Can active learning improve knowledge retention? Two undergraduate calculus-base

Question

Can active learning improve knowledge retention? Two undergraduate calculus-based engineering statistics courses were taught in different academic quarters, with one employing active-learning methods and another using traditional learning methods. The traditional class was taught lecture-style with relatively little in-class interaction between peers and with the instructor. The active-learning course integrated four group projects into the curriculum, with in-class time devoted to group work on the projects and fewer homework assignments. To assess knowledge retention, two five-question versions of a test were created. They had similar but not identical questions covering core statistics topics, worth a total of 18 possible points. All students in both sections were randomly given one version of the test as part of their final . Then, eight months later, a volunteer subset of the original students were given the version that they had not taken previously. To encourage students to take the second version , a $10 gift card to the university bookstore was given to each participant. The change in the score from the first version to the second is used to measure a student's long-term ability to retain the course material.

Here are the changes in scores for the 15 students in the active group.

The changes in scores for the 23 students in the traditional group are as follows.

SOLVE: What is the test statistic? (Round your answer to two decimal places.)

Explanation / Answer

Solution:

Here, we have to use two sample t test assuming equal population variance.

Test statistic formula for pooled variance t test is given as below:

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

Where Sp2 is pooled variance

Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

From the given data, we have

X1bar = 3.6

X2bar = 4.73913

S1 = 2.414243

S2 = 2.847924

n1 = 15

n2 = 23

Degrees of freedom = n1 + n2 – 2 = 15 +23 – 2 = 36

Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

Sp2 = [(15 – 1)*2.414243^2 + (23 – 1)*2.847924^2]/(15 + 23 – 2)

Sp2 = 7.2232

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

t = (3.6 – 4.73913) / sqrt[7.2232*((1/15)+(1/23))]

t = -1.1391/0.8920

t = -1.2771

Test statistic value = t = -1.28

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