Steve Kramer & Amy Roth-McDuffie
The Center for Mathematics Education
Department of Curriculum & Instruction
Room 2226 Benjamin
University of Maryland, College Park
College Park, Maryland 20742
Department of Mathematics
Towson, Maryland 21204
A paper presented at the annual meeting of the American Educational Research Association, San Diego, California, April 13-17, 1998.
The preparation of this manuscript was supported in part by a grant from the
National Science Foundation
(Cooperative Agreement No. DUE 9255745).
This study reports the use longitudinally of a valid and reliable instrument to measure teacher candidates' attitudes and beliefs about the nature of and the teaching of mathematics and science. The instrument used, Attitudes and Beliefs about the Nature of and the Teaching of Mathematics and Science, was developed for the Maryland Collaborative for Teacher Preparation (MCTP), a National Science Foundation funded undergraduate teacher preparation program for specialist mathematics and science elementary/middle level teachers. In the current analysis, we report how MCTP teacher candidates' attitudes toward and beliefs about mathematics and science evolved over a two-year period. During the Fall 1995 and Spring 1996 semesters the instrument was administered in MCTP classes twice each semester to the study participants (N=104; 100% response). During the Fall 1996 and Spring 1997 semesters the instrument was mailed to the study participants at the end of each semester (N=96; 46% Fall response; 75% Spring response). Since individual responses to the questionnaire were not independent, we used as the unit-of-analysis responses from five institutions participating in the program. We aggregated survey responses within each institution, and analyzed changes (repeated-measures t-test design). We determined that the MCTP appears to be affecting participating teacher candidates' attitudes towards and beliefs about mathematics and science in the direction intended. In particular, the MCTP teacher candidates' attitudes and beliefs moved in the desired direction on all five subscales of the instrument. Moreover, the magnitude of change was statistically significant at the .01 level for the subscale measuring "Beliefs about the Nature of Mathematics and Science" and for the subscale measuring "Beliefs about Teaching Mathematics and Science". In addition, the magnitude of change for the subscale measuring "Attitudes towards Mathematics and Science" approached statistical significance. These findings make a highly significant contribution to the science and mathematics education research communities interested in charting the attitudinal and belief journeys of teacher candidates participating in a reform-based teacher preparation program.
Context Of The Study
Theoretical Assumption And Research Question
A fundamental assumption of the MCTP is that changes in pre-secondary level mathematics and science educational practices require reform within the undergraduate mathematics and science subject matter and education classes teacher candidates take throughout their teacher preparation programs (NSF, 1993). One of the ways reformed undergraduate classes can change teaching practices is by changing the attitudes and beliefs of teacher candidates. The MCTP Research Group is investigating whether enrollment in MCTP classes encourage teacher candidates to adopt more positive attitudes towards mathematics and science, and towards the teaching of these subjects. We also want to determine whether the MCTP fosters beliefs about the nature of mathematics and science, and about the best ways to teach mathematics and science, that are compatible with the program's goals: use of constructivist instructional strategies, emphasis on connections between mathematics and science, appropriate use of technology when teaching mathematics and science, and encouragement of students from diverse backgrounds to participate in challenging and meaningful learning.
Specifically, the research question investigated in this study is:
Do MCTP teacher candidates' attitudes toward and beliefs about mathematics and science change over time as they participate in the MCTP?
In the current analysis, we report how MCTP teacher candidates' attitudes toward and beliefs about mathematics and science evolved over a two-year period. In order to do so, we found it necessary to modify one of the five subscales described in McGinnis, et. al. (1997a). Specifically, one of the subscales, which we had labeled "X4: Attitudes towards learning to teach mathematics and science" contained two items which we dropped. These items asked teacher candidates to rate their agreement with the statement "I expect that the college courses I take will be helpful to me in teaching mathematics in elementary or middle school," and "I expect that the college courses I take will be helpful to me in teaching science in elementary or middle school". As MCTP students filled out the questionnaire during multiple occasions over a 2-year period, many of them completed a significant portion of their undergraduate classes, and their responses to these two items, instead of measuring the attitudes we had intended, began to reflect their expectation that they did not need to take many more college courses to complete their teacher preparation program. This precipitated a reliability issue. Therefore, we dropped the two items from the "X4" subscale. The remaining two items on the subscale focused rather narrowly on students' attitudes towards learning to use technologies to teach mathematics and science. Consequently, we have renamed the subscale to more accurately reflect its new emphasis.
In grades K-9, truly understanding mathematics requires special abilities that only some people possess.1
In grades K-9, truly understanding science requires special abilities that only some people possess.
The use of technologies in mathematics is an aid primarily for slow learners.
The use of technologies in science is an aid primarily for slow learners.
Getting the correct answer to a problem in the mathematics classroom is more important than investigating the problem in a mathematical manner.
Getting the correct answer to a problem in the science classroom is more important than investigating the problem in a scientific manner.
The primary reason for learning mathematics is to learn skills for doing science.
The primary reason for learning science is to provide real life examples for learning mathematics.
Mathematics consists of unrelated topics (e.g., algebra, arithmetic, calculus and geometry).
Science consists of unrelated topics like biology, chemistry, geology, and physics.
To understand mathematics, students must solve many problems following example provided.
To understand science, students must solve many problems following example provided.
Theories in science are rarely replaced by other theories.
Science is a constantly expanding field.
X2. Attitudes towards mathematics and science: Cronbach's a=.81
I am looking forward to taking more mathematics courses.
I am looking forward to taking more science courses.
I like mathematics.
I like science.
I enjoy learning how to use technologies in mathematics classrooms.
I enjoy learning how to use technologies in science classrooms.
X3. Beliefs about the teaching of mathematics and science: Cronbach's a=.69
Using technologies in mathematics lessons will improve students' understanding of mathematics.
Using technologies in science lessons will improve students' understanding of science. Calculators should always be available for students in science classes.
Students should be given regular opportunities to think about what they have learned in the mathematics classroom.
Students should be given regular opportunities to think about what they have learned in the science classroom.
Students should have opportunities to experience manipulating materials in the mathematics classroom before teachers introduce mathematics vocabulary.
Students should have opportunities to experience manipulating materials in the science classroom before teachers introduce science vocabulary.
Small group activity should be a regular part of the mathematics classroom.
Small group activity should be a regular part of the science classroom.
X4. Attitudes towards using technology to teach mathematics and science: Cronbach's a=.80
I want to learn how to use technologies to teach mathematics.
I want to learn how to use technologies to teach science.
X5. Attitudes towards teaching mathematics and science: Cronbach's a=.60
The idea of teaching mathematics scares me.
The idea of teaching science scares me.
I prefer to teach mathematics and science emphasizing connections between the two disciplines.
I feel prepared to teach mathematics and science emphasizing connections between the two disciplines.
1. Note: items in italics have been reversed, so that a response of "strongly agree" is scored as a "1" and a response of "strongly agree" is scored as a "5".
In this study, we are investigating how MCTP students' attitudes towards and beliefs about mathematics and science changed over time as they remained in the program. Two years of data are available to us. The simplest question to ask, and the one we address statistically, is "Were MCTP students' attitudes and beliefs different in the spring of 1997 from what they had been in the fall of 1995?"
Administrations of the Instrument
2) the "post test" given in all MCTP classes at the end of the fall semester, 1995;
3) the "pretest" given in all MCTP classes at the beginning of the spring semester, 1996;
4) the "post test" given in all MCTP classes at the end of the spring semester, 1996;
5) the mail-in survey, conducted in December, 1996;
6) the mail-in survey, conducted in May, 1997.
However, the timing of students' changed attitudes did raise one possible doubt about this conclusion. As can be seen in Figures 1 through 5, a large positive change occurred on four of the five subscales between when the questionnaire was administered in class at the end of the spring, 1996 semester, and when the questionnaire was first administered as a mail-in survey in December, 1996. On two of the subscales (X1: Beliefs about the nature of Mathematics and Science and X2: Attitudes towards Mathematics and Science) average scores on the questionnaire increased more between those two administrations than at any other time. Could the apparent improvement in students' attitudes and beliefs be attributable merely to the difference between how students respond to an in-class survey, and how they respond to a mail-in survey? Perhaps students respond more positively to a questionnaire if the fill it out at home than if they fill it out in a classroom setting. Or, perhaps those who didn't have attitudes and beliefs desired by MCTP were disproportionately among non-respondants to the mail-in questionnaire. Finally, it is possible that the in-class sample of "MCTP students" was contaminated by some non-MCTP students in the same class, who mistakenly identified themselves as being enrolled in the MCTP.
Educational Significance Of The Study
American Association for the Advancement of Science (1989). Science for all Americans. New York: Oxford University Press.
American Association for the Advancement of Science (1993). Benchmarks for Science Literacy. New York: Oxford University Press.
Ball, Deborah L. (1990a). Breaking with experience in learning to teach mathematics: The role of a preservice methods course. For the Learning of Mathematics, 10(2), 10-16.
Ball, Deborah L. (1990b). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 10-16.
Brickhouse, N. W. (1989). The teaching of philosophy of science in secondary classrooms: Case studies of teachers' personal theories. International Journal of Science Education, 11(4), 437-449.
Brickhouse, N. W. (1990). Teachers' beliefs about the nature of science and their relationship to classroom practice. Journal of Teacher Education, 41(3), 53-62.
Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87-103.
Cohen, J. (1977). Statistical power analysis for the behavioral sciences. New York: Academic Press.
Dillman, D. A. (1978). Mail and telephone surveys: The total design method. New York: John Wiley & Sons.
Driver (1989). The construction of scientific knowledge in school classrooms. In R. Miller (Ed.) Doing science: Images of science in science education. London: Falmer Press.
Huling-Austin, L. (1990). Teacher induction programs and internships. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 535-548). New York: Maxmillan.
Lederman, N.G. (1992). Students' and teachers' conceptions of the nature of science: a review of the research. Journal of Research in Science Teaching, 29(4), 331-359.
Likert, R. (1967). The method of constructing an attitude scale. In M. Fischbein (Ed.), Attitude theory and measurment (pp. 90-95). New York: John Wiley & Sons.
Maryland Collaborative for Teacher Preparation (1996). Remarks for December 9, 1996 NSF Review. Unpublished manuscript. University of Maryland, College Park.
McGinnis, J. R., Watanabe, T., Shama, G., & Graeber, A. (1997, March).
Development of an instrument to measure teacher candidates' attitudes and beliefs about a and science. A paper presented at the National Association for Research in Science Teaching, Oak Brook, Illinois. (ERIC Document Reproduction Service No.ED406201).
McGinnis, J. R., Shama, G., Graeber, A., & Watanabe, T. (1997, March). The assessment of elementary/middle level candidates' attitudes and beliefs about the nature of and the teaching of mathematics and science. A paper presented at the American Educational Research Association, Chicago, Illinois. (ERIC Document Reproduction Service No. ED 407235).
Moreiri, C. (1991). Teachers' attitudes towards mathematics and mathematics teaching: Perspectives across two countries. Presented at and published in Proceedings of PME-15: The Fifteenth Conference of the Psychology of Mathematics Education. Vol. II. Italy, Assisi., 17-24.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Research Council (1996). National Science Education Standards. Washington, D. C. : National Academy Press.
National Science Foundation (1993). Proceedings of the National Science Foundation Workshop on the role of faculty from scientific disciplines in the undergraduate education of future science and mathematics teachers. (NSF 93-108). Washington, D.C.: National Science Foundation.
Peterson, P. L., Fennema, E., Carpenter, T. P., and Loef, M. (1989). Teacher's pedagogical content beliefs in mathematics. Cognition and Instruction, 6, 1-40.
Schoenfeld, A. H., (1985). Mathematical problem solving. Orlando, Florida: Academic Press.
Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20(40), 338-355.
Silver, E. A. (1985). Research on teaching mathematical problem-solving: Some under represented themes and directions. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247-266). Hillsdale, New Jersey: Lawrence Erlbaum.
Stevens, J. (1996). Applied multi variate statistics for the social sciences, third edition. Mahwah, New Jersey: Lawrence Erlbaum.
Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on science teaching and learning (127-146). New York: MacMillan.
Tobin, K., Tippins, D. J., & Gallard, A. J. (1994). Research on instructional strategies for teaching science. In D. White (Ed.), Handbook of research on science teaching and learning
(45-93). New York: Macmillan.
University of Maryland System (1993). Special teachers for elementary and middle school science and mathematics: A proposal submitted to the National Science Foundation Teacher Preparation and Enhancement Program. Unpublished manuscript.
von Glasersfeld, E. (1987). Learning as a constructivist activity. In C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics. Hillsdale, New Jersey: Lawrence Erlbaum.
von Glasersfeld, E. (1989). Cognition, construction of knowledge, and teaching. Synthese, 80 (1), 121-140.
Watanabe, T., McGinnis, J. R., & Roth-McDuffie, A. (1997, March). University faculty "modeling" good instruction in mathematics and science courses for prospective middle grades teachers: Voices from the MCTP. A paper presented at the American Educational Research Association, Chicago, Illinois. (ERIC Document Reproduction Service No.ED406896).
Figure 1. Change over time in mean beliefs about the nature of mathematics and science.
Figure 2. Change over time in mean attitudes towards mathematics and science.
Figure 3. Change over time in mean beliefs about the teaching mathematics and science.
Figure 4. Change over time in mean attitudes toward using technology to teach mathematics and science.
Figure 5. Change over time in mean attitudes towards teaching mathematics and science.