Incorporating Inquiry-Based Class Sessions with Computer Assisted Instruction
Since our goal is to compare three pedagogical treatments within an over-arching context of computer-assisted instruction, our methodology seeks to remove from consideration as many confounding factors as possible. All students involved in the courses will have identical computer-assisted instruction provided. A student's grade is determined by total number of points earned out of 1000 with the following thresholds: A-880, B-750, C-620, D-500. About 79% of the grade in the course is determined by evaluation in the computer-assisted context: lab attendance (70 points), online homework (70 points), supervised online quizzes (70 points), and supervised tests (580 points). The remaining 21% of their grade, but reflecting more like 30% of their time on task, is determined by one of three pedagogical treatments, described below.
Students registered for one of three time periods (Section) in the Fall 2008 semester schedule, an early morning, mid-morning, or mid-afternoon time slot, two days a week, for their 50 minute class meeting and 50 minute required lab meeting in Finite Mathematics. Students in each time slot were randomly assigned to one of the three treatments. Three instructor/teaching assistant pairs agreed to participate in the experiment. Each instructor/TA pair teaches in each time slot, employing exactly one of the treatments, as pre-assigned to that subsection, thus administering one of each treatment over the day.
The three pedagogies to be compared are:
- Group: inquiry-based group work without prior instruction, on problems intended to motivate the topics to be covered in computer-assisted instruction later;
- Lecture: a summary lecture with graduated examples on the topics to be covered in computer-assisted instruction later; and
- Quiz/Lecture: a briefer summary lecture with a 10 minute quiz each weekly class meeting on the material covered in the previous week's lecture.
Group. In the group work treatment, students are divided randomly at the beginning of each class into groups of four. All groups are given the same problem situation to investigate as a group, and strive to arrive at an understanding and solution. Discussion within each group takes place independently with the instructor and teaching assistant each playing the role of a Socratic facilitator, answering questions with questions. The problem is posed without prior instruction in the topic being introduced. An example of a problem is below. This problem is intended to bring out some of the mathematical and modeling issues involved in apportionment.
Problem. Andy, Bert, and Connie are farmers. Their neighbor who is also a farmer is retiring next month and wishes to sell her 12 pigs for $480. Andy, Bert, and Connie can only afford to purchase the pigs if they pool their money. Andy can contribute $97, Bert can contribute $210, and Connie can contribute $173. How many pigs each should Andy, Bert, and Connie get?
Challenge. After all of the money contributed to the purchase is tabulated but before the pigs are distributed, an extra pig is discovered hiding in the pen (13th pig). The neighbor decides to just include the extra pig in the $480 purchase. How many pigs each should Andy, Bert, and Connie get now?
Each student turns in each class meeting a written report on his/her investigation and solution of the problem(s) posed in that class period. The report is evaluated based upon the same rubric as the Pre- and Post-Test (described below). Response to the Challenge portion can only help, not hurt, a student's score. Students are aware of the rubric and receive written feedback consistent with the rubric. Time is allowed in each period for one or two of the groups of four to report voluntarily on their findings to the whole class.
Lecture and Quiz/Lecture. In the lecture treatment, the instructor gives a traditional lecture introducing the upcoming material. For instance, the concept of apportionment, distribution of indivisible objects in proportion to some entitlement, would be defined and examples, isomorphic to the above problem, would be worked through by the instructor. In the lecture/quiz treatment, the lecture is necessarily briefer, and the quiz is on basic material and examples from the previous lecture. The quiz is graded traditionally (correct answer with work shown) and returned.
The 21% of the final grade determined by the class meeting differs among the treatments as follows, each of 14 class meetings:
- for the group work, 10 points are earned for attendance and up to 5 more for evaluation of the solution and explanation turned in;
- for the lecture, 15 points are earned for attendance;
- for the quiz/lecture, 10 points are earned for attendance and up to 5 more for evaluation of the quiz.
The classes took place in Fall Semester, 2008. Data gathered includes
- course grades,
- Pre-Test and Post-Test content knowledge evaluation according to a rubric* that weighs problem identification, evidence of problem-solving, and adequacy of explanation (including accuracy), to extended responses on three problems typical of the material in the course,
- pre and post responses to a Survey of Mathematical Self-Efficacy [BH, HP],
- focus groups selected from each of the nine class sections,
- student course evaluations using the online IDEA system [ID], and
- RTOP observations of the instructors in each of the nine class meetings [RT].
(*All students were given copies of the grading rubric prior to both the Pre-Test and Post-Test.)
