Student Magnitude Knowledge of Negative Numbers

Abstract

Numerous studies have demonstrated the relevance of magnitude estimation skills for mathematical proficiency, but little research has explored magnitude estimation with negative numbers. In two experiments the current study examined middle school students' magnitude knowledge of negative numbers with number line tasks. In Experiment 1, both 6th (n = 132) and 7th grade students (n = 218) produced linear representations on a -10,000 to 0 scale, but the 7th grade students' estimates were more accurate and linear. In Experiment 2, the 7th grade students also completed a -1,000 to 1,000 number line task; these results also indicated that students are linear for both negative and positive estimates. When comparing the estimates of negative and positive numbers, analyses illustrated that estimates of negative numbers are less accurate than those of positive numbers, but using a midpoint strategy improved negative estimates. These findings suggest that negative number magnitude knowledge follows a similar pattern to positive numbers, but the estimation performance of negatives lags behind that of positives.

Distinct Representations of Magnitude and Spatial Position within Parietal Cortex during Number–Space Mapping

“…To our knowledge, our study is the first to study the neural basis of mapping both positive and negative numbers onto space. We are aware of only two previous behavioral line-marking experiments using both positive and negative numbers ( Young & Booth, 2015;Ganor-Stern & Tzelgov, 2008). Because the effects of range on spatial bias and landmarking behavior were not the focus of either article, it is not possible to extract strong conclusions about these topics.…”

How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares

“…This logarithmic‐to‐linear shift extends to larger number ranges and older people. Middle school students’ estimates of integers in the negative range −10,000 – 0 and the combined range −1,000 – 1,000 are linear, though with lower accuracy for negative numbers (Young & Booth, ). Adults’ estimates of integers in the combined range −100 – 100 are linear and show comparable accuracy for positive and negative numbers (Ganor‐Stern & Tzelgov, ).…”

Commentary: The mental representation of integers: An abstract-to-concrete shift in the understanding of mathematical concepts

“…They concluded that practice and experience help to integrate negative numbers into an extended mental number line. In addition, Young and Booth ( 2015 ) found results both in line with an extended MNL and in line with a rule-based MNL account in two pointing experiments with middle school students. The authors concluded that this conflicting pattern could reflect under-developed number knowledge and differences in previous number exposure.…”