Every word problem has a solution—The social rationality of mathematical modeling in schools

The Effects of Learning Experience on the Ability of Elementary School Students to Deal With Math Problems Requiring Multiple Solutions

“…In addition to the results obtained in previous studies (Kinda, 2003;Reusser & Stebler, 1997;Verschaffel et al, 1994;Wyndhamn & Säljö, 1997;Yoshida et al, 1997), the results of Investigations 1 and 2 reveal the following.…”

“…Previous studies have revealed that elementary school students have a single-solution tendency (Reusser & Stebler, 1997;Verschaffel et al, 1994;Yoshida et al, 1997) and that they need to spontaneously notice the existence of multiple solutions and identify the cases possible in order to produce multiple solutions when solving word problems requiring them (Kinda, 2003). However, these studies do not clarify the way in which students are able to spontaneously notice the existence of multiple solutions and identify the cases possible.…”

“…Several empirical studies (Kinda, 2003;Reusser & Stebler, 1997;Verschaffel, De Corte, & Lasure, 1994;Wyndhamn & Säljö, 1997;Yoshida, Verschaffel, & De Corte, 1997) have used multiple-solution word problems. The results of these studies provide information regarding such a single-solution tendency in elementary school students.…”

“…Verschaffel et al (1994), Reusser and Stebler (1997), and Yoshida et al (1997) used countless-solution word problems (see Table 1) to examine whether 4th and 5th grade elementary school students could apply their knowledge of multiple solutions from the real world in the context of solving mathematics problems at school. The results showed that approximately 95% of the students produced only one solution to the problem (Reusser & Stebler, 1997;Verschaffel et al, 1994) even when they were provided with an extra hint, such as "the test contains several problems that are difficult or impossible to solve because of certain unclarities or complexities in the problem statement (Yoshida et al, 1997)." However, in group learning situations wherein students could interact with one another (Wyndhamn & Säljö, 1997), as a result of group discussions, approximately 88% of the 10-to 11-year-old students were able to understand that the problem had countless possible solutions.…”

“…The results indicated that the correct response rates under Conditions 1, 2, and 3 were 0%, 4%, and 42% respectively in the countlesssolution word problem, and 11%, 41%, and 88% respectively in the two-solution word problem. Verschaffel et al (1994), Reusser and Stebler (1997), and Yoshida et al (1997) provided students with no prior information regarding multiple solutions; therefore, the conditions employed in their studies were equivalent to Condition 1 in Kinda (2003). In Wyndhamn & Säljö (1997), group discussions enabled students to identify multiple cases; therefore, this situation was almost equivalent to Condition 3 in Kinda (2003).…”