Are Thinking Classrooms Out of Step With Cognitive Science? (Part 1)

Last summer, the Fordham Institute published an editorial piece by Daniel Buck called "The Latest Math Fad is Another Excuse to Teach Nothing."  ​The "latest math fad" in question is Building Thinking Classrooms in Mathematics, and the editorial can be quickly summed up as asserting:

• Building Thinking Classrooms in Mathematics is not direct instruction
• Cognitive science has unambiguously found that direct instruction is the best instruction
• Ergo, Thinking Classrooms are out of step with cognitive science
• Also, here are a bunch of bad analogies for Thinking Classrooms that allow the author to make fun of it, separate from the cognitive science

If you're new to reading my work, I spent the last two years implementing Building Thinking Classrooms on my own and documenting how it was going and what I was learning about it.  It has gone extremely well for my students, both in terms of their achievement and of their classroom experience.  So, to be transparent, I'm a fan of the philosophy and framework, and I've spent a lot of time and effort contributing to the conversation of how to make it a positive and transformative experience in classrooms.
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"It says here that we're participating in the "latest excuse to teach nothing."

That said, I'm also an academic at heart.  Once upon a time, I stopped teaching for four years and earned a PhD from a full-time, residential program at a major university.  I regularly read books on cognitive science intended for teachers (I recommend that every educator read this one and this one, at a minimum).  I have written one hundred long-form posts on my website, most of which detail the implementation of research-backed practices.

All this to say, while I'm not an academic, I am about as well-versed in research, in cognitive science, and in writing professionally-informed articles as any practicing teacher out there.

And having written now fifty posts on the implementation of Building Thinking Classrooms in Mathematics, I am genuinely and sincerely interested in the question posed:

Are Thinking Classrooms out of step with cognitive science?

Daniel Buck certainly thinks they are.  He cites a "seminal article" from 2006 that he thinks unequivocally supports his position.  If pressed, I think quite a few of the scholars and practitioners I respect most would say that they are, too.

Are they right?
 
There's a lot to unpack in that question.  I'm not exactly sure where this research project will take me, but it certainly seems clear where to start.  A few months ago, I wrote a piece suggesting that there is good reason to heed the warning of Craig Barton when it comes to a key pillar of Building Thinking Classrooms in Mathematics. ​

Should we heed Daniel Buck's warning as well?

Who is Daniel Buck?

A good starting place when scrutinizing any editorial opinion piece (including mine) is to inspect its author and to become aware of an agenda or incentives he or she may have in writing the piece.  

I don't know Mr. Buck, but several key pieces of information about him were easy to find with some basic web searching:

• Mr. Buck has degrees in English Literature, Spanish Language, and Curriculum and Instruction
• Mr. Buck is a former English teacher
• Mr. Buck is now an assistant principal at Lake Country Classical Academy
• Lake Country Classical Academy is trained by and uses a curriculum published by Hillsdale College.  Yes, that​ Hillsdale College.
• Mr. Buck writes opinion-editorial pieces, not research
• His other linked publications - all of which can be found in publications with a reputation for sensationalism and one-sided political leanings - include pieces called Education Schools Have Long Been Mediocre.  Now They're Woke, Too and Don't Spare the Rod. ​

The picture of Daniel Buck from his online profile seems pretty clear to me.  His writing is overtly political and consistently critical.  He espouses a specific and inflexible philosophy about teaching and learning.  He has no experience whatsoever with any of the ideas that he lambastes; he merely dismisses them on philosophical grounds.
​

With all that in mind, we are to consider Mr. Buck's assertion that Building Thinking Classrooms in Mathematics is out of line with cognitive science.

Mr Buck is not a cognitive scientist.  He is not a math teacher.  He cites no experience with Building Thinking Classrooms ​(or anything else he criticises).  And he isn't writing from a position of genuine, neutral curiosity.

But is he wrong?
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"You guys aren't going to believe what I was able to find out about this guy from a quick Google search!"

Breaking Down Mr. Buck's Argument

My interest in writing this is to begin a sincere investigation into the question: is Building Thinking Classrooms in Mathematics out of step with cognitive science?  

I need to be clear that this was not Daniel Buck's interest in writing his piece speaking against it.  In fact, I only draw attention to it - and begin my investigation here - because the piece circulated so widely among the Building Thinking Classrooms community, and because he says it is out of step with cognitive science.

But you have to read pretty far to get to to that assertion.
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The piece starts out with three paragraphs that patently mischaracterize the book and the philosophy.  The first paragraph paints a picture of Liljedahl telling a successful teacher that "everything she does has to change" in the book's introduction (which he does not).  The second says that "to Liljedahl, thinking only occurs when students are fumbling to solve problems for which they receive little instruction or guidance. It’s only swimming if Uncle Joe pushes you into the deep end" (Liljedahl at no point says any such thing).  The third claims that BTC demands that teachers "shed the burden of curriculum to instead busy students with various mind games, brain teasers, and even card tricks" (also not the case).

My face when I first read Mr. Buck's blatant mischaracterizations of the Building Thinking Classrooms in Mathematics philosophy and practices.

​​At this point, there is no point in continuing to read his piece.  Looking at it in the context of his other publications, this is his mode of writing.  He wishes to paint anything new as foolish and woke, and makes fun of it and lies about it to make his point.  He cites no experience, and it is a long time before he mentions any actual research.  Since he obviously mischaracterizes the book he is criticizing, it stands to reason that he will obviously mischaracterize the research he will use to support his claim, too.

Mr Buck has written a politically opinionated, misinformation hit piece, and nothing more.

But -

He does eventually reference some real work and some real science, even if still not from an open-minded, genuinely curious perspective.  Finally, eight paragraphs into his piece, we get this:

"Found some evidence!  You have to go all the way to paragraph 8."
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"[Benjamin Bloom, of the famed "Bloom's Taxonomy," published in 1956] refers to knowledge acquisition as the “primary” objective in education. Knowledge and comprehension are the bases of far more complex thinking. If students are busy counting out basic math facts on their fingers, they can’t attend to more difficult math problems. If they’re busy sounding out words, they can’t attend to higher-order thinking, such as evaluating the text in hand or creating their own poems. Factual knowledge, memorization, and comprehension facilitate and allow robust analysis, synthesis, and creation."
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Everything here is right on target when it comes to cognitive science.  While Mr. Buck doesn't cite anything after the first sentence, he could have.

Allow me to do it for him.

University of Virginia cognitive scientist Daniel Willingham - who has written four books, dozens of scholarly articles, a host of opinion-editorials, and who has a regular column called "Ask the Cognitive Scientist" - makes this exact assertion in chapter two of his outstanding book Why Don't Students Like School, a summary of major cognitive science principles I think every educator should read.  The guiding principle of the chapter is "thinking skills depend on factual knowledge," and Willingham deftly makes his case using evidence, examples, references, and reasoning.  The chapter (and the whole book) is a masterpiece, and it directly backs up the claim made in paragraph 8 of Mr. Buck's op-ed.

​As an astute reader, you've probably know what should come next.  Mr. Buck has accurately offered a fair representation of a major pillar of cognitive science.  From here, it stands to reason, he gives an example of how Building Thinking Classrooms in Mathematics is out of alignment with this pillar.

That's how evidence-based, persuasive writing works, right - here's my claim, and here's supporting evidence."

Right?

He does not.

Not once.

He wants us to take his word for it that Thinking Classrooms do not value factual knowledge or comprehension.  He characterizes Thinking Classrooms as "busy[ing] students with various mind games, brain teasers, and even card tricks" rather than doing real mathematics.

Which, of course, is precisely Liljedahl's recommendation... for the first 3-5 days of the year. The non-curricular tasks that Mr. Buck speaks of are intended to be high-engagement, culture-building activities that allow students to learn the foundational skills and procedures necessary to learn high-level mathematics through his practices.

3-5 days.

That's it.

After which point, Liljedahl says that "the trick is to maintain the positive effect and the positive affect [of those non-curricular tasks] while turning our attention back to the reality of curriculum" (p. 26; a full description of task implementation and sequencing, including the "shed the burden of curriculum" quote that Buck takes out of context, can be found from pp. 25-30).

In fact, the primary task example used in the text is a factual knowledge, comprehensive, skill-based task.​

How would students learn this foundational skill in a Thinking Classroom?  In a scientifically-sound way, it turns out - with prior knowledge activated (another pillar of cognitive science) during a task launch (practice #6), with their working memory expertly managed (yet another pillar of cognitive science) through hints and extensions (practice #9), and through systematic instruction (practice #1, and one of the highlighted findings of a study that Mr. Buck himself cites in his piece).

Mr. Buck, of course, mentions none of this, instead closing his piece with two more paragraphs making fun of another nonsensical mischaracterization of Thinking Classrooms that he has fabricated out of thin air.

So there you have it.  If you want no part of a Thinking Classroom and want to defend your stance with the opinion of someone who knows nothing about it, hasn't tried it, and does not even appear to have read the book, Mr. Buck is your scholar.
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"It's laughable that an English teacher thinks this qualifies as effective persuasive writing."

If you're looking for an honest assessment of whether Building Thinking Classrooms in Mathematics is out of step with cognitive science, he is not.

He does, however, cite two legitimate scholarly publications that he says do answer that question.

• Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching
• ​Effectiveness of Explicit and Constructivist Mathematics Instruction for Low-Achieving Students in the Netherlands

What are we to make of those?  Does the actual research Mr. Buck purports to have read make the point that he wasn't able to?

That'll be my question for part 2.

Am I just participating in the "latest fad" and "another excuse to teach nothing?"  If so, I'm not convinced just yet.

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