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Studying Wrong Answers Helps Learn the Right Ones
Andrew Watson
Andrew Watson
March 18, 2019

Studying Wrong Answers Helps Learn the Right Ones

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With teaching as with baking, sometimes you should follow steps in a very particular order. If you don’t do this, and then that, and then the other, you don’t get the best results.

Two researchers in Germany wanted to know if, and when, and how, students should study incorrect answers.

To explore this question, they worked with 5th graders learning about fractions. Specifically, they taught a lesson about comparing fractions with different denominators.

(When studying this topic, students can’t rely on their instincts about whole numbers. For that reason, it’s a good subject to understand how students update conceptual models.)

They followed three different recipes.

One group of 5th graders saw only correct answers.

A second group saw both correct and incorrect answers.

A third group saw correct and incorrect answers, and were specifically instructed to compare correct and incorrect ones.

Which recipe produced the best results?

The Judges Have Made Their Decision

As the researchers predicted, the third group learned the most. That is: they made the most progress in updating their conceptual models.

In fact: the group prompted to compare right and wrong answers learned more than the group that saw only the right answers. AND they learned more than the group that saw (but were not prompted to compare) right and wrong answers.

In other words: the recipe is very specific. For this technique to work, students should first get both kinds of information, and second be instructed to compare them.

Important Context

I’ve held off on mentioning an important part of this research: it comes in the context of problem-based learning.  Before these 5th graders got these three kinds of feedback, they first wrestled with some fraction problems on their own.

In fact, those problems had been specifically designed to go well beyond the students’ mathematical understanding.

The goal of this strategy: to make students curious about the real-world benefits of learning about fractions with different denominators in the first place.

If they want to know the answer, and can’t figure it out on their own, presumably they’ll be more curious about learning when they start seeing all those correct (and incorrect) answers.

As we’ve discussed before, debates about direct instruction and problem-based learning (or inquiry learning) often turn heated.

Advocates of both methods can point to successes in “their own” pedagogy, and failures in the “opposing” method.

My own inclination: teachers should focus the on relevant specifics. 

In the link above, for example, one study shows that PBL helps 8th graders think about deep structures of ratio. And, another study shows that it doesn’t help 4th graders understand potential and kinetic energy.

These German researchers add another important twist: giving the right kind of instruction and feedback after the inquiry phase might also influence the lesson’s success.

Rather than conclude one method always works and the other never does, we should ask: which approach best helps my particular students learn this particular lesson? And: how can I execute that approach most effectively?

By keeping our focus narrow and specific, we can stay out of the heated debates that ask us to take sides.

And: we can help our students learn more.

Evaluating the Best Classroom Practices for Teaching Math
Andrew Watson
Andrew Watson
November 06, 2018

Evaluating the Best Classroom Practices for Teaching Math

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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..

Homework Improves Conscientiousness: Do You Believe It?
Andrew Watson
Andrew Watson
March 29, 2018

Homework Improves Conscientiousness: Do You Believe It?

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Teachers have many reasons to assign homework. In particular, we want our students to practice whatever they’re learning, so they can get better at it.

homework improves conscientiousness

We might also plausibly hope that homework benefits students in other ways. Perhaps it helps them get more organized. Perhaps it involves parents in learning. Or, perhaps homework improves conscientiousness.

This last option seems especially intriguing.

Obviously, conscientiousness improves the likelihood that students will do homework. But, does that causal process flow the other way? Do people who do more homework become more conscientious?

Promising Signs

To answer that question, several researchers gathered data from German middle school students, and — crucially — their parents.

Then, they crunched a lot of numbers. I mean, A LOT of numbers.

Early results showed that, for these middle schoolers, homework effort and conscientiousness change in tandem. More specifically, both homework effort and conscientiousness increased from 5th to 7th grades, and then declined quite sharply from 7th to 8th grades.

(My condolences to 8th grade teachers.)

These correlations also appeared when analyzing parents’ points of view. Like their children, they saw that the effort going in to homework correlated with their children’s conscientiousness in other areas of life.

Researchers then ramped up their analytical methodology to explore causal direction. They used a particular statistical method to contrast students whose effort did not go up with those who did, and to compare their conscientiousness levels.

Is it true that doing more homework improves conscientiousness? Here is their summary:

We are willing to tentatively propose that changing one’s homework effort may lead to changes in conscientiousness, but obviously, this inference and our results await more rigorous testing.

In other words: based on the data they have and the methods they can use, it seems so. But, these methods have limits, so we need to explore this question further.

Homework Improves Conscientiousness: Not So Fast…

This study appeals to me because its authors recognize not only the limits of their methods, but also the limitations of its implications.

For instance, teachers might conclude “if homework improves conscientiousness, then we should all assign more homework. It will be good for them, and not just their learning.”

NOT SO FAST, the authors respond.

First, not all students do the homework we assign. After all, in the dry language of research, they note that “students differ in the extent to which they ascribe value to the activity of doing homework.” (Ain’t that the truth…)

Second, an increase in homework might (might!) increase conscientiousness, but it might harm other important things: like, say, happiness, or relationships with peers.  Conscientiousness is an important part of life, but it’s not the only important part of life.

What’s Next

Reasonably enough, these researchers call for more investigation of this question. In particular, they hope for a study that controls the amount of homework that students do, and learns from what happens next.

(The current study, remember, simply looks at what students did.)

But what should we teachers do because of this research?

Schools are having a healthy and important debate right now about the benefits of homework. (For earlier posts on this topic, click here and here.) Reasonably enough, we want to ensure that its benefits outweigh its potential harms: lost time, increased stress.

This research encourages us to remember the non-academic benefits of homework. If we cut back on practice problems, what can teachers and parents do in their stead to help young children develop the healthy characteristics essential for a productive adult life?

I don’t know the answer, but I do know that’s an important question.

Teens and Cell Phones: The Good, The Bad, The (Not So) Ugly
Andrew Watson
Andrew Watson
March 19, 2018

Teens and Cell Phones: The Good, The Bad, The (Not So) Ugly

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Teens and Cell Phones

A recent article in Nature magazine wisely captures the complexities of the Great Cell Phone Debate.

Will they transform human potential?

Will they destroy our children’s self-confidence, not to mention their ability to hold a simple conversation? Their ability to pay attention in class?

(For earlier articles on these topics, see here and here.)

Researcher Candice Odgers offers a simple formula to answer those questions:

“In general, the adolescents who encounter more adversity in their offline lives seem most likely to experience the negative effects of using smartphones and other digital devices.”

That is, the cell phone isn’t causing the problems. For children who already struggle, however, it might exacerbate existing problems.

Teens and Cell Phones: The Good

You might be surprised to read Odgers’s list of digital benefits. Several studies show that teen texting can foster healthy relationships.

6-12 year-olds with solid social relationships are likelier to keep in digital communication with peers as they get older.

Virtual conversations can even help teens “bounce back after social rejection.”

Clearly, cell phones aren’t destroying our children’s ability to create healthy relationships. (Of course, the form those relationships take looks quite different from those of our youths. Or, at least, my youth.)

Teens and Cell Phones: The Bad

As Odgers sees the research, socio-economic status might be a key variable.

The “digital divide” used to mean that rich people had technology that others didn’t. Today, it’s more likely to mean that affluent parents can supervise their children’s digital lives more consistently than less-affluent parents.

“What we’re seeing now is a new kind of digital divide, in which differences in online experiences are amplifying risks among already-vulnerable populations.”

So: for low-income families, online fights lead to real world fights more often. So too bullying.

A Final Point

Complaints about teens and cell phones often miss a crucial point: they get those cell phones from us.

Odgers’s own research shows that 48% of 11-year-olds in North Carolina have cell phones. I’m guessing that relatively few of those 11-year-olds bought those phones — and the data plans — with their own money.

Also: adolescents did not invent the cell phone. They aren’t running companies that make huge profits from their sale.

Odgers’s article suggests that we should focus our concerns not on teens overall, but on those who are already struggling in their daily, non-virtual lives. I suggest, in addition, that we should focus on adult participation in this digital culture.

We are, after all, the ones who make their digital lives possible.

The Benefits (?) of Interactive Online Science Teaching
Andrew Watson
Andrew Watson
March 12, 2018

The Benefits (?) of Interactive Online Science Teaching

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Few educational innovations have gotten more hype than online learning, and few have a more checkered track record.

interactive online scienceFor every uplifting story we hear about a Khan Academy success, we get at least one story about massive drop-out rates for MOOCs.

You’d be forgiven for thinking that people are just better at learning face to face than from a computer.

And so a recent study deserves our attention. And — like all other research — it also merits our respectful skepticism.

Three Headlines, and a Warning

First Headline: middle schoolers learned A LOT more science from an interactive online curriculum than from a more traditional one.

Second Headline: learning gains seem impressive for students with learning disabilities, and for English language learners.

and

Third Headline: the program was tested with more than 2300 students and 71 teachers in 13 schools in two different states: Oregon and Georgia. That is: this study isn’t about 30 college students in a psychology lab. It’s about real students in real classrooms at opposite ends of the country.

And now, the Warnings: I’m going to give you reasons to be skeptical about all of this. (Well, at least the first two headlines.)

Interactive Online Science Teaching

Researchers developed four units aligned with national science standards. These units, each roughly 10-14 weeks long, covered such topics as Knowing My Body and Our Place in the Universe.

We should note that researchers brought several theoretical perspectives to these science units. They took care to make them culturally relevant to the learners. They designed each unit with project-based learning principals in mind.

And, they made sure that students could interact with the material in different ways. Middle schoolers could control the pace of the lesson, move images around on the screen, get feedback, and navigate among several sources of information.

Even from this brief description, you can see how this interactive online science lesson could be especially appealing — and potentially especially effective — for 7th and 8th graders.

(You can learn more about the curriculum at this website.)

Results: By The Numbers…

First, the online units helped students learn.

In the control group, where teachers taught as they typically had done, students improved 5.7% from pretest to posttest. In the treatment group, where teachers used the units described above, students improved 16.7%.

When the researchers looked at students with learning disabilities and at English language learners, the raw data also showed promising improvements.

For ELL students, for example, the control group improved 4.9%, whereas the treatment group improved 15.0%.

Reasons for Concern #1: “Active Controls”

Researchers compared students who used their online curriculum to others who did not. This comparison to a “control group” allows them to say that their curriculum is better than the old way.

However, it’s quite possible that the students in the treatment group responded well simply because they did something different. In other words: perhaps the online curriculum didn’t help students learn, but the change of daily routine did.

The only way to rule out this possibility is to have the control group do something new as well. If the new online curriculum produces more learning than some other new curriculum, then we can reasonably conclude that the curriculum itself made the difference.

After all, in this hypothetical case, we can’t say that just changing something made a difference; both groups changed something.

However, because the control group in this study wasn’t “active” — that is, they didn’t do anything different or special — we can’t be certain why the researchers found the results they did. Maybe it was the interactive online science curriculum. But maybe it was just the change of pace.

The researchers’ own video — linked to above — highlights this concern. One of the teachers who used the online units says that she liked them because teachers simply hadn’t had an organized curriculum in the past. Each teacher had put something together on her own.

If that’s true for the schools in the control group, then this study compares schools that had no consistent, professionally developed curriculum at all with schools that had a curriculum developed by a Oregon University’s School of Education.

In other words: the benefit could come from having any well developed curriculum, not specifically this curriculum. Or not an online curriculum.

We simply can’t know.

Reason for Concern #2: Goodies

There’s no neutral way to say this. Teachers assigned to the online curriculum got a big gift bag. Teachers in the control group got dinky gift bags.

More specifically: teachers in the control group got a $300 bump. (Admittedly, that’s a nice perk for not having to do anything special.)

Teachers who used the online curriculum got $1500. (That’s a REALLY nice perk.) It’s five times as much.

And, they got some cool technology. And, they got extra PD and instructional resources. They even got 2 days of paid subs so they could attend that PD.

For all these reasons, it’s possible that the students did better with the online science curriculum because it helped them learn. It’s also possible that they did better because their teachers were really excited by all the loot they got.

Again, because of the study design, we simply can’t know.

What Should Teachers Do?

In my view, the jury is still out on online curricula.

On the one hand, they seem like a really good idea. On the other hand, the evidence in their favor is, at best, equivocal.

I wouldn’t be surprised if, 20 years from now, we all clapped our hand to our foreheads and asked, what were we thinking?

In other words: we can’t yet look to research to be certain of an answer. If you have an opportunity that appeals to your teacherly instincts, give it a try.

If it works, let me know. If not, don’t worry that you might be doing something wrong. After all: humans evolved learning face to face. It’s just possible that the e-version of that experience will never be as good.

Growth Mindsets Help All Subgroups Learn
Andrew Watson
Andrew Watson
January 22, 2018

Growth Mindsets Help All Subgroups Learn

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Growth mindset helps subgroups

Research into Growth Mindsets often focuses on small groups of people: a class or two of 5th graders, a few dozen college students.

These studies allow researchers to draw conclusions about this specific group of students. However, we’re less sure about the sub-populations.

How does Mindset influence English Language Learners? Female students? Students from different social strata?

(more…)