Opportunity-to-Learn to Solve Context-based Mathematics Tasks and Students’ Performance in Solving these Tasks – Lessons from Indonesia

Abstract

This study investigated whether providing opportunity-to-learn can improve Indonesian students' performance in solving context-based mathematics tasks. On the basis of an inventory of Indonesian students' difficulties with these tasks and an analysis of textbooks and classroom practices, an intervention program for mathematics teachers was developed. This program contained tasks with relevant and essential contexts with missing or superfluous information, but without explicitly given mathematical procedures. The program also comprised guidelines for a consultative teaching approach with metacognitive prompts and questions for discussion to promote reflection in class. A field experiment with a pretest-posttest control-group design was carried out in six junior high schools in Indonesia involving 299 eightgraders. Students in the experimental group made significantly more progress on solving context-based mathematics tasks than students in the control group. Furthermore, an analysis of students' errors revealed that experimental students made significantly fewer task comprehension errors than control students. These results show that providing opportunity-to-learn, that is offering context-based tasks to students, which require mathematical modeling, and having teachers knowing the characteristics of such tasks and using a consultative teaching approach, can improve students' ability in solving context-based tasks.

Do students like us because we teach well? The popularity of high school mathematics teachers

“…Most importantly, it seems that the individual support for students, and teachers’ appreciation of students, which are interwoven with the appropriateness of mathematical examples and challenging teaching methods might have won the hearts of many students. This result is akin to the findings of previous studies which have concluded that adaptive support builds confidence and enhances self-regulated learning in students (Corno, 2008), challenging level of tasks motivates students to learn mathematics (Livy et al, 2018), and relevance of tasks make mathematics real to students (Wijaya et al, 2018) provided that teacher quality (to wit mathematics teachers enact quality instruction) made popular teachers (Fauth et al, 2014). Interestingly, the finding that providing challenging tasks to activate students’ cognition positively related to teacher popularity was noteworthy considering concerns raised by Anthony (1996).…”

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“…Furthermore, Rittle-Johnson and Schneider (2014) We used context-based problems to measure conceptual knowledge, while procedural knowledge is assessed using simple fractional multiplication operations. Students must understand problems and relevant information in context-based problems, analyse, and evaluate what decisions are appropriate when determining problem-solving methods in that context (Purnomo et al, 2019;Wijaya et al, 2015Wijaya et al, , 2018. Context-based problems are also required to connect mathematics to everyday life, which has various implications for understanding concepts, such as determining examples and non-examples.…”

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“…An examination of the effect of the intervention on students' errors showed a positive influence of the opportunity-tolearn on reducing students' errors. Students who received the opportunity-to-learn could better understand the instruction for a context-based task and had improved performance in selecting relevant information (Wijaya, Van den Heuvel-Panhuizen, Doorman, & Veldhuis, 2018).…”