Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations

Abstract

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics "Pythagoras' theorem" and "linear functions". The study aimed to answer the following research questions: (1) Do students' enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a "directive", teacher-centred instruction and an "operative-strategic", more studentcentred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students' enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.

“Why do I have to learn this?” A case study on students’ experiences of the relevance of mathematical modelling activities

“…There is ample evidence that students are motivated when they engage in mathematical modelling activities (e.g. Bonotto 2010;Cardella 2010;Kaiser et al 2011;Maaß 2010;Schukajlow et al 2012;Stillman et al 2013a), although this effect is task-specific, context-specific, and short-term. Also, motivation in modelling activities does not automatically translate into motivation for mathematics at large.…”

Sami Culture and Values: A Study of the National Mathematics Exam for the Compulsory School in Norway

“…Competence aims are written in the same frame for all subjects, starting with "[t]he aims for the education are that students shall be able to ..." (ibid.). The competence simplified model is presented from the start (Schukajlow et al 2012). All data necessary to solve the dressed-up problems are given in advance, and the task does not contain any unnecessary data.…”

“…The tasks are first categorized by whether they are modeling problems, dressed-up word problems or intramathematical problems (Schukajlow et al 2012), and subsequently the tasks are categorized with respect to Here culture and context is interweaved with mathematics and pedagogy. Nutti (2013) points out that the goal of Indigenous education is that it should be based on Indigenous culture and language.…”

Attitudes, Beliefs, Motivation, and Identity in Mathematics Education

“…In addition, there have recently been several pleas to further develop the available educational and psychological measuring instruments by taking into account subject-specific aspects and to study student affect in a domain-specific, subject-oriented way, particularly by using tasks (Schukajlow et al 2012). Aligned with these appeals, a recent instrument was developed by Pampaka et al (2011) that was designed to measure mathematics self-efficacy as a learning outcome of students following post-compulsory mathematics programs.…”

“…In a recent study by Schukajlow et al (2012), 224 ninth grade German students were asked about their enjoyment, interest, value, and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems, and modelling problems. Half of the students received studentcentered teaching while the other half teacher-centered teaching.…”