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Adult students are often better motivated than traditional-age students, but many have not taken an examination for many years. Thus, finding appropriate methods of assessment poses a challenge.
Background and Purpose
The Houston Community College System's Central College has about 27,000 full-time equivalent students who have various goals including changing careers, acquiring associate degrees and transferring to programs which will result in 4-year degrees. There are no residential facilities at the college which is located in downtown Houston, Texas. Some students are homeless, physically challenged, in rehabilitation programs; and others are traditional students. The average age of our students is 27 years old.
Older students present the faculty member with unusual challenges since they don't necessarily respond well to traditional methods of teaching and assessment. However, they are capable of succeeding in learning mathematics if given appropriate support and opportunities to show what they have learned. Many students have personal difficulties at the beginning of the semester. They are challenged with housing arrangements, parking and transportation problems. Day care is also a problem for many single or divorced women. Although the students have social problems and economic constraints, they are motivated to strive toward the academic goals of my class. They honestly communicate their difficulties and they share their successes. I design activities and assessment in my class to address these special needs of my students. Flexibility and compassion create an environment rich with opportunities to learn, while the expectations of excellence, mastery and skills acquisition are maintained.
These non-traditional students usually begin my course in college algebra with little confidence in their abilities. They are reluctant to go to the board to present problems. Older students tend to do homework in isolation. Many of them do not linger on campus to benefit from interaction with their classmates. College Algebra students at Central College have no experience with mathematics software or computer algebra systems such as DERIVE, and are uncomfortable with computer technology generally. While older students may be uncomfortable with reform in college algebra, with time they do adjust and benefit from a pedagogical style which differs from the one they expected. In this article, I discuss some assessment techniques which I have found help these students grow, and allow them to show what they have learned.
Method
I usually start my college algebra classes with a 10 or 15 minute mini-lecture. I pose questions which encourage discussion among the students. These questions are sequenced and timed to inspire students to discover new ways of approaching a problem and to encourage them to persist toward solutions. Students are invited to make presentations of problems on the board.
Cooperative Learning
Cooperative Learning offers opportunities for sharing information and peer tutoring. Students are invited to form groups of four or five. I assign the work: for example, the section of Lial's College Algebra test on word problems. Each group selects its group leader. Participants keep a journal of their work, and each member must turn in a copy of all solved problems in their own handwriting. Students are warned that each group member must be an active problem solver and no one is to be a "sponge." One class period is dedicated to forming the groups and to establishing the rules for completion of the assignment, and a second to work on the assignment. If the word problems are not completed in the designated class period, the assignment become a homework assignment to be completed by each group. Approximately 30 word problems requiring the use of equations are solved using this method.
As a result of this activity, students become aware of their strengths and weaknesses and become better at pacing themselves and at self assessment. Although I give a group grade for projects, I do not give a group grade for classwork or participation in discussion groups: each individual receives a grade for work completed.
Projects
Projects provide an opportunity for students to become familiar with the Mathematics Laboratory. The goal of the project is graphing and designing at least three images: a cat's face, a spirograph and a flower. Most designs are accomplished using lines and conics such as circles, ellipses and parabolas.
Some students do library or internet research for their projects: they look up trigonometric equations and discover the appropriate coefficients to produce the best (and prettiest) flowers, or use polar coordinates or parametric equations. An objective of the research is to identify role models and people of diverse backgrounds who persisted and succeeded in mathematics courses or professions that are mathematics dependent. A second objective is to inspire students to write about mathematics and to record their attitude toward mathematics and technology. I had the students in summer school find a web page on Mathematics and Nature, and write a short report. They also did research on biomimetics and composites to become aware of the usual connections in science, mathematics and nature. Connecting mathematics to the world around them helps motivate them to work harder learning the mathematics. The Mathematics and Nature web site that the students found is the one that I have linked to my page. I encouraged the students to use e-mail and to provide feedback to me by e-mail.
Examinations
Examinations usually contain 14-20 questions requiring the students to "show all work." This gives me an opportunity to see exactly what their needs are. Four examinations and a comprehensive final are administered. The student is given the option to drop the first examination, if the grade is below 70. This option provides a degree of flexibility and often relaxes tension.
Findings
Our most successful endeavor has been the establishment of my web page, using student research and feedback to improve the design. The web page can be accessed at http://198.64.21.135. I have an instructional page (with information for my students on syllabus, expectations, etc.) and a personal page that students viewed and provided corrective feedback. This activity inspired many students to do more research using World Wide Web. Encouraging students to use this technology helps some of those who are feel bypassed by technology overcome their fears. One student sent me an e-mail message: "This project to research your webpage was not only educational to students it gave them an opportunity to use current fast moving technology." Another commented, "I have been meaning to start on my own for quite some time, and now you have inspired me to do so." Attitudinal learning took place and students seemed more excited about the mathematics class and the use of technology.
The college algebra classes have developed into a stimulating and broad intellectual experience for my students. They gained the algebra skills and a new attitude about mathematics and careers in mathematics. The drop out rate in my college algebra classes is lower than most classes in my department. Approximately 89 percent of the students passed the course with grade C or above, while others realized that they did not have the time nor dedication to do a good job and they simply dropped the course. I believe students made wise judgments about their own ability and that they will probably re-enroll at a later date to complete the coursework.
With persistence on the instructor's part, older students become more confident learners. For example, toward the beginning of the semester, a 62-year-old businessman would often ask me to do more problems on the board for him. He would say, "Darling, would you work this problem for me?...I had a hell of a time with it last night." I didn't mind his style as long as he continued doing the work. Eventually, he would put forth more effort and go to the board to show the class how much progress he made. He would point to the area where he was challenged, and then a discussion would ensue. As I observed his change in behavior I noted that he and other students were taking more and more responsibility for their learning.
Participants in my classes seem more appreciative of the beauty of mathematics and mathematics in nature. Students who successfully completed their designs using DERIVE discovered the beautiful graphs resulting from various
types of mathematics statements. They learned how to use scaling and shifting to design images that were symmetric with respect to a vertical axes. While designing, for example, the cat's face, they learned how to change the radius and to translate small circles to represent the eyes of the cat. Some students used a simple reflection with respect to the x-axis to obtain a portion of their design. As they pursue their work, they had conferences with me to gain more insight.
Many students needed to learn basic computer skills: how to read the main menu of a computer, search and find DERIVE, and author a statement. Tutors were available in the Mathematics Laboratory and I assisted students when questions arose. It was the first time many of my students had ever made an attempt to integrate the use of technology into college algebra.
More students are enthusiastic about the use of technology in mathematics. Three years ago only about 5 percent of the Central College students owned graphing calculators or used a computer algebra system. In 1997, approximately 35 percent of them are active participants in the Mathematics Laboratory or own graphing calculators.
Use of Findings
As a result of student input, via informal discussions and e-mail, I will lengthen my mini-lectures to 20-25 minutes. Furthermore, at the end of each class I will review concepts and provide closure for the entire group. More demonstrations using the TI-92 will help prepare the students for their project assignments and a bibliography on "Diversity in Mathematics" will assist the student research component. I usually document class attendance on the first and last day of class so that I have a photographic record of retention. The inspiration to design a more suitable attitudinal study using a pre-test and post-test to measure change in is my greatest gain as a result of these experiences.
Success Factors
The adult learner can be an exceptional student; adults
learn very rapidly in part, because they don't need to spend
time becoming adults, as traditional-aged students do.
However in my experience, adults may be more terrified of tests,
they may feel a great sense of failure at a low grade, they may
be slower on tests, and they may have lost a lot of
background mathematical knowledge. Also they have more
logistical problems which make working outside of class in
groups harder, thereby not benefitting from explaining and
learning mathematics with others. The methods I have used
are specifically designed to bring the adult learners together,
to relieve anxiety, to encourage group work, the "OK-ness"
of being wrong.
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