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International Journal of STEM Education

Table 2 Pairwise comparisons of instructional practices by instructional style

From: Individual and situational factors related to undergraduate mathematics instruction

Fig.

Item

Global test statistics1

Post hoc comparison2

Extensive moderate

Extensive limited

Moderate limited

3

I pause and ask students if they have questions.

H = .428, n = 218, p = .808

E ~ M

E ~ L

M ~ L

I have students engage in small group discussions or problem-solving.

H = 46.904, n = 214, p < .001

E < M (p < .001)

E < L (p < .001)

M < L (p = .006)

I use visual and/or physical representations of groups and group elements.

H = 10.366, n = 219, p = .006

E < M (p = .004)

E ~ L

M ~ L

I use diagrams to illustrate ideas.

H = .958, n = 218, p = .619

E ~ M

E ~ L

M ~ L

I have students ask each other questions.

H = 23.720, n = 219, p < .001

E < M (p = .022)

E < L (p < .001)

M < L (p = .004)

I include informal explanations of formal statements.

H = .035, n = 219, p = .983

E ~ M

E ~ L

M ~ L

4

Showing students how to write specific proofs.

H = 12.393, n = 218, p = .002

E ~ M

E > L (p = .002)

M > L (p = .013)

Having students work with one another in small groups.

H = 50.474, n = 215, p < .001

E < M (p < .001)

E < L (p < .001)

M < L (p = .005)

Having students give presentations of completed work.

H = 27.924, n = 213, p < .001

E < M (p = .006)

E < L (p < .001)

M < L (p = .003)

Have students work individually on problems or tasks.

H = 13.031, n = 216, p = .001

E < M (p = .009)

E < L (p = .003)

M ~ L

Lecturing

N/A

E > M

E > L

M > L

Holding a whole class discussion.

H = 13.8, n = 216, p = .001

E < M (p = .039)

E < L (p = .001)

M ~ L

Having students explain their thinking.

H = 17.055, n = 215, p < .001

E < M (p = .007)

E < L (p < .001)

M ~ L

5

Have students present a proof or counterexample to the class.

H = 52.174, n = 219, p < .001

E < M (p < .001)

E < L (p < .001)

M < L (p < .001)

Have students develop their own definitions.

H = 11.302, n = 219, p = .004

E < M (p = .021)

E < L (p = .005)

M ~ L

Have students develop their own conjectures.

H = 18.426, n = 219, p < .001

E < M (p = .002)

E < L (p < .001)

M ~ L

Have students develop their own proofs.

H = 33.914, n = 219, p < .001

E < M (p < .001)

E < L (p < .001)

M < L (p = .013)

Lead discussions in which students discuss why material is useful and/or interesting.

H = 28.729, n = 219, p < .001

E < M (p < .001)

E < L (p < .001)

M ~ L

  1. 1The family-wise error rate for the global tests was controlled by use of the Bonferroni correction by cluster (i.e., 3, 4, 5). Post hoc testing was performed only in cases where this threshold for significance was achieved
  2. 2The p values reported here have been adjusted with a Bonferroni correction. In the cases where “a ~” is used to describe a relationship, it does not mean that there is no ordering between the groups, but rather that it did not achieve the desired significance level. Furthermore, in cases where seemingly contradictory results appear (i.e. M < E and L ~ M should imply that L < E but L ~ E is reported), this is not to say that one cannot infer the ordered relationship but the power reduction caused by dissimilar sample sizes and the FWER correction does not allow for the reporting of the latter pairwise comparison with significance. We explain this to differentiate between describing trends (i.e., L < M < E) versus declaring differences between groups. The former case does not necessarily achieve statistical significance, whereas the latter does
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