Abstract
We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards’ suggestions for teaching fractions, would improve children’s fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards.
Highlights
Many children and adults struggle with fractions
Participants in the control group practiced placing fractions on a number line for the same number of trials as participants in Study 1, but did not receive feedback or instruction, whereas the experimental group received the same instruction as in Study 1. This control group was designed to examine if the gains seen in the first study were due to additional exposure to fractions and fraction number line estimation or if the gains were due to some combination of the instruction, game and feedback
Children who received conceptual instruction about fractions that was in accord with the Common Core State Standards and played Catch the Monster with Fractions showed large improvements in fraction magnitude understanding
Summary
On one National Assessment of Educational Progress (NAEP), a nationwide test given to a very large, representative sample of U.S children, only 49% of eighth graders correctly ordered 2∕7, 1∕2 and 5∕9 from least to greatest. On another NAEP, only 55% of 8th graders correctly solved a simple word problem involving fraction division [1, 2]. Despite fraction instruction beginning in elementary school, many people fail to gain a firm understanding of fractions and harbor misconceptions through high school and college [3,4,5,6]. A sample of 1,000 U.S Algebra 1 teachers identified a lack of fraction understanding as one of the two largest problems hindering their students’ algebra learning [10]
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