The author discusses assessment techniques which she has found to be particularly effective with female students.
Background and Purpose
Some women students, including most of us who have acquired Ph.D.s in mathematics, excel at demonstrating what they've learned on traditional tests. However, most women students are less successful than men with comparable levels of understanding when only these instruments are used. It is thus important to look for assessment methods that allow women to demonstrate as well as men what they have learned. Cedar Crest College is a four year liberal arts women's college in Allentown, Pennsylvania. As a professor in a women's college, I have experimented with a variety of assessment techniques over the past 14 years. These include journal writing, group work, individual and group tests, and creative projects. My findings are that journals help form positive attitudes in females through encouragement and weekly guidance. Formative evaluation improves the teaching/learning process.
A research study of students enrolled in college remedial mathematics courses [4, p. 306] supported the assertion that beliefs such as self-confidence were more important influences on mathematics achievement and success for females than males. Research indicates that sex differences in mathematics self-efficacy expectations are correlated with sex differences in mathematical performance [2, p. 270]. Mathematics self-efficacy expectations refer to a person's beliefs concerning ability to succeed in mathematics. Such beliefs determine whether or not a person will attempt to do mathematics and how much effort and persistence will be applied to the task at hand and to obstacles encountered in the process. Suggestions for improving learning experiences of females include changing students' perceptions of the nature of mathematics by emphasizing creativity in mathematics, making connections to real life situations, permitting students to engage in problem posing, and encouraging debates, discussions, and critiques of mathematical works [1, p. 89-90].
I find that our students learn mathematics better with a hands-on teaching approach and with daily assessment activities to boost their self-esteem and to build their confidence as successful problem solvers. Making models helps our students visualize mathematical concepts. Since many women lack experiences with objects of physics which motivate much of mathematics, they require experience with such objects to continue studying mathematics successfully.
Creative projects help students visualize a mathematical concept. Also, projects require students to reflect on how all the concepts they learned fit together as a whole.
Women as nurturers thrive on cooperation and collaboration rather than competition. The first attribute of women leaders is collaboration [3, p. 26]. Women leaders elicit and offer support to group members while creating a synergistic environment for all and solving problems in a creative style.
Classes used in the following assessments include: Precalculus, Finite Math, Calculus I, II, III, and IV, Probability and Statistics, and Exploring Mathematics for Preservice K-8 teachers over the past fourteen years.
1. Group Work Group work in class gives instantaneous assessment of each individual's daily progress. Students thrive as active learners receiving constant feedback and positive reinforcement. Problems can be solved by groups working with desks drawn together or working in groups on the blackboard. When groups work on the blackboard, I can watch all the groups at the same time. It is easy for me to travel around the room from group to group giving encouragement to those who are on the right track and assisting those who are stuck. This works successfully with classes as large as thirty-two.
A natural outgrowth of working in teams during class is to have team members work together on an exam. All team members receive the same grade for their efforts if all contribute equally to the end result. Teams are given 7-10 days to complete the test, and hand in one joint solution. Each problem is to be signed by all team members that contribute to its solution. Teams are only allowed to consult each other and their texts.
A good group teaching technique is to play "Pass the Chalk." When the teacher says to pass the chalk, then the person with the chalk passes it to another group member who continues solving the problem. This technique brings everyone into the problem solving process. No spectators are allowed: all are doers.
Group work leads to working together outside of class. The class mathematics achievement as measured by hourly tests improves. They feel comfortable as a successful working unit and take tests together as a team. For more detailed discussion of group work, see articles by Crannell (p. 143), Hagelgans (p. 134), and Roberts (p. 137) in this volume.
2. Journal Daily journal writing provides a one-on-one con-versation with the teacher about progress and stumbling blocks. I answer student inquiries about learning or about homework, and dispel negative feelings with encouragement. Students require about 5 minutes to complete a daily journal entry. Weekly reading of journal entries takes about 3-5 minutes per student. Scoring consists of a point for each entry. Total points are used as an additional test grade.
SAMPLE JOURNAL WRITING TEMPLATE
1. In class, I felt...
2. In class, I learned...
3. The most positive result of class was...
4. The least positive result of class was...
5. Some additional comments related to class are...
I use the same questions (replacing "In class," by "While doing homework") for responding to homework. Questions 3 and 4 are both formed in terms of a positive response and not with the words, "most negative result," to emphasize a positive frame of mind. Question 5 allows individuality in response. Students freely share their progress and problems in these entries.
3. Creative Projects In Calculus II, for instance, I assigned students the task of making a model of an inverse function. One ingenious model was made from hospital-sized Q-tips. This student made a three dimensional cube using these over-sized Q-tips. Inside the cube she placed three axes. With wire, she constructed a physical representation of a function and its inverse. Another movable model was made from a pipe cleaner and ponytail beads. The function (a pipe cleaner attached to a piece of cardboard by the ponytail beads) was attached to a two-dimensional axes model. Then by lifting and rotating the pipe cleaner, a student could view a function and its inverse function by rotating the function (pipe cleaner) about the line y = x. One student brought in her lamp as an illustration since the contours of the lamp's shadow were representative of a function and its inverse function.
A possible assignment in precalculus is to draw a concept map, a scaffold, or a flow chart to classify conic sections. For additional information on concepts maps, see article by Dwight Atkins in this volume, p. 89.
I am always amazed at how creative projects put a spark of life into mathematics class and that spark sets off a chain reaction to a desire to succeed in the day-to-day mathematical activities in the rest of the course. These creative projects range from bringing in or constructing a model of a calculus concept, writing a poem or a song, or developing a numeration system and calendar for a planet in the solar system. In the latter case, students are required to explain their numeration system and why it developed as it did on this planet using relevant research from the Internet. Enthusiasm for mathematics increases as students research mathematical ideas and concepts, brainstorm, and engage in critical thinking and reasoning.
In the fall of 1996, I used journals, group work, a group test, and creative projects in Calculus I and Finite Math.
Final grades included two individual tests, one group test, and an individual comprehensive three-hour final. In comparing student grades on the first test of the semester to their final grades, I found that students performed substantially better on the final tests.
Written student final evaluations note that journal writing gives students time to reflect on how they learn best, a focus on class work, and a link between the professor and the student. In addition, journals provide the teacher an opportunity to view student thought processes and use this knowledge to teach more effectively. Group work increased student confidence in mathematics, replaced competition with cooperation, emphasized hands-on problem solving, and individual contact with the teacher. Projects enabled students to review and reflect on major concepts from the course.
Use of Findings
I find journal writing improves my students' attitudes towards mathematics, and thus their success in doing mathematics. As the course progresses, journal entries provide the stimulus for making changes in the learning environment. If many student responses indicate that a definite change is required, then the teacher may decide to reteach a concept or proceed at a slower pace. If just a handful require additional help, then the teacher may schedule an additional study session with these students.
Students realize that I care about their learning because I require and grade their journals each week. In turn, they work harder and harder to understand mathematics. I will solve original problems that they pose in the journal. So the journals become written, one-on-one, semester-long conversations and dialogues.
Group work helps the teacher view the interactions within a group, notice which group members need additional help in graphing or algebra skills, and provide help while the group is problem solving. I find group work invaluable. I do not enjoy giving long lectures anymore. I want to present a concept briefly and then solve problems in groups at the blackboard for the rest of the class period. I teach individual groups and assess learning effectiveness as they learn in small groups. My students always write in their journals of the value of the board work. It prepares them for the homework for that night. They are successful on the homework assignments because of the struggles in class that day.
Creative projects provide a needed respite to talk about concepts and to bring them to life in the classroom. I am always intrigued by student creativity and originality. A group in Finite Math shared a counting technique they found on the Internet for making sand patterns in India. The class went to the blackboard to draw these patterns because they were intrigued with this concept and wanted to try it also. Wanting to learn more than is required by the coursework and bringing mathematics into their lives to me makes our students mathematically literate and aware of the power, beauty, and mystique of mathematics.
1. Start on a small scale.
2. Be willing to fail and to try again.
3. Do not abandon lectures. Students cannot succeed unless you give them the background needed.
4. Answer everything asked in the journal. Try to be positive.
5. Shuffle group members during the semester. Working with a variety of partners encourages students to explore various ways to solve a problem, requires that our students be active learners, and increases communication within the class.
These techniques are especially helpful with female students yet they can also be beneficial for all students.
 Barnes, M. "Gender and Mathematics: Shifting the Focus," FOCUS on Learning Problems in Mathematics, Vol. 18, No. 1, 2, & 3, 1996, pp. 88-96.
 Hackett, G. and Betz, N.E. "An Exploration of the Mathematics Self-Efficacy/Mathematics Performance Correspondence," Journal for Research in Mathematics Education, Vol. 20, No. 3, 1989, pp. 261-273.
 Regan, H.B. and Brooks, G.H. Out of Women's Experience: Creating Relational Experiences. Thousand Oaks CA: Corwin Press, Inc., 1996.
 Stage, F. and Kloosterman, P. "Gender,
Beliefs,and Achievement in Remedial College Level
Mathematics." Journal of Higher
Education, Vol. 66, No. 3, 1995, pp. 294-311.