Incorporating Inquiry-Based Class Sessions with Computer Assisted Instruction
What is the effect of incorporating inquiry-based group work sessions in a Finite Mathematics course in which the primary pedagogy is computer-assisted instruction? Our research at a major state university investigates in a randomized study the relative effect of combining computer-assisted instruction with inquiry-based group work sessions, traditional summary lectures of material to be covered in the computer-based part, and the latter combined with regular in-class quizzing on lecture material. Student success as measured by grades, and greater efficiency in terms of cost effectiveness, have been a driving force in "course reform" over the past 15 years, particularly at large state universities [NCAT]. One prevalent direction of course reform has been the development of, and widespread use of, sophisticated computer-assisted instruction. This approach has been often applied to large-enrollment service courses in mathematics. One such course is the Finite Mathematics course taken by non-technical students to fulfill a "university mathematics requirement."
Finite Mathematics is taken by most pre-service elementary and middle school teachers at our university. Pre-service elementary teachers are required to take four 3-credit-hour mathematics courses, two of which must be courses that satisfy the university Core Curriculum requirement in mathematics. Finite Mathematics is the lowest level such course and most pre-service elementary teachers take it. Pre-service middle school teachers, in accordance with the mathematics curriculum of the Mathematical Reasoning track in the mathematics major, are required to take the Finite Mathematics course.
One goal of such a course might be to foster an appreciation of how mathematics, even simple mathematics, can be employed to solve approachable problems. Thus, the goal may well be more developing quantitative reasoning than training to acquire a specific compendium of skills [W]. We take the position that incorporating an inquiry-based component into a computer-assisted instructional environment enhances student learning (compare [MR]). Specifically, we will examine inquiry-based plus computer-assisted instruction against lecture plus computer-assisted instruction for effectiveness. However, what we investigate, and our methodology of simultaneously comparing different pedagogies within one term, has few direct comparisons in the literature that we have found (but see [DO]). A number of studies similar to [GN] and [HMK] have compared different pedagogies over a longer time frame.
Our theoretical perspective is that of constructivism, somewhat informally described by D. Blais [DB]. (Re)invention and active (re)construction are essential for the development of knowledge. The students in the course that we have first investigated, Finite Mathematics, are generally speaking mathematics-avoiders. Construction of mathematical concepts, as opposed to being told algorithms then being asked to implement them, is far from their experience. Nevertheless, we contend that the opportunity to construct will positively affect their self-efficacy and confidence, as well as their ability to explain and defend their conclusions. We contend that this will occur in conjunction with the algorithmic learning emphasized in the computer-assisted instruction.
