elementary school – Education & Teacher Conferences

Evaluating the Best Classroom Practices for Teaching Math

Andrew Watson

November 06, 2018

Evaluating the Best Classroom Practices for Teaching Math

What strategies work best for 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..

3rd Graders Beware! The Perils of Mindfulness Research

Andrew Watson

May 11, 2018

3rd Graders Beware! The Perils of Mindfulness Research

In our frantic, stressed-out, technology-addled world, it just makes sense: we should all take some time to rest our brains.

And: what better way than mindfulness?

We’ve all heard so much about the benefits of focused breathing. The energy that derives from specific poses. The insights that come from curious attention to our bodies.

So: what’s not to love about mindfulness?

Yoga and Mindfulness in 3rd Grade

In 2016 and 2017, researchers worked with high-anxiety 3rd graders at a school in New Orleans.

20 of these students went through a combined yoga and mindfulness program. This program has good research behind it, and was led by an experienced professional. As the researchers describe it,

The session content included breathing exercises, guided relaxation, and several Vinyasa and Ashtanga poses appropriate for third graders.

And, the school devoted real time to this program. Students met before school 10 times, for forty minutes each session. 400 minutes shows real commitment!

Researchers also kept track of 33 other high-anxiety 3rd graders who had been randomly selected as the control group.

Both before and after the yoga/mindfulness program, the students answered a list of questions that measure physical, emotional, and social quality of life. (It’s euphoniously called the PedsQL.)

So: did those 400 minutes help?

The Benefits of Mindfulness

In part, it seems the program helped.

For example, the 3rd graders who participated in yoga and mindfulness saw an increase in their emotional PedsQL score of more than 18 points. Given that the scale ranges from 1 to 100, and that they started with an average score of 52, AND that the control group’s average fell by just under a point — that’s a dramatic improvement!

Researchers also found a statistically significant improvement in their psychosocial PedsQL score.

In a parallel track of this investigation, researchers offered a professional development session on mindfulness for the school’s teachers.

As a result, they found that more teachers used mindfulness and yoga with their students during the class day. Depending on how you count, teachers roughly doubled the number of sessions they used in their classrooms.

So far, so good.

The Perils of Mindfulness Research

Despite all these measurements, I remain unpersuaded by this study.

Three concerns jump out at me.

First: the study includes a control group…but the control group didn’t do anything different from their normal routine. (They were treated for anxiety in the school’s usual way.)

So: the benefits described above might have resulted from the yoga and mindfulness. But, it might just have well resulted from doing something different. Maybe these students would have scored higher on the PedsQL if they’d gone hiking. Or, made music. Or simply arrived at school 40 minutes early and done something relaxing.

We just don’t know.

Second: the students did score higher on the emotional and psychosocial PedsQL, but those are only 2 of the 6 measures on the test. Their scores on the other scales — school, social, physical, and overall — weren’t statistically significantly improved.

In fact, if you look at table 2 instead of table 3, it seems that only the emotional and not the psychosocial scores improved. (Table 3 shows the results of more sophisticated statistical modelling.)

Even in the best case, then, the yoga and meditation helped students on some measures. On 2/3 of the measures, however, it didn’t make a measurable difference.

Third: in this study, classroom teachers started doing additional yoga with their students as well.

So, perhaps the change we saw resulted from the special yoga and mindfulness intervention. Or, perhaps it resulted from the additional classroom yoga. Or, perhaps from the combination.

Again: we just don’t know.

The Perils of Mindfulness Research: The Big Picture

My point here is not to criticize this study. I am, in fact, quite glad that researchers are working with students in schools.

In fact, these researchers — quite helpfully — asked teachers about the biggest impediments for having a mindfulness program in the school.

Instead, I want to highlight how difficult it is to be confident about cause and effect.

In truth, I really want to be persuaded. I want to be able to tell teachers that we’ve got a sure-fire solution to real school problems.

But, my desire to be persuaded means I must be especially vigilant about the research I rely on.

In fact, as noted before on this blog, research in this field isn’t improving as fast as we’d like it to.

Ultimately, if we’re going to tell students to come to school early, if we’re going to ask them to spend 400 minutes doing something, if we’re going to create new programs and hire more staff, we need to be sure that this cause produces this effect.

As of today, I don’t think we’re sure enough.

Surprise! The Unexpected Outdoor Class Advantage

Andrew Watson

February 11, 2018

Surprise! The Unexpected Outdoor Class Advantage

“Can we have class outside today?”

If you’re like me, you get this question often. Especially on a beautiful spring day…

But do your students have a point? Might there be good reasons to move class outside every now and then?

Outdoor Class Advantage: What We Know

We’ve already got research suggesting that your students might be on to something.

Some researchers suggest that classes outside help restore student attention.

Other studies (here and here) indicated that they might enhance student motivation as well.

We’ve even got reason to think that exposure to green landscape helps students learn. For example: this study in Michigan suggests that natural views improve graduation rate and standardized test scores.

None of the evidence is completely persuasive, but each additional piece makes the argument even stronger.

Outdoor Class Advantage: Today’s News

If I’m a skeptic about outdoor class, I might make the following argument. Outdoor classes might be good for that particular class. However, they might be bad for subsequent classes.

That is: students might be so amped up by their time outside that they can’t focus when they get back indoors.

To explore this concern, Ming Kuo and colleagues put together an impressive study.

Over ten weeks, two teachers taught several pairs of lessons. Half of the time, the first lesson was taught outside. For the other half, the first lesson was taught inside.

Researchers then measured students’ attentiveness during the second lesson in these pairs.

The results?

The Results!

Students were more attentive — A LOT more attentive — after outdoor classes than indoor classes.

In almost 50% of the lessons, attention was a full standard deviation higher after outdoor classes. In 20% of the lessons, it was two standard deviations higher.

Technically speaking, that difference is HUGE.

(By the way: the researchers came up with several different ways to measure attention. Outdoor classes led to improved attention in four of the five measures.)

The Implications

This research suggests that teachers needn’t worry about outdoor classes leading to distraction in subsequent classes.

That finding doesn’t necessarily mean that outdoor classes benefit learning, but it does mean we have fewer potential causes for concern.

The Struggles of Young-for-their-Grade Students

Andrew Watson

January 14, 2018

The Struggles of Young-for-their-Grade Students

Several years ago I taught Jacob: an affable high school sophomore notable for his quick wit, his impressive height…and his immaturity. He was, technically speaking, goofy. Jacob’s peers noticed, and didn’t appreciate his antics. (Neither did I.)

When I met his parents for a teacher conference, I commented on his surprisingly juvenile behavior. They exchanged glances, and his mother said: “Well, he is the youngest student in the sophomore class. He could be a freshman.”

This news made all the difference to me. I had been fooled by Jacob’s 6′ 2″ frame. His behavior, odd for a 10th grader, was entirely appropriate for a 9th grader. When I started giving the structure he needed, he calmed down. And grew up.

By the end of the year, he worked with his classmates very effectively.

The Travails of Relatively Young Students…

A recent BrainBlogger post describes the Jacobs of the educational world. If a school has a strict cut-off date for a particular grade, then some students will be almost a full year younger than others.

In college, this difference shouldn’t matter much. After all, 19-year-olds and 20-year-olds should be emotionally and cognitively well matched.

In younger grades, however, that age difference can be huge. The age-appropriate developmental differences between the youngest and the oldest kindergartener might be substantial.

BrainBlogger’s author–identified only by her first name Naomi–outlines the alarming and ongoing consequences of this early developmental gap.

Relatively young students are likelier to be criticized for their immaturity–as happened with my student Jacob.
They are likelier to be diagnosed with ADHD.
Relatively older students are likelier to be accepted into Gifted programs, even if they’re not gifted.
Relatively young students are less likely to take the high-stakes exams that shape educational possibilities in some countries.
They are less likely to attend college, and also less likely to graduate from college.

…and, some benefits

At the same time, Naomi is careful to note the complexity of the question.

In the first place, as she writes, “the impact of [relative age effects] on educational attainment is…probabilistic not deterministic.” That is, some younger students will do just fine, even if their group is less likely to do so.

In fact, some research shows the advantages of being at the younger end of a grade’s age spectrum. For instance, younger students get the message that they need to work harder to succeed as much as their older peers, and so might have a better work ethic.

Next Steps

If you’d like to think more about this complex question, I’d start by looking over Naomi’s article. She lays out the research well, and includes sources from many different countries.

In the meanwhile, you’ve now got a helpful new question to ask. When working with students whose behavior makes you wonder about ADHD, you might start by looking up their age.

Andrew Watson

June 05, 2017

Head Start: Getting To Yes

Loyal blog readers know that Austin Matte is our local expert on Head Start. To follow up on his recent article, I want to highlight study published in Child Development.

Studying records of nearly 3000 students, the authors find that attendance matters. Head Starters who miss class don’t make as much progress in math and literacy as those who do.

That news might not sound surprising–of course attendance matters!–but it contributes to an important debate about the value of Head Start in the first place.

The Argument, Part I

We’ve got some good research showing that, although Head Start produces impressive gains among its participants, those gains just don’t last. This review, for example, finds that–by 3rd grade–Head Start participants no longer stand out from their non-Head-Start peers.

In the biz, they call this result “fadeout.” Some people argue that fadeout suggests we should give up on Head Start altogether. After all, given that its results don’t last, we should spend our money elsewhere.

Austin’s response to this argument (a response I find persuasive, by the way) is that fadeout in fact demonstrates the benefits of Head Start.

Here’s an analogy:

I’m overweight and my cholesterol is high. My doctor tells me to exercise and eat right. I start jogging four times a week and eating like Tom Brady. A year later–voila!–my doctor reports that I’m the picture of health.

So, I stop with the jogging, and go back to potato chips and lard burgers. Fairly soon, I’m back to my old weight and cholesterol level.

Now: do you blame the jogging? Or, do you blame the end of the jogging?

People who say that “Head Start” doesn’t work are blaming the jogging. But, it just seems obvious that the jogging helped. It was my decision to stop–not to start–jogging that caused the problems.

Isn’t the straightforward conclusion that we should add more years to Head-Start, not eliminate the program that’s clearly working?

The Argument, Part II

Today’s study gets at the same question a different way. If Head Start programs didn’t really help, then doing less of them wouldn’t matter. Gaps in attendance shouldn’t be a problem, because the program being attended wouldn’t actually accomplishing anything.

This research, however, gives the lie to that logic. Clearly, less time in Head Start leads to less learning; or–said the other way around–more time produces more learning.

(In the biz, they call this “the dosing effect.” A higher dose of something–in this case, Head Start–leads to greater benefits–in this case, greater learning.)

Given that we see a dosing effect, we can have confidence that Head Start does, in fact, cause the changes it claims to cause.

I + II = Yes

Austin’s argument about “fadeout” helps us see the long-term benefits of Head Start. And today’s study about “dosing” helps us see the short-term effects of Head Start.

Convinced yet? Just say yes…

Andrew Watson

May 24, 2017

School, Self-Regulation, and the Brain

The Study

A just-published study asks about the effect of schooling on the brain. (A chatty, readable summary by one of the authors can be found here.)

More specifically, it looks at a young child’s ability to self-regulate: a skill that early schooling emphasizes–and, of course, one that’s highly necessary for sustained success in almost any meaningful activity or relationship.

The authors take advantage of the arbitrary cut-off date for schooling, and look at brain development for children who were just old enough–or not quite old enough–to enroll in 1st grade.

The research question was: can we find meaningful differences in self-regulatory areas of the brain after a year of 1st grade (children just within the cut-off date) compared to a year of kindergarten (children just beyond the cut-off date)? Did these brains develop alike over the course of this year, as part of typical human development? Or, did the more academic structure of 1st grade influence brains to develop differently than the more playful freedom of kindergarten?

The result:

The research team found meaningful developmental differences in a specific region of the prefrontal cortex, and also in the posterior parietal cortex. Earlier work has shown both regions to be parts of neural networks that participate in self-regulation.

In other words: the greater structure of 1st grade seemed to bulk up neural regions often used for self-regulation.

In quite predictable ways, that is, schooling changes brains.

The Bigger Picture

I was drawn to this study because of a headline: “How does going to school change your brain?”

In the current world of education, we hear this phrasing quite often:

Taxi drivers in London–who must learn very complex street maps–have different brains from people who don’t learn those maps. Map learning changes your brain!
Learning a foreign language actually changes your brain!
Playing the bagpipes not only makes you sexy, but it also changes your brain!

You may well have heard this claim quite often in the world of education. It’s an especially popular point among folks who have something to sell.

So here’s an important secret: if you do something often, practically everything changes your brain.

If you nap regularly at 3, I suspect your brain is different from the brains of people who don’t. If you run marathons, doing so changes your brain. Or, juggling. Or, learning calculus.

Or–I don’t know–walking up stairs backwards.

Brains change. Often. It’s what they do.

I honestly don’t quite understand the reverence with which people utter the words “collecting chia pets actually changes your brain!” Over a decade ago, neuroscientists believed that brains didn’t change much once they were fully formed, so I understand why they are still awestruck by this fairly recent discovery.

But the rest of us? I’m surprised most non-neuroscientists are invested enough in the changelessness of brains to care one way or the other.

Here’s a test I occasionally use: when I hear the words “actually changes your brain,” I mentally substitute the words “happens while you’re breathing.” If that second sentence would surprise me, then I’ll be surprised by the first.

So, for example: “Ball-room dancing classes actually change your brain!” becomes “Ball-room dancing classes happen while you’re breathing.” Nope, not surprised.

Back to Where We Started

If it’s not surprising that a structured academic environment (1st grade) affects brains differently than a playful environment (kindergarten), what should we do with this study?

For teachers, the answer is: not much. This research result is interesting, but not at all surprising. When one group of students spends a year in a somewhat different environment than another group, those groups develop differently–both in their behavior and in their neural structures.

Put differently, we might summarize the research result this way: at the neural level, 1st grade works. It creates the changes we want it to change. (Or, more precisely: the changes we see in neural networks make sense given what we know about their behavioral correlates.)

For neuroscientists, the answer is: celebrate. Given that neuroplasticity is a relatively recent finding, it’s quite amazing that specialists can now predict where brain changes might happen, and then find those very changes after 9 months. 20 years ago, all of this would have been impossible. Today, it’s not only doable–it’s been done.

In other words: I don’t think you and I will teach any differently because of these findings. But, this study gives us even more confidence that neuroscience and education will come to inform each other more and more often.

Andrew Watson

May 10, 2017

Once Upon a Digital Time…

A recent study suggests that 3- and 4-year old children understand as much, and learn as much vocabulary from, digital books as from read-alouds with adults.

This study hasn’t been published–it was presented at a recent conference–so we can’t look at all the details with the specificity that we usually do. (And, skeptics will rightly be concerned that the research was funded by Amazon: a company that might well profit from its conclusions.)

At the same time, the description I’ve linked to sounds plausible and responsible, so I’m not inclined to dismiss this finding out of hand.

The authors’ conclusions conflict with some other findings in related fields. You may remember a recent blog post discussing Daniel Willingham’s conclusion that, on the whole, students learn more from books than from e-readers.

I’ve also been interested in a study by Ackerman and Goldsmith showing that students regulate their learning better with books than e-readers.

But the current study isn’t about college students trying to learn from books; it’s about pre-readers trying to follow a story that’s being read to them. In this one paradigm, the researchers have found that the right kind of e-book can do the job as well as the right kind of adult.