24 SES 09 B, Paper Session
Most of the time, mathematics has been found to be one of the hardest courses in terms of learning, interpreting and understanding the concepts effectively to be able to integrate them in authentic contexts. Mathematics topics are in close relation for development with many fields such as Economics, Physics, Physics, Engineering, Medicine, and understanding key concepts in mathematics plays an important role in the improvements at those areas. Moreover, Calculus is one of the major topics that forms the basis of main subjects (Orton, 1980); as it facilitates to form the fundamental principles at various discipline areas. However students face with many difficulties to interpret and understand the concepts of Calculus (Keith, 1989; Orton, 1980). Like every mathematics topics, interpretation of Calculus concepts well enough would facilitate problem solving in different contexts. Perkins & Salomon (1988) emphasize that students who do not understand the key mathematical concepts well enough, will not gain much enough from the general strategy of defining the problem and representing it well before the start. Thus, transfer of learning plays an important role in problem solving.
Transfer of learning has been defined in similar ways but in different wording by educational experts. One of the definitions that Erik de Corte (2003) suggested is that “transfer of learning is the broad, productive and supported use of acquired knowledge, skills, and motivations in new contexts and learning tasks” (p.143).Transfer is acknowledged as a fundamental theory in learning connecting process and outcome.Thinking critically, making plans, giving reasons,metacognition activities and problem solving strategies are all the results of transfer of learning. Hence transfer of learning is the core concept in understanding and interpretation. It is classified in categories due to learning outcome and application of knowledge. Perkins and Salomon (1988) state that transfer of learning is essential as the aim of education is not raising the students only for narrow school tasks but for authentic context.
Therefore, the purpose of the study is to explore the contributions of learning tasks-involving worked examples, diverse worked examples, completion examples, self-explanations and online group discussions on near transfer and far transfer of learning towards learning, understanding and interpretation of mathematics.
Tthis study aimed to investigate the answers for the following research questions:
- RQ.1. Is there a significant mean difference between pre and post achievement test scores of students who were exposed to learning activities in mathematics lesson designed based on cognitive load theory principles ?
- RQ 1.1 Is there a significant mean difference between pre and post near transfer scores of students?
- RQ.3.2 Is there a significant mean difference between pre and post far transfer scores of students?
- RQ2. What are the indications of near and far transfer of learning in students’ self-explanations and online group discussions?
Erik De Corte (2003), “Transfer as the Productive Use of Acquired Knowledge, Skills, and Motivations,” Current Directions in Psychological Research 12, 142-46. Keith, Z. S. (1989). Writing for educational objectives in a calculus course. Using writing to teach mathematics. MAA Notes, No.16, Sterrett, A. (Eds.), 6-10. Orton, A. (1980). Elementary calculus in adolescents and young adults. Unpublished Doctoral Dissertation, University of Leeds, UK. Perkins, D. &Salomon, G.(1988) Teaching for Transfer. Educational Leadership. September 1988 22-32.
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