Teachers’ pedagogical content knowledge in teaching word problem solving strategies

Abstract

This research addressed Hungarian pre-service and in-service (both elementary and lower secondary) teachers' pedagogical content knowledge concerning the teaching of word problem solving strategies. By means of a standardized interview protocol, participants (N = 30) were asked about their judgement on the difficulty of teaching word problems, the factors they find difficult, and their current teaching practice. Furthermore, based on a comparative analysis of Eastern European textbooks, we tested how teachers' current beliefs and views relate to the word problem solving algorithm described in elementary textbooks. The results suggest that in the teachers' opinion, explicit teaching of a step-by-step algorithm is feasible and desirable as early as in the 1st school grade. According to our results, two approaches (namely, paradigmatic-and narrative-oriented) concerning how to teach the process of word problems solving, originally revealed by Chapman, were found. Furthermore, teachers in general agreed with the approach taken in the textbooks on the subject of what kinds of word problems should be used, and that explicit teaching of word problem solving strategies should be introduced by using simple, routine word problems as examples.

Mathematical word problem solving strategy for middle school students

“…Una parte importante de la investigación sobre representaciones visoespaciales se centra en diagramas pictóricos y esquemáticos. Hegarty llevaron a cabo una investigación fundamental sobre los efectos de estas imágenes visuales y espaciales; para ello, especificaron lo que podría contener un diagrama dentro de cada una de estas categorías [11]. Una representación pictórica es aquella en la que un estudiante simplemente identifica objetos o personas a las que se hizo referencia en el problema, mientras que una representación esquemática se categoriza como aquella en la que el estudiante hace referencia a relaciones espaciales entre objetos y personas a partir del problema [12].…”

Word problems in different textbooks at the early stage of teaching mathematics comparative analysis

“…There is a danger that the otherwise useful and justified solution steps that may really be valuable when solving more difficult tasks will be considered as part of the hidden curriculum or "didactic contract" (see Verschaffel, Greer, & De Corte, 2000). According to our results (Csíkos and Szitányi, 2019), Hungarian teachers would use a scoring system when assessing students' solutions according to the step-by-step solution strategy, and the lack of any explicit solution step may result in unfavorable test results even though the students have excellent arithmetic skills and a high level of sensemaking.…”

“…According to Csíkos and Szitányi (2019), Hungarian elementary teachers do not find it problematic to introduce a linear, step-by-step solution strategy as early as in grade 1, but they also find it natural to introduce those steps by means of applying them on relatively simple, straightforward, routine word problems. However, while applying a linear, step-by-step solution strategy on a simple arithmetic word problem, there is a chance that many children will find the explicit and consciously followed steps unnecessarily since they immediately and easily would solve the task by mental calculations.…”

An investigation of the use of specific problem-solving strategies by mathematics teachers in lessons

“…Özmen et al (2012) similarly reported that teachers make more frequent use of problems that are routine and brief in terms of their quantitative data content; that are loosely aligned with the curriculum; that lack a connection to daily life and do not contain unrelated data; or that do not lack required data. Furthermore, Ishida (2002) and Özmen et al (2012) point out that teachers employ problems that can be solved using a variety of strategies, while Csíkos & Szitányi (2020) revealed that teachers generally agree that problem-solving strategies should be taught explicitly. In this regard, Ling and Maat (2020) investigated the strategies used by teachers and to what degree they applied them, using a Likert-type scale to present the names of strategies to participants and asking them to indicate the degree to which they used them.…”

“…Other researchers (e.g., Foong & Koay, 1997;Ho & Hedberg, 2005;Ishida, 2002;Ling & Maat, 2020;Özmen et al, 2012) have provided insights into the types of problems applied in classrooms and make it clear that mathematics teachers utilize problems requiring various strategies in their lessons. In some cases (e.g., Bruun 2013;Csíkos & Szitányi, 2020;Ling & Maat, 2020), studies have examined teachers' ideas about the use of strategy in lessons and their views on their experiences, but these do not provide information about their actual classroom practice. Overall, the problemsolving strategies employed by the teachers, as well as whether they employ multiple strategies for the solution of individual problems, have not been studied comprehensively; yet the literature is virtually unanimous in noting the importance of the experiences provided to students with respect to different problem-solving strategies (Baki, 2015;Ling & Maat, 2020;Olkun & Toluk, 2003;Silver, Ghousseini, Gosen, Charalambous, & Strawhun, 2005).…”