Developing Integer Understanding Through Board Games

• In Event: Excellence in Education Research: Early Career Scholars and Their Work

Abstract

Students who have numerical experiences at home that support the development of a mental number line (Case, 1996) come to school with deeper numerical understanding than students without those experiences; fortunately, curricula which emphasize the order and value of numbers can help students catch up (Griffin, 2005). One experience children have outside of school, which is positively correlated with number knowledge, is playing board games (Ramani & Siegler, 2008). Early experiences with negative integers can help students make sense of the multiple meanings of the minus sign, and research suggests that Case’s mental number line theory could accommodate negative integers when children are at the uni-dimensional level (~age 6-8) (Bofferding, 2014). Therefore, I investigate the following question:
What is the influence of playing a linear board game on first-graders’ development of a mental number line for integers?
Participants and Methods
Forty-eight first graders from a diverse school in Indiana completed a pretest and posttest, given as individual interviews. Test items were similar to those from Siegler and Ramani (2009) but also involved negative integers. Further, several questions were added to confirm that students were at a uni-dimensional level of numerical understanding (Case, 1996; Griffin, 2005). The questions involved (1) counting forward and backward, (2) identifying numbers, (3) ordering numbers, (4) determining which number is greater/closer to or less/farther from 10, (5) solving arithmetic problems, and (6) marking the location of integers on a series of number lines (where only a few numbers were given).
After the pretest, students were randomly assigned to either a control group or board game group. In either condition, students met individually with a researcher for three, fifteen-minute sessions. Students in the control group completed a series of numerical tasks (counting backward from 10, counting objects, putting integer cards in order, and playing an integer matching game). Students in the game group counted on as they moved along a board game numbered from -10 to 10.
Data Analysis and Results
For this preliminary analysis, I scored each participant’s items according to correct and incorrect, with an initial focus on tasks (1), (2), and (4) and used multivariate analysis on the gain scores to determine if there were any significant differences between groups. Additionally, I investigated the overall trends of students’ numeral placements on the number lines in task (6).
There were significant differences in the groups’ gains on the counting, numeral identification, and value tasks, with students in the board game group showing more improvement than the students in the control group. However, gains were smallest on the value items. Students across groups frequently interpreted negative numbers as positive. Further, on their number lines, about half of the students placed 1 to the left of 0 and near the left edge of the page, explaining that 1 comes after 0 and 0 always starts on that side. They maintained this reasoning even after being shown where 0 was located on the number line.

Author

• Laura Bofferding, Purdue University