Kien H Lim

The Role of Prediction in the Teaching and Learning of Mathematics.

The prevalence of prediction in grade-level expectations in mathematics curriculum standards signifies the importance of the role prediction plays in the teaching and learning of mathematics. In this article, we discuss benefits of using prediction in mathematics classrooms: (1) students’ prediction can reveal their conceptions, (2) prediction plays an important role in reasoning and (3) prediction fosters mathematical learning. To support research on prediction in the context of mathematics education, we present three perspectives on prediction: (1) prediction as a mental act highlights the cognitive aspect and the conceptual basis of ones prediction, (2) prediction as a mathematical activity highlights the spectrum of prediction tasks that are common in mathematics curricula and (3) prediction as a socio-epistemological practice highlights the construction of mathematical knowledge in classrooms. Each perspective supports the claim that prediction when used effectively can foster mathematical learning. Considerations for supporting the use of prediction in mathematics classrooms are offered.

Addressing the Multiplication Makes Bigger and Division Makes Smaller Misconceptions via Prediction and Clickers

This article presents a lesson that uses prediction items, clickers and visuals via PowerPoint slides to help prospective middle-school teachers address two common misconceptions: multiplication makes bigger and division makes smaller (MMB–DMS). Classroom research was conducted to explore the viability of such a lesson. Results show that the lesson was effective in creating awareness that multiplication does not always make bigger and division does not always makes smaller, uncovering students’ misconceptions, and providing opportunities for students to learn from mistakes. Students liked the activity for various reasons, such as getting to learn certain mathematical ideas, to think about the problems, to work in groups and to have fun. The lesson was implemented slightly differently in two classes. The class with an additional phase involving prediction and voting via clickers in the PowerPoint lesson showed a gain of 36 points (an effect size of 1.3 standard deviations, SDs) from the pre-test to the exit-test whereas, the comparison class showed a gain of 25 points (an effect size of 0.87 SDs). In terms of students’ written responses with regards to addressing the MMB–DMS misconceptions, there was however not much difference between the two classes.

Integrating Programming into Physics and Algebra (Abstract Only)

We are infusing inquiry-driven programming activities into algebra and physics courses with the objective of strengthening disciplinary understandings and providing all students a meaningful first experience with programming. The majority of students who complete 9th grade algebra fail to connect its syntactic and graphical representations to concepts related to rate of change. These learning deficits contribute to the well documented failure of high school and college physics courses to effectively convey conceptual understandings of the relationships between force, acceleration, velocity and position. Our programming activities for algebra and physics classrooms focus student attention towards the principles underlying symbolic and graphical representations of slope. Implementations of these inherently multi-disciplinary activities within math, physics, and even computing classes have previously only been successful when instructors have broad content and pedagogical knowledge. For our most recent implementations within physics lab courses led by inexperienced TAs, instructional modules that introduce and explore the lab courses conventional kinematic experiments were developed.