Learning Smarter

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Do Students Know Enough Smart Learning Strategies?

March 22, 2012 | 11:16 AM | By

Lenny Gonzales

What’s the key to effective learning? One intriguing body of research suggests a rather gnomic answer: It’s not just what you know. It’s what you know about what you know.

To put it in more straightforward terms, anytime a student learns, he or she has to bring in two kinds of prior knowledge: knowledge about the subject at hand (say, mathematics or history) and knowledge about how learning works. Parents and educators are pretty good at imparting the first kind of knowledge. We’re comfortable talking about concrete information: names, dates, numbers, facts. But the guidance we offer on the act of learning itself—the “metacognitive” aspects of learning—is more hit-or-miss, and it shows.

Research has found that students vary widely in what they know about how to learn, according to a team of educational researchers from Australia writing in this month’s issue of the journal Instructional Science. Most striking, low-achieving students show “substantial deficits” in their awareness of the cognitive and metacognitive strategies that lead to effective learning—suggesting that these students’ struggles may be due in part to a gap in their knowledge about how learning works.

Teaching students good learning strategies leads to improved learning outcomes.

Teaching students good learning strategies would ensure that they know how to acquire new knowledge, which leads to improved learning outcomes, writes lead author Helen Askell-Williams of Flinders University in Adelaide, Australia. And studies bear this out. Askell-Williams cites as one example a recent finding by PISA, the Programme for International Student Assessment, which administers academic proficiency tests to students around the globe, and place American students in the mediocre middle. “Students who use appropriate strategies to understand and remember Continue reading →

FILED UNDER: Teaching Strategies

Can Stereotyping Girls Harm Boys Too?

March 9, 2012 | 9:21 AM | By

Getty

When Larry Summers, then the president of Harvard, made his infamous remark in 2005 about “intrinsic aptitude” in explaining part of the gap between men and women’s performance in math and science, he was accused of making it harder for women and girls to succeed in those fields. He wasn’t blamed for hobbling the performance of men and boys—but maybe he should have been.

According to new research, both males and females do worse on a spatial reasoning task when they’re told that intrinsic aptitude accounts for the gender gap in the test’s results—even though the gap favors men.

In the study, published in the February issue of the journal Learning and Individual Differences, psychologist Angelica Moè told a group of 201 high school students that they would be taking a test that measured how well they could mentally manipulate imagined objects. They were also told that males perform better than females on this exercise, known as the Mental Rotation Test. Such pre-test comments are a standard way of inducing what psychologists call “stereotype threat.”

“What makes the difference is the belief that failures are dependent on genetic reasons.”

Research shows that when women or minorities are reminded before being evaluated that the group to which they belong commonly scores poorly, they themselves do worse than if they had received no such reminder. Anxiety about confirming the negative stereotype hampers their performance.

But Moè went a step further. She divided the students into four groups and offered each one a particular explanation for women’s comparative disadvantage. One group was told that the gap resulted from genetic differences between men and women. A second group was told that time limits were the problem: women could do as well as men on the test, but they were more affected Continue reading →

FILED UNDER: Big Ideas, Teaching Strategies, math, stereotypes

Why It’s Important to Talk Math With Kids

March 2, 2012 | 8:27 AM | By

Flickr: Benjamin Rossen

Do you speak math with your kids?

Many of us feel completely comfortable talking about letters, words and sentences with our children—reading to them at night, helping them decode their own books, noting messages on street signs and billboards.

But speaking to them about numbers, fractions, and decimals? Not so much. And yet studies show that “number talk” at home is a key predictor of young children’s achievement in math once they get to school. Now a new study provides evidence that gender is part of the equation: Parents speak to their daughters about numbers far less than their sons.

The report, published in the Journal of Language and Social Psychology, drew on a collection of recordings of mothers talking to their toddlers, aged 20 to 27 months. Alicia Chang, a researcher at
the University of Delaware, and two coauthors determined that mothers spoke to boys about number concepts twice as often as they spoke to girls. Children this age are rapidly building their vocabularies, Chang notes, and helping them become familiar with number words can
promote their interest in math later on.

That was made clear in another study, published in Developmental Psychology in 2010, which also used recordings of parents talking to their children to gauge how often number words were used (the kids in this study were between the ages of 14 and 30 months). Psychologist Susan Levine of the University of Chicago and her coauthors found huge variation among the families studied: Some children were hearing their parents speak only about two dozen number words a week, while others were hearing such words about 1,800 times weekly.

The frequency of number talk in the children’s homes had a big impact on how well the youngsters understood basic mathematical concepts such as the cardinal number principle, which holds that the last number reached when counting a set of objects determines the size of the set (“One, two,
three—three apples in the bowl!”). A subsequent study by Levine found that the kind of number talk that most strongly predicted later knowledge of numbers involved counting or labeling sets of Continue reading →

FILED UNDER: Teaching Strategies, math

What’s Your Best Guess? Predicting Answers Leads to Deeper Learning

February 24, 2012 | 8:12 AM | By

Flickr: saxtourigr

Predictions pique our interest. Once we wager that our favorite sports team will win, we want to know the final score. Once we guess the identity of the murderer in a mystery novel, we keep reading to find out if we were right.

The same holds true, it turns out, in the learning of mathematics. A new study published by two Michigan psychologists reports that middle-school students asked to anticipate how linear and exponential factors work—before this information was taught—became more curious about the content of the lessons they then proceeded to learn. Even more importantly, the act of venturing predictions prompted them to understand the material more deeply as they engaged in reasoning and sense-making about math instead of mere memorization.

Students who view mathematics as only memorizing facts and procedures are often unsure of when or how to apply what they have learned.

To test their theory that making predictions would facilitate learning, Lisa Anne Kasmer of Grand Valley State University and Ok-Kyeong Kim of Western Michigan University designed a lesson plan in which the teacher started off the class with a series of prediction questions. Students were asked to imagine, for example, that a boy named Alejandro was cutting a paper ballot in half, then in half again, and so on. “If Alejandro makes ten cuts, can you predict how many ballots Alejandro might have?” the teacher asked. “What is your reasoning?”

The pupils wrote down a prediction, along with explanations supporting their guess, and then discussed their responses with their classmates. After telling the students that it was their Continue reading →

FILED UNDER: Teaching Strategies, math

How Much Practice is Too Much?

February 17, 2012 | 10:41 AM | By

Flickr: WoodleyWonderWorks

More practice cuts down on unnecessary movements and eliminates wasted energy, a new study shows.

By Annie Murphy Paul

Why do I have to keep practicing? I know it already!”

That’s the familiar wail of a child seated at the piano or in front of the multiplication table (or, for that matter, of an adult taking a tennis lesson). Cognitive science has a persuasive retort: We don’t just need to learn a task in order to perform it well; we need to overlearn it. Decades of research have shown that superior performance requires practicing beyond the point of mastery. The perfect execution of a piano sonata or a tennis serve doesn’t mark the end of practice; it signals that the crucial part of the session is just getting underway.

New evidence of why this is so was provided by a study published in the Journal of Neuroscience earlier this month. Assistant professor Alaa Ahmed and two of her colleagues in the integrative physiology department at the University of Colorado-Boulder asked study subjects to move a cursor on a screen by manipulating a robotic arm. As they did so, the researchers measured the participants’ energy expenditure by analyzing how much oxygen they inhaled and how much carbon dioxide they breathed out. When the subjects first tackled the exercise, they used up a lot of metabolic power, but this decreased as their skill improved. By the end of the learning process, the amount of effort they expended to carry out the task had declined about 20 percent from when they started.

“The lesson here is keep on practicing, even after it seems the task has been learned.”

Whenever we learn to make a new movement, Ahmed explains, we form and then update an internal model—a “sensorimotor map”—which our nervous system uses to predict our muscles’ motions and the resistance they will encounter. As that internal model is refined over time, we’re able to cut down on unnecessary movements and eliminate wasted energy.

Over the course of a practice session, the subjects in Ahmed’s study were becoming more efficient in their muscle activity. But that wasn’t the whole story. Energy expenditures continued to decrease even after the decline in muscle activity had stabilized. In fact, Ahmed and her coauthors report, this is when the greatest reductions in metabolic power were observed—during the very time when it looks to an observer, and to the participant herself, as if “nothing is happening.” Continue reading →

FILED UNDER: Teaching Strategies

Beyond Strategy and Winning, How Games Teach Kids Empathy

February 9, 2012 | 1:30 PM | By

Getty

By Annie Murphy Paul

Until I had children, I couldn’t be bothered with playing games. Couldn’t stand poker, pinochle or gin rummy. Bored out of my mind by Sorry! and Stratego. Never understood the appeal of chess, checkers or backgammon.

But once I had kids, games took on a new appeal. Apart from entertaining my kids on rainy afternoons, I saw how many different skills games helped to develop. Card games like Uno and Go Fish helped my sons learn to recognize colors and numbers. Board games like Candyland and Chutes and Ladders reinforced their burgeoning conception of a linear number line. And word games like Scrabble and Boggle, which we’re just beginning to try out, promise to expand their vocabularies and enhance their understanding of word stems and endings.

But the biggest benefits of playing games, I’ve come to see, are social. The same kid who responds to the question, “What did you do at school today?” with an impassive “Nothing,” suddenly grows loquacious once there’s a pair of dice or a pack of playing cards between the two of you. Games teach children how to take turns, lose stoically and win graciously (well, most of the time). And there’s another skill that game-playing promotes, one I hadn’t thought about until I read a study published last month in the Proceedings of the National Academy of Sciences: Games push players to try to understand the minds of the other participants. Is she bluffing? Is he

Continue reading →

FILED UNDER: Big Ideas, Teaching Strategies, Games