How kids learn math and science:
Stimulate learning by asking kids to explain

© 2009 - 2017 Gwen Dewar, Ph.D., all rights reserved

Want to help your kids learn math and science? Ask them to explain what they are learning in their own words.

Experiments suggest that self-explanation can help children grasp concepts, learn procedures, and transfer knowledge to new situations. But it's important to provide kids with the right support.

Here is an overview of the research, and tips for getting the most from self-explanation.

The benefits of self-explanation

You've might have noticed it yourself: We're more likely to really "get" a concept if we go to the trouble of explaining what we think.

For instance, novice chess players appear to hone their skills faster when they make explaining an explicit part of their training process. In one experiment, people asked to watch and explain a computer’s moves became better players than did people who simply observed the computer’s moves (de Bruin et al 2006).

Similarly, the act of explanation may help students may improve their understanding of mathematics -- even if nobody else is listening.

When researchers asked 9th graders to study for a geometry test by "self-explaining," these teens earned higher scores. Compared with students who studied in other ways, the "self-explainers" were better able to solve new problems that conceptually connected with the subject matter (Wong et al 2002).

But some of the most interesting research concerns younger children. In a study of 5-year-olds, Bethany Rittle-Johnson and her colleagues (2008) gave kids some pattern-detection problems to solve.

Each problem consisted of a sequence of 6 plastic bugs like this:

and kids were asked what comes next (e.g., a red spider).

After children answered, they were told the official solutions. Then they were asked to explain why the official answers were correct. The researchers put another group of kids through the same procedure, but without asking them to explain. Which group developed better pattern-detection abilities? When given new puzzles to solve, the "explainers" performed better.

Why does self-explanation help kids learn?

Perhaps it forces them to wrestle with the underlying concepts, making them discover connections we might otherwise overlook.

That's the contention of Cristine Legare and her colleagues.

They believe that preschoolers are especially likely to attempt explanations when they encounter new data that don't jibe with their prior beliefs. Inconsistent outcomes prompt kids to think about possible, hidden causes and unseen mechanisms. The explanations they generate then inspire them to actively test their hypotheses (Legare et al 2010; 2012).

Intriguing studies support this idea.

For instance, Legare's team observed that 2-year-olds spent more time exploring a new toy after offering explanations about it. The toddlers were also more systematic in their investigations (Legare et al 2012).

Other experiments suggest that asking children to explain makes them focus on causation. When researchers have asked preschoolers to explain how a new device works, these children were subsequently more likely remember the unseen, causal properties of the device (Walker et al 2014; Legare and Lombrozo 2014).

So explaining may be valuable because it makes us aware of what we don't yet understand. If that's true, then we might expect self-explanation to be less helpful when kids are already well-informed about the concepts. And that seems to be the case. When researchers provided school-aged children with high-quality, concept-driven instruction in mathematics, kids received no added benefits from self-explanation (Rittle-Johnson 2008).

On the flip side, self-explanation might fail if kids possess too little information. It isn't realistic to expect kids to rediscover major mathematical concepts on their own. There's a reason why humanity existed for eons without anyone stumbling across these ideas!

So if we don't provide kids with enough instruction in the underlying concepts, we shouldn't expect self-explanation to aid conceptual learning.

In one experiment, Bethany Rittle-Johnson (2006) presented elementary school kids with unfamiliar algebraic problems like these:

3 + 4 + 8 = _ + 8

Some kids were given explicit instructions on a procedure to follow (e.g., "Add together 3+4+8, then subtract 8 from the sum..."). Others were simply asked to discover their own procedure. Neither group of kids got instruction in the underlying concept of equivalence.

Afterwards, half the kids in each group were asked to provide explanations for their solutions. The researchers found that self-explanation helped reinforce a child's mastery of the procedures, and it helped kids apply their procedures to new problems.

But kids didn't show an improved understanding of why the procedures worked. They weren't more likely to understand that the equal sign means sums on both sides must be equal.

What about the role of listeners? 

We've seen that kids benefit from trying to explain. Does it matter if there is an audience? Probably.

In the bug experiment for 5-year-olds, Rittle-Johnson and colleagues found that self-talk helped kids learn. But kids made even bigger gains when they explained their ideas to their mothers.

In addition, an experiment on college students suggests that learners benefit when they teach others. The students were given a passage to read and randomly assigned to one of three conditions:

  • some students were told they would be tested on the material later
  • some students were told they would have to teach a lesson about it (but did not end up doing so)
  • some students were told they would have to teach and they did go on to teach it

Who learned the material the best? On a reading comprehension test, students who had been told they would teach got higher scores than other students did. And the students who performed best were the ones who had actually delivered a lesson (Annis 1983).

Of course, we can't assume that kids would benefit in the same way that college students do. But a clever experimental study by Brown and Kane (1988) offers intriguing hints than even 3-year-olds get a boost from trying to teach.

The study worked like this. Kids were given a chance to try to solve a problem encountered by a character from a story--a man who couldn't reach a high shelf.

If the kids were stumped, the researchers gave them the solution: There were some spare tires nearby. Stack the tires to make a stool.

Afterwards, kids were presented with a second, analogous story about a farmer who needed to stack hay bales on a tall tractor.

Could the children solve this problem by themselves? It depended on what happened  next. Some kids were told to simply recount the story before answering. Others were told to teach a puppet the solution. And that simple difference had a big impact. The kids who were asked to teach were twice as likely to solve the problem on their own.

How can we reap the biggest benefits?

Four tips for making self-explanation an effective learning tactic

As noted above, self-explanation isn't always helpful. Bethany Riddle-Johnson and her colleagues (2017) have identified some of the pitfalls, and offered suggestions for making self-explanation an effective learning tactic. Here are some tips based on their ideas.

1. If there are abstract concepts to learn, don't expect kids to discover these on their own.

Give them the necessary background information. 

2. Help kids develop high-quality explanations by modeling, or providing partial answers.

For example, in the case of the pattern detection bug sequence (above) you might first walk your child through an example that you solve and explain. Describe the sequence you see, and point out the repeated pattern. Then show how your answer (the next proposed bug in the sequence) fits.

For an alternate approach, you can offer kids with a partial explanation, and ask them to fill in the missing steps. In some studies, teachers have presented students with several explanations, and asked them to choose the best one.

3. Ask kids to explain why correct information is correct.

Most experiments of self-explanation have asked students to explain a correctly worked out example. If a child has come up with an incorrect solution, and doesn't realize that, asking him or her to justify the solution may not be terribly helpful.

4. Point out errors that are based on common misconceptions, and ask kids to explain why such errors are wrong.

This is different than asking kids to justify an incorrect answer. The child begins with the knowledge that something is incorrect, and attempts to explain the nature of the mistake.

Riddle-Johnson and her colleagues note that research is limited in this area. But several studies suggest that identifying and explaining flawed reasoning can help students better understand correct reasoning. It may also teach kids to avoid using flawed reasoning themselves.

More information

For a related look at self-explanation and learning, see my article about the role that gestures play in helping kids learn math, science, and the meaning of new words. 

For more information about science education, visit my page,  "Science for kids: How to raise a science-minded child."


References: How self-explanations and teaching tasks can help kids learn math and science

Annis LF. 1983. The processes and effects of peer tutoring. Human learning: Journal of Practice and Research Applications 2(1): 39-47.

Benware CA and Deci EL. 1984. Quality of learning with an active versus passive motivational set. American Educational Research Journal 21(4): 755-65.

Brown AL and Kane MJ. 1988. Preschool children can learn to transfer: Learning to learn and learning from example. Cognitive Psychology 20: 493-523.

de Bruin ABH, Rikers RMJP, and Schmidt HG. 2007. The Effect of Self-Explanation and Prediction on the Development of Principled Understanding of Chess in Novices. Contemporary Educational Psychology 32(2):188-205.

DeCaro MS, Rittle-Johnson B. 2012. Exploring mathematics problems prepares children to learn from instruction. J Exp Child Psychol. 113(4):552-68.

Legare CH and Lombrozo T. 2014. Selective effects of explanation on learning during early childhood. J Exp Child Psychol. 126:198-212.

Legare C. 2012. Exploring explanation: explaining inconsistent evidence informs exploratory, hypothesis-testing behavior in young children. Child Dev. 83(1):173-85.

Legare CH, Gelman SA, and Wellman HM. 2010. Inconsistency with prior knowledge triggers children's causal explanatory reasoning. Child Dev. 81(3):929-44.

Matthews P and Rittle-Johnson B. 2009. In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools J Exp Child Psychol. 104(1):1-21.

Rittle-Johnson B. 2006. Promoting transfer: effects of self-explanation and direct instruction. Child Dev. 77(1):1-15.

Rittle-Johnson B, Saylor M, Swygert KE. 2008. Learning from explaining: does it matter if mom is listening? J Exp Child Psychol. 100(3):215-24.

Rittle-Johnson B, Loehr A, and Durkin K. 2017. Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM Mathematics Education 49: 559-611.

Walker CM, Lombrozo T, Legare CH, and Gopnik A. 2014. Explaining prompts children to privilege inductively rich properties. Cognition. 133(2):343-57.

Wong RM, Lawson MJ, and Keeves J. 2002. The effects of self-explanation training on students' problem solving in high-school mathematics Learning and Instruction 12(2): 233-26. 

Image of boy with skull: NPS Photo/Nathan Kostegian

Image of preschool in Indore: Globe Tot'ers / wikimedia commons

Content of "How kids learn math and science" last modified 11/2017




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