A recent New York Times commentary by American engineering professor **Barbara Oakley** has, once again, stirred up much public debate focused on the critical need for **“Math practice”** and why current **“Discovery Math”** methodologies are hurting students, and especially girls. *“You and your daughter can have fun throwing eggs off a building and making paper-mache volcanoes, “* she wrote, “*but the only way to create a full set of options for her in STEM is to ensure that she has a solid foundation in math.” *Mathematics is “the language of science, engineering and technology,” Oakley reminded us. And like any language, she claimed, it is “best acquired through lengthy, in-depth practice.”

That widely-circulated commentary was merely the latest in a series of academic articles, policy papers, and education blog posts to take issue with the prevailing ideology in North American Mathematics education, championed by **Professor Jo Boaler** of **Stanford University’s School of Education** and her disciples. Teaching the basics, explicit instruction, and deliberate practice are all, in Boaler’s view, examples of “bad math education” that contribute to “hating Math” among children and “Math phobia” among the populace. Her theories, promulgated in books and on the * “YouCubed” *education website, make the case that teaching the times tables and practicing “multiplication” are detrimental, discovering math through experimentation is vital, and making mistakes is part of learning the subject.

Boaler has emerged in recent years as the leading **edu-guru** in Mathematics education with a wide following, especially among elementary math teachers. Under the former Ontario **Kathleen Wynne** government, Boaler served as a prominent, highly visible member of the **Math Knowledge Network (MKN)** **Advisory Council** charged with advancing the well-funded **“Math Renewal Strategy.” **Newsletters generated by the MKN as part of MRS Ontario featured inspirational passages from Jo Boaler exhorting teachers to adopt ‘fun’ strategies and to be sensitive to “student well-being.”

While Boaler was promoting her “Mathematics Mindset” theories, serious questions were being raised about the thoroughness of her research, the accuracy of her resources, and the legitimacy of her claims about what works in the Math classroom. Dr. Boaler had successfully weathered a significant challenge to her scholarly research by three Stanford mathematics professors who found fault with her **“Railside School”** study. Now she was facing scrutiny directed at **YouCubed** by cognitive science professor **Yana Weinstein** and New York Math teacher **Michael Pershan**. Glaring errors were identified in YouCubed learning materials and the research basis for claims made in **“Mistakes Grow Your Brain”** seriously called into question. The underlying neuroscience research by Jason S Moser and his associates does not demonstrate the concept of “brain sparks” or that the “brain grows” from mistakes, but rather that *people learn when made aware of their mistakes. *

Leading researchers and teachers associated with **researchED** are in the forefront of the current wave of evidence-based criticism of Boaler’s theories and contentions. Australian teacher-researcher** Greg Ashman,** author of ** The Truth About Teaching** (2018), was prompted by Jo Boaler’s response to the new

**UK math curriculum**including “multiplication practice” to critically examine her claims. “Memorizing ‘times tables,’ “she told

*was “terrible.”*

**TES,***“I have never memorised my times tables,” she said. “I still have not memorised my times tables. It has never held me back, even though I work with maths every day.” Then for clarification:”*

*“It is not terrible to remember maths facts; what is terrible is sending kids away to memorise them and giving them tests on them which will set up this maths anxiety.”*

Ashman flatly rejected Boaler’s claims on the basis of the latest cognitive research. His response tapped into “cognitive load ” research and it bears repeating: *“Knowing maths facts such as times tables is incredibly useful in mathematics. When we solve problems, we have to use our working memory which is extremely limited and can only cope with processing a few items at a time. If we know our tables then when can simply draw on these answers from our long term memory when required. If we do not then we have to use our limited working memory to figure them out when required, leaving less processing power for the rest of the problem and causing ‘cognitive overload’; an unpleasant feeling of frustration that is far from motivating.”*

British teachers supportive of the new Math curriculum are now weighing-in and picking holes in Boaler’s theories. One outspoken Math educator, * “The Quirky Teacher,” *posted a detailed critique explaining why Boaler was “wrong about math facts and timed tests.” Delving deeply into the published research, she provided evidence from studies and her own experience to demonstrate that ‘learning maths facts off by heart and the use of timed tests are actually beneficial to every aspect of mathematical competency (not just procedural fluency).” “Children who don’t know their math facts end up confused,” she noted, while those who do are far more likely to become “better, and therefore more confident and happy, mathematicians.”

Next up was University of Pennsylvania professor **Paul L. Morgan**, Research Director of his university’s Center for Educational Disabilities. Popular claims by Boaler and her followers that “math practice and drilling” stifle creativity and interfere with “understanding mathematical concepts” were, in his view, ill-founded. Routine practice and drilling through explicit instruction, Morgan contended in *Psychology Today*, would “help students do better in math, particularly those who are already struggling in elementary school.” Based upon research into Grade 1 math achievement involving 13,000 U.S. students, his team found that, of all possible strategies, “only teacher-directed instruction consistently predicted greater first grade achievement in mathematics.”

Critiques of Jo Boaler’s theories and teaching resources spark immediate responses from the reigning Math guru and her legions of classroom teacher followers. One of her Stanford Graduate Education students, **Emma Gargroetzi, **a PhD candidate in education equity studies and curator of **Soulscrutiny** Blog, rallied to her defense following **Barbara Oakley’s** New York Times piece. It did so by citing most of the “Discovery Math” research produced by Boaler and her research associates. She sounded stunned when Oakley used the space as an opportunity to present conflicting research and to further her graduate education.

Some of the impassioned response is actually sparked by Boaler’s own social media exhortations. In the wake of the firestorm, Boaler posted this rather revealing tweet: * “If you are not getting pushback, you are probably not being disruptive enough.” *It was vintage Boaler — a Mathematics educator whose favourite slogan is

**“Viva la Revolution.”**In the case of Canadian education, it is really more about defending the status quo against a new generation of more ‘research-informed’ teachers and parents.

Far too much Canadian public discourse on Mathematics curriculum and teaching simply perpetuates the competing stereotypes and narratives. Continued resistance to **John Mighton** and his **JUMP Math** program is indicative of the continuing influence wielded by Boaler and her camp. **Doug Ford’s Progressive Conservative Government** is out to restore *“Math fundamentals”* and determined to break the curriculum gridlock. The recent debate over **Ontario Math** education reform on **Steve Paikin’s TVOntario **program * The Agenda* featured the usual competing claims, covered familiar ground, and suggested that evidence-based discussion has not yet arrived in Canada.

**What explains Professor Jo Boaler’s success in promoting her Math theories and influencing Math curriculum renewal over the past decade? How much of it is related to YouCubed teaching resources and the alignment with Carol Dweck’s ‘growth mindset’ framework? Do Boaler’s theories on Math teaching work in the classroom? What impact, if any, have such approaches had on the decline of Math achievement in Ontario and elsewhere? When will the latest research on cognitive learning find its way to Canada and begin to inform curriculum reform?**

on September 11, 2018 at 4:25 pm |John MyersWith all the furor about math in Ontario, I have a few questions to ask all who feel we are in a crisis or at least are combatants in the math wars. Given that math and other curricula have been subject to change and criticism since the mid-1980s. An assertion is NOT evidence.

– Are we clear on the goals of learning math in K-12 and beyond?

– Apart from anecdotes do we REALLY know how math is taught in the majority of classrooms?

– When curriculum is up for change, do elementary, secondary, post-secondary and other stakeholders WORK TOGETHER to set learning goals, identify best teaching strategies, and determine evidence to show the results?

I wish that in my lifetime we get satisfactory answers to these questions. Tant pis 😦

In my own thinking math is a language, through its numbers so

– practice on learning its arithmetical “grammar” counts, as it does for me as I am consolidating on my use of more than half a dozen languages

– while math is not sufficient to make sense of our world, it is necessary (read Hans Rosling’s Factfulness which I first saw in Swedish but it is easier to read in English 🙂 )

– practicing “basics” does NOT have to be boring nor lead to students hating math; there are ways to practice without being bored (I am told that Jump math does this but I do not know first hand). Decades ago I did an experiment (requested by a frustrated math teacher) to instill a “growth mindset in high school students in math and it was successful enough so that they did not give up but at least passed. You teach a love of or respect for math from the outset. Here the data is clear if they come to middle or high school hating math, they will not likely change their minds.

on September 12, 2018 at 8:42 am |Jo-Anne Grossoh John…ugh!

on September 12, 2018 at 9:12 am |John MyersI have no understanding of your response.

on September 12, 2018 at 11:04 amPaul W. BennettYour comment is most welcome and I think it provides a valuable contribution. My former teaching colleague, Peter Crippin, modeled an early form of “Guided Discovery” for me and taught me a lesson. There are different ways of achieving success in teaching Mathematics. The most compelling research finding — for me — is that learning challenged kids seem to respond better to explicit instruction and deliberate practice. It confirms my observation that academically able kids can handle “problem solving” challenges, but struggling kids can and do experience frustration and confusion.

on September 12, 2018 at 9:49 am |teachingbattlegroundReblogged this on The Echo Chamber.

on September 12, 2018 at 11:06 am |Paul W. BennettThanks for the reblog! Great to see the commentary finding a wider audience in the United Kingdom.

on September 12, 2018 at 11:46 am |lemieux2016Yes, John and Paul. I taught math successfully to wide range of students using what I would call guided inquiry/ discovery approach that incorporated mixture of student investigation ( supported by varying degrees of scaffolding/ prompts as needed), close monitoring (assessment) and feedback in- lesson as well as post, and lots of explicit direct instruction depending on stage of teaching/ learning sequence, learning goals, and student needs.

No teacher worth her salt would leave students floundering/ feeling anxious or frozen- cognitive research has long told how brains freeze under such emotions. Key things are know what one is trying to teach, know variety of approaches that work, know your students- then follow closely and support and adjust to achieve best possible learning for all.

Am so tired of the arguments about the best way to teach mathematics. All the well- founded approaches are needed plus a solid teacher understanding of mathematics and how people learn mathematics.

Lastly, begin by finding out what students know and can do. Different ways exist to do that. Then go from there.

on September 12, 2018 at 12:17 pm |John Myersagree Lynn,

false dichotomies are wasteful

People should note as L does

– guided and scaffolding are NOT “discovery”

In my old instructional strategies course at OISE Models of Teaching, we explored this when we taught inquiry models which we did along with direct instruction etc.

on September 12, 2018 at 2:00 pm |Paul W. BennettNice to hear from you, Lynn. My commentary responds to the latest research findings with respect to multiplication and math practice. Your success as a Math teacher and openness to “working out what works” speaks volumes. I remain skeptical about the wisdom of implementing Dr. Jo Boaler’s theories, particularly with struggling students. The research conducted by Paul L. Morgan looks sound and rather compelling.

on September 12, 2018 at 4:57 pm |Tara Houleummm…that is not accurate. Many kids in classrooms these days are left floundering. Both mine floundered for 4 years before their Gr.5 actually taught them math. Many, 1000s of parents report the same because of the existing pedagogy being flaunted at pro D workshops these days, such as Ms. Boaler’s ill fated “memorization harms kids”. This is so incredibly damaging to a child’s cognitive development! Kids today learn how to solve 8×2 7 different ways. Many are instructed to just work through the problem and not worry about the answer. Others are told just to estimate cuz that’s what calculators are for!! Kids go to tutors because they are taught different ways to solve basic arithmetic problems AT EVERY SINGLE GRADE LEVEL. We know what works yet many workshops and overzealous School Admin rush to implement failed edufads in lieu of proper math instruction.

Great that you know how to teach basic math. Most kids in today’s classroom aren’t so lucky.

on September 12, 2018 at 8:24 pmlemieux2016Hi Tara. I said “Any teacher worth her salt would not leave students floundering.” The “many kids” of which you speak must unfortunately have come from classrooms with teachers who are not as competent as we wish they were. My point was that guided inquiry/ exploration teaching/learning sequences need not lead to floundering children if done well. My thoughts are , as I had posted later on, are that students do need to know their multiplication facts. How they learn them is another point. But I also think that showing them or having them share different ways of solving 8×27 is not harmful. If students can solve correctly, consistently, and efficiently then whatever they are doing is working for them.

on September 13, 2018 at 12:26 pm |Tara HouleLynn we have been through this before. I don’t disagree about what constitutes proper math instruction; i do disagree that it’s only happening some of the time. It’s happening in most classrooms these days, as evidenced by the appalling results being gathered right across the country-with one exception: Quebec. Where, as you have already highlighted, it’s where effective math instruction is being taught.

It’s not about the teachers. This is about ineffective, weak curricula, which then allows for convoluted teaching strategies, and terrible resources meant to fail our kids, AND our teachers. In BC the Ministry, in conjunction with the teacher’s Union, has decided that teachers are now responsible for their own resources under “teacher autonomy”. The curriculum guidelines state that memorization of facts is not expected in both Gr.3 and Gr.4. There are no set goals for ANY mastery of basic math facts at the elementary level. Adding/subtracting fractions doesn’t happen until Gr.8 under the new revamp. Textbooks aren’t used unless they’re already in classrooms; Ministry isn’t providing them anymore. As for resources? The BCTF established this one https://teachbcdb.bctf.ca/list?q=math&p=1&ps=25. #1 on the list is using kittens and puppies created by the BCSPCA … how much research went into THAT?

It’s deplorable and the SYSTEM is to blame. Not the teachers.

on September 13, 2018 at 11:57 pmlemieux2016Hi Tara.

I agree with you that the Ontario elementary mathematics curriculum needs to have some additions, deletions, and some rewrites to make expectations clearer for teachers. I agree that by grade 3 and 4, there should be expectations that students develop good working knowledge of multiplication facts and strategies for figuring out when they forget a fact. As for fraction operations, by grade 7 I think students should be adding fractions using common denominators: – I used manipulatives and/or diagrams only to illustrate what was happening to help with understanding.

The BC situation sounds quite dire. I hope things improve.

on September 12, 2018 at 12:21 pm |John MyersResponding to Paul

– one wonders why some students are frustrated and struggle?

– what can we do to teach them to problem solve, perhaps not like professional mathematicians but as citizens in a democracy?

My reference to the experiment I did indicated one method to encourage students to persist in the struggle.

on September 12, 2018 at 5:01 pm |Tara HouleJohn your queries, and questions have been answered multiple times throughout the years yet you fail to acknowledge our answers BACK, to you.

The frustrating aspect of these discussions is how so many say, “In my experience i did this…” well today’s experience in today’s classroom is different. We have the performance data, along growing numbers of innumerate kids behind declining math trends. Parents AND teachers telling us what the reality is and it’s frustrating their concerns aren’t being acknowledged.

Number one concern is weak curriculum guidelines which have been prevalent in Canadian schools for over 30 years now, terrible resources, and ill fated pedagogy which shapes prevailing methodology at the District level. Try addressing that first and see what happens.

on September 12, 2018 at 4:29 pm |Tunya AudainCurriculum + Method = Education

The Curriculum says What to teach: Teach Math. The question then arises: How? The Answer is: The teacher has autonomy re Method(s). Supposedly this is to accommodate variability in the student body, allowing the teacher to be flexible with methods.

Today’s Globe&Mail says many teachers do not even have the basic grounding in Math, thus the recommend is for teacher upgrading. This addresses the Curriculum part of the education equation.

As far as methods go — to answer Paul’s question: “When will the latest research on cognitive learning find its way to Canada to begin to inform curriculum reform?” — the research has been there since 2006! Is there a deliberate rejection of the conclusion for reasons of politics (challenge to established orthodoxy), doubt re validity of the research or something else? The research was so convincing that the original 12 page academic paper was reworked (to 6 pages 6 years later) to be more understandable to the average teacher and this was done by an editor at the offices of the AFT (American Federation of Teachers).

What was the bottom line that has been ignored, snubbed and disparaged for so long? Here is the last paragraph of the reworked paper:

“After a half century of advocacy associated with instruction using minimal guidance, it appears that there is no body of sound research that supports using the technique with anyone other than the most expert students. Evidence from controlled, experimental (a.k.a. “gold standard”) studies almost uniformly supports full and explicit instructional guidance rather than partial or minimal guidance for novice to intermediate learners. These findings and their associated theories suggest teachers should provide their students with clear, explicit instruction rather than merely assisting students in attempting to discover knowledge themselves.”

https://www.aft.org/sites/default/files/periodicals/Clark.pdf Putting Students on the Path to Learning: The case for fully guided instruction (2012) This paper is the shorter form of the longer research (which BTW was approved and signed-off by one of the authors as being true to the original meaning) http://www.cogtech.usc.edu/publications/kirschner_Sweller_Clark.pdf Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching, 2006, Kirschner, Sweller, Clark

If this bottom-line were to be accepted would it throw a wrench into the current dominating discovery/inquiry etc. methods. No, not necessarily. Read the bottom line again — where three learner levels are noted — novice, intermediate, expert. The direct instruction applies particularly to the first two levels, and this would apply to most subjects, be they reading, math, science, piano, sports . . .

What remains to be done to answer Paul’s question is the mobilization of well-developed professional development respectful of this research to date.

on September 13, 2018 at 7:48 pm |lemieux2016Hello Tunya. I agree with you that the cognitive studies research on how people learn has been around for a while. I also agree that the presentation of those findings e.g., in ” How People Learn: Brain, Mind, Experience and School” by Bransford , Brown, and Cocking (hope spelling correct) was likely heavy reading for teachers not knowledgeable in the helpful science or psychology background. I am sad that instead of finding ways to help teachers learn about and understand the findings, and spend the requisite time helping them to then develop lessons that reflected what they had learned, education boards tended to present abbreviated info sheets meant for quick perusal in one or half day workshops, and then expectations that teachers change their teaching accordingly. It did not work well.

Follow up to workshops has been increasingly pushed onto teachers who attended, with often little engagement and support from administration, although that is not always the case by any means. For example, I and 6 of my Intermediate and Junior grade colleagues were once sent by our board to a full day workshop but Robert Marzano. I was thrilled because I thought finally, after 20 years of silently using his and his colleagues huge volume of research into instructional approaches that work, along with ways to analyze curriculum , determine learning goals, and select instructional approaches to suit each category, my school board was going to promote something useful board wide. After an exciting day, I returned to school to never hear another word about any of it. An incredible waste of money to say the least.

Last year, about 7 years after the workshop and 4 years into retirement, I was chatting with an admin who excitedly said, “Have you heard of Marzano’s stuff.” I have no words left to describe my frustration.

That being said, I could share several rebuttals to the ” only direct instruction works, ” bit, and the claim ” don’t have kids discover what you can teach them directly.” But instead, I will simply say one more time, that a lot of the good research you speak of suggests you need different approaches for different learning goals.

For example, if I want to address the curriculum expectations that say that students are to analyze, compare, predict, etc when working with content, I will teach those skills directly ahead of time. It would make no sense not to!

Then, I will ask them to practise those skills while investigating, exploring, etc. with new content. The goal I have then is different; I now want them to practise/ apply the skills I have taught them to look at and explore new content, as I guide them with prompts and scaffolds. Afterwards, my goal then becomes having them understand the content,and I will discuss findings and directly teach the facts, concepts, relationships etc that came out of the inquiry/ investigation practice.

on September 13, 2018 at 7:53 pm |lemieux2016A big yes to Tunya’s end comment re need for “mobilization of well- developed professional development respectful of this research to date” But not if the research being referred to is only that which calls for explicit , direct instruction and excludes the research showing the efficacy of of well- guided inquiry / investigative instructional methods.

on September 14, 2018 at 9:15 amJohn MyersI agree on all of Lynn’s points re

– poor professional development

– role of direct instruction (necessary but not sufficient)

– need to learn key skills and concepts in order to apply to new situations

on September 13, 2018 at 8:08 pm |lemieux2016https://lexiconic.net/pedagogy/edu-103-1-1.pdf

A link to an excellent, oft-referenced article the conclusion of which strongly supports considering well- done guided inquiry as an effective instructional approach.

on September 12, 2018 at 5:27 pm |John MyersWhich of my questions has been answered?

– Are we clear on the goals of learning math in K-12 and beyond?

– Apart from anecdotes do we REALLY know how math is taught in the majority of classrooms? (why do PISA results paint a better picture?)

– When curriculum is up for change, do elementary, secondary, post-secondary and other stakeholders WORK TOGETHER to set learning goals, identify best teaching strategies, and determine evidence to show the results?

if the last question were a “yes” one might think that over 30 years with different governments the guidelines would have been improved.

on September 12, 2018 at 7:12 pm |Tara HouleI’m not sure i’ve ever given you anecdotes John, and I’m pretty sure you’ve attended researchED events where credible researchers have already reviewed, analyzed and answered these questions for you.

Educrats and Ed Ministries aren’t interested in improving the situation that they themselves created, because THAT would mean it’s the end of the money train for them. We know what works, those in charge refuse to acknowledge to implement it -see D. Staples latest as yet another illustration ignites about how ed officials like to ignore what the mathematicians says what works, and what should be done https://edmontonjournal.com/news/local-news/david-staples-new-k-4-math-curriculum-promising-but-has-some-defiencies.

Rehashing the same questions is tiresome, as more kids continue to flounder and fall through the cracks whilst the bobbleheads at the control panel continue to push through ineffective curricula and ed policies.

on September 12, 2018 at 7:16 pmJohn MyersI have never received answers to these questions. In fact, I wrote a letter to the editor of a newspaper which was published a decade ago when a university spokesperson said it was the first time they had had a meeting with their high school math counterparts.

on September 13, 2018 at 7:08 am |Jo-Anne GrossOur resource includes inquiry-based, open-ended mathematical problems to support student voice, the multiple intelligences and the diversity of the students in our classrooms.

“edubabble at it`s best”

on September 13, 2018 at 12:27 pm |Tara Houleyup.

on September 16, 2018 at 6:40 pm |J. DalesInteresting commentary. I find myself wondering a few things – such as, how accurate is that Globe & Mail article claiming that “most” elementary school teachers don’t have enough math background knowledge to teach elementary school math? I question the likelihood of that – after all, you need at least a Bachelor’s degree in order to even enter pre-service teacher training in Ontario, and a bare pass won’t cut it either. There are very few degree programs that a person could enter which do not require at the very least, grade 12 University level math. Many elementary teachers such as myself have math or science degrees. Mine is a science degree – between the math & physics courses I took, I have more than enough math background to teach elementary math. I don’t think I’m so rare in my profession.

I also wonder how clear the researchers are on how PD actually plays out in real schools. From the teacher perspective (well, mine at least), boards love to push “flavour of the moment” pedagogy. This year’s Must-Do approach combines, usually, with the latest Miriam Small (or whoever) Must-Use-Only-This resource. After a couple of years, this same approach & resource become the “Never-Do” and “Never-Use” way of teaching. When teachers point out a problem we see in our classrooms daily, we are ignored and the “party line” is pushed, regardless of how ridiculous. Teachers are micro-managed and pressured to teach in lock-step with each other, despite the diverse needs of learners within & between our classes. We are strongly discouraged from trying out a variety of approaches and then picking and choosing whatever works for our kids. The main pressure, in the end, is anything that is perceived as having the ability to plump EQAO scores. Truly examining how students learn and what knowledge gaps they demonstrate is not looked at with favour by math coaches, superintendents and sometimes, school administrators.

How does this play out in terms of PD? It becomes difficult to make any real movement in our pedagogy when all PD sessions are aimed at pushing an upper-level administrator’s agenda that frequently has no relation to student needs. It’s limiting when teachers are not encouraged, and in fact are sometimes flat-out forbidden from, teaching any in a balanced way that’s responsive to the individual students in our classrooms. Oh sure, the idea of responding to student needs, informing our practice with good diagnostic data and all the rest is given reverant lip service, but when it gets down to actual practice any teacher who uses any approach other than the current flavour of the moment must be ready to stand up for it in the face of flack. This is true whether or not the flavour of the month approach is actually working.

I don’t know if that answered any of the questions proposed – it became sort of ranty, for which I apologize – but possibly there’s some useful thing in there somewhere for someone.

on September 22, 2018 at 9:23 am |John MyersAll too true on the lack of quality or impact of much PD. How many of us have experienced “death by powerpoint” especially when the presenter spends their time reading the slides?

on September 30, 2018 at 2:01 pm |lemieux2016Your comments express much of the same thoughts I have, J Dales, about the experiences of teachers with regards to using a range of different approaches and trying to determine gaps in students learning and best ways to close those gaps. As you described, I too experienced an overriding emphasis on teaching through problem using the 3-part lesson plan, and using open ended problems and small group work, to develop both conceptual and procedural learning. Little mention was made beyond the approaches pushed in PD of other instructional methods that could be used to help students develop understanding of the most challenging concepts and procedures.

When trying to teach parts of curriculum at any grade level that are notoriously challenging for students, teachers need resources beyond textbooks and commercial worksheets etc, to help them develop sequences of connected lessons that build progressively on one another and which have been shown to support the development of understanding, as well as strategies for assessing and remediating student learning as needed along the way.

Stepping away from the math wars fuming around the best way to teach would open up room to discuss approaches such as teaching with variation, and learning progressions, among others.

on September 22, 2018 at 4:20 pm |lemieux2016Hi Paul. I too am sceptical about using jo Boaler’s theories, as I understand them, with struggling students unless teachers closely monitor and support them.

As I and many of the commentators on this blog have said, no matter what pedagogy is being used, timely assessment and feedback during teaching and learning in association with altered instruction methods and/or content as indicated are essential elements of good teaching to ensure that all students are learning optimally and not floundering and/or feeling overwhelmed/confused.

Those aspects of what I term good teaching for all students, not just “struggling “ones, can and will look different in each classroom; however, if all the valid evidence from research into how people learn and effective teaching strategies that have been discussed in this blog are taken into account, then we could see some of Jo Boaler’s theories in action, along with explicit, direct instruction, guided inquiry/discovery, and sufficient use of independent and guided practice with feedback used at different times in iterative spirals of instructional sequences.

One thing missing from this discussion of the seeming buy in to growth mindset, Jo Boaler’s stuff, You used, etc, is the fact that unless teachers of mathematics have a strong foundation in how the learnihbjlng of mathematics progresses, common learning errors and how to remediate them, and are able to effectively analyze and interpret the curriculum documents to discern what are the foundational concepts, facts, skills, relationships etc that are implied in the learning expectations, then none of the instructional methods being discussed and argued over will be of much help to students, especially struggling ones.

From National Academy of Sciences: “How Students Learn: Mathematics in the Classroom” – there are four interacting lenses through which to approach thinking about and planning instruction:

1. Learner- centred( what students bring to class- what math students know and can do prior to beginning an instructional sequence, and their attitudes and beliefs about maths);

2. Knowledge-centered:

– what is important for students to know and be able to do?

– what are the core concepts that organize our understanding of mathematics and what concrete cases and detailed knowledge will allow students to master those concepts effectively?

– How will we know when students achieve mastery? (Overlap of knowledge-centred and assessment-centered lenses)

3. Assessment-centered: formative assessment essential -designs to make students’ thinking visible; permit teachers to grasp students’ preconceptions so they can build on those. Assessment permits teachers and students to monitor their progress towards mastering the knowledge to be learned, and where students are along a path from informal to formal thinking and design instruction that is responsive to student progress.

4. Community-centered: fostering discussion and sharing of ideas -in short.

None of this is new but all of it still holds as solid principles upon which to base teaching and learning.

Do people who supposedly know this stuff and are in positions of power and control over public education choose to think that those principles and all the other reputable research from the past two decades into how students learn can and should be replaced by the newest ideas that come along, such as Jo Boaler’s theories, YouCubed, or Growth Mindset? I can only wonder.

Each of the four principles suggest the need for differing instruction depending on the knowledge to be learned, what students bring, what assessment shows, and the desire to build a community of learners led by a competent, knowledgeable teacher. So we need more clarity yet complexity of thinking, more openness to other’s ideas.

Why a local school board supposedly has erroneously blacklisted Mighton’s Jump Math allegedly for being too rote learning in nature is completely beyond me. Yet the board embraces Boaler’s theories and Growth Mindset.

This speaks of power being misused, and personal agendas getting in the way of what is best for students and teachers.

Politics ruining chances to do something amazing.

on September 22, 2018 at 5:18 pm |Paul W. BennettWell said, Lynne. The double-talk concerning John Mighton and JUMP Math is indicative of what’s standing in the way of progress in Ontario.