Abstract
This study focuses on students in first year enviro nmental science degree programs where traditionally mathematical emphasis has been much less than the strict science or math majors. The importance now placed in applied mathematics means that students n eed to gain more conceptual and quantitative knowledge in not only the environmental degree programs but also in most if not all non-mathematical majors. In this study, the authors attempt to gain insights into why students fail in mathematical cou rses where the mathematical requirements are not as demanding as other strict math degree programs. This is done by examining student conceptual thinking patte rns and strategies as evident in student prepared scripts. A total of 133 students were requested to prepare a focus sheet to summarize their knowledge on topics learned but they were also told that the foc us sheets could be used in exams for notes. This motivated their sheet preparation. The students pre pared weekly summaries and later revised and summarized them for later use. Detailed examination of such sheets allowed researchers to study students’ knowledge in terms procedural work, math skills, strategies and conceptual knowledge. A stud y of linear, quadratic and limit sections led to inte resting insights not only regarding revision strate gies, knowledge of content, but also conceptual and proce dural knowledge base and higher order skills such a s problem solving focus. Logical and creative competencies were assessed in terms of how and what studen t focused upon or linked to in order to facilitate ap plication of knowledge. The results show average le vels of procedural and conceptual competence but rather low levels in logical and creative competence in preparation of scripts. Almost 50% lacked competency in procedural work while around 54% lacked conceptual competency. Given the emphasis placed procedural skills by students, the levels were lower than expected. However, the lack of structure in their w ork and deeper levels of understanding of links bet ween the topics learned was concerning. These findings h ave implications for the first year mathematics tea ching teams at universities especially the non-specialist mathematical majors.
Highlights
Students still believe that to be successful in mathematics means that they can carry out procedures and use algorithms, formulae and mathematical rules (Kaldo, 2011; Tall, 2004; Tularam, 2013a; 2013b; 1997a; Tularam and Amri, 2011)
This study focuses on the depth of student cognitive structures and mathematical knowledge base; that is how deep are student conceptual structures and procedural competence for learning and problem solving when students are in their first year study at universities
The overall analysis conducted in this study showed that students did not show significantly developed procedural or conceptual understanding in some basic topics of mathematics
Summary
Students still believe that to be successful in mathematics means that they can carry out procedures and use algorithms, formulae and mathematical rules (Kaldo, 2011; Tall, 2004; Tularam, 2013a; 2013b; 1997a; Tularam and Amri, 2011). It is often easier to memorize mathematical rules and formulas without concerns about conceptual and more deeper and connected understanding but this is problematic later when students are expected to apply their knowledge to real life or abstract problems (Tularam, 1997b; 2013b). It is important to consider that the dispositions refer to affective aspects and to deeper abilities to problem solve, apply logical and creative thinking to address the problem at hand that are driven by well-structured knowledge base (Griese et al, 2011). Lester et al (1989) advocated the importance conceptual and procedural knowledge in the development of solution processes when problem solving Using this view, this study focuses on the depth of student cognitive structures and mathematical knowledge base; that is how deep are student conceptual structures and procedural competence for learning and problem solving when students are in their first year study at universities
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