Question

Can moving their hands help children learn math? This question was investigated by the authors of the paper "Gesturing Gives Children New Ideas about Math" (Psychological Science [2009]: 267-272). A study was conducted to compare two different methods for teaching children how to solve math problems of the form \(3+2+8=-8 .\) One method involved having students point to the \(3+2\) on the left side of the equal sign with one hand and then point to the blank on the right side of the equal sign before filling in the blank to complete the equation. The other method did not involve using these hand gestures. To compare the two methods, 128 children were assigned at random to one of the methods. Each child then took a test with six problems, and the number correct was determined for each child. The researchers planned to see if the resulting data supported the theory that the mean number correct for children who use hand gestures is higher than the mean number correct for children who do not use hand gestures.

Short answer

The question asked involves conducting a hypothesis test to compare the means of two groups - those children who used hand gestures while learning math and those who didn't. To answer the question, a hypothesis test should be set up, performed upon the test scores data, p-value determined and results interpreted in terms of the original question.

Step-by-step solution

Identify the Hypotheses

The first step in any hypothesis test is to define the null hypothesis and the alternative hypothesis. In this case, the null hypothesis (\(H0\)) would be that there is no difference between the mean score of children who used hand gestures and those who didn't. The alternative hypothesis (\(H1\)) is that the mean score of children who used hand gestures is higher than those who didn't.

Conduct the Test

Assuming the test is set up, the next step is conducting the test. Normally, this would involve gathering data (in this case, the test scores of the children) and performing a test statistic. The researchers did that already. The test statistic, which depends on the data and the type of test being run, will give us a measure of how much the observed data deviates from what was expected under the null hypothesis.

Determine the p-value

Once the test statistic is calculated, the next step is determining the p-value. This is the probability of observing a test statistic as extreme or more extreme given that the null hypothesis is true. If the p-value is smaller than the chosen significance level (commonly 0.05), then the null hypothesis is rejected and we say that there is evidence to support the alternative hypothesis.

Interpret the Results

Lastly, the figures obtained (both the test statistic and the p-value) need to be interpreted in context of the question under investigation. Here, this would mean stating whether there is strong evidence that using hand gestures improves student's performance compared to not using them, based on the p-value.