What did they learn?
- LESS instructor talk time, results in BETTER outcomes.
- Women in IBL classes reported as high or higher gains than their male classmates across all cognitive, affective and social gains areas (3.2.3). But women in non-IBL classes reported statistically much lower gains than their male classmates in several important domains: understanding concepts, thinking and problem-solving, confidence, and positive attitude toward mathematics.
- Among students who entered with low math GPAs (<2.5), IBL students generally earned better grades in later classes than did their non-IBL peers (6.4.1).
- Attitudinal changes were modestly positive in IBL groups, and mixed and somewhat negative in non-IBL groups. Overall, IBL math courses tended to promote slightly more sophisticated and expert-like views of mathematics and more interactive approaches to learning. In contrast, traditional mathematics courses appeared to weaken students’ confidence and enjoyment, and did not help them to develop expert-like views or skillful practices for studying college mathematics.
The overall results of the Colorado study points in the same direction as the bulk of the results from the Math Education literature. When students are (a) deeply engaged in high quality mathematical tasks requiring critical thinking and reasoning, and (b) have some form of collaboration, then student outcome are statistically significantly better compared to students in a non-IBL setting. (Collaboration is broadly defined here. Collaboration is not only group work, but includes activities such as class discussion and student presentations to the whole class. In this last instance, the class is peer-reviewing the presenter's work. This is collaboration.)
When the Colorado study is combined with the literature from Math Education, then we start to put together a rather clear picture. We have known already that students have historically had poor attitudes and beliefs about Math from K-college. Students have beliefs such as "all problems can be solved in 5-minutes or less" and "it's the form of the answer that important, not the quality of the process or content of the proof."
We also know that students, even college students, have limited ability in problem solving and proof. Students are rarely exposed to the kinds of experiences necessary to develop problem solving, the critical thinking and reasoning for proof, and other higher-level thinking strategies. High stakes testing and the drive for further standardization has made it more difficult for students to develop the kinds of attitudes and thinking skills needed to learn math beyond rote skill.
In light of this, the Colorado study shows that IBL methods (broadly defined) is a glimmer of hope. When students are given a chance to think for themselves and are properly supported by the instructor and their peers, that students are capable of rising up and fulfill their potential.
The data speaks -- all the vectors are pointing in towards IBL.