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

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.

The Effectiveness of using Conventional Whiteboard in Teaching Probability and Statistics Online

“…(Ares, 2022). In addition, many statistics students struggled to grasp the concept of normal distribution because of its complexity and lack of basic math skills (Delport, 2022).…”

“…Students have difficulty converting these statements into the proper probability notation, which frequently comprises letters and inequality symbols. As a result, when students are asked to calculate the chance of an event occurring, they shade the erroneous areas on the bell-shaped curve (Delport, 2022).…”

“…Despite its importance in statistics, many firstyear statistics students struggle to grasp the normal distribution because of its complexity and lack of basic math skills. Students are perplexed by the size and sequence of negative numbers when dealing with situations involving normally distributed random variables; z-scores on a typical normal curve are used (Delport, 2022). In addition, the study "How the Number Line Can Be Used to Promote Students' Understanding of the Normal Distribution" shows that teachers should employ an effective teaching tool to increase students' conceptual knowledge of the normal distribution (Delport, 2022).…”