Whatever you do, don't panic. There will not be 294
students in MS 090. But here is the ruthlessly raw first bloody look at
the math entrance test data. Consider this a disorganized meander through the
data. A journey led by a fool who is attracted to the next pretty number
or statistic.
| Course |
Raw
Placement |
Percent |
425 |
| 90 |
941 |
0.69 |
294 |
| 95 |
79 |
0.06 |
25 |
| 98 |
166 |
0.12 |
52 |
| 100 |
153 |
0.11 |
48 |
| 101 |
20 |
0.01 |
6 |
|
1359 |
1 |
425 |
1,359 students took the entrance test
Presume we get 425 new freshmen Fall 2003.
Then the bulk place into MS 090 followed by MS 098 and MS
100. The raw projected numbers in the rightmost column are
malarkey.
The problem with the above chart is a disaproportionate
number of projected MS 090 students are actually going to wind up at the state
campuses in either certificate or IEP programs. The MS 090 numbers are a)
wrong b) cannot be "fixed" until after the candidate selection process
concludes.
So what use is this data? The inter-course RATIOS
among MS 095, MS 098, MS 100, and MS 101 are likely to prove relatively
robust. The data indicates that excluding the MS 090 students, 80% of the
remaining may place into MS 098 and MS 100 with only 20% placing into MS
095.
The data also shows that, if the placement test is
reflective of our courses, then students who can handle MS 090 material can also
handle MS 095 material. Once a student succeeds in the first column, they
usually succeed in the second column. This suggests that the courses are
not strongly significantly different in level/content.
This also causes me to want to see the underlying
frequency curves for the four columns. Remember that the four columns are
MS 090, MS 095, MS 098, and MS 100. There are ten questions in each
column. This means students get a score from one to ten in each
column. Suppose one counts up the number of students who got a score of n
in each and every column. Four frequency curves result from this:
Obviously two is random, getting zero on a multiple
choice test requires extra work! The raw data under this graph is:
| Correct |
90 |
95 |
98 |
100 |
90 |
95 |
98 |
100 |
| 0 |
47 |
96 |
85 |
82 |
0.03 |
0.07 |
0.06 |
0.06 |
| 1 |
169 |
189 |
195 |
295 |
0.12 |
0.13 |
0.13 |
0.20 |
| 2 |
281 |
253 |
255 |
435 |
0.19 |
0.17 |
0.18 |
0.30 |
| 3 |
264 |
239 |
289 |
332 |
0.18 |
0.16 |
0.20 |
0.23 |
| 4 |
190 |
164 |
216 |
146 |
0.13 |
0.11 |
0.15 |
0.10 |
| 5 |
144 |
143 |
154 |
46 |
0.10 |
0.10 |
0.11 |
0.03 |
| 6 |
108 |
118 |
91 |
16 |
0.07 |
0.08 |
0.06 |
0.01 |
| 7 |
57 |
68 |
49 |
4 |
0.04 |
0.05 |
0.03 |
0.00 |
| 8 |
64 |
49 |
19 |
0 |
0.04 |
0.03 |
0.01 |
0.00 |
| 9 |
26 |
31 |
3 |
0 |
0.02 |
0.02 |
0.00 |
0.00 |
| 10 |
6 |
6 |
0 |
0 |
0.00 |
0.00 |
0.00 |
0.00 |
|
1356 |
1356 |
1356 |
1356 |
1 |
1 |
1 |
1 |
Bearing in mind that it looks like success in the MS 090
column meant success in the MS 095 column as well, I looked for evidence of this
in the frequency diagram.
090 and 095 both appear to peak in a similar location and
both appear to decay at about the same rate in the right tail.
I immediately decided I needed to know the mean values,
some other basic stats, and see a correlation cross:
|
90 |
95 |
98 |
100 |
| count |
1356 |
1356 |
1356 |
1356 |
| mean |
3.58 |
3.46 |
3.15 |
2.29 |
| mode |
2 |
2 |
3 |
2 |
| median |
3 |
3 |
3 |
2 |
| stdev |
2.17 |
2.29 |
1.88 |
1.27 |
|
|
|
|
|
|
90 |
95 |
98 |
100 |
| 90 |
1 |
0.62 |
0.44 |
0.19 |
| 95 |
0.62 |
1 |
0.52 |
0.22 |
| 98 |
0.44 |
0.52 |
1 |
0.18 |
| 100 |
0.19 |
0.22 |
0.18 |
1 |
The average "decays" from 90 to 100, but the big drops
are 95 to 98 and 98 to 100. The drop in the average from MS 090 to MS 095
is less than half of the next two drops:
|
90 |
95 |
98 |
100 |
| Decay |
|
-0.12 |
-0.31 |
-0.87 |
Although statistically separated due to the huge sample
size, the relative drop in the average is small from MS 090 to MS 095. The
above data suggests that students who did well on the MS 090 material did well
on the MS 095, or at least equally poorly if nothing else. And there is
the suggestion that the two columns do little to distinguish between the
students. These students are close to the same level (those that placed
into 090 and 095, NOT those that placed into 098!).
Turning to the correlation cross above, the MS 090 and MS
095 scores do show the highest correlation in the cross at 0.62. Of course
there should be a relationship! The strength simply lends support to the
theory that "As a student does in the 090 column, so shall they do in the 095
column."
I continue to favor running MS 090 students through an
exit exam that would then place the student into MS 095, MS 098, MS 100, or back
into MS 090 were they to fail the exit exam. Yes, this would be a binding
exit examination. It would "desequence" MS 090 in some sense. Sure,
many would simply place into MS 095 and continue the sequence. But some
would rise to the challenge and move more appropriately into a higher
level.
A couple other things to check out: There were six
perfects in column one and six in two. Underneath these numbers is the
following data:
| HS |
Last |
First |
MS090 |
MS095 |
MS098 |
MS100 |
Place |
| Xavier |
Tewailiig |
Arthur |
9 |
10 |
7 |
5 |
100 |
| Xavier |
Mori |
Donsean G.R. |
9 |
10 |
7 |
1 |
100 |
| KHS |
Nena |
Junior M. |
10 |
7 |
7 |
3 |
100 |
| KHS |
Mackwelung |
Sra |
10 |
8 |
8 |
5 |
100 |
| Xavier |
Semens |
Alan |
10 |
9 |
6 |
4 |
100 |
| PICS |
Hadley |
Salter |
10 |
9 |
8 |
4 |
100 |
| KHS |
Salik |
Horace |
10 |
10 |
9 |
7 |
101 |
| PICS |
Meninzor |
Makrihda |
10 |
10 |
5 |
5 |
98 |
The other thing to check out: the bottom line is that the
country is not producing students who can do any mathematics at all. Check
out the number of students who scored at or below random in the MS 090 column:
37% !!!! These students cannot do the most basic of arithmetic operations
- or, as Jonathan might note, there is a high likelihood that they cannot read
English and that this underlies their scores. To see what they cannot do,
check out: http://shark.comfsm.fm/~dleeling/math/practice.xml
*
There may be many more fun and shiny numbers to dig out
of the raw data, but these statistics above should serve as a fun starting point
for anyone who likes to stare at numbers and search for meanings
therein.
- Dana "While visions of sugar numbers danced in his
head" Lee Ling
Go Sharks!
*That web page will display correctly only
in the most recent browser versions. Microsoft Internet Explorer 6.0 can
display that page, but some of the fraction bars will be too big. There
may be other display problems. To fix these you need a browser helper, a
type of plug-in, from: http://www.dessci.com/en/products/mathplayer/
Browsers older than MSIE 5.5 cannot display the page properly even with
the browser helper. Go to the Help menu in your Internet Explorer and
choose About Internet Explorer to determine what version you have if the page
will not display correctly.
The practice test problem set is set at a
hairbreadth's higher level than the entrance test. The ability to do the
practice test should ensure the ability to do the entrance test.
I should
also note that printing the tests still remains problematic. The functions
do not always print as they display on PostScript and PCL printers (e.g.
laserjets). My experience has been that a cheap inkjet does a better job
of printing the tests.
The display and printing problems are connected
with my use of the leading edge technology MathML web language. For further
information on MathML please see http://www.w3.org/Math/
The new mathematics entrance test permits and encourages the
use of a calculator. The test is not designed to be completed in an hour
without a calculator. Students should be told to bring a calculator for the
College of Micronesia-FSM math entrance
test.
