Can Learning From a Classmate Help Children Understand Math?

Can Reciprocal Learning Improve Math Achievement and Reduce Math Anxiety?

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A child can arrive at the correct answer and still struggle to explain why the method works. For a teacher or parent, that raises a more useful question than whether the answer is right or wrong: has the child understood the idea, or learned to repeat a procedure?

That distinction is especially important in mathematics. A student may remember a formula, follow an example, and complete a worksheet successfully, yet become stuck when the numbers or wording change. One way to make that understanding more visible is to ask students to explain their reasoning to someone else.

That is the basic idea behind reciprocal learning. Instead of relying primarily on teacher explanations, students work with classmates and take turns helping one another understand mathematical ideas. The approach gives students more opportunities to explain, question, and work through a problem together.

But does that actually lead to better mathematics achievement? And can it make students feel less anxious about mathematics?

Gilbert Banguis Guita and Denis Abao Tan explored those questions in their 2018 study, Mathematics Anxiety and Students’ Academic Achievement in a Reciprocal Learning Environment. Their results offer an interesting answer, although not the simple one that a teaching-method comparison might suggest.

Both the reciprocal-learning group and the traditionally taught comparison group improved their mathematics performance. Both groups also reported lower mathematics anxiety after the teaching period.However, the researchers did not find a statistically significant advantage for reciprocal learning.

This is important. The study gives us a useful look at what happened when students learned in a reciprocal environment, but it does not establish that this approach is better than traditional instruction.

When Explaining Math Becomes Part of Learning

Reciprocal learning starts with a simple idea: students can learn by explaining, not just by listening. In a reciprocal learning environment, students work with a partner, talk through a problem, and take turns explaining their thinking. Instead of waiting for the teacher to provide every answer, they have to put their own reasoning into words and respond to another student’s ideas.

This kind of interaction can make learning more active. A student who has to explain why they chose a particular operation, for example, may notice gaps in their own understanding that are easy to miss when simply completing a worksheet. Le Cornu and Ewing also emphasized the value of learning through reciprocal relationships, noting that teachers and students can learn from one another rather than treating knowledge as something that moves in only one direction.

The idea is particularly relevant to mathematics. Students need more than the ability to remember formulas or follow procedures; they also need a foundation in basic concepts, problem-solving, and critical thinking. Lebens, Graff, and Mayer highlighted the importance of the learning experience surrounding mathematics, while Braza and Supapo identified weak conceptual foundations, limited problem-solving and critical-thinking skills, and unsuitable teaching approaches as some of the factors that can affect students’ mathematics achievement.

There is also an emotional side to the subject. Math anxiety can make an already difficult problem feel even harder. A student who is worried about getting an answer wrong may be less willing to ask a question, try a different approach, or explain an idea in front of others. That is why looking at both achievement and students’ feelings toward mathematics can give us a fuller picture of how a teaching approach works.

What Happened in the 76-Student Study?

The study was conducted at a high school and involved Grade 8 students who were studying Mathematics 8. The researchers selected two intact classes, with a total of 76 students participating in the study.

One group consisted of 38 students who learned through a Reciprocal Learning Environment.

The other group also consisted of 38 students and served as the non-RLE group.

Because the students came from existing classes rather than being randomly assigned individually to experimental conditions, the study used a quasi-experimental design. Put simply, the researchers compared existing groups instead of creating new ones through random assignment.

The researchers looked at two main outcomes:

1. Mathematics achievement
2. Mathematics anxiety

Students completed a pretest before the instructional period and a posttest afterward. The researchers also gave a retention test two weeks later. This provided a way to look not only at performance immediately after instruction, but also at whether students continued to perform at a similar level shortly afterward.

The most noticeable result was that both groups improved.

At first glance, the slightly higher scores for the reciprocal-learning group might seem encouraging. But the statistical comparison is what prevents us from turning that difference into a stronger claim.

Students in both learning environments performed better after the instructional period. Their anxiety also declined. However, the differences between the groups did not reach statistical significance according to the authors’ analysis. The improvement within each class does not establish that reciprocal learning produced greater gains than the comparison approach.

The finding is easier to understand when we separate improvement from comparison. Both classes made progress, but the study could not show that the reciprocal-learning class improved more because of the teaching approach itself. With only two existing classes in one school, there are simply too many factors to rule out.

The context also matters. The research involved 76 students from one school, focused on particular Grade 8 topics, and checked retention only two weeks later. It offers useful evidence from those classrooms, but cannot settle questions about longer-term learning or how the approach would work with other students and subjects.

A Correct Answer Does Not Always Tell the Whole Story

For parents and teachers, perhaps the most useful part of this research is not a particular teaching method. It is the attention given to how students explain their thinking.

Imagine a student solving a fraction problem correctly. If you stop at the answer, you know that the student reached the expected result. Ask the student to explain the first step, though, and a different picture may emerge.

Perhaps the student understands the relationship between the numbers and can explain it clearly. Perhaps the student remembers a procedure from a previous lesson but cannot explain why it applies here. Or perhaps the student made a lucky choice and cannot reproduce the reasoning on a similar problem.

Those differences matter.

This is where peer explanation can be useful even without claiming that reciprocal learning has been proven superior. Asking a student to explain a solution gives the teacher—or another student—a chance to hear the reasoning rather than seeing only the final answer.

A few simple questions can do this without turning homework into another formal lesson:

• “How did you figure that out?”
• “Can you show me your first step?”
• “Why did you choose that operation?”
• “What would you do if the numbers changed?”
• “How would you explain this problem to a classmate?”

The response can be more informative than the answer itself. If a child gives a confident explanation, the teacher may know that the concept is taking hold. If the explanation falls apart halfway through, that is useful information too.

And when a child says, “I don’t know,” it does not necessarily mean that nothing has been learned. Sometimes asking, “What part do you know?” is enough to find a starting point.

Mathematics Learning Has an Emotional Side

The anxiety results add another layer to the study.

A student who feels uncomfortable with mathematics may approach a difficult problem differently from a student who feels confident. They may rush, avoid trying a second method, or stop after the first mistake. For that student, giving more problems to complete is not necessarily the same thing as providing better support.

The study found that anxiety decreased in both groups, but it did not show that reciprocal learning was the reason.

That distinction should remain in place. It would be tempting to turn the findings into a simple message—“peer learning reduces math anxiety”—but the data do not support that conclusion.

What the study does show is that academic performance and students’ emotional responses to mathematics can change during the same instructional period. Looking at only test scores can therefore leave part of the learning experience out of view.

What Parents Can Learn From the Study

Parents often want to know which approach will work best when a child struggles with math. Should they explain the problem themselves? Find a tutor? Encourage independent practice? Have the child work with a classmate?

There is no single answer in this study.

The findings instead point toward a more practical habit: pay attention to the child’s learning process, not just the finished worksheet.

A child who gets an answer wrong may understand most of the concept but make one calculation error. Another child may get the same answer wrong because the underlying idea is unclear. Those two students need different kinds of help.

Likewise, two children who both get ten problems right may not have the same level of understanding. One may be able to explain the reasoning and adapt it to a new problem. The other may simply remember the sequence of steps.

That is why explanation is worth making part of everyday math conversations.

The goal is not to question children constantly. In fact, too many questions can make a struggling student feel as though every answer is being tested.

Sometimes the best response is simply to listen.

If a child’s explanation reveals a misconception, that gives the parent or teacher somewhere specific to begin. If the child can explain the reasoning clearly, there may be no need to add another worksheet or another round of instruction.

The study does not give parents a single teaching method to follow. What it does offer is a useful reminder to look beyond the final answer. A child may need more practice, a clearer explanation, a chance to talk through the problem, or simply more time to work out what they already know.

Reciprocal learning may provide one setting for that kind of interaction, but Guita and Tan’s findings do not show that it produces better results than traditional instruction. For parents and teachers, the more practical takeaway is to listen to how a child thinks, not just check whether the answer is correct. Sometimes that explanation reveals more about the next step than another completed worksheet ever could.

References:

Braza, M. T., & Supapo, S. S. (2014). Effective solutions in the implementation of the K to12 mathematics curriculum. West Visayas State University. Iloilo City.

Guita, G.B & Tan, D. A. (2018). Mathematics Anxiety and Students’ Academic Achievement in a Reciprocal Learning Environment. International Journal of English and Education, 7(3), 112-124.

Lebens, M., Graff, M., & Mayer, P. (2011). The affective dimensions of mathematical difficulties in schoolchildren. Education Research International, 2011(1), 487072.

Le Cornu, R., & Ewing, R. (2008). Reconceptualising professional experiences in pre-service teacher education… reconstructing the past to embrace the future. Teaching and teacher education, 24(7), 1799-1812.

Simon Holmes | Contributing Education Reporter

Simon Holmes is an education reporter who contributes to WuKong Education, covering K–12 education, education technology and issues affecting students and families around the world.

With a background in education and experience as a teacher, Simon brings firsthand insight into classroom learning, student development, and the challenges educators face.

For WuKong Education, he reports on education research, emerging learning trends, policy developments, technology in the classroom, and issues relevant to parents, teachers, and students.