The Number Line Test

Learning decimals and fractions is challenging. Too often, students memorize calculation procedures without truly understanding a number in terms of its size and its position compared to other numbers. grandeur et de position par rapport aux autres nombres.

We offer a simple and effective test: placing a number on a graduated number line. placer un nombre sur une ligne numérique graduée.

At each trial, the learner sees a number and must place it on a number line ranging either from 0 to 20 or from 0 to 5. The number may be a whole number (e.g., 4), the result of an operation (e.g., 7–4), a decimal (e.g., 2.4), or a fraction (e.g., ½).

Instruction:

Ask your child to look carefully at the number displayed in the center box, then point to where that number should be placed on the line. We suggest that you look at your child’s errors and provide them with feedback as they go so that they can progress in understanding how to find the correct response.

This test has been administered to a large, representative sample of students entering sixth grade. The results show that it is highly sensitive to students’ strengths and weaknesses. Learners generally place whole numbers correctly and manage simple operations well. However, decimals—and especially fractions—cause significant difficulties. In fact, 78% of students at the start of sixth grade could not correctly place ½ in the middle of the interval [0,1]!

Error analyses reveal that students often confuse a fraction with one of its whole-number components (e.g., treating ½ as 1 or 2) or with a decimal (e.g., 1.2). 

Research shows that a strong understanding of number lines is a powerful predictor of later success in mathematics. Training in this area, combined with appropriate pedagogy, has proven positive effects. We therefore encourage students in primary and lower secondary levels to practice placing numbers on number lines to better understand quantities and to help teachers identify learning difficulties.

To learn more about how we used this test in research, you can download the test explanations, written by France’s Scientific Council for Education.