Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

Abstract

BACKGROUNDDemands by engineering faculties of mathematics departments have traditionally been for teaching computational skills while also expecting analytic and creative knowledge-based skills. We report on a project between two institutions, one in South Africa and one in Sweden, that investigated whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than the traditional more procedurally oriented way of teaching. PURPOSE (HYPOTHESIS)We focus on how second-year engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between Swedish and South African groups of students in answering conceptual and procedural mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. DESIGN/METHODAn instrument consisting of procedural and conceptual items as well as items on student opinions on the roles of the different types of knowledge in their studies was conducted with groups of second-year engineering students at two universities, one in each country. RESULTSAlthough differences between the two countries are small, Swedish students see procedural items to be more common in their mathematics studies while the South African students find both conceptual and procedural items common; the latter group see the conceptually oriented items as more common in their studies outside the mathematics courses. CONCLUSIONSStudents view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics. The use of mathematics in other subjects within engineering education can be experienced differently by students from different institutions, indicating that the same type of education can handle the application of mathematics in different ways in different institutions.

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum – Comparing Views of Junior and Senior Engineering Students in Two Countries

“…Engelbrecht, Bergsten and Kågesten (2012) designed a questionnaire to investigate junior engineering students' achievement and views on mathematics tasks that were either conceptually or procedurally focused. The students found procedural tasks to be more common than conceptually focused tasks in their mathematics courses, while the latter were more common in engineering subjects; they also reported a higher confidence in their performance on procedural tasks.…”

“…In our previous study (Engelbrecht et al, 2012) we investigated how second year engineering students respond to the conceptual-procedural distinction made in research, as discussed above. In the study presented here, we surveyed senior (4 th year) engineering students, comparing the results of these students with those of the junior students.…”

“…The development and piloting of the questionnaire that was used to address our research questions is described in Engelbrecht et al (2012). In its final version four pairs of calculus tasks (questions) in a multiple choice format were used.…”

Contextualizing Calculus with Everyday Examples to Enhance Conceptual Learning

“…17 Similar studies by Simpson and Zakaria found that conceptually-oriented students use linking words, like "then" and "because" to explain their solutions. 22 This indicates that they are confident about the solution and, unlike procedurally oriented students, do not resort to external authority to justify their solution.…”

“…There is also good reason to believe that the students, like those in the Chappell and Killpatrick study above, will be able to reconstruct the concepts at will and apply them in the future. 17 Ultimately, using everyday examples is a conscious action where affordances for conceptual understanding are designed into the course and not only left to the student to attain in future once they have reached mathematical maturity through procedural struggle.…”