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Bit by Bit, Putting It Together
Andrew Watson
Andrew Watson

Over at Teacherhead, Tom Sherrington has posted a form that teachers can use for lesson plans.

He has put together different versions: one filled-in with explanations, another left blank for teachers to use, yet another for adapting and editing.

The Bigger Picture

In the world of Learning and the Brain, researchers explore precise, narrow questions about learning. The result: lots of precise, narrow answers.

For instance: Technique X helped this group of bilingual 5th graders in Texas learn more about their state constitution.

How might Technique X help you? With your students? And your curriculum?

And, crucially, how does Technique X fit together with Technique Y, Technique 7, and Technique Gamma — which you also heard about at the conference?

As you’ve heard me say: only the teacher can figure out the best way to put the research pieces together. Once you’ve gathered all the essential information, you’re in the best position to conjure the optimal mix for your specific circumstances.

All Together Now

And, that’s why I like Sherrington’s lesson planning form so much.

You’ve seen research into the importance of “activating prior knowledge.” You’ve also seen research into the importance of “retrieval practice.” You know about “prior misconceptions.” And so forth…

But, how do those distinct pieces all fit together?

This lesson planning form provides one thoughtful answer.

To be clear: this answer doesn’t have to be your answer. For this reason (I assume), Sherrington included a form that you can edit and make your own.

The key message as you start gearing up for January: research does indeed offer exciting examples and helpful new ways to think about teaching and learning.

Teachers should draw on that research. And: we’ll each put the pieces together in our own ways.

New Year, New Habits: More Learning!
Andrew Watson
Andrew Watson

When the school year starts back up in January, teachers would LOVE to use this fresh start for good.

new learning habits

In particular, our students might have developed some counter-productive habits during the first half of the year. Wouldn’t it be great if we could help them develop new learning habits?

Maybe homework would be a good place to start. Better homework habits should indeed lead to more learning.

The Problem: Old Habits

When I sit down to do my homework, the same problems always crop up.

My cell phone buzzes with texts.

I’m really tired. SO tired.

The abominable noise from my brother’s room (heavy metal horror) drives me crazy.

I try to solve all these problems when they appear, but they get me so distracted and addled that I just can’t recover quickly. Result: I’m just not very efficient.

Wouldn’t it be great if I could develop new habits to solve these problems? What would these new learning habits be?

New Learning Habits: “Implementation Intentions”

We actually have a highly effective habit strategy to deal with this problem. Sadly, the solution has a lumpish name: “implementation intentions.”

Here’s what that means.

Step 1: I make a list of the problems that most often vex me. (In fact, I’ve already made that list — see above.)

Important note about step 1: everyone’s list will be different. The problems that interfere with my homework might not bother other people. (Apparently, some folks like my brother’s dreadful music.)

Step 2: decide, IN ADVANCE, how I will solve each problem.

For example, when my cell phone buzzes, I won’t look at the message. Instead, I will turn the phone to airplane mode.

When I feel tired, I’ll do 20 jumping jacks. If that doesn’t work, I’ll take a quick shower. That always wakes me right up.

When my brother cranks his stereo, I’ll move to my backup study location in the basement.

Just as everyone faces different problems, everyone will come up with different solutions.

Step 3: let the environment do the work.

Here’s the genius of “implementation intentions”: the environment does the work for us.

Now, when my phone buzzes, I already know what to do. I’ve already made the decision. I don’t have to make a new decision. I simply execute the plan.

Phone buzzes, I switch it to airplane mode. Done.

New Learning Habits: the Research

Now, I have to be honest with you. When I first read about this strategy, I was REALLY SKEPTICAL.

I mean, it’s so simple. How can this possibly work?

The theory — “the environment does the work, activating a decision chain that’s already been planned” — sort of makes sense, but: really?

In fact, we do have lots of good research showing that this strategy works.

For instance, Angela Duckworth (yes, that Angela Duckworth) found that students who went through this process completed 60% more practice problems for the PSAT than those who simply wrote about their goals for the test.

You read that right: 60% more practice problems.

How’s that for new learning habits?

Classroom Applications

What does this technique look like in your classroom?

Of course: everyone reading this blog teaches different content to different students at different schools. And, we are all different people.

So, your precise way of helping your students will differ from my way.

I’m including a link to Ollie Lovell’s post on this topic. To be clear, I’m not suggesting that you follow his example precisely. After all, you and Ollie are two different people.

However, I am suggesting that his example helpfully illustrates the concept. And, it will give you ideas on how best to apply it in your world.

Escaping the “Inquiry vs. Direct Instruction” Debate
Andrew Watson
Andrew Watson

If you’d like to stir up a feisty argument at your next faculty meeting, lob out a casual observation about direct instruction.

Almost certainly, you’ll hear impassioned champions (“only direct instruction leads to comprehension”) and detractors (“students must construct their own understandings”) launch into battle.

For Example…

Back in September, I reviewed two studies contrasting these approaches.

One study, looking at science instruction with 4th graders, found that direct instruction led to more learning. The second study argued for a constructivist approach — yet lacked a remotely plausible control group.

So, in that post at least, it made sense to tell students what experts had already concluded.

One Study, Two Perspectives

I’ve found another study that helpfully reopens this debate.

Daniel Schwartz and colleagues helped 8th grade science students understand concepts like density, speed, and surface pressure.

Crucially, all these concepts share an underlying “deep structure”: ratio.

That is: “speed” is distance divided by time. “Density” is mass divided by volume.

Schwartz wanted to see if students learned each concept (density, spring constant) AND the underlying deep structure (ratio).

Half of the 8th graders in this study heard a brief lecture about each concept — and about the underlying structure they shared. They had a chance to practice the formulas they learn.

That is: this “tell and practice” paradigm is one kind of direct instruction.

The rest of the 8th graders were given several related problems to solve, and asked to figure out how best to do so.

This “invent with contrasting cases” paradigm enacts constructivist principles.

Findings, and Conclusions

Schwartz and Co. found that both groups learned to solve word problems equally well.

However — crucially — the contrasting cases method led to deeper conceptual understanding.

When this group of students were given a new kind of ratio to figure out, they recognized the pattern more quickly and solved problems more accurately.

So, the obvious conclusion: constructivist teaching is better. Right?

Not so fast. Schwartz’s study includes this remarkable pair of sentences:

“There are different types of learning that range from skill acquisition to identity formation, and it seems unlikely that a single pedagogy or psychological mechanism will prove optimal for all types of learning.

Inventing with contrasting cases is one among many possible ways to support students in learning deep structure.”

That is: in this very particular set of circumstances, a constructivist approach helped these students learn this concept — at least, in the way it was tested.

What Next?

If the purists have it wrong — if both direct instruction and constructivist pedagogies might have appropriate uses — what’s a teacher to do?

Schwartz himself suggests that different approaches make sense for different kinds of learning.

For instance, he wonders if direct instruction helps learn complex procedures, whereas constructivist methods help with deep structures (like ratio).

Perhaps, instead, the essential question is the level of difficulty. We have lots of research that says the appropriate level of cognitive challenge enhances learning.

So: perhaps the “tell and practice” method of this study was just too easy; only a more open-ended investigation required enough mental effort.

However, perhaps the study with the 4th graders (mentioned above) included a higher base level of conceptual difficulty. In that case, hypothetically, direct instruction allowed for enough mental work, whereas the inquiry method demanded too much.

Two Conclusions

First: the right pedagogical approach depends on many variables — including the content to be learned. We teachers should learn about the strengths and weaknesses of various approaches, but only we can decide what will work best for these students and this material on this day.

Second: purists who insist that we must always follow one (and ONLY one) pedagogy are almost certainly wrong.

When Multitasking Helps (And Why Teachers Should Discourage It Anyway)
Andrew Watson
Andrew Watson

We all know that multitasking is baaaaad.

In fact, we all know that multitasking doesn’t happen. Instead, when we think we’re multitasking, we’re actually switching rapidly back and forth between two tasks. (Or, heaven help us, more than two tasks.)

multitasking

If either of those two tasks is cognitively complex, this rapid task switching imperils performance.

So, to repeat: multitasking is baaaaad.

Surprising New Research…

But what if, under unusual circumstances, it were beneficial?

More precisely, what if the perception that I’m multitasking improves my performance.

Here’s how you might test such a question (especially if your name were Shalena Srna):

Ask two groups of students to transcribe a Shark Week video.

Tell half of them that they’re doing two things: learning by watching, and also transcribing.

Tell the other half that they’re doing one thing: learning by watching and transcribing.

In other words, both groups of students do the same thing. But: one group thinks they’re multitasking, and the other doesn’t.

Sure enough, in this study, students who thought they were multitasking did better. They wrote more words, and they remembered more of the video.

Wow.

Curiouser and Curiouser

Srna and company didn’t stop there. They kept testing their hypothesis.

In another study, they asked students take a virtual art-museum tour. They told half of them that this required distinct tasks (listening and looking); the other half didn’t get that instruction.

Same results.

In another version, they had participants solve two kinds of puzzles simultaneously: word searches and anagrams. Rather than tell half that the puzzles required dual-tasking (or not), they asked participants what they thought.

Here again, those who spontaneously thought they were multitasking did better on the puzzles than those who didn’t – even though they were all doing the same task.

In Search of an Explanation

This result, to put it mildly, seems bizarre. If multitasking makes me worse at something, why would believing that I’m multitasking make me better?

Srna & Co. suggest one plausible explanation. If I think I’m multitasking, then I might concentrate harder on the task.

To test their hypothesis, they measured participants’ pupil dilation when they did (or didn’t) think they were multitasking. (We’ve got good research showing that people who are more engaged in material have greater dilation.)

Sure enough, people who believed they were multitasking had bigger pupils than those who did not.

In fact, they rated themselves as less bored by the work they were doing.

Teaching Implications

This research strikes me as a) fascinating, b) thorough and thoughtful, and c) a smidge dangerous.

Here’s what I mean.

Given these (highly persuasive) studies, we might be tempted to tell our students that they’re multitasking when they’re not – because their extra level of concentration will improve their learning.

Alas, such a response would mistake research benefits for school benefits.

In this case, if we tell our students that they’re multitasking, good things might happen in the short term. However, in the long-term, they get the message that we think it’s okay.

But, it isn’t. Rapid task switching reduces learning. It really does.

In fact, students get counter-productive, pro-switching messages all the time. We need to work against this cultural programming.

(One key strategy: they should see us conspicuously refusing to multitask. Hard-core monotasking adults are great role models.)

Reality Check

Srna and Co. begin their article with some amazing statistics. According to their survey, 84% of people think they’re better-than-average multitaskers. In fact, almost 50% say they’re tops in the field.

Rather than use students’ false beliefs to help them today, we should correct their beliefs to help them for a lifetime.

“We Can No Longer Ignore Evidence about Human Development”
Andrew Watson
Andrew Watson

The more teachers learn about neuroscience and psychology, the more we admire Dr. Mary Helen Immordino-Yang.

Unlike most researchers, she has spent time as a classroom teacher.

And, her extensive research—in both neuroscience and psychology—offers us wise perspectives on our craft.

For instance, she has zealously emphasized the inextricable connection between emotion and cognition—although we live in a society that wants to keep the two apart. As she has shown in her books and articles, we can’t think deeply about thinking without understanding the importance of feelings.

Thinking and feeling aren’t two different things. They’re names for distinct perspectives on the same thing.

(You can check out her essay in Mind, Brain, & Education: Neuroscience Implications for the Classroom, edited by David Sousa.)

More recently, working with Linda Darling-Hammond and Christina Krone, Dr. Immordino-Yang has published a lucid and practical summary of our field. In 20 jargon-free pages, she makes a strong case for focusing on development as an essential variable in schools and in learning.

You can download The Brain Basis for Integrated Social, Emotional, and Academic Development here.

That’s a mouthful of a title. But it synthesizes an impressive range of complex and vital topics: age-appropriate teaching strategies, neural development across the lifespan, epigenetics, even cultural well-being.

As an introduction to The Brain Basis, I interviewed Dr. Immordino-Yang. This transcript is edited for clarity and brevity.


Andrew:

You’ve packed a lot of information into this document. What’s your goal in putting it all together this way?

Mary Helen:

I wanted to tell a story about what it means to be a human being.

From there I thought we could think back to retrofit what are we doing in schools to support the development of our full humanity.

And so I aimed to tell a story of many fields—of biological, genetic, developmental, and cognitive research that would help people understand why human development and learning are so closely tied together.

Schools really can no longer ignore the new evidence about human development in thinking about our aims and our strategies in educational environments.

Andrew:

A big chunk of this brief talks about different developmental stages, and the appropriate educational strategies to use during each one.

Where you get the most pushback? What are people most surprised about?

Mary Helen:

One of the things that people have been very surprised about, and where I get a lot of pushback, is in adolescence. I talk about adolescence being a fundamental time of plasticity—but also of vulnerability.

And this means that teenagers really need deeply supported opportunities to explore alternate identities: scholarly ways of thinking and being, social ways of thinking and being.

This is a time when kids can develop very deep interests, and connect those interests to their world—how it is now, how it has been in the past, and how it could be different in the future– like they never have been able to do before to the same extent.

Schooling needs to capitalize on that. Yet we really do not in the way that standard schools are designed. In fact we directly undermine that kind of agency, that kind of exploration of self and ideas that’s just fundamental to adolescence.

Andrew:

In schools, I’m guessing that would mean more electives, fewer requirements. You’d like more open-ended, freeform opportunities for high school students?

Mary Helen:

Well, yes. But all that in the context of very strategic support and close relationships, in addition to intellectual and social opportunities to really get invested in important work: more like an apprenticeship model of schooling in adolescence, as compared to a didactic transfer model.

There are schools doing this extremely well. They tend to be schools built for kids one step away from failing out of society, though.

For example: The New York Performance Consortium Schools got special dispensations to not have standardized testing. Instead they do performance-based portfolio work as a graduation requirement.

These students were mostly at risk of failing [in their prior schools]. And then lo and behold, when you redesign their educational experience so it’s more of this apprenticeship model—students focus on broad, relevant problems—they begin to think in scholarly ways. They develop deep understanding and explore innovative solutions.

These kids go on to college at far higher rates. They’re graduating college. They’re just ever so much more engaged than their peers.

We’ve got this misunderstanding that when kids are doing poorly and flailing around, you want to double down on discipline. You want to straighten them out and get them on the straight and narrow. Control them first, and then you can teach them.

In fact what you need to do is offer them opportunities to really utilize the energy that they have, and to question and rethink their ideals, to build their deep desire for inventing themselves. And give them a creative, scholarly, structured outlet in which to productively explore that.

Andrew:

And, as you say, that makes a lot of developmental sense.

Let’s change gears. This document talks about three essential brain networks: the Executive Control Network, the Default Mode, and the Salience Network.

This is essentially a neuroscientific way of thinking about learning.

Another approach is the psychological approach: let’s think about motivation, let’s think about attention, let’s think about working memory.

When you talk with teachers about this neuroscientific approach, does it deepen their understanding of the psychological framework? Does it conflict with it? Does it confuse it?

Mary Helen:

I think it really does [deepen their understanding]. I hope it does. My aim was to teach educators about the dominant models of brain development right now.

There are hundreds and hundreds of studies demonstrating how these networks work. And those networks had really not been explained to educators to this point.

What you notice about them is: none of them is emotional or cognitive. These networks are both [emotional and cognitive] all the time. No one of them is the social network. They all have a role to play in sociality.

Andrew:

In the past you’ve written that there’s relatively little neuroscience that teachers need to know. So this approach is quite a change for you.

Mary Helen:

Well, not really. What I really think people do need to know is about human development. And one of the sources of evidence is neural development.

Understanding the basic functionality of the [neural] system is important for supporting the development of the person.

And don’t get me wrong: in some of the best schools in the world the teachers don’t know diddly squat about brain development.

But they really, really understand what their aim is for their students. They know in a deep way about the kinds of thinking and relating and reflection that they want their students to be capable of.

And in that case you don’t need the neuroscience anymore.

I think we need it in the United States because we have such a faulty model of how learners learn, and what to do when they’re not doing as well as we would like.

I’ve written several papers about the default mode network for example. We in education are potentially undermining the development of deep thinking, deep understanding, deep integration of content because of our overly task-oriented focus.

We shift people into an outwardly directed task-oriented state too much at the expense of reflection and synthesis that happens internally in a narrative constructive process.

Andrew:

So much of our vision of good teaching is a kind of a performance. It’s external, it’s what the students are doing.

Mary Helen:

That’s right. It’s about what you do, it’s not about how you think. And good thinking takes time. It takes skills for reflecting. Those skills are often neglected in our schools.

We have this kind of “frantic productivity model” which is basically a lie about what meaningful accomplishments students are actually accomplishing.

Andrew:

The “frantic productivity model” sounds a lot like schools where I’ve worked.

American education has been battling between constructivism—“inquiry-based” and “project-based learning”—on the one hand, and direct instruction on the other.

Your brief is calling for a truce. You say that these approaches can work well together, and we’re looking for a wise balance.

My question is: as a teacher how do I know when I’ve gotten that balance right? What does that feel like? What does it look like?

Mary Helen:

Yeah, great question.

So here’s the thing: this is where the teaching skill comes in.

And what skill do you need to have? What teaching artistry do you need to have? You need to deeply understand your students, and deeply understand your aim for them.

What’s your intent in the lesson?

Too much of what we do in education is designed around an outcome—a “learning outcome.”

Instead, it should be designed around this question: what are the kinds of mental capacities and habits of minds that students will be practicing?

To balance constructivism with direct instruction, think about the how much more than the endpoint. And then the answer will look really different in different contexts: different kids, different content, different supports and scaffolds, at different times.


At this point, our conversation turned to a description of a specific school focusing exactly on these complex questions and difficult choices.

That discussion was so interesting that it deserves its own blog post. I’ll have that live for you within the month.

Why Do Choices Interfere with Your Learning?
Andrew Watson
Andrew Watson

Perhaps you’ve heard of the famous experiment.

If you give shoppers many jam choices to sample, they’re delighted to taste your wares. But, if you give them fewer choices, they’re more likely to — ahem — buy some jam.

choices harm learning

In other words: choices both motivate and demotive in a complex pattern.

What effect might this finding have on education?

Choices Overwhelm Brains? Choices Harm Learning?

In a recent study, Elena Reutskaja and colleagues explored the neural basis of this intriguing finding.

They gave study participants choices about the image to be printed on a tee-shirt or mug. Crucially, some got a few choices: 6. Others got more choices: 12. And others got A LOT more: 24.

What happened in participants’ brains?

The short version: two crucial brain regions behaved differently with 12 choices.

The anterior cingulate cortex (ACC) and the striatum showed more activity when given a manageable number of choices than when they had too many or too few.

By the way: the prefrontal cortex showed a similar pattern, but to a smaller degree.

(Important wonky caveat: more brain activity ISN’T always better. In this case, more activity in these regions coincided with self-reports of greater pleasure.

In other cases — say, dyslexia — more brain activity coincides with lots of reading difficulty.)

These results mean that we’ve got two reasons to think too many choices are bad.

Firstbehaviorally, people react badly with too many choices. (If you try to navigate the toothpaste section of your local CVS, you know what I mean.)

Secondneurobiologically, brains react badly with too many choices.

In other words, those people running the behavior experiments weren’t making things up or misreading the data. Instead, they identified real problems.

Teaching Implications

We might reasonably start with the presumption that choices enhance learning. The more that our students get to choose what they’re doing, the more intrinsically motivated they will be.

However, as we see more and more studies like this one we realize that — just possibly — choices harm learning. Faced with more options than they can readily process, students feel their ACC shut down.

The result: not more learning and motivation, but less.

What, then, is the perfect number of choices?

One answer is: the authors suggest between 8 and 15.

A much better answer: honestly, research really can’t answer that question.

In the first place, they’re currently doing research with consumers getting choices to buy stuff. That’s not the situation our students are in.

In the second place, this research pool works with adults. Almost certainly, younger students can manage fewer choices than older students — who manage fewer than adults.

In the third place, the “choices” that students make vary in complexity. If I have to define 5 of 6 vocabulary words, that’s a straightforward process.

If, however, I have to solve 5 of 6 calculus problems, then I’m likely to start the early steps of solving each one to test out their trickiness.

In this case, I’ve got A LOT more info rattling around in working memory, even thought the number of choices has remained the same.

In other words, the correct number varies from case to case to case. As is so often true, you — the classroom teacher — will have the best vantage point from which to suss out the answer.

 

Choosing a Knowledge-Rich Curriculum: Pros and Cons
Andrew Watson
Andrew Watson

Should our curriculum focus on knowledge or skills?

Jon Brunskill debates this question with himself in this thoughtful post.

Brunskill does offer a strong conclusion in this debate. But just as important: the way he frames the discussion.

Following Rapoport’s Rules to Promote Civil Discourse (which I haven’t heard of before), Brunskill sets himself several tasks.

First, he summarizes the opposite belief as accurately and fairly as he can. (The goal, according to Daniel Dennett, is that the other person say “Thanks, I wish I’d thought of putting it that way.”)

Second, he notes his points of agreement with that position, and (third) what he has learned while thinking about it.

Only then, fourthdoes he get to express his disagreement, and advocate for a distinct point of view.

(By the way: you haven’t accidentally skipped a paragraph. I’ve deliberately not said what his conclusion is, because I want to focus on his methodology.)

The Takeaway

You might agree with Brunskill’s conclusion. Or, you might emphatically disagree with it.

If the latter, great news! You have an opportunity to follow his example.

How might you summarize his position as fairly as possible?

What do you agree with?

What did you learn?

Once you’ve answered those questions, then your rebuttal will be more persuasive, and more beneficial to the debate. I suspect it will also be more beneficial to you.

Ask a Simple Question, Get an Oversimplified Answer
Andrew Watson
Andrew Watson

handwritten notes

If learners were widgets, then educational research would be simple. The same teaching technique would work (or not work) equally well for all students.

It would also help if all teachers were widgets. And, if we all taught the same topic the same way.

We could ask simple research questions, get uncomplicated answers, and be ENTIRELY CERTAIN we were doing it right.

A Sample Case: Handwritten Notes

For example, if all students were identical, then we could know for sure the best way to take notes in class.

(It would help if teachers all taught the same way too.)

Are handwritten notes better than laptop notes? Vice versa? The study design couldn’t be simpler.

Mueller and Oppenheimer famously argue that “the pen is mightier than the keyboard.” (I’ve argued strenuously that their research does not support this claim, and probably contradicts it.)

But what if the question just can’t be answered that simply?

What if students do different things with their notes?

What if the classes in which they take notes are different?

Really, what then?

Mixing It Up

Linlin Luo and colleagues explore these questions in a recent study.

Happily, they start from the assumption that students use notes in different ways. And, that professors’ lectures include important differences.

For example: some students take notes, but don’t review them. (They probably should…but, there are LOTS of things that students probably should do. For instance, attend lectures.)

Others students do review the notes they take.

Some lectures include lots of visuals. Others don’t include many.

Once we start asking more complicated questions … that is, more realistic questions … we start getting more interesting answers.

More Interesting Answers

What did Luo and colleagues find? Unsurprisingly, they found a complex series of answers.

First: students who didn’t review their notes before a quiz did better using a laptop.

Second: students who did review their notes did better taking handwritten notes.

Third: in both cases, the differences weren’t statistically significant. That’s a fancy way of saying: we can’t say for sure that the laptop/handwriting distinction really mattered.

Fourth: unsurprisingly, students who took handwritten notes did better recording visuals than did laptop users. (Students who took laptop notes basically didn’t bother with visuals.)

Advice to Teachers and Students

What advice can we infer from this study? (And: from its analysis of previous studies?)

A: teachers can give students plausible guidance. “If you really will study these notes later, then you should take them by hand. But, if you really won’t, then use a laptop.”

B: teachers who present a lot of visuals should encourage handwritten notes. Or, make copies of those visuals available.

C: given that the differences weren’t statistically significant, we might encourage students to use the medium in which they’re more comfortable. If they (like me) have dreadful handwriting, then maybe they should use a laptop no matter what.

D: I continue to think — based on the Mueller and Oppenheimer study — that we should train students to take notes in a particular way. If they both use laptops AND reword the teachers ideas (rather than copying them verbatim), that combination should yield the most learning.

Most importantly, we should let this study remind us: simple answers are oversimplified answers.

If you’d like to meet two of the researchers who worked on this study, check out this video:

https://www.youtube.com/watch?v=BfCZ0K0HoJE

 

 

 

Evaluating the Best Classroom Practices for Teaching Math
Andrew Watson
Andrew Watson

What strategies work best for math teaching?

math teaching

And, crucially, how do we know?

To answer this question, we might rely on our teacherly instincts. Perhaps we might rely on various educational and scientific theories. Or, we might turn to data. Even big data.

Researchers in Sweden wondered if they could use the TIMSS test to answer this question.

(“TIMSS” stands for “Trends in International Mathematics and Science Study,” given every four years. In 2015, 57 countries participated, and 580,000 students. That’s A LOT of students, and a lot of data.)

3 Math Teaching Strategies

When students take these tests, they answer questions about their classroom experience.

In particular, they answer questions about 3 math teaching strategies. They are asked how often they…

Listen to the teacher give a lecture-style presentation.

Relate what they are learning in mathematics to they daily lives.

Memorize formulas and procedures.

Researchers want to know: do any of these teaching practices correlate with higher or lower TIMSS scores? In other words, can all these data help us evaluate the effectiveness of specific teaching practices?

2 Math Teaching Theories

Helpfully, the researchers outline theories why each of these practices might be good or bad.

As they summarize recent decades of math-teaching debate, they explain that “researchers with their roots in psychology and cognitive science” champion

formal mathematical notions,

explicit instruction where teachers show students how to solve math problems,

practicing and memorizing rules and worked examples.

On the other hand, “researchers with their roots in the reform movement” champion

connecting math to students’ daily lives,

a problem-solving approach,

understanding ideas and connections, rather than memorization.

Doubtless you’ve heard many heated debates championing both positions.

Predictions and Outcomes

These theories lead to clear predictions about TIMSS questions.

A cognitive science perspective predicts that “lecture-style presentations” and “memorizing formulas” should lead to higher TIMSS scores.

A reform-movement perspective predicts that “relating math to daily life” should lead to higher scores.

What did the data analysis show?

In fact, the cognitive science predictions came true, and the reform predictions did not.

In other words: students who listened to presentations of math information, and who memorized formulas did better on the test.

Likewise, students who applied math learning to daily life learned less.

An Essential Caveat

As these researchers repeatedly caution, their data show CORRELATION not causation.

It’s possible, for instance, that teachers whose students struggle with math resort to “daily life” strategies. Or that both variables are caused by a third.

Potential Explanations

“Connecting new math learning to real life situations” seems like such a plausible suggestion. Why doesn’t it help students learn?

These researchers offer two suggestions.

First, every math teaching strategy takes time. If direct instruction is highly effective, then anything that subtracts time from it will be less effective. In other words: perhaps this strategy isn’t harmful; it’s just less effective than the others.

Second, perhaps thinking about real-life examples limits transfer. If I use a formula to calculate the area of a table, I might initially think of it as a formula about tables. This fixed notion might make it harder for me to transfer my new knowledge to — say — rugby fields or floor plans.

At present, we can’t know for sure.

A final point. Although this research suggests that direct instruction helps students learn math, we should remember that bad direct instruction is still bad.

Lectures can be helpful, or they can be deadly tedious.

Students can memorize pertinent and useful information. Or, they can memorize absurd loads of information.

(A student recently told me she’d been required to memorize information about 60 chemical elements. Every science teacher I’ve spoken with since has told me that’s ridiculous.)

And so: if this research persuades to you adopt a direct-instruction approach, don’t stop there. We need to pick the right pedagogical strategy. And, we need to execute it well.

Cognitive science can help us do so..

Can Quiet Cognitive Breaks Help You Learn?
Andrew Watson
Andrew Watson

We write a lot on the blog about “desirable difficulties” (for example, here and here). Extra cognitive work during early learning makes memories more robust.

cognitive breaks

Retrieval practice takes more brain power than simple review — that is, it’s harder. But, it helps students remember much more.

Wouldn’t it be great if some easy things helped too?

How about: doing nothing at all?

Cognitive Breaks: The Theory

When a memory begins to form, several thousand neurons begin connecting together. The synapses linking them get stronger.

Everything we do to help strengthen those synapses, by definition, helps us remember.

We know that sleep really helps in this process. In fact, researchers can see various brain regions working together during sleep. It seems that they’re “rehearsing” those memories.

If sleep allows the brain to rehearse, then perhaps a short cognitive break would produce the same result.

Cognitive Breaks: The Research

Michaela Dewar and colleagues have been looking into this question.

They had study participants listen to two stories. After one story, participants had to do a distracting mental task. (They compared pictures for subtle differences.)

After the other, they “rest[ed] quietly with their eyes closed in the darkened testing room for ten minutes.”

Sure enough, a week later, the quiet rest led to better memory. As a rough calculation, they remember 10% more than without the quiet rest.

10% more learning with essentially 0% extra cognitive effort: that’s an impressive accomplishment!

Classroom Questions

A finding like this raises LOTS of practical questions.

Dewar’s study didn’t focus on K-12 learners. (In fact, in this study, the average age was over 70.) Do these findings apply to our students?

Does this technique work for information other than stories? For instance: mathematical procedures? Dance steps? Vocabulary definitions?

Does this finding explain the benefits of mindfulness? That is: perhaps students can get these memory benefits without specific mindfulness techniques. (To be clear: some mindfulness researchers claim benefits above and beyond memory formation.)

Can this finding work as a classroom technique? Can we really stop in the middle of class, turn out the lights, tell students to “rest quietly for 10 minutes,” and have them remember more?

Would they instead remember more if we tried a fun fill-in-the-blank review exercise?

I’ll be looking into this research pool, and getting back to you with the answers I find.

Cognitive Breaks: The Neuroscience

If you’d like to understand the brain details of this research even further, check out the video at this website. (Scroll down just a bit.) [Edit 11/4/19: This link no longer works; alas, I can’t find the video.]

The researchers explain a lot of science very quickly, so you’ll want to get settled before you watch. But: it covers this exact question with precision and clarity.

(By the way: you’ll hear the researchers talk about “consolidation.” That’s the process of a memory getting stronger.)

If you do watch the video, you might consider resting quietly after you do. No need to strain yourself: just let your mind wander…

hat tip: Michael Wirtz