### MS 100 College Algebra: faint signal of knowledge extinction during short term?

I realized last night as I fell asleep that I had all of the data I needed to run a trend analysis by outline item. I added a couple columns to my item analysis bank:
 i Src Q Description l Outref SLO Corr Corr%
 1 t1 8 linear motion 3 3c Write mathematical models for direct, inverse, and joint variation. 6 0.5 1 t1 9 linear motion 3 3c Write mathematical models for direct, inverse, and joint variation. 6 0.5 2 t2 1 Solve quadratic 1 1b Solve linear, quadratic, polynomial, and radical equations. 6 0.55 2 t2 2 Solve quadratic 1 1b Solve linear, quadratic, polynomial, and radical equations. 6 0.55

The i and l columns are added. i tracks the nth evaluation instrument, l is the left digit of the outline reference (outref)  - the major category of the outline. Running a pivot of outline reference against i allows one to create a table against which a slope analysis can be run:
 Average - Corr% i Outref 0 1 2 3 4 5 6 7 Total Result slope 1_ 58% 27% 14% 60% 41% 0.01 1a 50% 58% 59% 36% 50% 52% -0.01

This analysis can then be made more comprehensible by putting back in the appropriate labels. The first horizontal row is the evaluation instrument, the first vertical column is the item on the MS 100 outline. The last vertical column is the slope or trend. I am unable to run a significance analysis, but the underlying small sample size inveighs against significance - so we can only have the tantalizing hint of possible signals in the noise.

 Outline Pre t1 t2 mx t3 t4 t5 fx Mean Slope 1_ 0.58 0.27 0.14 0.6 0.41 0.01 1a 0.5 0.58 0.59 0.36 0.5 0.52 -0.01 1b 0.5 0.58 0.48 0.48 0.55 0.5 0.52 0 1c 0.76 0.64 0.4 0.66 -0.07 1d 0.91 0.64 0.5 0.68 -0.07 2_ 0.27 0.82 0.55 0.55 2a 0.61 0.5 0.58 -0.03 2b 0.63 0.27 0.36 0.7 0.49 0.02 2c 0.67 0.65 0.77 0.68 0.03 2d 0.88 0.64 0.75 0.69 -0.02 2e 0.18 0.2 0.19 0.01 3_ 0.45 0.4 0.43 -0.05 3a 0.64 0.68 0.66 0.02 3b 0.7 0.8 0.75 0.05 3c 0.53 0.36 0.6 0.52 0.02 4_ 0.5 0.63 0.4 0.49 -0.05 4a 0.05 0.05 4b 0.35 0.5 0.4 0.08 4c 0.5 0.67 0.82 0.35 0.71 0.86 0.71 0.04 5_ 0.5 0.5 Pre 0.75 0.83 0.88 0.81 0.04 Mean 0.67 0.6 0.53 0.6 0.55 0.51 0.67 0.64 0.6 0

Note the downward trend in outline items 1c and 1d - covered early in the term. Back when these were actually covered - at the time of test two, performance was strong. By the time the final rolled around, performance on these outline items had fallen, hence the negative trend line.

Meanwhile, 4b and 4c show a positive trend over the evaluation instruments. These items were touched on early but only come to full fruition late in the course. There is the hint that performance climbed.

I realize that one reaction is "teach and reteach everything" yet that is easier said than done given the amount of material to be covered and the limited amount of time. Guns and butter: you can reteach more material to gain the effect of 4b and 4c, but you cannot then cover the same amount of material.

The next follow-on reaction might be, "Alright then, go deep and narrow instead of wide and shallow so you can reteach throughout the term."  Bear in mind that college algebra is a fairly standard course across thousands of colleges - reduce the scope and articulation becomes problematic. The outline is what it is based on, if you will, industry standards.

That said, the data hints at loss of knowledge even during a single term. I have often cited knowledge loss between terms as problematic and as being a part of the puzzle of why students do well one term and then seem so clueless in the next term. I have noted this anecdotally when I have taught "vertically" - MS 095 one term and MS 098 the next. My "A" students fall to a "B," the "B" to "C", and the "C" to a "D."  Documentation of this effect in the mid-1990s lead to the "promote only on a 'C' or higher" rule.

The data above, using the new l column, can also be "sliced and diced" by the four course level student learning outcomes:
 Outline Pre t1 t2 mx t3 t4 t5 fx Mean Slope Pre 0.75 0.83 0.88 0.81 0.04 1 0.55 0.58 0.58 0.47 0.45 0.5 0.53 -0.01 2 0.75 0.27 0.67 0.56 0.65 0.61 0 3 0.53 0.36 0.45 0.59 0.68 0.59 0.03 4 0.5 0.67 0.82 0.4 0.7 0.67 0.62 0.02 5 0.5 0.5 Mean 0.67 0.6 0.53 0.6 0.55 0.51 0.67 0.64 0.6 0

Note that the "5" is due to "material beyond the outline" and should be ignored. Here too we have the hint of knowledge loss.

In a separate vein I have always felt strongly that the instructor ought to be a researcher in their own classroom. My own interest in getting a handle on learning in my own classroom is a driving reason why I asked not to be put on additional committees such as the midterm report. By not having to run a division, attend meetings, or generally get bogged down in administrivia, I have - I hope and believe - had a chance to do some learning assessment and analysis. Assessment takes time and energy - and this may be one reason there is resistance out there in the faculty trenches. Assessment adds to one's workload. Only by escaping the world of the national campus have I had the chance to really focus on learning, and for that I remain in debt to the Kosrae campus for providing me with what feels like a sabbatical.