Can moving their hands help children learn math? Eighty - five children in the t
ID: 3158272 • Letter: C
Question
Can moving their hands help children learn math? Eighty - five children in the third and fourth grades who did not answer any questions correctly on a test with six probles 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 givien 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 tught 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 fromm a graph in the paper are given below.
n x s
no gesture 42 1.3 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 highter mean number of correct responses? Test the relvant hypotheses using = .01.
Explanation / Answer
Let
u1 = mean of no gesture
u2 = mean of with gesture
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0
At level of significance = 0.01
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 1.3
X2 = 2.2
Calculating the standard deviations of each group,
s1 = 0.3
s2 = 0.4
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 42
n2 = sample size of group 2 = 43
Thus, df = n1 + n2 - 2 = 83
Also, sD = 0.076575371
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -11.75312628
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = - 2.372118621
Also, using p values,
p = 1.19563E-19
As t < -2.372, and P < 0.01, WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence to support the theory that learning the gesturing approach to solving problems of this type results in a highter mean number of correct responses. [CONCLUSION]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!