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# How the Number Line Can Be Used to Promote Students' Understanding of the Normal Distribution

## Keywords

quantitative literacy, number sense, number line, the normal distribution, probabilities, bell-shaped curve

## Abstract

A strong foundation in early number concepts is crucial for students’ future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or when problems about normally distributed random variables are presented in word questions which involve phrases that indicate inequalities. As a result, students shade wrong areas on the bell-shaped curve when they have to calculate probabilities for normally distributed variables. Visual representations such as the number line can support students’ development of quantitative literacy or number sense by helping them create a mental representation of the order and magnitude of numbers as well as inequalities. Based on a comprehensive investigation of evidence demonstrating this weakness, this experienced-based perspective proposes a framework that demonstrates how the number line can be used as a powerful teaching tool to promote students’ conceptual understanding about the normal distribution. The framework illustrates with authentic examples how the number line relates to the horizontal axis of the normal and standard normal curve and how it can be used to address erroneous quantitative reasoning when students are required to calculate probabilities for normally distributed variables. To determine if the number line teaching intervention affects student performance, the researcher adopted a non-equivalent pretest-posttest design with two intact classes. The results of the analysis show that students who received the intervention performed significantly better in the posttest.

## DOI

https://doi.org/10.5038/1936-4660.15.2.1403