Support for Relational Learning in Japanese Math Textbooks

• In Event: 2-084 - Relational Learning in Real-World Contexts: Cognitive, Educational, and Socio-Cultural Factors

Integrative Statement

Relational learning involves drawing comparisons among examples on the basis of underlying similarities (Gentner, 1983). Promoting relational learning (via comparing examples) improves learning across a range of topics, including math, science and language (Alfieri, Nokes-Malach, & Schunn, 2013). Further, comparison is a recommended instructional method for math education in many countries (Australian Education Ministers, 2006; NCTM, 2014; Singapore Ministry of Education, 2006). Specifically, comparison of multiple strategies supports learning and flexible use of new strategies (Rittle-Johnson & Star, 2007). Further, comparing strategies is reported as most common in Japanese math classrooms relative to six other countries, including the U.S. (Hiebert et al., 2003). The goal of the current study was to identify how often Japanese math textbooks support comparing strategies, describe how comparing strategies was supported, and identify whether it varied by grade level.
Japanese textbooks for 3 grade levels (5th, 7th and 9th) in two widely used text series were analysed. Worked examples (i.e., a problem and solution strategy, see Figure 1) in the first half of each textbook were coded.
As shown in Table 1, comparing strategies occurred occasionally in 5th grade, with about 1 to 2 instances per chapter. However, it rarely occurred in 7th grade and never occurred in 9th grade. Most instances of comparing strategies were like the one in Figure 1, with presentation of each strategy by a fictitious student (i.e., person-presentation). Indeed, all instances of comparing strategies used person-presentation except for the instances in the 7th grade textbook for Text 2. Most often 2 strategies were compared, except 5 of the 10 instances in the 5th grade textbook for Text 1 included 3 or 4 strategies to compare.
Japanese mathematics education researchers note that comparing strategies is common in elementary school math instruction (Shimizu, 1999), and textbooks are providing some support for this. Person-presentation of the strategies in textbooks mirrors the practice of real students sharing different strategies during class in Japan (Hiebert et al., 2003). However, recent evidence suggests person-presentation of strategies may interfere with strategy generalization (Riggs, Alibali & Kalish, 2017), so the advantages and disadvantages of person-presentation in classroom instruction need to be better understood.
It is unclear why comparing strategies virtually disappeared in junior high school math textbooks. Videos of 8th grade math lessons in Japan gathered as part of the TIMSS video project suggest that comparing strategies is more common in class (Hiebert et al., 2003). In those videos, 17% of problems per lesson included comparing strategies and 42% of lessons included at least one problem in which comparing strategies was used. Conversations and classroom observations I have conducted in Japan indicate that comparing strategies is considered an ideal that teachers strive for, especially when doing specially prepared demonstration lessons for observers. However, it is not considered typical of daily instruction in secondary education. Although experimental evidence supports the effectiveness of comparing strategies (Rittle-Johnson & Star, 2007), its use may be infrequent in secondary education, even in Japan.

Author

• Bethany Rittle-Johnson, Vanderbilt University
  Presenting Author