Question

14.25 Can moving their hands help children learn math? This question was investigated in the paper "Gesturing Gives Children New Ideas About Math" (Psychological Science [2009]\(: 267-272\) ). Eighty-five children in the third and fourth grades who did not answer any questions correctly on a test with six problems of the form \(3+2+8=+8\) were participants in an experiment. The children were randomly assigned to either a no-gesture group or a gesture group. All the children were given a lesson on how to solve problems of this form using the strategy of trying to make both sides of the equation equal. Children in the gesture group were also taught to point to the first two numbers on the left side of the equation with the index and middle finger of one hand and then to point at the blank on the right side of the equation. This gesture was supposed to emphasize that grouping is involved in solving the problem. The children then practiced additional problems of this type. All children were then given a test with six problems to solve, and the number of correct answers was recorded for each child. Summary statistics follow.

Short answer

The conclusion will depend upon the results of the hypothesis testing phase. If the p-value is less than the significance level (typically 0.05), then there is strong evidence to suggest that using gestures can help children learn math more effectively.

Step-by-step solution

Identifying the data

Begin by identifying and extracting the data values from both the gesture and no-gesture group. This will include the total number, mean, standard deviation, and individual test scores from both groups.

Conducting hypothesis test

Carrying out a hypothesis test will provide statistical evidence to suggest if there is a significant difference between the two groups. Set up the null hypothesis that there is no difference in the test results between the gesture and no-gesture group. In contrast, the alternate hypothesis assumes that there is a statistically significant difference between the two groups. Use a t-test if the data follows a normal distribution and variances are unequal in the two groups.

Evaluating test results

After the T statistic and the corresponding P value is calculated, compare the P value with the significance level, often 0.05. If the P value is lower than the significance level, there is strong evidence to reject the null hypothesis.

Drawing conclusions

Depending on the results of the hypothesis test, deduce if gestures have an impact on children learning math. If the null hypothesis is rejected, it suggests that there is a significant difference between the two groups, thus indicating gestures do have an impact on maths learning.