Criterion D: Results
Type II, Mathematical Modeling: Interpretation
Achievement level
0 The student has not arrived at any results.
1 The student has arrived at some results.
2 The student has not interpreted the reasonableness of the results of the model in the context of the task.
3 The student has attempted to interpret the reasonableness of the
results of the model in the context of the task, to the appropriate
degree of accuracy.
4 The student has correctly interpreted the
reasonableness of the results of the model in the context of the task,
to the appropriate degree of accuracy.
5 The student has correctly
and critically interpreted the reasonableness of the results of the
model in the context of the task, including possible limitations and
modifications of these results, to the appropriate degree of accuracy.
D0 Type II The student has not arrived at any results.
D1 Type II The student has arrived at some results.
D0
indicates that "the student has not done the task," pretty much. D1 is
when there's a function found, but that's all. No mention of whether it
works, nothing else. Don't be that guy.
D2 Type II
The student has not interpreted the reasonableness of the
results of the model in the context of the task.
This criterion is the most oddly worded of them all, in that it doesn't say what the student has
done to get past level 1. Elsewhere, IB made a clarification, and the
"positive" form indicates that the student has interpreted the results
of the model as it describes the raw numbers, but has not gone on to
compare that to the real situation underlying those values. In this
example, I have included the entire first page of the task. Aside from
the first sentence, she makes absolutely no reference to the usefulness
of the model as a predictor for medication concentrations. (Also, her
graph here does not include the original points for comparison, but
that's a problem with communication, not interpretation.)
D3 Type II The student has attempted to interpret the reasonableness of the
results of the model in the context of the task, to the appropriate
degree of accuracy.
In
this excerpt, the student has immediately come to the correct
conclusion as to what type of function should model the data -- an
exponential one. She then tries four different types of functions,
including a logistic, and concludes, despite the requirement for rate
of change, that the logistic is the best one to model the data. If
there were some underlying reason that she could point out to suggest
that a logistic made more sense in context, this could have been okay,
but as it is, she has more or less ignored the context, which is how
the kidneys clean a fixed percentage of the chemicals out of the blood
every hour. In addition, "appropriate degree of accuracy" in the
descriptor definitely would not mean 14 significant figures, especially
since the original data was only available to two significant figures.
D4 Type II The student has correctly interpreted the
reasonableness of the results of the model in the context of the task,
to the appropriate degree of accuracy.
The
reasonableness in this model is okay, but she didn't check to see if
there were any things that could be better given the context. In
particular, the initial dose is 10 μg,
but the model predicts about 10.5. That's not very hard to fix, and at
the very least she should have pointed out the inconsistency.
If you're an excellent speller, you may notice that I did not point out
the misspelling of "minuscule" (she made the beginning say "mini"
rather than "minus"). That's because I didn't remember it myself, and
have only really learned that spelling quite recently.
The
"appropriate degree of accuracy" is an issue in this next passage. She
mentions using more decimal places without realizing that she might be
getting results that exhibit a false precision not warranted by the
initial data.
D5 Type II The student has correctly
and critically interpreted the reasonableness of the results of the
model in the context of the task, including possible limitations and
modifications of these results, to the appropriate degree of accuracy.
This
example shows clearly how the student arrived at the model and how the
results apply in the dosing situation. On the next page, that analysis
continues for another several lines in the same vein (pun intended).
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