Documenting and Diagnosing Deficiencies in Basic Math Skills: Two Years of Data
Simcha Pollack, Department of Computer Information Systems/Decision Sciences, The Peter J. Tobin College of Business
This research has four main goals. First, to document the extent of deficiency in St. John’s students’ basic math skills. Second, to devise a method of diagnosing the specific skills that need improvement. Third, to ascertain whether these deficiencies are correlated with the grades in an introductory business statistics course. Fourth, to develop and test methods of remediation. This presentation focuses on the progress made to date toward the first three objectives.
Anecdotal experience and prior pilot data strongly suggest that a significant number of our students are deficient in some basic mathematical techniques. Perhaps it is due to the prevalence of the calculator, poor study habits or poor elementary school teaching but for whatever reasons a subset of students can not add and multiply fractions, convert a fraction to a decimal, a decimal to a percent or solve a simple word problem.
This has serious adverse academic affects because so many classes are quantitative. This includes, of course, all the hard sciences and math but also psychology, management etc. Indeed, one can not function well in almost any endeavor in or out of school without basic math skills. No wonder so many students’ eyes glaze over when an equation is presented to them. The lack of confidence when it comes to any quantitative material begins with a fear of even simple operations or concepts.
In order to document the problem, to teach at the appropriate level and to help remediate my students’ deficiencies, I have devised a simple twenty question, ten minute quiz of basic math operations. Results from this instrument are correlated with the quantitative outcomes in an introductory statistics class. Factor analysis of the results are used to discover groupings of questions which can be used to diagnose underlying problems. Analysis of variance models are used to compare results across business disciplines (i.e. Economics, Finance, Accounting, Management, Marketing). Mixed models analysis of variance is used to compare skills within students.
The mean score in the sample of 338 students was 84% (sd=15%). About a fifth made six or more mistakes. The correlation with grades was significant but moderate in magnitude (r=0.27, p=0.0001). The factor analysis reveals a pattern among the questions that highlights the major problems for a particular student. There is considerable heterogeneity in results. i.e. students who have deficiencies in one area may not have deficiencies across the board.
The heterogeneity in deficiencies makes a program of remediation practicable. Only a minority of students require remediation and only a much smaller subset require remediation in several areas.