told a group of parents and educators gathered at the 2015 Innovative Learning Conference. “But it turns out there’s no such thing as a math brain.” Unfortunately, many parents, teachers and students believe this myth and it holds them up every day in their math learning.

“We live in a society with lots of kids who don’t believe they are good at math,” Boaler said at an Education Writers Association conference. “They’re put into low groups; they’re given low-level work and their pathway has been set.” But math education doesn’t have to look like this.

Neuroscience research is now showing a strong connection between the attitudes and beliefs students hold about themselves and their academic performance. That’s a departure from the long-held traditional view that academic success is based only on the quality of the teacher and curriculum. But researchers like Carol Dweck, Camille Farrington and David Yeager have shown repeatedly that small interventions to change attitudes about learning can have an outsized effect on performance.

Neuroscientists now know that the brain has the ability to grow and shrink. This was demonstrated in a study of taxi drivers in London who must memorize all the streets and landmarks in downtown London to earn a license. On average it takes people 12 tries to pass the test. Researchers found that the hippocampus of drivers studying for the test grew tremendously. But when those drivers retired, the brain shrank. Before this, no one knew the brain could grow and shrink like that.


“We now know that when you make a mistake in math, your brain grows,” Boaler said. Neuroscientists did MRI scans of students taking math tests and saw that when a student made a mistake a synapse fired, even if the student wasn’t aware of the mistake. “Your brain grows when you make a mistake, even if you’re not aware of it, because it’s a time when your brain is struggling,” Boaler said. “It’s the most important time for our brains.”

A second synapse fires if the student recognizes his mistake. If that thought is revisited, the initial synapse firing can become a brain pathway, which is good for learning. If the thought isn’t revisited, that synapse will wash away.

A recent study of students with math learning disabilities found in a scan that their brains did behave differently from kids without the disability. “What they saw was the brain lighting up in lots of different areas while working on math,” Boaler said. The children were recruiting parts of the brain not normally involved in math reasoning.

The researchers tutored the group of students with math disabilities for eight weeks using the methods Boaler recommends like visualizing math, discussing problems and writing about math. At the end of the eight weeks, they scanned their brains again and found that the brains of the test group looked just like the kids who did not have math disabilities. This study shows that all kids can learn math when taught effectively. Boaler estimates that only 2 to 3 percent of people have such significant learning disabilities that they can’t learn math at the highest levels.

People who learned math the traditional way often push back against visual representations of math. That kind of thinking represents a deep misunderstanding of how the brain works. “When you think visually about anything, different brain pathways light up than when we think numerically,” Boaler said. The more brain pathways a student engages on the same problem, the stronger the learning.

An example of many ways to visually represent 18 x 5.
An example of many ways to visually represent 18 x 5. (Jo Boaler/YouCubed)

GROWTH MINDSET AND MATH

Increasingly, educators are buying into the compelling research showing that what students believe about themselves affects how their brains approach learning. Growth mindset is probably the best known aspect of this research, and many school leaders are trying to figure out how to implement growth mindset programs in their classrooms.

“More kids have a fixed mindset about math than anything else,” Boaler said. And it’s no coincidence that they feel this way. Teachers often believe their students can’t achieve at the highest levels, and in turn, students believe that about themselves. Plus, the tasks themselves communicate a fixed mindset.

“It is very difficult to have a growth mindset and to believe that you can grow or learn if you are constantly given short, closed questions with a right or wrong answer,” Boaler said. Instead, she recommends giving visual problems that provoke discussion and have multiple ways they could be solved.

She also says kids should not be grouped by ability or tracked into “advanced” or “remedial” groups. That common practice sends fixed mindset messages to students, both the “advanced” ones and the “low-performing” ones. Kids considered to be “gifted” suffer from ability grouping the most because they develop the ultimate fixed mindset. They become terrified that if they struggle they’ll no longer be considered smart.

Instead, mixed ability grouping can work if the tasks are open-ended and what Boaler calls “low-floor/high-ceiling” tasks that allow every student to participate, while allowing lots of space within the task for students to grow in their thinking.

Boaler has lots of example tasks on her website, YouCubed, and on the NRICH website.

PUTTING IT INTO PRACTICE

During the summer of 2015, Boaler invited 81 seventh- and eighth-graders from a low-income district near Stanford to come to a summer math camp focused on algebra concepts. She gave the students a pre-test and found that their abilities ranged from very low (getting 0 answers correct) to fairly high. Then, for 18 days she taught them math well.

The instructional program focused on mindset messages, was full of inquiry-based, low-floor/high-ceiling tasks, was visual and used mixed achievement groups. At the end of 18 days, when Boaler gave them another test they had improved on average by 50 percent.

“They improved because they changed their beliefs that they were not a math person to believing they were a math person,” Boaler said. After the course, students said they looked forward to math and saw math as a creative subject.

Administrators from the district came to observe partway through the camp and couldn’t tell who was a low achiever and who was a high achiever in the class. Boaler also makes it clear to the students in the workshop what she expects from them, and speed is not something she’s evaluating. Instead, they do norm building so that everyone knows how to appropriately work in groups, help one another and be supportive.


“If we don’t pay attention to those kinds of interactions, and kids are dominating, or thinking they’re smarter, then we’re really in trouble,” Boaler said.

Removing the time pressure from math is another important issue for Boaler. Neuroscience research out of Sian Beilock’s lab at the University of Chicago has shown that time pressure often blocks the brain’s working memory from functioning. This is particularly bad for kids with test anxiety.

“The irony of this is mathematicians are not fast with numbers,” Boaler said. “We value speed in math classrooms, but I’ve talked with lots of mathematicians who say they’re not fast at all.” But it is common for math teachers to call on the kids who get the answer quickly, reinforcing the idea for all students that rapidity is what matters.

COMMON PUSHBACK

Math education experts have been making the same case as Boaler for decades, and yet math education in the U.S. has not shifted much. Teachers often say they have to cover all the topics in the curriculum to prepare students for the tests they will be expected to pass, leaving them with no time for the kinds of open-ended, discussion-based math that Boaler advocates.

Boaler agrees with teachers that there is way too much to cover in the curriculum, especially because she finds much of it to be obsolete (don’t get her started on the textbooks themselves). “The most important thing we can give kids is to think quantitatively about the world and apply a mathematical lens to different situations,” she said.

In addition to teaching students, Boaler trains teachers in her methods. Often they go back to their classrooms and apply these theories, which means they aren’t covering every topic in the textbook, and yet their students do better on the standardized tests anyway. Boaler is not a fan of all the tests American students must take, but she says teaching math the right way deepens kids’ understanding of math in real ways that show up on tests, too.

Teachers and parents often push back against this kind of math. They wonder where memorization of math facts fits into the model, given the belief that kids must know their times tables to succeed in higher-level math. Boaler says that’s unnecessary. She is a math education teacher and has risen to high levels of math learning without ever learning her math facts. She has number fluency, knows how to manipulate numbers and understands concepts, but she doesn’t have her math facts memorized.

The Programme for International Student Assessment test (PISA), which is often used to compare achievement across countries, has a section about attitudes and beliefs. Those surveys show that kids who approach math as memorization are the lowest achievers in the world. “America has more memorizers than almost any country in the world,” Boaler said. The highest achievers are those who think about the big ideas and make connections.

Likewise, repetition of math tasks is not helpful to deep learning. The same kind of problem with different numbers does not improve understanding, Boaler said. What students really need is “productive practice,” approaching the problem from different directions, applying the ideas and explaining reasoning.

Boaler is on a mission to “revolutionize” how math is taught in the U.S. She has written several books to help teachers learn to teach with her methods, offers a free online course, and even gives away curriculum for teachers, students and parents on her YouCubed website. During one week at the start of the 2015 school year Boaler gave away five free math lessons, encouraging teachers to try this approach. She’s pleased that 100,000 schools tried the lessons, and teachers could see the difference in their students. A survey of students found that after the lessons and the growth mindset videos, 96 percent believed they should keep trying after making a mistake in math.

Boaler said a big problem is that math teachers themselves are math-traumatized. They came through a system very similar to the one in which they work. Elementary school teachers in particular often feel insecure about math.

“When they try math in these ways they get it, too,” Boaler said. “They can see this is much more valuable and enriching.”

‘Not a Math Person’: How to Remove Obstacles to Learning Math 30 November,2015Katrina Schwartz

  • Educational leader

    Excellent article and absolutely agree! This movement is necessary and we need to keep moving forward in this direction.

  • Kim

    boaler’s work is very compelling and, as a parent with two kids in high-need san francisco public schools, i agree with most of her conclusions. unfortunately, my kids’ 3rd and 7th-grade classrooms do not mirror the laboratory conditions her team carefully creates and cultivates, and i expect most comparable schools’ don’t either (our schools are 65% and 75% free/reduced, respectively; their teachers have ranged from good to excellent). i am a fan of common core math generally; it’s great. i am not a fan of SFUSD’s untested, undefined, unsupported and grossly undervalidated reliance on “differentiation” as a replacement for the rigor of the middle-school and 9th/10th grade “honors” math curriculum, which SFUSD has eliminated in a scorched-earth campaign as part of its detracking effort. (in an impressive sleight of hand, SFUSD pretends that taking algebra I off the table in middle school is dictated by common core implementation, when in fact, nearly all other large urban districts maintain it as an acceleration option so students can follow a normal path to AP calc by 12th grade and become competitive STEM program applicants.) in any case, two of boaler’s statements in particular raised red flags for this veteran equity school parent: “’low-floor/high-ceiling’ tasks that allow every student to participate” and “instead, they do norm building so that everyone knows how to appropriately work in groups, help one another and be supportive.” sounds sensible, don’t it? even innocuous. well, let me tell you: it looks a little different in heterogenous classrooms with 8-year — yep: 8 YEARS — ability spreads, undersupported teachers and kids with social-emotional-behavior issues requiring level 2 and 3 intervention. kids who are ready to move faster find the pace in these classrooms much too slow to provide an adequate challenge. some students are incapable of participating for a variety of reasons (illiteracy, EL, trauma, etc.), making this utopian ideal of participation by all a pipe dream. and norm building? sounds great; i’m sure my kid’s friend would have been better able to exercise her right to an “equal” education if she had not been forced to “tutor” a classmate who called her “bitch” on the daily, or if he had been gently informed by ms. boaler that one should refrain from calling one’s classmates by that term during long division. my 7th grader never complains and has had a decent experience overall, but i worry about the long-term effects of the tactics used in boaler’s name, and in the name of detracking: if higher achievers with discipline, interest, stamina and hunger for learning math are constantly told they are “elitist” or “racist” for wanting more, wanting it faster, or wanting it delivered in a civil manner, why should they persist in caring?

  • Comprendio

    I love this article. Explaining one’s reasoning for math problems (and other problems in various subjects) is something that’s definitely needed in the classroom environment, but the difficulty is really finding a safe space where students can do this and receive quality feedback. Comprendio’s platform bit.ly/demo_comprendio has been designed to provide a safe space where students CAN explain their reasoning and receive immediate and individualized feedback based on their responses. Here’s our most recent piece on how Comprendio supports the growth mindset in students and educators: bit.ly/mindset_comprendio

  • StopItJoBoaler

    Kim below makes some extremely important points about the inability to replicate Boaler’s “research” and the KQED writer certainly should mention the decades of controversy about that very point. She was caught red-handed fabricating and manipulating research.

    Her free lessons are worth exactly what you pay for them. She is flat out wrong about memorization. KQED and Stanford are doing students and teachers a grave disservice continuing to give her this platform to spread these “beliefs.” And disappointed KQED presents so much of it as “the right way.” That’s simply untrue.

    There are at least a few vaild points here and you can see Boaler trying to pivot to points that are slightly more logical and fact based. But by the end of the story we are back in dangerous story saying “memoriziation is bad and harmful” and “develop multiple strategies with open ended discussions” and “wrong answers are OK.”

    ANy news organization that covers her certainly could do ten minutes of work to find out how much DoE and NSF grant money she has eaten up propagating this drivel.

    • Jo Boaler

      This comment comes from a person who calls themselves “stopJoBoaler”. This should be the first sign to everyone that the comment comes from someone with no legitimacy who is pushing a position. I should point out to this person that any public comment accusing me of fabricating/manipulating research goes straight to my lawyer. This claim has been made before and people can read about it here: http://stanford.edu/~joboaler/

      Stanford University rejected the false claims (made by retired, white males who don’t want math change) of manipulating data . It turns out that it is illegal to make untrue statements about people to damage their reputation. It is called “defamation”. My advice to “stopJoBoaler” is: look it up. Honest and collegial debate is a great thing, retorting to defamatory comments is not.

      • Wise Mathbc

        “…made by retired, white males who don’t want math change”. Now who’s making the racist comments? I’m all for following research as long as its valid, quantitative and easily adaptable to enforce. Hard to find that here. And puhleeze…your claim that memorization harms children is more damaging than any timed multiplication test will ever inflict.

    • Michael

      As WW Sawyer put it in 1943 – memorising without understanding is just an “imitation of math”. It might appear to work for some who can jump through the hoops to pass math exams, but if math education needs more of the same diet it has laws had, why are US and UK falling behind. I understand the fear of change (I’m a math teacher), and no doubt anyone can take a good idea and make it a failure if they want to, but Jo Boaler’s research and methods work for more pupils than ‘traditional’ (and dull) drill and practice (in my experience)

      The world has moved on from the Dickensian utopia some long for – pupils deserve a math education that excites and engages them rather than suffering with the sense of failure that many feel about math.

    • rad76dude

      StopItJoBoaler,

      Your comment seems like an answer to a Presidential debate question. Bold statements without your owning research backing anything, and cherry picking sentence fragments out of context and blowing them out of proportion.

      “memorization is bad and harmful” – If you watched the video lessons, Jo says that memorization has it’s place, but to only teach memorization and to assess students on it is harmful. As students come to my middle school math class, one of the biggest struggles is breaking students of the mindset that if they can’t answer 30 math facts in 120 seconds, then they are bad at math and will never be able to achieve in the subject.

      “wrong answers are OK.” – As long as you learn from them. When students know that, Mistakes are Expected, Respected and Inspected, they are more likely to take chances, try new things and believe they can learn.

      I offer up my class as an opportunity for you to come observe how these beliefs can be instilled in students, and still maintain high mathematical expectations for students. And if you are not open to observing the benefits of these beliefs, then you can keep your Fixed Mindset drivel to yourself.

      • Maestra Malinche

        I like that: “Mistakes are Expected, Respected, and Inspected”. I often give prizes for interesting mistakes in my Spanish classes!

  • ACClark

    Unfortunately for the author of this article, the methods used to tutor kids to ameliorate their math performance issues included just those types of methods this article cautions against. So which is it: learn math facts to automaticity via timed exercises to free up working memory as the research you cite used, or follow Boaler’s unpublished theories?

    “Tutoring sessions. All children took part in an 8-week math tutoring program
    adapted from MathWise17,19,40. The tutoring combined conceptual instruction
    with speeded retrieval of arithmetical facts. The focus of the tutoring included
    strengthening of number knowledge (for example, cardinality) and relations within
    and between operations (for example, commutativity and inverse relation between
    addition and subtraction) that facilitate the use of sophisticated counting
    procedures and retrieval-based processes. The tutoring also incorporated a strategic
    practice component, that is important for building automaticity40, and decreasing
    load on cognitive resources (for example, working memory and non-verbal
    reasoning)62. This practice was designed to promote quick responding and use of
    efficient counting procedures to generate as many correct responses as possible,
    which in turn supports the formation and strengthening of representations in longterm
    memory63,64. Similarly to MathWise40, the tutoring involved a total of 15–
    20 h of tutoring. Differently from MathWise, for which tutoring occurred over the
    course of 15–16 weeks, the present tutoring was condensed to 8–9 weeks. Thus, the
    current tutoring had longer sessions—from 40 min to 50 min—to equate overall
    time on tutoring. Specifically, the present tutoring consisted of 22 lessons of
    increasing difficulty (details of each lesson and the tutoring material are described
    in the Supplementary Methods).”

    • ACClark
      • RCraigen

        Well caught! From the same article,

        We used a tutoring program that
        combines conceptual aspects of number knowledge and speeded
        practice
        on efficient counting strategies and systematic learning of
        number families. These components are designed to facilitate
        arithmetic fluency, and have previously been validated in school
        settings
        17–19,39–41 (Fig. 1a,b).

        Note: “speeded practice”

  • ACClark

    And the paper you cite to support the claim that “time pressure often block’s the brain’s working memory from functioning” doesn’t even contain any mention of “time pressure”, and instead is about how math anxiety impacts math performance. Did the author of this article even read the abstract?

    “Although math anxiety is associated with poor mathematical knowledge and low course grades
    (Ashcraft & Krause, 2007), research establishing a connection between math anxiety and math
    achievement has generally been conducted with young adults, ignoring the emergence of math
    anxiety in young children. In the current study, we explored whether math anxiety relates to young
    children’s math achievement. One hundred and fifty-four first- and second-grade children (69 boys,
    85 girls) were given a measure of math achievement and working memory (WM). Several days later,
    children’s math anxiety was assessed using a newly developed scale. Paralleling work with adults
    (Beilock, 2008), we found a negative relation between math anxiety and math achievement for
    children who were higher but not lower in WM. High-WM individuals tend to rely on WM-intensive
    solution strategies, and these strategies are likely disrupted when WM capacity is co-opted by math
    anxiety. We argue that early identification and treatment of math anxieties is important because these
    early anxieties may snowball and eventually lead students with the highest potential (i.e., those with
    higher WM) to avoid math courses and math-related career choices.”

  • LaurieHRogers

    Jo Boaler has been a long-time advocate of concepts and processes and approaches like those that have been failing children for the last 30 years. In answer to the charge that an over-emphasis on inquiry-based math interferes with the learning of math, advocates of inquiry-based math just say, “The schools aren’t doing it right.” They’ll say that until they run out of breath, which will be long after our children have been harmed for life.

    The article says this: “Boaler said a big problem is that math teachers themselves are math-traumatized. They came through a system very similar to the one in which they work. Elementary school teachers in particular often feel insecure about math.”

    Those two sentences, taken out of the context of the rest of the article, are true. How infuriating to know that the math teachers – and elementary school teachers in particular — have been completely damaged by the foolishness espoused by people who do not believe in direct instruction, memorization, or systematic practice to mastery of the most-efficient, most-effective algorithms.

    So many of the talking heads who prattle at length in the media about how to teach math do not actually use math in their daily lives as it is meant to be used, as a tool to get a job done. In math, correct answers are everything — in building roads, measuring medicine, constructing the skyscraper, and calculating one’s finances. People need to understand each other, so they need to use the same math language. They need to check each other’s work, so they need to know what they’re looking at. They need to get their answers quickly and efficiently, so number sense is important, knowing their math facts is critical, and being able to estimate before the calculator does the work is incredibly helpful.

    Jo Boaler and her work are well known in math advocacy circles. It is the opinion of many in those circles that she has not been a friend to the proper instruction of math.

  • Wayne Bishop

    Jo Boaler’s response to StopItJoBoaler’s comment refers to a self-serving “poor me” non-response to a study done by three of us including a Stanford PhD in statistics who used the very carefully selected and selective data from the state database included in her own articles then on her website to uniquely identify the 3 schools of her famous, five-year, NSF-funded “study” (school’s names available on request). The schools of the data were scrupulously not revealed to independent researchers in clear violation of Stanford’s policy on openness of research for the most obvious of reasons; the full state data of the schools reveal the exact opposite of her assertions. Her justification for concealing their names is a standard education industry misinterpretation of human subjects research restrictions – identification of the individual students is illegal but not the schools or even the instructors involved unless, by implication, students could be identified. As she freely admitted, her conclusions were based on her own assessments – see Debra Viadero’s almost offhand statement in this EdWeek article long ago (in which I was accurately quoted as an agnostic):

    http://www.edweek.org/ew/articles/2005/02/16/23math.h24.html?querystring=viadero&levelId=2300

    “On California’s state-mandated tests, Railside students did no better than those in demographically similar schools.”

    “Did no better” was quite an understatement – in fact it was the lowest of the low across the entire state of California. In the last year of the data of her study, Railside was the least effective regular public high school in California. To start with, it was a 1-1 school – in the bottom 10% of all high schools overall and in the bottom 10% of 100 comparable schools. Restricting the data to those schools that were 1-1 (different schools in the 1st decile have different comparable schools so hundreds of schools, not 10% of 100), it was the absolute lowest except for six or seven special schools (a state school for the deaf and several “continuation” schools, schools that districts set aside for their especially problematic students, in affluent districts such as Palo Alto). Other misleading claims as reported by Viadero? “41 percent of the Railside students had taken calculus by the end of 12th grade, compared with 29 percent of the students at each of the other schools.”

    Reality? As opposed to those other two schools, no one at Railside took the national AP Calculus test in the entire 5 years of her study and, based on Venn diagram analysis of CSU admissions and the ELM (the system-wide Entry Level Math exam), many of those “had taken calculus” students who were admitted to some CSU campus had to begin in noncredit remedial math.

    Do take her warning about criticisms being turned over to Stanford’s lawyers seriously; she did exactly that with me after that Viadero article appeared. Ironically, her paranoia was what saved me. Because she had refused to name the schools to the reporter and to me, I started my search identify the schools and fortunate that I did. She started a serious inquiry and, when their lawyers contacted ours who reported my discretions to my campus president, he appointed a committee to inquire into the damning details of my supposedly unprofessional activity. The first meeting with the committee was really quite scary. Since I had never seen the indictment (or knew that there was one), I strongly felt that I was being assumed guilty unless proven innocent. On receipt of same, I prepared a rather lengthy point-by-point response to the accusations including quotations from links to the situations so badly misinterpreted by Boaler to her lawyers and submitted it – along with the actual school data – to the committee before our second meeting. That meeting never occurred. On the strength of my rebuttal, the committee recommended to the president that no action was warranted and he sent me a letter assuring me that there would be no record in my file.

    Years ago, she promised to provide a point-by point rebuttal to the peer-reviewed, but never published, article referred to in her website link in her short response. If it ever appeared, which I doubt, I would like to see a copy. Why was the article never published? In response to the concern at Stanford, she resigned her post and returned to her native England so we pulled the article to avoid making Stanford look bad by association since it seemed to be no longer needed. No one anticipated her return or her level of vindictiveness. The article is still available at the website of one of the authors:
    http://math.stanford.edu/~milgram/combined-evaluations-version3.pdf

    wbishop@calstatela.edu

    • Doug Holton

      This page has some info on Wayne Bishop in connection with Jo Boaler: https://web.stanford.edu/~joboaler/

      • beaminup

        If you read the respons(ehttp://math.stanford.edu/~milgram/Jo-Boaler-reveals-attacks-AccusationsResponse-trans.html) to that website it would appear that Dr. Boaler is in fact the bully. She is the one who tried to ruin Dr. Bishop’s career based on information that she received through nefarious channels. She is the one who seems to threaten anyone that would cross her with a lawyer whether truth or not, http://blogs.discovermagazine.com/neuroskeptic/2016/03/26/brain-on-maths-educational-neurononsense/#.VxO8ImN7gyx She tries to win her arguments, not by logic, reason and debating the issue with supported data but by an appeal to authority. https://twitter.com/doctorwhy/status/713941135819935744

        She gives advice to parents on how to “help” kids in which she encourages parents to lie about their own math ability. Item number 4 from the following document
        https://iusd.org/ea/documents/Parent-Night-Handout-vF.pdf

        And yet her ‘research for which she has never answered the legitimate questions raised in Dr Bishop’s and Dr. Milgram’s paper, is fausted on my school and I am forced as a parent to deal with her nonsense indirectly as a parent. It infuriates me that those in high castles never demanded that such an important study be replicated before being passed on to entire nations. She used a ridiculously small sample size. Is there a possibility that the results she found in some way reflect the demographic of the city she chose, and not her purported variable of interest? A question which was never asked. Why on earth did they not try to replicate this, not in a measly 3 schools in a single state in CA. It should have been tested in multiple states and methods should be readily available. I deserve as much being the parent of children who will have to suffer if in fact hidden variables that she did not account for were responsible for the results she achieved. But hey, her results are so important that instead of finding a way to let it be replicated, she does all in her power to hide the process.

        Thanks Dr. Boaler for performing your experiment on my children without proper research to back up your claims, and without my permission. If you’re wrong do I get to sue you in 15 years when my kids graduate, and can’t do math because your ideas were incorrectly tested? Didn’t think so. At that point what good would it do my children anyhow? They will have been forced to go down a path because of your pride. Please do me a favor as a parent. Get over yourself and let your work be validated, and that is not the same as your university vouching for you. You really can’t win by an appeal to authority no matter how you try it is a logical fallacy.

  • Lcs

    Look, if you have to resort to some special tricks or dog and pony show to get the slower kids to learn math, ok. But don’t hold back the smart ones who have a natural affinity for math. This silly notion that everyone has equal ability to fathom abstractions is obviously wrong to anyone who has spent time around bright kids and dumb ones.

    • Maestra Malinche

      Everybody has a natural affinity for learning languages; this is why we speak. I have many special Ed students who are bilingual. By your assumption, we can pick out those who can and those can’t by some measure of “natural affinity”. If this were the case, then we would see equal proportions of rich and poor, female, male, black, brown, white and Asian in our tracked math classes. I think Jo’s work is important for bringing in more students, and to expand on all of our students’ natural affinity for abstract thought, creativity and collaboration. At the same time, I agree with Kim’s argument that you can have too wide of a spread in your classes. I also think that memorizing certain math facts is important for speed and math fluency. I have newcomers from war torn countries who are learning how to count at age 15. It would be a disservice to not teach them basic survivor math skills first- and create some math facts memories.

  • Ki Sung

    A previously removed comment has since been restored.

  • Carissa

    I want to do the free online course about adjusting our thinking about math, and the 5 free math lessons with my kids over the summer. Should I do the courses first, then do the lessons, or do they dovetail so that we should do them somewhat simultaneously?

  • I watched your little, 7-minute video about Complex Instruction and I was in tears by the end of it – tears for myself as a child who, as one of the smart ones who was taught all along that I was smarter, only got thru math classes because I could memorize! I never like math and never understood it until years later, in teachers’ college, I took a course in how to teach math and I had a chance to play with cuisinaire rods. Those experiences helped me understand math in ways that fit my brain. But the tears were also for my several years of grade school teaching experience, when I felt I had no choice but to encourage 4th graders to memorize their times tables and division tables. I love that new teaching methods are being developed to actually help children explore and learn how math works and to enjoy the learning process!

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Author

Katrina Schwartz

Katrina Schwartz is a journalist based in San Francisco. She's worked at KPCC public radio in LA and has reported on air and online for KQED since 2010. She's a staff writer for KQED's education blog MindShift.

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