The recent study by the Mathematical Society of Japan has revealed that Japanese university students can calculate according to standard formulas within a limited time but they cannot explain why they use particular calculation methods because they do not understand the basic theories behind them.
Only 1.2 per cent of the university students surveyed answered all five questions correctly, even though the questions were primary and middle school level. Lack of mathematical skill is a serious problem even among students in science and engineering majors and those who took a math exam at the preliminary university entrance examinations administered by the government.
University of Tokyo Prof. Takashi Tsuboi, an executive board member of the society, said the decline in students’ math ability has become more serious. “We are in a new phase,” Tsuboi said at a press conference at the Education, Culture, Sports, Science and Technology Ministry. Experts say students’ academic ability has fallen since the 1990s.
However, the number of university professors who decry their students’ lack of academic ability has increased particularly quickly in the last several years. They say students can do calculations but do not answer proof questions, make illegible responses or do not understand the textbook. The society conducted its latest survey to verify whether the professors’ impressions are correct.
In examining students’ math ability, the society made several hypotheses. For example, students can calculate an average but they may not be able to deduce the entire picture on which the average is based as they do not understand the meaning of average. The result was exactly what experts had predicted.
One in four students answered incorrectly and about 20 per cent of students majoring in science and technology did not understand the concept of average. One question was a construction question that required students to explain step by step how to trisect a straight line. This applied question is carried in almost all math textbooks for third-year middle school students in the category of similar figures.
Only 4 per cent answered correctly, the lowest among the five questions. Even among students at a competitive national university, 11 per cent answered, “Trisect the line by measuring it with a ruler” and 26 per cent left the answer blank. The fact supported the hypothesis that students might lack application skills.
Entrance exams blamed
The questions were prepared by Noriko Arai, a professor at the National Institute of Informatics, who said the decline in students’ math ability was largely due to the university entrance exam system. The survey asked students whether they took a math exam for university entrance exams.
Students who had taken a math exam that included many questions in which they had to draw figures and provide proofs, rather than a computer-scored math exam, had a high percentage of right answers. The students targeted by the survey are from the generation of “cram-free education.” Many experts believe their lighter curriculum simply reduced learning for primary school students at schools where their thinking powers should have been cultivated.
A new course of study that includes nurturing the ability to think logically was implemented at primary schools last year and it is scheduled to be implemented at middle schools from this spring. However, experts believe this curriculum change will not solve the problem unless the current entrance exam system is changed.
According to Keitaro Kamata, chief researcher at Benesse Educational Research and Development Center, who is in charge of surveys on academic ability at Benesse Corp., the survey results highlighted the fact that more students are entering university through admission offices or recommendations, as universities have adopted these systems to secure students.
“In addition to math, our survey shows a big difference in academic ability between students who entered university via such admissions and students who passed the entrance exam on reading ability in the Japanese language,” he said.