The influence of questions on mathematical achievement

As research has shown, asking higher-level questions – even when students do not succeed in giving correct answers – can increase learning. Studies indicate that preparing to communicate an answer involves higher-level thinking, which can lead to increased learning. Given the consistently superior performance of Asian students over U.S. students in math beginning as early as first grade, Michelle Perry, University of Illinois, and Scott W. VanderStoep and Shirley L. Yu, University of Michigan, researched the types of questions asked in first-grade addition and subtraction lessons in Japan, Taiwan and the United States. Perry et al. examined the questioning patterns of teachers in these three cultures in an attempt to determine if there was a difference in the degree to which teachers’ questions engage students in higher-order thinking.

Differences in schooling

Previous studies of classrooms have revealed that in contrast to Japanese and Chinese children, who spend most of their time paying attention to the teacher, American students spend more than half their time working alone. Asian children also receive more instruction because they spend more time in school. Asian teachers emphasize whole-class evaluation of problems and their solutions, enabling all students to learn how to approach different types of problems. These researchers state that the individual evaluation common in U.S. classes allows students to learn only if they solved the problem correctly.

The study

A total of 311 first-grade math lessons in the three countries were observed and analyzed. Two classrooms were observed in each of 10 schools in Japan, 10 schools in Taiwan and 20 schools in the U.S. Lessons were recorded by trained observers native to each country. Observers were told to record all behavior and discussion during math lessons, as well as the materials used and the content of the lesson. Particular attention was to be paid to the oral remarks of students and teachers. Observers were not informed of the purpose of the study. Following the observations, all the questions asked by the teachers were coded into one of six categories. The categories were:

1. Computation or rote recall (“What is 7+5?”).

2. Rule recall (“What rule applies in this example?”).

3. Computing in context (problem involves the use of concrete manipulative or a realistic context).

4. Make up a problem (teacher requests that students make up but not necessarily solve a problem).

5. Problem-solving strategies (teacher asks students to go beyond actual computation and to explain how a problem was solved).

6. Conceptual knowledge (questions that ask for principles underlying addition or subtraction; teacher asks children to transcend the specific problem and to attempt to construct general, abstract or conceptual knowledge).


No significant difference in the proportion of computation questions, rule recall questions or requests to make up problems was found between each of the three countries. Computation questions were asked frequently in all three countries, but very few teachers asked rule-recall questions or asked students to make up their own math problems.

Asian students, however, were engaged by their teachers in a greater proportion of lessons involving computing in context. These questions typically involved contexts or materials with which students were very familiar. For example, questions about the cost of items they buy and use regularly were asked frequently and Japanese teachers, in particular, stressed that context questions had to be understood before they could be solved. Often students were read a problem off the blackboard by the teacher and then were instructed to copy it into their notebooks to be read silently. Following this, students were asked to put down their pencils and to look up at the blackboard and to follow along as the teacher read it aloud again. Often students were then chosen to read the problem aloud for the class once more. The problems usually were illustrated with pictures or manipulatives.

Lessons pertaining to computing in context were used less frequently in U.S. classrooms and were significantly different than Asian context problems. Although these researchers found many examples of effective computing-in-context lessons in U.S. classrooms, the general quality of such lessons varied greatly. In the U.S., the contexts of questions was often arbitrary rather than familiar:

“She walked into the store with eight cents and earned four cents more. How much does she have now?”

“We have six yellow houses and two green houses. How many houses do we have in all?”

Although more or less plausible, the context of these questions is not sufficiently meaningful to first graders.

Based on the information gathered by observers, Perry et al. conclude that although the number and types of lower-level questions asked of students was similar across cultures, significant differences were apparent in the two higher-level categories of questions. Compared to U.S. students, Asian students were engaged much more frequently in lessons containing problem-solving strategies. When problem-solving lessons were given by U.S. teachers, however, they were similar to those used in Asian classrooms. In such lessons, students in all three countries were asked to explain how they got an answer or how they would go about solving a particular problem.

Asian students were also asked a significantly greater proportion of conceptual-knowledge questions than were U.S. students, and Japanese students were asked the most conceptual questions by far.


On the basis of this one study, these researchers do not conclude that certain question types are more effective than others in increasing academic achievement. However, they speculate that Asian students may be helped to construct more sophisticated mathematical knowledge by the kinds of questions they typically are asked in their classrooms. These researchers recommend that this hypothesis be tested further. They also suggest that U.S. teachers experiment in their own classes with more lessons pertaining to problem-solving strategies and conceptual knowledge, and that they design their own math questions in contexts relevant and familiar to their students.

“Asking Questions in First-Grade Mathematics Classes: Potential Influences on Mathematical Thought”, Journal of Educational Psychology, Volume 85, Number 1, pp. 31-40.

Published in ERN May/June 1993, Volume 6, Number 3

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