### Update on MS 150 Statistics for curriculum committee

#### 15 September 2007

MS 150 Statistics as a course is more than an outline and I would hope that no instructor anywhere in the system would only be given the outline and asked to teach the course. The course includes on line resources such as syllabi going back to 2000, and a textbook.

Instructors who teach MS 150 will also have to determine a manner of assessment for the course - reporting into the same five course level outcomes into which I report. I view decisions on the specific mechanism of formative assessment to be best left up to the individual instructor. I feel it would be overly prescriptive and curtail academic freedom and syllabus design choices to force my item-analysis aggregation approach on other faculty.

Every Friday there is a quiz or test, and each weekend I item analyze the current quiz or test. This results for this past Friday were:

 Q Description l Outref SLO Corr Corr%
 1 direct variation calculation 1 1 Calculate basic statistics 24 53% 2 linear, non-linear, or random 5 5 Perform a linear regression and make inferences based on the results 26 58% 3 slope 5 5 Perform a linear regression and make inferences based on the results 43 96% 4 intercept 5 5 Perform a linear regression and make inferences based on the results 42 93% 5 correlation r 5 5 Perform a linear regression and make inferences based on the results 45 100% 6 positive or negative relation 5 5 Perform a linear regression and make inferences based on the results 44 98% 7 strength of relationship 5 5 Perform a linear regression and make inferences based on the results 34 76% 8 coefficient of determination 5 5 Perform a linear regression and make inferences based on the results 42 93% 9 perc var x that explains var y 5 5 Perform a linear regression and make inferences based on the results 13 29% 10 predict y given x 5 5 Perform a linear regression and make inferences based on the results 28 62% 11 predict x given y 5 5 Perform a linear regression and make inferences based on the results 26 58%

From the above data I gain insight into what has been learned and what has not. Note that the percentage is the percentage of students answering that item correctly. So every single student can calculate the correlation r - a phenomenal result.

Of interest is also that while 62% of the students can predict a y value given an x value (using the slope and intercept they calculated in 3 and 4 above), when asked how much fifty feet of wire at 15 cents a foot would cost, only 53% answered this correctly. As this would seem to be a precursor skill to number ten, this lower result for number one would seem to a a puzzle. I attribute it to the "extinction of knowledge" effect - I have not been teaching this specific precursor skill, so it is a) surprisingly forgotten and b) not all that strongly impacting current skills. As much as mathematics instructors might want their students to not memorize solution processes but rather to work things out from the rules of mathematics, our students will still fall back on sheer memorization.

Based on the above, I will work with the students on Monday to run another linear regression, with a special focus on the meaning of the coefficient of determination as performance was weak on interpreting the coefficient of determination (29%).

Aggregating the above plus prior quiz and test results yields a report on the accomplishment of course learning outcomes as of then end of week four:

 Outref Students will be able to: Sum Count Avg 1 Calculate basic statistics 20.51 37 55% 2 Represent data sets using charts and histograms 2.96 8 37% 3 Solve problems using normal curve and t-statistic distributions including confidence intervals for means and hypothesis testing 0 0 0% 4 Determine and interpret p-values 0 0 0% 5 Perform a linear regression and make inferences based on the results 8.07 15 54% PSLO define mathematical concepts, calculate quantities, estimate solutions, solve problems, represent and interpret mathematical information graphically, and communicate mathematical thoughts and ideas. 29.26%

Outcomes three and four are not covered until close to and after the midterm, there is precursor material to introducing the normal curve between now and the midterm. Histograms and charts will be covered again at midterm and on the final, so there is room for that metric to improve as well.