Analysis of Post Test Question 2 Rough Draft 2
Lincoln Elementary Snookerpuss Intervention
For the second post test question in the intervention, the students were presented with some given data points and a blank grid. They were asked make a prediction that would require extrapolating the data. The student graphs fell into some general categories.
Graph Categories ( not
mutually exclusive )
A – 45% of the student graphs fell into
this category. Graphs marked with an
“A” indicate that the student was able to set up a reasonably good graph that
they could make an accurate prediction from.
B – 25% of the students had trouble with the horizontal spacing on their graph. These students did not use even column widths when making their graph, which hinders their ability to make predictions from the graph.
C – 25% of the
class were thrown off by the vertical spacing of the graph. The posttest intentionally gave the students
a grid that was too small to label the vertical axis in increments of one. Students who had this problem attempted to
extend the grid by hand, but were unable to get an accurate prediction.
All together, 40% of the students had problems with spacing on their graphs. (Some students fell into the B & C categories.)
D – Graphs that fall in this
category indicate that the student wasn’t quite sure how to extrapolate. 40% of the class only graphed the given data
points, and did not extend the data points to make a prediction. It should also be noted that the
extrapolation that was done in class only extended one time period past the
collected data, while we were asking the students to extend the data 3 time
periods on the post test. Given that
this was the students’ first taste of extrapolation, it is quite encouraging
that 60% of the students were able to use, and extend their first lesson on
extrapolation.
E – 10% of the students did
not explicitly draw the best-fit line in their graph. However, their responses suggest that they did use the best-fit
line method.
F – The students have had most of their previous graph experience with bar graphs. 10% of the students set up their graphs as a bar graph instead of plotting data points. These students were able to successfully adapt extrapolation to a bar graph.
There does not seem to be any correlation between the students’ performance on the second posttest question and the treatment group they were in. This question relied more heavily on the classroom discussion about graphing. Even students that did not participate in the VR portion of the intervention had reasonable success with the graphing. 4/7 of the trace group created successful graphs. ¾ of the blip and 1/5 of the map group were successful. A successful answer was one in which the students correctly graphed the data, and made a correct prediction that was supported by their graph.
It seems that the most common error that prevented
students from successfully answering the question, was to only allocate space
on their graph for the data we provided them.
Often there was not enough room left for the extrapolation. The next most common errors were to not
allocate enough vertical space, or to not use even horizontal spacing. After going through the posttests, it looks
like the lesson would benefit greatly from actually setting up the graph we
used with the class. When we performed
the intervention, the graph that we used to plot data was already set up, and
labeled for the students. I believe
that taking a few minutes of the lesson to walk the students through setting up
the graph would improve the educational value of the lesson.
One particularly exiting effect of this intervention is that it seems that it has started the students thinking about slope and rates of change. With the idea of the best-fit line, students are introduced to the idea of an average rate of change implicitly, while the lesson explicitly introduces extrapolation and interpolation. Below is an example of a student thinking about the rate at which the mushrooms are increasing.
As mentioned before,
the students’ primary experience with graphing has been with bar graphs. Their classroom is decorated with several
bar graphs the class has made. It seems
that many of the problems the students had with the graphing may stem from
sheer inexperience with point and line graphs.
The student example below shows this problem. Many of the students had problems with the graphing because of
uneven horizontal spacing on their graphs.
I suspect that this could be because the students are used to making bar
graphs of things like “how many siblings do you have,” where the importance of
even horizontal spacing is not emphasized, and possibly not corrected when
wrong. 
Half of the students, spanning all the treatment groups, produced reasonably good-looking graphs that supported a correct answer. With the limited amount of graphing experience the students had before the lesson, I think the posttest results are very encouraging.
|
Subject # |
Treatment Group |
Student Graph |
Student Prediction |
|
1 |
Trace |
A |
A |
|
2 |
Trace |
A F |
D |
|
3 |
Trace |
B C |
C |
|
9 |
Trace |
A |
A |
|
10 |
Trace |
A |
A |
|
12 |
Trace |
B |
A |
|
16 |
Trace |
B D |
C |
|
8 |
Blip |
A |
A |
|
14 |
Blip |
B D |
A |
|
20 |
Blip |
A E |
A |
|
17 |
Blip |
B C D |
C |
|
7 |
Map |
C D |
C |
|
5 |
Map |
D |
B |
|
19 |
Map |
C |
E |
|
15 |
Map |
A |
A |
|
11 |
Map |
D |
B |
|
13 |
No VR |
A |
A |
|
18 |
No VR |
C D |
C |
|
6 |
No VR |
D |
C |
|
4 |
No name |
A E F |
D |
KEY
|
|
A – a good graph B – poor horizontal spacing C – poor vertical spacing D – only graphed given months F – used bar graph |
A – correct ( supported by graph ) B – incorrect C – correct ( not supported ) D – did not answer, but graph indicates a correct answer E – did not answer, graph doesn’t suggest an answer |
|
|
|
|
|