Friday

2:25 – 2:55 pm

Session 15 – Contributed Reports

Marquis A

Graphing habits: ÒI just donÕt like thatÓ

Kevin Moore, Teo Paoletti, Irma Stevens and Natalie Hobson

StudentsÕ ways of thinking for graphs remain an important focus in mathematics education due to both the prevalence of graphical representations in the study of mathematics and the persistent difficulties students encounter with graphs. In this report, we draw from clinical interviews to report ways of thinking (or habits) undergraduate students maintain for assimilating graphs. In particular, we characterize aspects intrinsic to studentsÕ ways of thinking for graphs that inhibited their ability to represent covariational relationships they conceived to constitute some phenomenon or situation. As an example, we illustrate that studentsÕ ways of thinking for graphs were not productive for their representing a relationship such that neither quantityÕs value increased or decreased monotonically.

Paper

2

Marquis B

The Effect of Mathematics Hybrid Course on StudentsÕ Mathematical Beliefs

Kuo-Liang Chang, Roxanne Brinkerhoff and Ellen Backus

Computer-based courses (e.g., online or hybrid) have significantly changed the design of pedagogy and curriculum in the past decade, which include online teaching and learning on mathematics education. As beliefs play an essential role on achievement, the impact of computer-based courses on mathematical beliefs is still underdeveloped. In particular, we are interested in whether mathematics hybrid class (blend of online and face-to-face) has different impact on studentsÕ mathematical beliefs compared to regular face-to-face class. A two-by-two design of instruction method (hybrid vs. regular) and mathematics performance (high vs. low) was employed. The results showed that both hybrid and regular class students believed understanding and memorization were equally important in mathematics learning. Hybrid class students showed more flexibility in selecting solution methods compared to regular class students on their beliefs about problem solving.

Paper

13

Marquis C

Using the effect sizes of subtasks to compare instructional methods: A network model

Garry Johns, Christopher Nakamura and Curtis Grosse

Networks have become increasingly important in studying air pollution, energy use, genetics and psychology. These directed graphs also have features that may be useful in modeling student learning by answering questions such as the following: How can we determine if one teaching approach has better outcomes than a second method? In this paper we present a framework for dividing an approach into subtasks, assigning a numerical value (such as an effect size) to each subtask and then combining these values to determine an overall effectiveness rating for the original approach. This process allows researchers to investigate potential causes for student achievement rather than simple correlations, and can compare the effectiveness of a method for various types of students or instructors.

Paper

18