Middle Grade Students’ Evoked Concept Images of Number Line Models and Their Calculation Strategies with Integers Using These Models
Number line models provide a visual aid for students to examine therelationship of integers with each other and facilitate learning of integersand integer operations. Such models are typically used when students are asked real-lifeproblems. This study employs a qualitative case study design to perform anin-depth analysis of how middle grade students use number line models and whichmodels they instinctively prefer for different real-life contexts. Tounderstand students’ way of thinking, a questionnaire including real-lifecontext problems about integers was used. Additionally, interview data was usedto get a deep insight into students’ written responses. The results indicatedthat middle grade students have three evoked concept images of number linemodels namely, horizontal, vertical, and the Cartesian plane combining the two.The horizontal number line model was found to dominate over the other twomodels even in contexts that are typically associated with a vertical one. Thestudy also found that more than half of the students that took part in thestudy could not properly use any number line model. Finally, the study added tothe evidence that there was a symbiotic relationship between arithmeticcalculation and using number line in that errors made during one are oftencorrected with the other.
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