Mathematical Modelling and Applications: Ability and Competence Frameworks

Haines, Chris; Crouch, Rosalind

doi:10.1007/978-0-387-29822-1_46

Cited by 50 publications

(35 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The foregoing conclusion is in agreement with several studies that showed students' lack of experience in a particular type of task corresponds to their difficulties with the task. For example, Haines and Crouch (2007) mentioned that particular difficulties of students in mathematical modeling are due to unfamiliarity with tasks in which students have to identify what mathematics is appropriate to solve the problem. Similarly, Stein and Smith (1998) reported that students' lack of prior experience with open-ended tasks leads to difficulties when solving tasks in which the mathematical procedure is implicit.…”

Section: Opportunity-to-learn and Students' Difficultiesmentioning

confidence: 99%

Opportunity-to-learn context-based tasks provided by mathematics textbooks

2015

View full text Add to dashboard Cite

Based on the findings of an error analysis revealing that Indonesian ninth-and tenthgraders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these tasks. An analysis framework was developed to investigate the characteristics of tasks in textbooks from four perspectives: the type of context used in tasks, the purpose of context-based tasks, the type of information provided in tasks, and the type of cognitive demands of tasks. With this framework, three Indonesian mathematics textbooks were analyzed. Our analysis showed that only about 10 % of the tasks in the textbooks are context-based tasks. Moreover, at least 85 % of these tasks provide exactly the information needed to solve them and do not leave room for students to select relevant information by themselves. Furthermore, of the context-based tasks, 45 % are reproduction tasks requiring performing routine mathematical procedures, 53 % are connection tasks requiring linking different mathematical curriculum strands, and only 2 % are reflection tasks, which are considered as tasks with the highest level of cognitive demand. A linkage between the findings of the error analysis and the textbook analysis suggests that the lacking opportunity-to-learn in Indonesian mathematics textbooks may cause Indonesian students' difficulties in solving context-based tasks. Based on the results of this study, recommendations are given for improving the opportunities-tolearn to solve context-based tasks as well as for doing further research on this topic.

show abstract

Section: Opportunity-to-learn and Students' Difficultiesmentioning

confidence: 99%

Opportunity-to-learn context-based tasks provided by mathematics textbooks

2015

View full text Add to dashboard Cite

show abstract

“…Mathematical Modeling: Haines and Crouch (2007) characterize mathematical modeling as a cyclical process in which real-life problems are translated into mathematical language, solved within a symbolic system, and the solutions tested back within the real-life system. According to Verschaffel, Greer, and De Corte (2002), mathematical modeling is a process in which reallife situations and relations in these situations are expressed by using mathematics.…”

Section: Mathematical Models and Concrete Materialsmentioning

confidence: 99%

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Erbaş¹,

Kertil²,

Çetinkaya³

et al. 2014

ESTP

View full text Add to dashboard Cite

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and learning mathematics in terms of definitions of models and modeling, the theoretical backgrounds of modeling, and the nature of questions used in teaching modeling. This study focuses on two issues. The first section attempts to develop a unified perspective about mathematical modeling. The second section analyzes and discusses two approaches to the use of modeling in mathematics education, namely modeling as a means of teaching mathematics and modeling as an aim of teaching mathematics.

show abstract

“…The stages are simplifying, mathematizing, working within mathematics, interpreting and validating. Some versions of the modeling process also include a stage of writing up the report (Haines & Crouch, 2007). Blomhøj and Jensen (2007) presented similar mathematical activities through a different diagram, the KOM flower.…”

Section: Literature Review: From Learning Process To Task Design the mentioning

confidence: 99%