Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

Abstract

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layersgeneral strategies, which adopted Pólya's four-stage problem-solving model, and specific strategies, which consisted of 17 different problem-solving heuristics such as 'acting it out,' 'looking for a pattern,' 'working backwards,' etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study.

The Effect of Comprehension and Problem Solving Strategy Training on 5th Graders’ Non-Routine Problem Solving Success

“…Stratejinin seçimi sürecinde belirlenecek problem çözme stratejisi önem arz etmektedir. Literatürde toplam 19 farklı problem çözme stratejisine rastlanmış olup (Altun, 2005;Baykul, 2005;Fan ve Zhu, 2007;Ulu, 2008), bu stratejilerden bu çalışmada kullanılan sekiz tanesi Tablo 1'de verilmiştir.…”

“…Problem çözme stratejileri eğitimi etkinlikleri bir program geliştirme, bir matematik ve bir sınıf öğretmenliği alan uzmanı tarafından yapılandırılmıştır. Fan ve Zhu (2007) tarafından yapılan çalışmada toplam 19 problem çözme stratejisi olduğu ifade edilmiş olup; çalışmanın 8 stratejiyle sınırlı kalmasının nedeni, bu stratejilerin ROPÇBT2 ve ROPÇBT3'teki soruların çözümüne uygun olmalarıdır, bu karara bir matematik alan uzmanı ve bir sınıf öğretmenliği matematik alan uzmanının ortak görüşleri doğrultusunda varılmıştır. ROPÇBT2 ve ROPÇBT3'ün her bir sorusunda kullanılabilecek stratejiler Tablo 8'deki strateji sıralamasına göre Tablo 9'da verilmiştir.…”

Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

“…Fan and Zhu (2007) compared China, Singapore, and USA mathematics textbooks for problemsolving procedures in terms of two layers: general strategies referring to Polya's four-stage problem-solving model (understanding the problem; devising a plan; carrying out the plan; and looking back); and specific strategies. The Chinese and Singapore textbook series merely presented the 'carrying out the plan'; while more than two-thirds of problem solving procedure presented in USA textbooks adopted at least two stages.…”

Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: two contrasted case studies in France and Norway

“…attitudes); or they have investigated particular features in textbooks (e.g. problem solving procedures-see Fan and Zhu 2007). However, there are relatively few studies investigating textbooks (in connection with curricular documents and practice) with respect to the educational traditions.…”