Blending Inquiry-Based and Computer-Assisted Instruction 1 Running Head : Blending Inquiry-Based and Computer-Assisted Instruction Blending Inquiry-Based and Computer-Assisted Instruction in a Basic Algebra Course : a Quasi-Experimental Study

In an experiment conducted at the University of Alabama at Birmingham in Fall Semester, 2009, we compare the effect of incorporating inquiry-based group work sessions versus traditional lecture sessions in an elementary algebra course in which the primary pedagogy is computer-assisted instruction. Our research hypothesis is that inquiry-based group work sessions differentially benefit students in terms of mathematical self-efficacy, content knowledge, problem-solving, and communications. All students receive the same computer-assisted instruction component. Students are randomly assigned to a treatment (group work or lecture). Measures, including preand post-tests, are described. Statistically significant differences have previously been observed in a similar quasi-experimental study of multiple sections of a finite mathematics course in Fall Semester, 2008. Undergraduates who do not place into a credit-bearing mathematics course take this developmental elementary algebra course. Many pre-service elementary school teachers place into elementary algebra, thus making this course a significant component of preparing K-6 teachers. 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, 2008). 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, including Basic Algebra, a non-credit developmental course, Intermediate Algebra, Pre-Calculus Algebra, and Pre-Calculus Trigonometry. Basic Algebra is taken by undergraduate students who do not place into a creditbearing course. Traditionally, the goal of such a developmental algebra course has been to enhance students' “algebra skills. ” Because much of the instruction is focused on the difficulties students' have with specific algebra skills, such as dealing with rational numbers and expressions, for example, higher-order thinking may be less engaged. Motivating Question. The research in this proposal investigates the relative effect of combining computer-assisted instruction with, respectively, inquiry-based group work sessions, and traditional summary lectures of material to be covered in the computer-based part. The hypothesis is that inquiry-based group work sessions differentially benefit students in terms of self-efficacy, content knowledge, reasoning and problem-solving ability, and communications. Theoretical Perspective. We take the position that incorporating an inquiry-based component into a computer-assisted instructional environment may enhance student learning (compare Marrongelle and Rasmussen, 2008). We examine inquiry-based group work sessions plus computer-assisted instruction against lecture sessions 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 Doorn and O’Brien, 2007; Gautreau and Novemsky, 1997; Hoellwarth, Moelter, and Knight, 2005). Blending Inquiry-Based and Computer-Assisted Instruction 3 Our theoretical perspective is that of constructivism (Blais, 1988). Reinvention and active reconstruction is essential for the development of knowledge. Students relegated to Basic Algebra have probably been told at one time or another all the basic algebra algorithms. However, we conjecture that construction of mathematical concepts, as opposed to being told them, is far from their experience. We contend that the opportunity to construct will positively affect their self-efficacy and confidence, as well as their ability to solve problems, explain their thinking, and defend their conclusions. We contend that this will occur in conjunction with the algorithmic learning emphasized in the computer-assisted instruction. Prior Research. In Fall Semester, 2008, we conducted a similar experiment in Finite Mathematics (MA 110), an entry-level course taken by non-technical students to satisfy a university mathematics requirement. The results of this quasi-experimental study (the methodology was essentially the same as described in the next section) are presented in our paper (Mayer, et al., 2009). In that study, when we compared outcomes for students participating in group work sessions versus traditional lecture, or lecture with a daily paper and pencil quiz, we found that students in the group work treatment did significantly better (p<0.05) comparing pre-test and post-test performance in the areas of problem identification, exhibiting problem-solving, and explaining their reasoning. All students, regardless of treatment, performed similarly (no statistically significant differences) when compared on the basis of course grades, course test scores, and gains in accuracy on the pre-/post-test items. All students exhibited similar gains in mathematical self-efficacy. There were no significant differences among treatments with regard to instructors or time-of-day. The lack of effect of treatment was contrary to our hypotheses regarding gains in accuracy and self-efficacy, but confirmed our hypotheses with regard to gains in problem identification, problem-solving, and explanation. Research Design and Methodology The course we studied experimentally was Basic Algebra (MA 098), a developmental noncredit-bearing course in elementary algebra for students that did not place into a credit-bearing course. Since our goal was to compare two pedagogical treatments within an over-arching context of computer-assisted instruction, our methodology removed from consideration as many confounding factors as possible. All students involved in the courses had identical computerassisted instruction provided. All students were required to purchase the textbook for the course, which was designed in a workbook style. 90% of a student’s grade in the course was determined by evaluation in the computer-assisted context (lab attendance, online homework, and supervised online quizzes and tests). The remaining 10% of the student’s grade, but reflecting more like 2025% of his/her time on task, was determined by one of two pedagogical treatments, described below. The course was graded Pass/Fail based upon total number of points accumulated through homework, quizzes, tests, and lab and class participation. Students registered for one of four time periods in the Fall 2009 semester schedule: 9 AM – Monday and Wednesday, 9 AM – Tuesday and Thursday, 10 AM – Tuesday and Thursday, or 12 Noon – Monday and Wednesday, for their 50 minute class meeting and 50 minute required lab meeting. Students in each time slot were randomly assigned to one of the two treatments. Four instructors agreed to participate in the experiment. Each instructor taught in two time slots. In one slot the instructor administered the inquiry-based group work treatment, assisted by a graduate teaching assistant, and in another time slot, the lecture treatment. Each instructor also Inquiry with Computer-Assisted Instruction 4 met with each class in the mathematics computer lab. The teaching assistant who assisted with the group work treatment also assisted in the lab. The two pedagogies compared were as follows. Group work (random, weekly changing, groups of four) without prior instruction, on problems intended to motivate the topics to be covered in computer-assisted instruction later. A traditional summary lecture with teacher-presented examples on the topics to be covered in computer-assisted instruction later. In the group work treatment, groups worked together on a problem, but each student turned in each class meeting a written report on his/her investigation and solution of the problem(s), posed in that class period. All sections of the course received the same problem(s) for the group work. The report was evaluated based upon the same rubric as the pre/post-test. Students were aware of the rubric and received written feedback consistent with the rubric. Time was allowed in each period for one or two of the groups of four to report voluntarily on their findings to the whole class. In the lecture treatment, the instructor gave a traditional lecture on the upcoming material. All instructors operated from the same outline of topics and objectives for each lecture, but were free to lecture in their own style. The lectures usually closely followed the workbook sections on the topics of the week. The 10% of the final grade determined by the class meeting differed between the treatments as follows: (1) for the group work treatment, 5 points were earned for attendance and up to 5 more for evaluation of the solution and explanation turned in, and (2) for the lecture treatment, 10 points were earned for attendance, for each class meeting. Specific Hypotheses. We report in this paper on two specific hypotheses regarding the two treatments. 1. Grades will be similar regardless of treatment (as measured by computerized test sum). 2. Group work treatment will have differentially improved problem-solving and communication skills (as measured by rubric). The research in Basic Algebra was undertaken in Fall Semester, 2009. Data gathered included (1) course grades and online test scores, (2) pre-test and post-test content knowledge evaluation according to a rubric* that weighs problem identification, evidence of problem-solving, and adequacy of explanation, as well as accuracy, to extended responses on three problems typical of the material in the course and one additional problem not addressed in the course (but algebrarelated), (3) preand post-responses to a survey of mathematical self-efficacy (Betz and Hackett, 1983; Hall and Ponton, 2002), (4) student course evaluations using the online IDEA system (Idea Center, 2009), and (5) R