A STUDY OF FIRST YEAR TERTIARY STUDENTS’ MATHEMATICAL KNOWLEDGE- CONCEPTUAL AND PROCEDURAL KNOWLEDGE, LOGICAL THINKING AND CREATIVITY

Abstract

This study focuses on students in first year environmental 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 need 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 courses where the mathematical requirements are not as demanding as other strict math degree programs. This is done by examining student conceptual thinking patterns 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 focus sheets could be used in exams for notes. This motivated their sheet preparation. The students prepared 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 study of linear, quadratic and limit sections led to interesting insights not only regarding revision strategies, knowledge of content, but also conceptual and procedural knowledge base and higher order skills such as problem solving focus. Logical and creative competencies were assessed in terms of how and what student focused upon or linked to in order to facilitate application of knowledge. The results show average levels 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 work and deeper levels of understanding of links between the topics learned was concerning. These findings have implications for the first year mathematics teaching teams at universities especially the non-specialist mathematical majors

The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra

“…They had low levels of both procedural and conceptual knowledge of algebra. It is inconsistent with Tularam and Hulsman's (2013) and Egodawatte's (2011) findings that discovered that the learners in their studies had average levels of both procedural and conceptual knowledge of algebra.…”

“…They had a very low mean score in the overall knowledge of algebra that could be attributed to the low-level procedural and conceptual knowledge of algebra. Learners with low levels of both procedural and conceptual knowledge were observed by Tularam and Hulsman (2013) to have a lot of misconceptions on variables, algebraic expressions, equations, and word problems. On a similar note, Ho (2020) discovered that students with higher procedural knowledge than conceptual knowledge had a very low ability to integrate the two types of knowledge.…”

“…Algebra is one of the branches of mathematics that challenge many learners because of the level of abstract thinking involved (Star, et al, 2015;Tularam & Hulsman, 2013;Egodawatte, 2011). Success in algebra requires a learner to master various representations (e.g., symbols, equations, tables, and graphs) and reason logically.…”

“…Learners' difficulties in learning mathematics, misconceptions, and poor performance in mathematics seem to be connected to their levels of procedural and conceptual knowledge of mathematics. Studies by Syam (2019), Tularam and Hulsman (2013), Egodawatte (2011) and Figueras, Males and Otten (2008) reveal that learners with average levels of procedural and conceptual competence in algebra had a lot of misconceptions on variables, algebraic expressions, equations, and word problems. A study by Ndemo and Ndemo (2018) in Zimbabwe on secondary school learners' errors and misconceptions in learning algebra revealed a prevalence of both procedural and conceptual errors among the learners.…”

Traditional vs Non-traditional Teaching and Learning Strategies - the case of E-learning!

“…This paper concerns the author's reflection upon more than twenty-five years of in class teaching of students in high school and tertiary levels across several countries. It is also a critical examination of much of research done by the author and colleagues concerning the teaching of mathematics and STEM (Science, Technology, Engineering and Mathematics) subjects more generally (Albano et al, 2013;Bryan, 2015;Caiazzo et al, 2013;Tularam 2013, Tularam andAmri, 2011;Tularam and Hulsman, 2013). In the past thirty years, there has been a concerted effort to develop, in STEM students, a strong conceptual understanding of mathematical principles, often at the expense of practice, memory, and negatively labelled instrumental learning.…”