Are Thinking CLassrooms Out of Step With Cognitive Science? (Part 3 - The Big One)

The Science of Learning is coming.

The pendulum swings.  Initiatives come and they go.  They rise and they fall. 

Chances are, your school's most recent or next big initiative will be called "The Science of (Something)." 

While the branding may be new, cognitive science is not.  It is a fully formed, well researched learning theory. Pendulum wise, we're in the "back to basics" part of the school reform initiative cycle after the rise and fall of several recent innovation attempts, and this time, we're hoping to ground "back to basics" in "the science of learning."

Count me in. 

While I like much of what I see in this rapidly spreading initiative, I have some concerns about it, too.  One of those concerns is that it will presuppose that only a narrow, inflexible set of teaching strategies and learning outcomes are "supported by cognitive science," functionally discarding highly effective teaching philosophies like Building Thinking Classrooms in Mathematics.  While I recently predicted that BTC would ultimately rise and fall by 2031 anyhow, this wasn't the reason that I first foresaw.  Now, however, I'm concerned that it will fall even faster as it gets painted as out of step with the new big thing.

And I have good reason to think so.

Last summer, a poorly written op-ed piece making precisely that claim circulated widely and no doubt caused many teachers to abandon ambitions to Build Thinking Classrooms and no doubt caused many leaders to outlaw them in their schools and districts.  I recently addressed that piece, showing that it was based in ideology rather than evidence, but nonetheless, plenty of damage had probably already been done, as publication - regardless of context or quality - is often held up as gospel by those in power. 

Opinion isn't the only opposition circulating, however.  There are also proclamations that "the research" supports that claim, which I addressed in another recent post.  I'm most worried about this form of attack.  For my whole career, I've heard school and district leaders tell me that "the research supports x" when they want me to buy in to an initiative or decision of theirs, all the while not having read that research, considered the context in which the supported result was situated, nor examined the specificity of the operational definitions, methods, or effect sizes therein.  Research can be improperly weaponized in a number of ways.  I addressed some of those in part 2, and another big one in part 2½ of this series. 

All that having been said, the claim that Building Thinking Classrooms in Mathematics is out of step with cognitive science could still be right.  While I don't think existing research has proven such, making that claim with no support would be me weaponizing research to make my own claim appear true.  While it will probably take decades for the full body of academic research to be developed that proves or disproves its effectiveness, I think the question of fit with cognitive science can be mostly assessed with what is available today. ​

The practices of Building Thinking Classrooms in Mathematics were effective for forty-some teachers that Liljedahl worked with.  It has been effective for me.  It has been effective for Julia, who left a stunningly insightful comment on part 2 of this series.  It has surely worked for countless others, or it wouldn't be proliferating across the world at such a staggering pace.

And if it works, it can't possibly be out of step with cognitive science research.

Right?

Right?
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How Do Practitioners Use Research?

Educators most often read books, not individual research studies.  Books for practitioners - at least some of them - are attempts to take decades worth of research results and to summarize the findings in a way that makes them useful in classrooms.  This type of practitioner book is similar to a meta-analysis, which I covered in part 2, except that a meta-analysis is intended to serve that purpose for further research and for fellow academics rather than for educators to use in schools and classrooms.

There are two practitioner books I lean on which summarize decades of research in cognitive science and attempt to translate their findings into actionable work in the field - Teach Like A Champion 3.0 by Doug Lemov and Why Don't Students Like School? by Daniel Willingham.

What I plan to do here in part 3 is to look at five major "pillars" of cognitive science presented in these texts and then to analyze whether or not the practices of Building Thinking Classrooms in Mathematics are aligned therewith.

In all honesty, even having completed parts one, two, and two-and-a-half of this series and having written this introduction so far, I haven't already looked into this.  

I'm not asking this question - are Thinking Classrooms out of step with cognitive science - already knowing the answer.

I'm investigating this in real time.

And I'll be honest with what I find.

Are Thinking Classrooms out of step with cognitive science?

Let's finally find out.
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Pillar #1 - Unless the cognitive conditions are right, the brain will avoid thinking

Willingham, p. 1

Willingham's wonderful book starts with a provocative claim on the very first page - the mind is not designed for thinking.  Thinking, as compared to other functions of the brain, he teaches us, is "slow... effortful... and uncertain" (p. 4), and thus it is one the mind is programmed to employ sparingly.
 
Willingham uses the word "thinking" in his book to mean, generally, complex mental activity of the problem solving sort.  It is distinct as a mental activity from memory, which will continue to be important.

Does the idea of "thinking" as an important, difficult-to-foster, complex mental activity that is distinct from memorizing sound familiar?  If it does, you probably heard it from... Peter Liljedahl.  "Thinking", he tells us, "is what you do when you don't know what to do," as distinguished from remembering, which is what you do when you do know what to do.

Perfect alignment so far.

Willingham goes on to teach us that while the mind avoids thinking in general, it can be pleasurable and people occasionally even seek it out (think crossword puzzles, for example) because it is very rewarding when successful.  So while the human mind is programmed by evolution to choose low-effort mental activities over high-effort ones, it doesn't avoid thinking at all costs.  The key, he tells us, is that the conditions must be right, namely:​

• There must be a problem to be solved
• The difficulty of the learning or problem solving task needs to be just right - not too easy, not too hard
• The brain requires an expectation that it will be able to learn or solve successfully
• The brain needs sufficient information stored in long-term memory to get started so that memory can "off load" some of the cognitive weight of the thinking task (pp. 8-18)

​All in all, it is hard to get people to think, but with the right conditions in place, people won't just think, they'll actually enjoy it and seek it out.

Thinking is not the mind's preferred action, but with the right conditions, it can be quite rewarding.

Again, Liljedahl is in complete alignment.  The introduction to the book is all about how difficult it was to get students to think in their math classes when they hadn't done so in a long time (BTC, pp. 1-15).  Chapter one is all about what kinds of tasks will invite thinking and how to move students from thinking about naturally inviting thinking tasks to tasks we need them to be willing to think about because curriculum demands it (BTC, pp. 19-37).  Chapter 9 is all about how to keep thinking tasks in the cognitive "sweet spot" of not too hard and not too easy that Willingham notes is essential to the conditions that support thinking (BTC, pp, 144-169).

One way to read Building Thinking Classrooms in Mathematics is to read it as a guide to mastering the cognitive conditions that invite and promote thinking - a process the mind naturally resists in their absence, and a process that is essential to learning.

Is Building Thinking Classrooms in Mathematics in alignment with pillar #1?  Perfectly, I'd say.

Pillar #2 - Thinking depends on factual knowledge

Willingham, p. 25, Lemov, p. 8

It has been fashionable recently for teachers to say things like "there's no point in having kids memorize dates, facts, times tables, or anything else they can quickly get from Google or a calculator.  They need to be thinking critically, not just memorizing." 

This, cognitive science would teach is, is partially true - they do need to be thinking critically and not just memorizing.  The difference is that, according to cognitive science, they need memorized factual knowledge in order to think critically.  As Lemov puts it, "critical thinking and problem solving are not the opposite of factual knowledge.  They rely on it.... Problem solving," he goes on to say, "is domain specific; for the most part, you can have deep thoughts only about things you know something about" (p. 8).  Willingham points out that factual knowledge is even one of the foundations of a cognitive process as complex as reading comprehension (p. 30).

This idea, also, was cited as one of the "conditions" for thinking to occur in pillar #1 - the brain needs sufficient information stored in long-term memory to get started so that memory can "off load" some of the cognitive weight of the thinking task.

This is a tough one with which to gauge alignment when it comes to Building Thinking Classrooms in Mathematics.  Explicitly, I don't know of any place where Liljedahl either confirms or contradicts this pillar.  I asserted in part 2 that BTC absolutely promotes the learning of factual knowledge, but I don't see anywhere that explains that this is in service of deeper thinking.

I'm going to consider this pillar as omitted from Liljedahl's work so far as I am familiar with it.  I might be able to piece together some fragments that infer it, but that's not what I'm trying to do here.  I'm trying to be clear and fair, and to be clear and fair, I don't see it.

There are two ways to consider whether this means BTC is out of step with this pillar or not.
​
One perspective is that omission is not evidence of contradiction.  Just because it isn't addressed doesn't mean the philosophy is at odds with it.  
​

"What do we do if it isn't in or out of alignment - it's just... not addressed?"

Another perspective is that its inclusion is important to alignment.  On page 14, justifying the entire existence of the book, Liljedahl says "In an effort to find a list of variables that impact thinking in a classroom... I was looking for a way to disaggregate teaching into discrete factors, each of which could act as a variable in our pursuit to improve thinking....  In the end, a list of fourteen [practices] emerged." 
​
Teaching factual knowledge - a pillar of cognitive science - isn't one of the practices, nor is it included in one to the best of my knowledge.  While I don't think Liljedahl would disagree with this pillar, he wrote a book about the major ways to promote thinking without including it.

Furthermore, I genuinely think that a lot of his followers would like to know his thoughts on teaching factual knowledge that is hard to "figure out."  There are pieces of it here and there, sure, but how do I use thinking tasks to teach kids things like...

• algorithms
• multiplication facts
• definitions of geometric shapes

is a common question that arises in the forums.  Are there times to forego thinking tasks?  Is there a way to teach factual knowledge through thinking tasks?  Is it a different thing?  I, at least, have had to come up with my own answers to these questions.  Others, I frequently see, use BTC sometimes and different teaching practices at others for precisely this reason.

I'm inclined to conclude that this omission is important.  Willingham and Lemov leave no doubt that the research on cognitive science clearly finds that factual knowledge promotes thinking. I believe it should be clearly included - rather than merely not contradicted - in a book about promoting thinking.

Is Building Thinking Classrooms in Mathematics in alignment with pillar #2?  Not sufficiently, no.
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Pillar #3 - Attention is required for Thinking

Lemov, pp. 19-23, Willingham pp. 58-59

I'll be referencing this diagram of memory structure that Willingham provides quite a bit in pillar #4, but for starting out with it, note the arrow labelled "attention."
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Cognitively, there are two "ingredients" necessary for thinking - attention and remembering.  The importance of remembering (facts) was addressed in pillar #2, and the pre-condition for thinking of having existing knowledge in one's memory was addressed in pillar #1.

We can remember something without thinking, however; remembering is an ingredient for thinking not to be confused for constituting thinking on it's own.  I remember how to square a number or find a square root.  I'm not thinking when I remember that.  However, when I combine that memory with my attention to this riddle from Ben Orlin that is in my immediate visual environment, I have the sufficient ingredients to start thinking.
​

Lemov tells us that "what students attend to is what they will learn about" and that "one major factor in the rates at which individuals learn is their ability to concentrate for a significant period of time" (p. 19).  Willingham, who supplies the diagram above, says that part of it "is a somewhat complex way of explaining the familiar phenomenon: if you don't pay attention to something, you can't learn it" (p. 59).

Thinking requires that we pay attention to something new (pillar #3), apply existing knowledge to it (pillar #2), and have sufficient reason to believe we can tackle the problem successfully so as to convince our mind that thinking will be rewarding and worthwhile (pillar #1).

Building Thinking Classrooms in Mathematics is littered with practices and details supported by the cognitive science pillar attention is required for thinking; the entire book is about thinking as delineated from or "mimicking," which Liljedahl roughly describes as classroom activity performed in the absence of genuine attention.

Practice #1 is all about using tasks that are worthy of students' attention, including the suggestion that non-curricular tasks be used as a transition to the method because they naturally invite attention, which students are largely not accustomed to in their math classes.  

Practice #3 suggests that students stand at erase-able surfaces because it focuses their attention faster and holds it longer by several measurable standards (p. 60).  Qualitatively, he also found that standing made students feel less anonymous, and "when students feel anonymous, they are more likely to disengage [their attention]" (p. 62).

Practice #4 suggests arranging furniture in a way that doesn't psychologically suggest that classroom activity will be on a teacher who will deliver content that can be mimicked without attention.  Practice #5 suggests not answering certain types of student questions that will permit the release of attention.  Practice #6 gives a time and place to maximize the initial attention given to a task.  Practice #9 promotes the management of attention by keeping students out of two "zones" - frustration and boredom - that will convince students to disengage their attention.

And that's likely not even an exhaustive list.

Building Thinking Classrooms in Mathematics is all about thinking.  Cognitive science tells us that thinking requires:

1. remembering (prior knowledge, factual knowledge)
2. attention (effortful concentration)

While, as I said in pillar #2, I think the book is short on its treatment of remembering, its treatment of attention is second to none.

​Is Building Thinking Classrooms in Mathematics in alignment with pillar #3?  Absolutely.
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Pillar #4 - Cognitive structure

Lemov, pp. 7-13, using Willingham's diagram of the human cognitive structure

For pillar #4 we need to complete the diagram of human cognitive structure that Willingham provides.

Thinking, which has been addressed in pillars 1-3, promotes learning, which you can see as another arrow in Willingham's diagram.

In order to learn something, the process is:

1. Attention brings the concept from the outside environment (classroom, in our usage) into working memory.
2. In the working memory, if properly "thought about" in combination with other information that is retrieved from long-term memory (background knowledge), the new learning will be encoded into long-term memory. 
3. If attention, thought, or relevant remembered information are missing, the concept will instead be forgotten immediately; it will be discharged from working memory without ever making it into long-term memory.
4. Once in long-term memory, the information needs to be remembered from time to time, or it will likely be forgotten as well.  To better remember something, one must practice remembering it (pillar #5, stay tuned). 

In classroom practice, then, the following elements are necessary for learning:

1. Students must pay attention
2. Attention alone is not sufficient for learning.  Once attentive to new content, students must operate with it in some mentally meaningful way - not just hear it or copy it down. 
3. Learning new content is much more reliable when recall of prior learning (long-term memory) is prompted to help connect it
4. In order to stay in long-term memory, students must be given multiple opportunities to practice remembering - or "retrieving" - that information.  

Students, if you recall cognitive science pillar #1, should avoid thinking in favor of mimicking; or at least, it is biologically understandable to expect them to do so.  The brain resists thinking unless the conditions are right, Willingham deftly tells us in his very first chapter, and students preferring mimicking to thinking is the classroom manifestation of that unfortunate evolutionary truth.  
​
Much of Building Thinking Classrooms in Mathematics was written with the express intent of optimizing this cognition system.  All throughout it, Liljedahl shares stories of students and teachers mimicking elements of this process rather than engaging in them with fidelity.  ​

Students' (and adults') minds naturally resist thinking, but with the right attention to cognitive structure and the surrounding conditions, thinking is not just effective - it is enjoyable and satisfying.​

​And unfortunately, as Liljedahl's observations show, the conditions are not right in most classrooms.  In many lessons, teachers attend to none of the four elements necessary for learning.

1. Attention is often not managed and left to the choice of the student
2. Many lessons leave no opportunities to operate with information being learned.  It is just said out loud and copied down in the hopes that students will study it on their own at a later time
3. Prior learning is often not activated
4. Once taught, there is no retrieval practice.  Students are expected to study their mindlessly copied notes on their own if they wish to strengthen their memory of new content

You can draw a straight line from most practices in Building Thinking Classrooms in Mathematics to one of those elements of cognitive structure; each one is designed to have an exponential positive influence on attention, operating with the concept while in working memory, and to give students their own path to encoding by building off of existing knowledge.  In fact, never have I seen a more comprehensive treatment of element #2, which in my experience is the most-often neglected element of the four.
​
​In so many math classes, students have no opportunity to engage with the content they're learning - it is merely told to them and they're instructed to copy it down.  In a Thinking Classroom, inordinate attention is paid to engagement of working memory - tasks, hints and extensions, looking at the work of other groups, consolidation, and even note-making are all practices that have students engage with and operate with information in their working memories for as long as and with as much depth as humanly possible. 

It pushes this element of cognition to its absolute limit.

The others are managed as well, however.  Attention is influenced through standing and using vertical surfaces (the psychology behind that is nicely explained).  Recall of prior learning is an element of the task-launch and innate in the task itself.  The foundational task used as an example throughout the book is a great example:
​​

Item #1 in this thinking task activates prior knowledge.

Check-your-understanding questions also deftly address recall practice.  Where as typical homework and practice sets may seem like opportunities for recall practice, without an answer key provided, they really aren't.

Not only are Thinking Classrooms in alignment with this pillar, they are explicitly designed to maximize every element therein.

Is Building Thinking Classrooms in Mathematics in alignment with pillar #4?  They are, and in certain cases, they are the best treatment of the matter that I'm aware of.
​​

Pillar #5 - Forgetting and Retrieval

Lemov, pp. 11-13, Willingham, chapter 5

"As soon as you learn something, you begin forgetting it almost immediately" (Lemov, p. 11).

Forgetting is a feature, not a bug, of the human cognitive system.  It's right there in Willingham's model of it!  Twice, in fact!

Cognitive Science tells us that we should expect students to forget what they learn, not be surprised or frustrated when they do.

Note that there are two "forgotten" arrows in the diagram.  Forgetting, it should be noted, isn't one thing.  It's  (at least) two distinct processes.

1. In one version of forgetting, the learning never makes it into long-term memory to begin with.  It is ejected from working memory because it was deemed by the mind to be insufficiently important to merit a spot in long-term memory.  This type of forgetting is more akin to never learning in the first place than to what we typically think of as forgetting.  The reasons for this type of forgetting were addressed in pillar #4 - there was insufficient attention, insufficient help from long-term memory, or insufficient opportunity to operate with the new  information, so the brain simply dropped it as not important. 
2. In another version of forgetting, information that did make it into long term memory is forgotten.  The hard work of getting it to the cognitive promised land was done, but it still got forgotten.

Pillar #5 - Forgetting and Retrieval - deals with the second version of forgetting.

"As soon as you learn something, you begin forgetting it almost immediately."

Lemov provides proof to back it up, too.
​

According to this "forgetting curve" Lemov provides, it is a normal process of the mind to forget half of new learning within the hour.

And more than 60% of it by the next day's class.

In this piece, I've tried to teach you five pillars of cognitive science.  According to this "forgetting curve" Lemov provides us, I'd be lucky if you remembered two of them by this time tomorrow.

Same goes for your students.  When they forget more than half of what you taught them yesterday, it isn't because you did a crappy job, it isn't because they're lazy and don't care, and it isn't because they rotted their brains on TikTok for 14 straight hours and got 3 hours of sleep after school ended yesterday.

It happened because that's what brains do.

Forgetting is a built-in feature of the human cognitive system.

Note from the "forgetting curve" graph, however, that there is an antidote to this type of forgetting - repetition.  The more times the mind practices retrieving something from long-term memory, the more likely it is to stay there.

In no uncertain terms, learners get better at remembering something by practicing remembering it.

This repetition is called retrieval practice.  It is an absolute must in any classroom and under any teaching philosophy.  Lemov delinates it as a discrete technique in Teach Like A Champion 3.0 - there is an entire chapter of the book devoted to it (pp 82-87).  I've written about both how I integrate that technique into my Thinking Classroom and how I did so beforehand. 

One last note on this pillar before we assess alignment.  There are two elements to "remembering" something from long-term memory:

1. It's storage in long-term memory in the first place, and
2. Efficacy in retrieving it

Ever have that experience where you know you remember something - maybe someone's name - but you just can't pull it from your memory?  That's a retrieval issue (#2), not a memory issue.  You remember that name, you just can't retrieve it easily. 

When it comes to learning something new, remembering the necessary prior knowledge at all is obviously important, but so is the ability to retrieve it quickly.  Long-term memory can only "off-load" the cognitive weight of new learning if it can be retrieved with ease.  If I'm trying to pay attention to my teacher's outstanding lesson on the Anterior Angles Theorem, but I'm devoting my entire working memory to oh, c'mon, what are anterior angles again?  Are those the ones that are... or the ones that are.... then my attention is toast.  Even though that memory is in there somewhere, my inability to retrieve it effortlessly is nearly as big a hurdle to my learning as forgetting it entirely would have been because the retrieval effort requires all my attention.

​Retrieval practice, luckily, supports both.  Regular retrieval practice makes use both more likely to remember something and better at retrieving it with minimal strain.

​The inability to recall something with ease is a major drain on attention.

So.

How well is Building Thinking Classrooms aligned with this pillar of forgetting and retrieval?

Spoiler: I think it has two very strong elements of alignment and one glaring omission.

Let's start with the good news.

First, as I said at the beginning of this section, forgetting isn't one process; it's two different ones.  In one version of forgetting, learning never makes it into long-term memory in the first place because the ingredients necessary for encoding to happen are not sufficiently present while that information is still in working memory.  This pillar is not referring to this "mode" of forgetting, but nonetheless, I think it merits remembering that, as I said in pillar #4, Building Thinking Classrooms in Mathematics is a magnum opus for avoiding it.

For the average teacher who doesn't care to worry about different kinds of forgetting, a well-run Thinking Classroom will absolutely have a dramatic, positive effect on memory.  I have noted many times that the learning I see in my students is more durable in my Thinking Classroom than it was before, and this is what I mean.  This type of forgetting is dramatically less common in my Thinking Classroom than it was before hand.

But what about the other kind of forgetting?

Let's stick with the good news.

Retrieval practice isn't complicated.  It's just practice.  Or drill, as Willingham calls it in chapter five of Why Students Don't Like School, when he says "it is virtually impossible to become proficient at a mental task without extended practice" (p. 119).  Sure, there's some nuance to retrieval practice (see Lemov pp. 82-87), but in essence, all it requires is a basic chance to remember and a way to know that you're correct.

Enter check-your-understanding questions (Liljedahl, chapter 7).

Check-your-understanding problems are practice problems with an answer provided.

Perfect.

Not only are check-your-understanding questions just what the doctor ordered when it comes to retrieval practice, they are specifically engineered to maximize the chances that a student completes them.  "In every case where we implemented check-your-understanding questions [instead of traditional homework],... usually 75-85% of the students were doing the questions, and doing them for the right reason...."  Plus, they include answers, which is an absolute must if we want drill to function fully as retrieval practice.

They are just what cognitive science calls for when it comes to this pillar.

But-

I can't give the alignment an A+ on this one, even though the two elements I addressed are not just in alignment, but at the top of their class for their respective goals.

Here's the thing.  Even though check-your-understanding questions are the perfect form of at-home or on-your-own retrieval practice, that's not nearly enough.  First of all, I've written that Liljedahl's experience that 75-85% of students are doing these is *a little* (he says sarcastically) high compared to my own.

Second of all, even if 100% of my students were completing check-your-understanding questions with complete fidelity (and I assure you they are not), one, single, same-day repetition or drilling of a new skill only puts us on the second forgetting curve.
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Not a great place to be.  Still a 70% forgetting rate by day 6.

I'm going to come right out and say it - retrieval practice has to be a regular event during class time.

It just has to be.

No matter what we're teaching or what philosophy we're teaching it with, we have to block out time for retrieval practice.  Full stop.  The cognitive science leaves no question about that.  Giving kids practice to do on their own - even if they do them in class, as Liljedahl's updated advice in "the green book" (p.74) -  isn't enough.

Retrieval practice has to be - has to be - a regular event during class time.

Even in a Thinking Classroom.

So adamant am I personally about this that I even wrote that doing retrieval practice at the beginning of every single class - in full violation of Liljedahl's "five-minute" rule ("orange book," p. 102) - literally completes my Thinking Classroom, almost like a 15th practice.

The cognitive science couldn't be more clear on this.

Nothing improves my students' chances of type #1 remembering like the practices of Thinking Classroom.

But nothing improves their chances of type #2 remembering like retrieval practice.

Is Building Thinking Classrooms in Mathematics in alignment with pillar #5?  My gradebook gives it two A+'s and an F.  You can use your grading system of choice to calculate a final grade for this pillar.
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Is Building THinking Classrooms in Mathematics Out of Step WIth Cognitive Science?

No way.

A quick recipe for learning, cognitive science tells us, is:

1. Attention
2. Background knowledge
3. Thinking 
4. Retrieval

Most teaching philosophies, books, etc, are heavy on #2 and #4, often neglecting #1 and #3 entirely.

Building Thinking Classrooms in Mathematics is a masterpiece when it comes to #1 and #3.  Yes, it is light on (though not in opposition to) #2 and #4, but why not be when all of that is already covered elsewhere?

There are other ways of optimizing attention and thinking.  Teach Like A Champion 3.0 is choc full of outstanding techniques for doing so.  You don't have to Build A Thinking Classroom to get those.

But make no mistake, cognitive science is clear that you do have to get those somehow if you want students to learn.

And Peter Liljedahl literally expanded the frontiers of how to optimize those elements of cognitive science in Building Thinking Classrooms in Mathematics.

"In an effort to find a list of variables that impact thinking in a classroom... I was looking for a way to disaggregate teaching into discrete factors, each of which could act as a variable in our pursuit to improve thinking....  In the end, a list of fourteen [practices] emerged" (BTC, p. 14).

A Thinking Classroom is a pursuit to improve thinking.

And the cognitive science leaves no doubt that thinking - done well - is essential for learning.

While Building Thinking Classrooms in Mathematics isn't a comprehensive textbook on cognitive science, it merits a place in the canon of work that has greatly contributed to the practice and implementation thereof.
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