From no to yes : the impact of an intervention on the persistence of algebraic misconceptions among secondary school algebra students

Abstract

Many students enter high school with persistent algebraic misconceptions that limit their success in mathematics and, by extension, limit potential educational attainment and future earnings.The purpose of this study was to assess the effectiveness of a warm conceptual change based intervention on remediating algebraic misconceptions held by students at a secondary school.The study used a quasi-experimental, pre-test post-test, control group design as well as student focus groups. In this eight-week classroom intervention, students first took a diagnostic pre-test to identify their misconceptions. For each of seven different misconception categories, students watched a video, took an online practice quiz, and then completed a series of short paper practice slips in class. Students then took a post-test and changes were analyzed. The videos were designed using augmented activation and refutational text to create cognitive conflict. The theorized causal relationship between engagement and conceptual change was explored through analysis of usage statistics, such as the number of times a video was watched. The intervention also explored how interleaved practice and process mnemonics could improve long-term learning retention. A repeated measures ANOVA showed that students in the intervention group made significantly fewer misconception errors than the control group, while regression analysis indicated that deeper engagement led to significantly greater conceptual change. Mann-Whitney U tests showed that the intervention was significantly effective at reducing errors in some misconception categories but not in others. Finally, student focus groups explored how students experienced the intervention. The findings gave strong support for the effectiveness of the intervention at reducing the number of misconception errors students made.

Refutation Text Facilitates Learning: a Meta-Analysis of Between-Subjects Experiments

“…In addition, the non-refutation text condition had to contain the same general instructional information as the refutation text, meaning studies with no instructional materials (Heddy et al, 2017) or filler texts (Kendeou et al, 2014) as the non-refutation text conditions were excluded. Additional inclusion criteria were that the study had to quantitatively measure learning outcomes of factual information rather than beliefs or opinions; report enough data to accurately calculate an effect size; report the number of participants in the experimental and control groups, as this allowed for a meta-analysis examining clear, transparent data and the ability to report the refutation text and comparison group numbers for each comparison; use a research design with few or minimal confounding variables (e.g., Zielinski, 2017 was excluded as it seemed one could not plausibly conclude that the refutation text alone caused any difference that may have occurred); be published in English; and be publicly available.…”

How a teacher professional development program influences students algebra performance Reflections from a web-based platform

“…Studies have revealed that students have difficulties in understanding the basic concepts of algebra and have misconceptions throughout their school life (Carraher, Schliemann, & Brizuela, 2005;Falkner, Levi & Carpenter, 1999, Stephens, 2008, and issues still apparent in the recent studies (Barbieri, Miller-Cotto & Booth, 2019;Mokh, 2019;Zielinski, 2017). According to Akkan, Baki & Çakıroğlu (2011), one of the main reasons for student difficulties is a cognitive gap possibly due to the rapid transition from the context of arithmetic to algebra.…”