Question

Can moving their hands help children learn math? This question was investigated in a study. 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 read from a graph in the paper are given below. n x s No gesture 42 1.4 0.3 Gesture 43 2.2 0.4 Is there evidence to support the theory that learning the gesturing approach to solving problems of this type results in a higher mean number of correct responses? Test the relevant hypotheses using α = 0.01. (Use a statistical computer package to calculate the P-value. Use μno gesture − μgesture. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.) t = df = P-value =

Answer 1

Null hypotbesis, 20 Alternative hypothesis, H: HM - Iu >0 [one tailed test] Significance level: a 0.01 Degree of freedom: n n -2 42+43 -2 83 The pooled standard deviation is: +2-2 (42-1)0.32 (43-1)0.4 42+43-2 0.3541 Test statistic: 14-22 0.3540,-+ V42 43

ー-10.41 -value: p1-(T.DIST(10.41.83,TRUE)) (Using ms-excel) 1-0.0000 1.0000 Since the p-value is greater than level of significance, so we fail to reject H Conclusion: Hence, there is no evidence to support the theory that leaming the gesturing approach to solving problems of this type results in a higher mean number of correct responses