“Let us discuss math”; Effects of shift‐problem lessons on mathematical discussions and level raising in early algebra

Abstract

We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N = 160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the shift-problem condition. The quality of the mathematical discussions in the shift-problem condition was better compared to that in the conventional textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the shift-problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that shift-problem lessons are powerful for eliciting mathematical discussions in seventh-grade shift-problem early algebra lessons.

Mathematical Problem-Solving on Slow Learners Based on Their Mathematical Resilience

“…S1 writes that the width of the playing page is − 2 which is not correct because − 2 should be the width of the gardening yard, while the width of the playing page is three times wider than the gardening yard. This error causes an incorrect result for question number 1, in line with previous research that substitution errors often occur, resulting in calculation errors even though the steps being carried out are correct (Calor et al, 2020;Islamiyah & Prayitno, 2017).…”

Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information

“…In particular, when multiple external representations are used to support learners in complex information processing or constructing deep understanding of new concepts, the translation between representations must explicitly be scaffolded in the learning process and cannot be taken for granted. These insights are in line with mathematics education research emphasizing the need to initiate processes of deliberately translating between representations (Calor et al, 2020;Duval, 2006;Lesh, 1979).…”

“…There has been wide practical consensus about the relevance of using and connecting multiple representations (Calor et al, 2020;Lesh, 1979;Moschkovich, 2013;NCTM, 2014), and a strong research tradition focusing on students' processes in dealing with representations (Ainsworth, 2006;Falcade et al, 2007;Renkl et al, 2013), including interactionist classroom studies showing that new visual representations require a careful negotiation of meanings (Meira, 1998;Steinbring, 2005). However, teaching with multiple representations has received much less research attention (Bossé et al, 2011;Dreher & Kuntze, 2015;Stylianou, 2010), so our aim was to decompose the teaching practices in detail.…”

“…Far beyond conditional probabilities, the use of multiple modes of representation has been promoted in mathematics education since the 1960s for enhancing students' understanding of abstract mathematical concepts and complex information with these multimodal resources (Bruner, 1966;Calor et al, 2020;Duval, 2006;Lesh, 1979;Mildenhall & Sherriff, 2018), including with dynamic representations through digital technologies (Falcade et al, 2007, and many others). In particular, the construct of semiotic mediation was used to explain the relation of external and internalized representations to promote the development of conceptual understanding (Falcade et al, 2007).…”

Elementary school students’ mathematical connection in problem-posing activities

“…The data relating to the spoken and written words and students' behavior were gathered from observation (Creswell, 2012). To choose the subject of the study, 34 candidates in V grades were asked to pose a mathematical problem which was analyzed based on problem complexity based on Calor et al (2019) as in the following Table 1. Representational Complexity The solution can be represented using diagrams or graphics.…”