Children’s Reactions to Verbal Arithmetical Problems with Missing, Surplus or Contradictory Data

Ewa Puchalska and Zbigniew Semadeni (1987)

The authors explore how children respond to MSCD (Missing, Surplus or Contradictory Data) problems in word problems in mathematics with introducing and summarizing several previous studies. In this paper, the authors give the participating students the word problems with unusual descriptions which provide insufficient/excess data or inappropriate information to find the targeted calculation. Their findings show that many students selected irrelevant data in given word problems to find the answer. The authors argue that those MSCD problems have the possibility to improve students’ careful meaningful, and critical thinking about the text of word problems.

Comment

In addition to their findings, their literature review invited me to find several interesting insights about word problems in mathematics. One is that school beginners tend to focus on a story in given word problem with attempting to make sense of and connecting it to their experience in real life whereas experienced students focus on numbers without thinking out-of-school life. Moreover, the other interesting finding is that some students who faced MSCD problems and could not find the answer believe that teachers or high achieving students can solve those ill-posed questions.

Their works including the study of Puchalska and Smadeni are consistent with what I experienced with my students in the Japanese school. The students seem to believe that there are no fragments in the description in textbooks. In other words, they think, each word problem must be solvable (has a solid answer), should be related to what they have learned before, and contain only necessary numbers they have to use for the solution. Originally, the reason why I provided my students several word problems with excess data is that the correct answer rate of a word problem with surplus data was relatively low in National Assessment of Academic Ability in Japan 2017. Additionally, many my colleagues in the Japanese school concern about the students’ reading comprehension of Japanese language regardless of subjects. I currently think it will be interesting if I give my students MSCD problems and make them discuss what kind of data will be needed to solve the question. We need to utilize information as many as possible when solving problems in the real world. In addition to students’ improvement of critical thinking, they may find the relationship between mathematics and real life.