First part of the talk on the "Shape(s) of Educational Data" delivered at the meeting SOED, April 2016

1. Shape of Educational Data
Yahya Almalki and Olga Caprotti
Florida State University
April 07, 2016

2. Vertices are graded activities of the course
Edges are different learning paths between graded activities

5. Look-back degree
Assume sections do not share resources, so that all resources L in a
course with t sections can be partitioned by section:
L =
0≤i≤t
Li
where Li are the resources in section i.
We then can also talk of Ln
0 resources as the set of resources
belonging to sections 0 to n.

6. We define the hop with target γn as the sequence of actions on
learning resources recorded in the log between the source of γn and
γn:
hopPA
(γn) = [λ1, . . . , λk] ⊂ 2L
Now we define the lookback degree
lbdPA
(γn) =
|hopPA
(γn) ∩ Ln−1
0 |
|Ln
0|

7. Mika Sepp¨al¨a suggested that a correlation distance between two
graded activities γi and γj in the space of graded activities is given
by
d(γi , γj ) = log
1
Corr(γi , γj )
where Corr(γi , γj ) is a measure of correlation between γi and γj .

8. Depending on which aspect of the learning we are studying,
we choose a measure of correlation.

9. Depending on which aspect of the learning we are studying,
we choose a measure of correlation.
Assume we want to study how much students recall.

10. Our candidate for this correlation is the lookback degree
Corr(γi , γj ) =
mean(lbdPA
(γj )) for i = j − 1
1 for i = j.

11. Our candidate for this correlation is the lookback degree
Corr(γi , γj ) =
mean(lbdPA
(γj )) for i = j − 1
1 for i = j.
This choice of the correlation does not define a metric
necessarily; the triangle inequality may not hold in certain
cases.

12. Our candidate for this correlation is the lookback degree
Corr(γi , γj ) =
mean(lbdPA
(γj )) for i = j − 1
1 for i = j.
This choice of the correlation does not define a metric
necessarily; the triangle inequality may not hold in certain
cases.
However, this correlation is still helpful when we visualize data.

13. Our candidate for this correlation is the lookback degree
Corr(γi , γj ) =
mean(lbdPA
(γj )) for i = j − 1
1 for i = j.
This choice of the correlation does not define a metric
necessarily; the triangle inequality may not hold in certain
cases.
However, this correlation is still helpful when we visualize data.
For visualization, we think of
d(γi , γj ) = log
1
Corr(γi , γj )
as the length of the cylinder joining γi and γj .