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Math Remediation and Tutoring

Monday, December 31st, 2012

Math Remediation

The following Abstract refers to a talk presented recently at my home university (British Columbia) by York University math professor Dr. Kim Maltman:

Abstract. At York, we have found first-year science majors coming to us from the
Ontario high school system in general rather poorly prepared for first-year
university mathematics. The result is very high drop-plus-fail rates in
our first-year math courses and a resulting high attrition rate in the
early years of our degree programs. A major source of the problem appears
to be the widespread use in the schools of an approach heavily emphasizing the
memorization of solution problem templates, an approach which leaves a
majority of our incoming science majors with deficiencies in very basic
algebra, trigonometry, and, even more problematic, their intuitive
understanding of the basic operations of arithmetic. In this discussion,
I will outline an approach I have developed involving 4-day, 4-hour-per-day
intensive remediation sessions focused on changing the way such students
approach mathematics. The program was begun in 2005 and significantly
expanded in 2009, now handling between 15 and 20% of the incoming
class each year. I will present statistics outlining the significant impact
we have seen on student performance.

It seems that the phenomenon of “high drop-plus-fail rates” is almost universal in North American colleges and universities. I don’t know how other universities are dealing with the problem, but at UBC until recently little was done, other than to provide students with a math-help facility where they could obtain help with their calculus courses. Many students still had difficulties, as attested to by the large number of posters advertising Math Tutoring. Besides this, almost every shopping mall in the area has an office advertising Help classes in Math.

Why is the phenomenon of high dropout rates so common and persistent? I think the Abstract has got it right – “…heavily emphasizing the memorization of solution problem templates,…which leaves incoming science majors with deficiencies in … algebra, trigonometry, [and] their intuitive understanding of … basic operations….” Just so.

But how to deal with the problem? Two possibilities are:

  1. Re-design the school curriculum to place more emphasis on understanding math.
  2. Provide assistance for poorly prepared college entrants.

The first alternative probably cannot be achieved easily, if at all. Remediation sessions are one approach to the second possibility, and it’s certainly impressive if a total of 16 hours’ class time can reverse 12 years of “math-is-memorization” instruction. I don’t know how  many universities are providing this service at the moment.

A second approach is streaming, with poorly prepared students being forced to take a course such as “Precalculus.”  But unless this course includes remediation for weak training and poor habits in arithmetic, algebra and geometry, I doubt if it will succeed in rescuing many students.

Tutoring

Private tutoring is yet another approach, but whether tutoring is likely to result in the necessary changes in the way that students perceive math is doubtful. Commercial tutoring may be better, but expensive.

Rather than hiring a tutor, a struggling student might try to re-learn math by searching the web. But what should they re-learn? Proofs? Set theory? Long division? Inverse functions?

Math Overboard!

These were the issues that prompted me to write Math Overboard! (Basic Math for Adults), which is a complete review of school math, emphasizing understanding and algorithmic, problem-solving skills. Math Overboard! is a self-study resource that helps motivated students to upgrade their comprehension of basic math to a level suitable for college math courses.

Here is what Prof. Marc Mangel (UC Santa Cruz) says:

I have now had a chance to read through MATH OVERBOARD and like it very much; I look forward to Part II. I will recommend it to grad students in biology as a reference book and once I am back on campus … I will hawk it to my colleagues who teach pre-calc and calculus. I think that for the calculus classes it would be wonderful resource book, if the students would use it.