Students’ Non-realistic Mathematical Modeling as a Drawback of Teachers’ Beliefs About and Approaches to Word Problem Solving

Abstract

Over the past decades numerous scholars have become aware of many compelling observations of students in mathematics classes abandoning their sensemaking capabilities when doing word problems, and, in particular, carrying out arithmetic calculations that do not make sense in relation to the situations described. This led us, together with several other scholars, to embark upon an extended investigation of the phenomenon, the results of which are reported, among others, in two books (Verschaffel L, Greer B, De Corte E, Making sense of word problems. Swets & Zeitlinger, Lisse, 2000; Verschaffel L, Greer B, Van Dooren W, Mukhopadhyay S, Words and worlds: modelling verbal descriptions of situations. Sense Publishers, Rotterdam, 2009). The goal of the present chapter is to bring together and critically review the theoretical analyses and empirical studies that have focused on major aspects of teachers' instructional practices that affect -directly or indirectly -students' non-realistic approaches to and beliefs about word problem solving. Special attention will be given to the problems that appear in students' mathematical textbooks as well as to teachers' beliefs about word problems and what are appropriate ways to solve them, and to their instructional behavior, and how these factors affect students' beliefs about and approaches to word problems. While the focus is on research that has been done in our own center, we also integrate relevant studies by others.

Teaching Writing-With or Without Metacognition : An Exploratory Study of 11- to 12-Year-Old Students Writing A Book Review

“…It should be noted, however, that the majority of researcher interactions with the teacher to address questions were in this area. This reinforces the idea that teachers do not feel secure in implementing metacognition-related instruction in their classrooms (Depaepe et al, 2015;Vlassis et al, 2014). Thus, it seems, and our results encourage this, that metacognition needs to take its place in teacher education programs.…”

The Impact of High School Life Science Teachers’ Subject Matter Knowledge and Knowledge of Student Misconceptions on Students’ Learning

“…Likewise, teachers' PCK, or KOSM, is also considered to be topic or domain specific (Blömeke et al, 2015), situated in varying contexts (Ball et al, 2008;Lee and Luft, 2008;Borowski et al, 2010;Depaepe et al, 2013;Gess-Newsome, 2015;Hayden and Eades Baird, 2018). Depaepe et al (2015) showed that students had lower scores on items that required a higher level of PCK of their teachers, compared with items that required only teachers' SMK. Regarding the combination of teacher SMK and PCK about a specific test item, Sadler et al (2013b) distinguished three categories: 1) teachers who have neither SMK nor KOSM; 2) those who have only SMK, but not KOSM; and 3) those who have both SMK and KOSM.…”

“…, 2013 ; Gess-Newsome, 2015 ; Hayden and Eades Baird, 2018 ). Depaepe et al. (2015) showed that students had lower scores on items that required a higher level of PCK of their teachers, compared with items that required only teachers’ SMK.…”

Mathematical modelling and verbal abilities: How they determine students’ ability to solve mathematical word problems?

“…The association between mathematical symbols and operations will result in simpler sentences, often called mathematical models. Solving mathematical word problems can be carried out in some steps (Uhden et al, 2012;Depaepe, De Corte, & Verschaffel, 2015), one of which is making mathematical models. According to Mulyana, Priyatno, and Dewi (2018), in the context of mathematical word problems, learning to understand problems constitutes learning that helps students turn words into mathematical models.…”