The Missing Ingredient

Kathy Pilger, Ed.D.

While working with incoming university students in introductory-level mathematics courses, it became apparent that most students are shortchanged in an extremely important aspect of their elementary and secondary mathematics training. Students are often not taught efficient methods of studying mathematics or how to prepare for and take a mathematics test. Therefore, college students regularly flounder in their study methods and often waste time in preparation for their mathematics classes. Students would benefit if elementary and secondary mathematics teachers would include training in efficient study skills while teaching content.

A survey of 149 introductory-level university mathematics students (Pilger, 1996) showed that 81.88% had received no training in how to study mathematics while they were in high school. Eleven percent had received part of one class hour of training in mathematics study skills during high school. Only 5% indicated that they had received adequate training in study skills for a mathematics course. It is no surprise, then, when students say, "I never study for a math test," or are extremely anxious about performance in a mathematics class. They have not been taught how to succeed in mathematics.

There are four major areas of study-skill instruction that should be incorporated in secondary mathematics courses. These areas are "Getting Ahead," "During Class," "Practice Time," and "Test Preparation."

The "Getting Ahead" skills focus on becoming familiar with instructional material before it is presented in class. These skills include pre-reading and outlining textbook material, reading supplementary material about the topic, and writing questions about the material. Students should be given instruction in these skills including the following procedures:

1. Read the material carefully. Use a reading procedure such as SQRQCQ:

S = survey (look at headings, look at italicized or highlighted terms).
Q = question (question yourself - what am I looking for?).
R = read (carefully note key words and ideas - write them down).
Q = question (question yourself - what operations should be used to solve these problems and how does this information fit with the material in the previous sections?).
C = compute (with pencil and paper find the answer to sample problems).
Q = question (question yourself - does the answer seem reasonable?).

2. Highlight or underline the main ideas in the text. But don’t highlight too much. No more than ten percent of the text should be highlighted.
   
3. Make a list of questions that occur to you while you are reading.
   
4. Ten minutes before class begins review your book notes and lecture notes from the previous class period.

The "During Class" skills focus on strategies to use during class to enhance perception and increase the ability to glean the most from the classroom experience. "During Class" skills include mental preparation immediately before the class begins, note-taking skills, and appropriate questioning techniques. Give the following suggestions to your students and help them develop skill doing them.

1. Be ready before the teacher begins his lecture. Your books and your notes from previous work and Getting Ahead work should be open. Be mentally prepared to begin.
   
2. Listen carefully while in class. Concentrate.
   
3. Be organized and neat in your note taking. Note the organization of the teacher’s or text’s presentation.
   
4. Be actively involved in the classroom experience at all times. Take notes, ask questions, think.
   
5. Get started on homework during class. If the teacher provides time to work during class, always be diligent to get started and to concentrate fully to get a good start on your out-of-class work.

"Practice Time" skills help students gain the most from their out-of-class homework time. Methods of study, location, and timing of study are important. Include the following ideas for your students.

1. Consistency and organization are keys to effective learning. Set up a study schedule for this class and stick to it.
   
2. Study in a quiet location where you can not be distracted (no music, no friends, etc.).
   
3. Summarize in your own words what you learned during the lecture or from textbook reading.
   
4. Attempt the assigned homework as soon as possible after class. Write all steps to solutions to problems.

"Test Preparation" skills help a student feel confident going into the testing situation. Long-range and short-range techniques should be emphasized. Specific strategies to use during the testing situation also help students take tests well. Suggest the following to your students.

1. Constant preparation and review is the key. A little study every day will produce extremely efficient learning.
   
2. Write all definitions, formulas, and important facts or theorems on 3" x 5" cards. Read through them each day.
   
3. When you complete a homework assignment, write on 3" x 5" cards at least three problems from each homework section similar to those problems assigned. Write the problem on one side and the solution on the other. Randomly select five of these problems each day to review. Actually work these five problems each day with pencil and paper.
   
4. Begin preparation for a test early.
   
1. Read through text and lecture notes at least five days before the exam.
   
2. Review all 3" x 5" cards (terms and problems) each day for four days before the exam.
   
3. Work the chapter review or chapter test found at the end of the chapter at least three days before the test.
   
5. At least two days before the test, prepare a practice test similar to what you expect on the test and work the problems on this test in the same amount of time and under the same circumstances as the test. Check to see how you did.
   
6. When taking the test, have a plan.
   
1. Go through the test quickly answering all questions that are apparent.
   
2. Go through the test again answering all questions that you now remember.
   
3. Go through the test again and answer the rest of the questions.
   
7. Go through the test a final time and double-check accuracy.

Students will benefit from a frank discussion concerning their responsibilities in learning. The teacher may want to choose one or two items from each area to help his students become efficient learners. If students are given the entire set of study skills at once, they may perceive that it is too much work, but if the teacher focuses on one or two study methods each year of high school, the students will build a repertoire of skills from which to choose when taking more advanced math courses. Teachers need not only instruct students in these study skills areas but must hold the student accountable for using them. Students will generally not do the extra "work" which produces efficient learning unless the teacher assigns study-skills tasks regularly and grades these tasks. If middle and secondary school teachers give graded assignments on a regular basis encouraging students to practice these skills, the students will become accustomed to using them and will see their benefit.

Teachers must not assume that students learn these skills elsewhere, because according to research, they do not. The mathematics teacher needs to incorporate study-skill training into the regular classroom experience. Students who learn and use these skills while in secondary school will be a step ahead of other students when they enter the university mathematics classroom.

References

Devine, T. G. (1981). Teaching study skills: A guide for teachers. Boston: Allyn and Bacon.

Pilger, K. D. (1996). The effects of different quizzing methods and study skills in introductory level university mathematics courses. Unpublished doctoral dissertation, Bob Jones University.

Poulsen, S. C. (1970, June). Study skills and mathematics achievement. Danish Institutes for Educational Research, Report No. 2.

Robinson, A. (1993). What smart students know. New York: Crown Publishers.

Shaughnessy, M. F. (1990). How to learn more in less time. ERIC, ED 322985. Eastern New Mexico University.

Smith, R. M. (1994). Mastering mathematics: How to be a great math student (2nd ed.). Belmont, CA: Wadsworth.

Reprinted from Balance, a publication of the School of Education, Bob Jones University. Used with permission of Bob Jones University. Please write BJU Press, for permission to reproduce this article.