Applying Psychology To The Teaching Of Basic Math: A Case Study

by W. George Jones

from Inquiry, Volume 6, Number 2, Fall 2001, 60-65

© Copyright 2001 Virginia Community College System

Return to Volume 6, Number 2

Abstract
An instructor of psychology uses a variety of techniques to reduce math anxiety.

Many students develop intense anxiety associated with math, especially math tests. Commonly termed "math anxiety," this phenomena can be a major barrier to gaining access to a variety of skills necessary for success in our increasingly technologically based society (Tobias,1978,1987; Zaslavsky,1994).

In a 1992 University of Florida Counseling Center Needs A ssessment Survey of 9,093 students, 25.9 % reported moderate to high need for help in managing math anxiety (Probert). Subsequent to two graduate degrees and five years employment, I experienced my first "math anxiety attack" while taking a mid-term examination in statistical analysis, a class in which I informally tutored a group of struggling upper division and graduate students to success. This experience, which could have compromised my beginning career as a community college instructor, made a powerful and lasting impression on me. Many of my students report similar anxiety experiences and often ask what can be done to escape the web of dread thus created.

In addition to thorough preparation (mastery/over-learning), clinical psychological theory suggests that this road-block can be ameliorated via a combination of user-friendly appropriate models, specifically (1) the exploration and modification of dysfunctional perceptions and conceptions, (2) the development of strategies for stress reduction and subsequent management, and (3) the use of a variety of behavioral techniques associated with establishing more functional patterns and schedules of reinforcement. Research was conducted to see whether or not these three factors would lead to improved student performance.

At Danville Community College, two basic math (MTH 02) classes composed of similar students were taught in the fall semesters 1999 and 2000. Conventional techniques were used in 1999 while a continuing systematic effort to reduce math anxiety was employed in 2000. Both classes met at approximately the same time of day and used Bittinger’s Basic Mathematics, 8th. Ed., and associated instructional and test resources. Anecdotally, students expressed similar math phobia and test anxiety in both classes. Tests and examinations were of equivalent difficulty, provided by the author of the text as part of the standard instructional package. Although the three-credit class was intended for students repeating the course, students in both classes were largely taking Basic Mathematics for the first time at Danville Community College. Performance statistics for the Fall 1999 class were consistent with departmental averages for that course (MTH 02) for the semester.

Teaching Strategy for Fall 1999: The instructor monitored and largely duplicated the instructional approach of a veteran mathematics teacher: effective presentation, overall instructional management, and communication of caring for the student.

Teaching Strategy for Fall 2000: The instructor consciously attempted to reduce math test anxiety and moderate risk-taking anxiety by creating a positive learning environment in which they did "live mathematics." Each class was started with a remark such as, "Isn’t it great that we get to do math today!" and other comments making light of what one might otherwise have to be doing, such as "Getting the groceries," "Doing taxes," etc. The instructor and students regularly created their own appropriate problems for demonstration. Although some students initially thought the math instructor to be a little "nutty"; in time most came to enjoy the necessary detours, etc. as they became more comfortable with the challenges of "live mathematics."

The instructor identified appropriate homework (largely odd-numbered problems in text exercises) but left the decision as to how much homework up to the individual student, emphasizing the need to become acquainted with one’s own learning style and characteristics and systematically stressing that it was the individual student’s responsibility to determine what kind and how much repetition was necessary for subject mastery and learning permanency. An incentive was given to all students to do at least the practice tests (Bittinger -Form D) by awarding up to 10 points based on the quality of work presented to be added to the upcoming chapter test score. However, the resultant score was not to exceed 100 points for the record. This arrangement required tedious scoring and feedback on each practice test, including "showcasing" and "troubleshooting" frequently missed problems.

Incentive for keeping previously learned techniques alive and continued thinking about "stretch" applications was provided by offering 5 to 6 optional review/challenge problems on both the practice tests and tests for the record. These problems, if executed successfully on the latter tests, could be substituted for missed required items, one for one. Unsuccessful attempts at such problems did not reduce the score based on required items (non-punitive for added incentive for risk-taking); such points could theoretically inflate scores by as much as 15 points on average, but the actual gain was typically more in the range of 5 to 8 points for challenged students. For consistently achieving students with the 100 points maximum in place, there was typically little or no point gain; their motivation appearing to be the "enjoyment" of a real security margin and the challenge of going beyond that which was required. Significantly, the typically achieving students consistently elected to attempt optional "opportunities" while the challenged students did so less frequently. For final grade purposes, the unit tests average awarded 60% of the semester grade; the comprehensive examination consisting of all required problems weighed in at 40%. Students were allowed to take a break and return to class at specified times and to leave early as appropriate on completing routine unit tests.

A structured systematic approach using repetitive questions was used:

Routine opportunities were created to include discussion of the processes of sensation, perception, conceptualization, retention, retrieval, and the management of anxiety with regard to the experiences associated with mathematical operations. These discussions were typically introduced and/or related to the aforementioned patterned questioning with sufficient redundancy to make retention-retrieval likely, sometimes to the degree of bordering on the ridiculous (humor and over-learning).

Rather than providing a scripted instructional performance, a casual "live"approach was used beginning with the identification of the learning task(s) from the textbook, then some "wondering out loud" as to how this might be approached, followed by the demonstration of appropriate "models"for solution finding and its possible value in living in "the real world."

Mnemonic strategies were used to make storage and retrieval of formulas, order of operations, conversions, and the metric naming system more readily accessible Frequently, the logic for the derivation of formulas temporarily inaccessible to memory was revisited in the context of: "Can’t remember? Don’t panic! If you stop and think carefully (rather than panic!) you can re-create that which we cannot immediately recall." (The instructor frequently remarked that he had to do this since his "aging brain" was often challenged to find all this stuff on demand.) Designed to lessen the likelihood of getting lost in doing a particular calculation, a "calculation tree" was used when doing order of operations problems, a procedure adapted from the "factorization tree" process introduced in finding the lowest common denominator, etc.

The instructor often verbally discovered/admitted getting lost, making an incorrect calculation and then calmly retraced his steps in order to get back on a promising path. Frequently, he requested the class’s assistance in identifying the miscue and what might be needed to recover from this deviation from the direct course. The "navigation" model became a prominent guide for maneuvering from where one is to where one wishes/needs to be mathematically, particularly useful in escaping the failure trap and the "learned helplessness" likely to follow. "Positive problem analysis-solution pursuit self-talk" was encouraged and repetitively modeled as much more desirable than the language of despair, self-humiliation, and/or resentment.

Where there were multiple solution options, such as the substitution of an equivalent in an equation or alternatively the use of a proportion, the merits of each approach were noted, and students were challenged to identify which should be used first. Subsequently, one approach was chosen to find the solution, and the other option was then used to check the accuracy of the initial solution, rather than checking in the back of the book or by duplicating the initial process. Basic short-cuts using algebraic procedures were modeled and used routinely in estimating and checking for solution accuracy with an "apology for leaking secrets of the craft!"

At the point where the use of calculators was allowed, such use was "restricted" to doing calculations after the problem was set up, which must include the designation of units of measure and the transformations mandated by the indicated calculations. Time was taken to explain the "logic" of the calculator, and walk-through demonstrations were shared, noting alternative keying possibilities. To check for accuracy, alternative keying was demonstrated and encouraged rather than simply duplicating the original keying. On homework problems, the use of the calculator to check accuracy of computations prior to looking for official answers in the back of the book was encouraged. Fortunately, occasional errors in book answers were discovered and noted in a low-key manner; moreover, students were calmly encouraged to trust in their own competence in such incidents rather than accept another’s "best guess."

The instructor requested complete problem set-up be shown on all application problems. On routine assignments, one-half credit was awarded for set-up success even if an incorrect calculation produced an inaccurate answer. The instructor discussed the appropriateness of set-up strategies and invited class members to identify alternate strategies, particularly those promising more direct ("easy") methods of calculation.

A comparison of the traditionally taught class in 1999 and the 2000 class structured around reducing math anxiety reveals the following:

Bittinger, M.L. 1999. Basic Mathematics (5th ed.). New York: Addison-Wesley.

Probert, B.S. & Vernon, A.E. 1992. "Overcoming Math Anxiety: Counseling Center Offers Math Confidence Groups." In Student Affairs Update 22 (2). University of Florida. Retrieved April 23, 2001 from the World Wide Web: http://www.ufsa.ufl/OVP/SAUpdate/counseling.html

Tobias, S. 1978. Overcoming Math Anxiety. New York: Norton.

Tobias, S. 1987. Succeed In Math: Every Student’s Guide To Conquering Math Anxiety. New York: College Board Publication.

Zaslavsky,C. 1994. Fear Of Math: How To Get Over It And Get On With Your Life. New Brunswick, NJ: Rutgers University Press.