Math society says university students’ skills don’t add up (Yomiuri, Feb.26)

The Yomiuri Shimbun

University students today lack sufficient mathematical and logical thinking skills, with 24 percent of them unable to grasp the concept of an average, according to a survey by the Mathematical Society of Japan.

The academic society attributes the university students’ poor academic performance not only to decades-long lax educational policies, but also to lowered entrance exam standards aimed at attracting students because of the low birthrate.

The society conducted the basic math survey–the first of its kind–from April to July last year, covering 5,934 students–mainly freshmen who had just enrolled in spring–from 48 national, public and private universities.

It featured a set of five problems, most of them at primary and middle school level, aimed at examining their skills in comprehending mathematical statements, providing written explanations and drawing figures.

The survey found only 1.2 percent of the students were able to answer all five questions correctly.

Only 19 percent of the students correctly answered a question in which they were asked to provide a logical explanation as to why the addition of an even and an odd number always results in an odd number–a question considered suitable for third-year middle school students.

In response to a problem on the arithmetic concept of an average–first learned in the sixth grade of primary school–many respondents mistakenly believed that if the average height of 100 students is 163.5 centimeters, half of them are taller than that and half of them are shorter.

Among respondents from middle-ranking private universities, nearly half of them answered incorrectly.

The survey found that many respondents who gave wrong answers in the survey tended to belong to either of two groups: non-science majors at private universities whose entrance exams do not include math tests, or those from colleges whose entrance exams include multiple-choice-only math questions.

Cram-free education lowers math abilities (Feb. 26, 2012)

Keiko Katayama and Mina Matsumoto / Yomiuri Shimbun Staff Writers

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 percent 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 percent 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 percent answered correctly, the lowest among the five questions. Even among students at a competitive national university, 11 percent answered, “Trisect the line by measuring it with a ruler” and 26 percent 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.


Universities filling the blanks

Officials of many companies’ personnel divisions are also furrowing their brows at some university students’ lack of mathematics ability.

“Since university entrance exams became more diversified in the 1990s, it’s become impossible to judge students’ scholastic ability only by the name of the university they went to or the department they were enrolled in,” a representative of a fabric maker’s personnel division said. “Even some students from famous universities lack basic knowledge that should’ve been learned at primary and middle schools.

“When we conduct job interviews, we judge a student’s ability by asking about the types of entrance exams they took, such as regular entrance exams or admissions-office method exams, as well as looking at recommendations from high schools or whether there were special quotas for students who have lived abroad. We also ask how they spent their time at high school.”

A recruitment official at a major telecommunications company said his company asks students about the entrance tests they took.

“Even students in science-related courses can’t write and speak logically. We’re sometimes left shaking our heads wondering how a student from a certain university could have such poor academic ability,” the official said.

Yoshihiro Toyoda, senior chief researcher at Recruit Co.’s Works Institute, said “it’s not uncommon” for companies to check the conditions under which students were admitted to their schools as reference material during the recruitment process.

In a bid to get their students up to speed, some universities have intensified their instruction of mathematics.

According to a Yomiuri Shimbun survey last year on university-level education, 31 percent of universities–mainly science and technology universities–have made mathematics compulsory.

Osaka Prefecture University started conducting math tests for freshmen seven years ago and set up a special room in which a teacher regularly stays to answer questions about mathematics.

The university started the program after a teacher of a humanities course complained it was impossible to teach classes smoothly “because some students don’t know how to read charts and graphs in social science and other classes.”

From April, the university will make mathematics compulsory for all students taking humanities courses.

Tetsuya Takahashi, vice president of the university, said, “Logical thinking picked up through mathematics will be useful for our students after they start working.”