Issues of assessment have obtained a prominent place in discussions of teaching and learning. Since teachers' own experiences with assessment practices are often limited to the traditional "tests" they have encountered throughout their own schooling, teacher education programs must not only discuss issues of assessment but also broaden the experiences of prospective teachers by using multiple assessment practices in teacher preparation courses.
To obtain a picture of the assessment practices being used in elementary mathematics teacher preparation courses a survey was conducted during Spring 1995. This article reports the results of that survey.
A survey on assessment practices was distributed primarily through the AMTE newsletter and the AMTE listserve. In addition, surveys were distributed through other, through email accounts, and handed out at a national mathematics meeting. An encouraging 109 replies were received from mathematics teacher educators throughout the United States and Canada. Even though the survey was anonymous, 84 percent of the surveys could be linked to a state because respondents revealed their identity or by use of postmarks; 29 states and one province were identified.
The respondents were asked to indicate the types of mathematics education courses they taught to prospective elementary teachers (see table 1). Two thirds (66.9 percent) of the respondents taught methods courses, 43.9 percent taught content courses, and 15.6 percent taught integrated methods/content courses. Close to two thirds (61.5 percent) of the respondents indicated there was a field experience component for the students in their courses.
Table 1. Mathematics Education Courses Taught by Respondents Mathematics Education Course Percent of Respondents Methods only 44.0 Content only 22.9 Methods & Content 17.4 Integrated Methods/Content only 8.3 Methods & Integrated Methods/Content 3.7 Content & Integrated Methods/Content 1.8 Methods, Content, & Integrated Methods/Content 1.8
A variety of assessment strategies are used in elementary mathematics education courses as shown in table 2. The most common strategies, used by over half of the respondents, were the use of student presentations in class, essay tests, and journals. In addition, a large number of respondents indicated using such innovative assessment strategies as portfolios, group assessment, and peer assessment. Some individuals described how they conducted group assessments. In one course, the professor has students take an individual part of an exam, turn it in, and then take the exact same test cooperatively. Another individual explained that she has her students work together on a problem solving experience and then has them prepare individual write-ups about that experience.
Respondents were also asked to describe other assessment strategies they use in their courses that were not listed on the survey. Performance tasks and demonstrations with manipulatives were mentioned several times. The following specific tasks were shared by some of the respondents. Preservice teachers in their courses were asked to:
- Interpret children's thinking by watching videotaped interviews of children solving problems or by analyzing student work samples.
- Develop two assessment tasks based on an activity presented in class.
- Write detailed solution paths to problems, including all wrong turns and changes in conceptual understanding.
- Write a letter to a hypothetical principal presenting a rationale for issues such as decreased use of the textbook, increased use of calculators, or the elimination of timed tests.
- Be interviewed, individually, by the instructor for half an hour on topics such as hands-on strategies for fraction instruction, calculator usage, or dealing with children's misconceptions.
Table 2. Assessment Strategies (in order of frequency high to low) Assessment Strategy Percent of Respondents Presentations in class 68.8 Essay tests 64.2 Journals 59.6 Student self-assessment 46.8 Quizzes 46.8 Short answer tests 45.9 Portfolios 22.9 Methods & Content 45.0 Group assessment 42.2 Peer assessment 35.8 Anecdotal records 17.4 Email journals 6.4
Assignments and Projects
In addition to the assessment strategies already discussed, respondents were asked to identify the assignments and projects they use for assessment purposes (see table 3). The most common assignment, used by 63.3 percent of the respondents, was having students write reaction papers to articles. Teaching Children Mathematics (TCM) was mentioned several times as the journal most frequently suggested for the assignment. Some twists on this assignment that were noted involved having students review an entire journal or write abstracts for articles. Other common assignments, used by about 45 percent of those replying, included having students develop a learning center/game/activity, teach lessons in elementary classrooms, develop lesson plans but not teach them, and prepare reports of interviews with children. About one third of the respondents required software evaluation and about one fourth required microteaching experiences, development of units (but not taught), and conference attendance.
Table 3. Assignments and Projects (in order of frequency high to low) Assignments and Projects Percent of Respondents Reaction papers to articles 63.3 Development of learning center/game/activity 46.8 Lesson plans taught in elementary school classrooms 45.9 Lesson plans developed, but not taught 44.0 Reports of interviews with children 44.0 Software evaluation 31.2 Lessons taught to peer groups(microteaching) 26.6 Units developed, but not taught 26.6 Conference attendance 22.9 Videotaped lessons 21.1 Research paper 19.3 Units developed and taught 14.7 Case study 11.0 Audiotaped lessons 3.7
Respondents were also asked to describe other assignments and projects used in their courses that were not listed on the survey. Critiques of classroom teachers' videotaped lessons, textbook reviews, development of interactive bulletin boards, problem-solving assignments, and group projects were mentioned several times. The following specific ideas were shared by some of the respondents. Preservice teachers in their courses were asked to:
- Interview classroom teachers.
- Compile a classroom observation log.
- Develop a lesson plan that integrates children's literature with mathematics.
- Write their math autobiography.
- Critique a videotaped lesson examining the actions of both students and teacher.
- Collect quotes from children that provide evidence about the children's mathematical thinking.
- Find someone who was taught an algorithm different than those traditionally taught in the United States and than describe the algorithm and explain why it works.
- Prepare position papers on controversial issues or myths; for example, men are better in mathematics than women because they have math minds, or calculators do not encourage students to think about the mathematics they are doing.
- Research a mathematics question or topic, prepare a poster displaying the results of the research, and then participate in an in-class, conference-like poster session.
- Conduct a small group independent study using video packages.
- Complete a computer project in Logo.
The final survey question asked respondents to indicate which assignments/projects or strategies were they considering using for assessment purposes in the near future. One strategy dominated the responses to this question, that being portfolios. In addition to the 45.0 percent of the respondents currently using portfolios, another 16.5 percent indicated that they were considering using portfolios in the near future. The next most common set of responses (9.2 percent responding) involved assignments related to the use of computer software, primarily designing and teaching lessons that utilize software. Other assessment practices that were being considered included the use of journals (7.3 percent), group assessments (5.5 percent), student self-assessment (5.5 percent), case studies (5.5 percent), videotaped lessons (3.7 percent), and peer assessment (3.7 percent). The following are some of the specific ideas respondents plan to incorporate into their courses in the near future for assessment purposes:
- Conduct an ethnography of a classroom focusing on mathematics teaching and learning.
- Review and teach a replacement unit.
- Prepare written reactions to articles from a content perspective.
- Use email journals to react to class activities and do follow-up or extension activities on ideas related to class topics.
- Conduct independent reading and research to investigate a question on mathematics teaching and learning; the question is either selected from those provided by the instructor or posed by the student.
- Plan open-ended assessment items.
- Develop rubrics for assignments and for self evaluation.
The survey results indicate that elementary mathematics teacher educators across the country are using multiple methods of assessment in their teacher preparation courses. Thus, prospective teachers are not only discussing and reading about assessment, but are gaining valuable experiences as learners being assessed by a variety of assessment strategies.
We would like to thank everyone who responded to this survey and so readily shared your own assessment practices with other mathematics teacher educators. This brief glimpse clearly illustrates that many of us are incorporating new assessment practices into our teaching. We plan to continue this focus on assessment practices.