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 0.2 2 281 253 255 435 0.19 0.17 0.18 0.3 3 264 239 289 332 0.18 0.16 0.2 0.23 4 190 164 216 146 0.13 0.11 0.15 0.1 5 144 143 154 46 0.1 0.1 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 8 64 49 19 0 0.04 0.03 0.01 0 9 26 31 3 0 0.02 0.02 0 0 10 6 6 0 0 0 0 0 0 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.