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 selfexplanation 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 selfexplanation.
The benefits of selfexplanation
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 "selfexplaining," these teens earned higher scores. Compared with students who studied in other ways, the "selfexplainers" 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 5yearolds, Bethany RittleJohnson and her colleagues (2008) gave kids some patterndetection 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 patterndetection abilities? When given new puzzles to solve, the "explainers" performed better.
Why does selfexplanation 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 2yearolds 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 selfexplanation to be less helpful when kids are already wellinformed about the concepts. And that seems to be the case. When researchers provided schoolaged children with highquality, conceptdriven instruction in mathematics, kids received no added benefits from selfexplanation (RittleJohnson 2008).
On the flip side, selfexplanation 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 selfexplanation to aid conceptual learning.
In one experiment, Bethany RittleJohnson (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 selfexplanation 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 5yearolds, RittleJohnson and colleagues found that selftalk 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 3yearolds 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 storya 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 selfexplanation an effective learning tactic
As noted above, selfexplanation isn't always helpful.
Bethany RiddleJohnson and her colleagues (2017) have identified some of the pitfalls,
and offered suggestions for making selfexplanation 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 highquality 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 selfexplanation 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.
RiddleJohnson 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 selfexplanation 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 scienceminded child."
References: How selfexplanations 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): 3947.
Benware CA and Deci EL. 1984. Quality of learning with an active
versus passive motivational set. American Educational Research Journal
21(4): 75565.
Brown AL and Kane MJ. 1988. Preschool children can learn to
transfer: Learning to learn and learning from example. Cognitive
Psychology 20: 493523.
de Bruin ABH, Rikers RMJP, and Schmidt HG. 2007. The Effect of
SelfExplanation and Prediction on the Development of Principled
Understanding of Chess in Novices. Contemporary Educational Psychology
32(2):188205.
DeCaro MS, RittleJohnson B. 2012. Exploring mathematics problems prepares children to learn from instruction. J Exp Child Psychol. 113(4):55268.
Legare CH and Lombrozo T. 2014. Selective effects of explanation on learning during early childhood. J Exp Child Psychol. 126:198212.
Legare C. 2012. Exploring explanation: explaining inconsistent
evidence informs exploratory, hypothesistesting behavior in young
children. Child Dev. 83(1):17385.
Legare CH, Gelman SA, and Wellman HM. 2010. Inconsistency with
prior knowledge triggers children's causal explanatory reasoning. Child
Dev. 81(3):92944.
Matthews P and RittleJohnson B. 2009. In pursuit of knowledge:
Comparing selfexplanations, concepts, and procedures as pedagogical
tools J Exp Child Psychol. 104(1):121.
RittleJohnson B. 2006. Promoting transfer: effects of
selfexplanation and direct instruction. Child Dev. 77(1):115.
RittleJohnson B, Saylor M, Swygert KE. 2008. Learning from
explaining: does it matter if mom is listening? J Exp Child Psychol.
100(3):21524.
RittleJohnson B, Loehr A, and Durkin K. 2017. Promoting
selfexplanation to improve mathematics learning: A metaanalysis and
instructional design principles. ZDM Mathematics Education 49: 559611.
Walker CM, Lombrozo T, Legare CH, and Gopnik A. 2014. Explaining prompts children to privilege inductively rich properties. Cognition. 133(2):34357.
Wong RM, Lawson MJ, and Keeves J. 2002. The effects of
selfexplanation training on students' problem solving in highschool
mathematics Learning and Instruction 12(2): 23326.
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