Yudariah Mohammad Yusof

Symbols and the bifurcation between procedural and conceptual thinking

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this article we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra, and calculus, then on to the formalism of axiomatic mathematics. This evidence is taken from a number of research studies recently conducted for doctoral dissertations at the University of Warwick by students from the United States, Malaysia, Cyprus, and Brazil, with data collected in the United States, Malaysia, and the United Kingdom. All the studies form part of a broad investigation into why some students succeed, while others fail.RésuméLes symboles jouent un rôle central entre les processus à accomplir et les concepts auxquels on doit penser. Ils nous permettent à la fois de résoudre des problèmes mathématiques et de réfléchir aux relations mathématiques. Dans cet article, nous examinons les discontinuités qui apparaissent le long du chemin d’apprentissage emprunté par différents élèves et qui entraînent une divergence entre la pensée conceptuelle et la pensée procédurale. Nous fournirons des exemples tirés de plusieurs contextes différents illustrant l’acquisition des symboles par l’intermédiaire de l’arithmétique, de l’algèbre et du calcul différentiel et intégral, pour ensuite passer au formalisme des mathématiques axiomatiques. Ces exemples proviennent d’un certain nombre d’études menées récemment à l’Université de Warwick par des doctorants américains, malaisiens, chypriotes et brésiliens, et qui portent sur des données recueillies aux États‐Unis, en Malaisie et au Royaume‐Uni. Toutes ces études s’inscrivent dans le cadre d’une vaste recherche visant à déterminer les raisons pour lesquelles certains élèves réussissent alors que d’autres échouent.

A framework for integrating cooperative learning and creative problem solving in engineering mathematics

Creative problem solving (CPS) is a multi-step method for solving problems in various disciplines that can support students in the learning of mathematics. Although CPS is cooperative in nature and is most productive when done as a team, CPS cannot utilize the full potential of teamwork to connect and share ideas among groups in the process of solving problems. Cooperative learning (CL) has additional elements designed to develop groups into a learning community. Both CL and CPS elements are combined to create a problem solving framework to guide students through the CPS cycle according to CL principles and to transform group discussions to class discussions. The main objective of this study is to propose a cooperative creative problem solving (CCPS) framework to support student problem solving in engineering mathematics. The designed framework can encourage engineering students to learn mathematics in their teams and overall class discussion.

Integrating mathematical thinking oriented problem solving approach with blended learning open source science or math studies (BLOSSOMS) modules

Research indicated that the major practices of engineers rely on mathematical thinking skills. Mathematical thinking and learning in engineering education must address the rapidly changing technological innovations and the associated expectations in terms of the quality of learning experiences. Thus, future engineers need to be actively engaged in deep and meaningful mathematical thinking and learning rather than passive information transmission during their engineering mathematics. This paper presents some results of a study carried out to investigate the potential of blended learning and its implication in supporting mathematical thinking among prospective engineers. Mason’s et.al. problem solving approach is integrated with BLOSSOMS modules first to produce activity based worksheets and then to conduct blended learning sessions to cultivate mathematical thinking skills among first year engineering students using duet teaching and collaborative learning approaches. The two staged interpretive data analy...

Teaching mathematical structures in differential equations using a computer algebra system to engineering students

Engineers often need to make sense of mathematical structures in differential equations to deal with real life problems. However, students showed difficulties in grasping them. This study presents the teaching of mathematical structures in differential equations using a computer algebra system. The computer algebra systems played the role as a pedagogical tool to enhance teaching mathematical structures. Findings showed the nature of the problems, prompts and questions assisted engineering undergraduates to make sense of mathematical structures. Explanations and links were the most frequent type of mathematical structures employed in solving real life problems. While techniques and representations were the most frequent mathematical structures adopted during solving procedural problems. This study implies that instructors should use computer algebra systems strategically to teach meaningful mathematics.