Relationship between Students' Self-Assessment of Their Capabilities and Their Teachers' Judgments of Students' Capabilities in Mathematics Problem-Solving

Abstract

The study examined the judgments made by four seventh-grade mathematics teachers of their 107 students' competence in solving mathematics problems. Simultaneously, the 107 students made self-efficacy judgments about their capability in solving mathematics problems. The two sets of judgments were tested for predicting students' mathematics performance. Also, students' prior mathematics achievement was studied for its influence on both teachers' and students' judgments and students' mathematics performance. Teachers were asked to make judgments of each student for every mathematics problem solved. Results were consistent with prior research indicating that students' mathematics self-efficacy beliefs were highly predictive of their performance. Path analysis indicated that the mathematics teachers' judgments were also highly predictive of students' performance and self-efficacy. In turn, these variables predicted students' postperformance judgments. Combining students' self-efficacy judgments and teachers' judgments of students increased predictiveness for students' mathematics performance. Educational implications were also discussed.

Get full access to this article

View all access options for this article.

References

Bandura

(1986) Social foundations of thought and action: a social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.

Bandura

(1997) Self-efficacy: the exercise of control. New York: Freeman.

Ball

D. L.

(2002) What do we believe about teacher learning and how can we learn with and from our beliefs? Paper presented at the proceeding of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Athens, GA.

Bol

Hacker

D. J.

(2001) A comparison of the effects of practice tests and traditional review of performance and calibration. Journal of Experimental Education, 69, 133–151.

Bol

Hacker

D. J.

O'Shea

Allen

(2005) The influence of overt practice, achievement level, and explanatory style on calibration accuracy and performance. Journal of Experimental Education, 73, 269–290.

Carpenter

T. P.

Fennema

Peterson

P. L.

Chiang

Loef

(1989) Using knowledge of children's mathematics thinking in classroom teaching: an experimental study. American Educational Research Journal, 26, 499–531.

Chen

P. P.

(2003) Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students. Learning and Individual Differences, 14, 79–92.

Cohen

(1992) A power primer. Psychological Bulletin, 112, 155–159.

Ewers

C. A.

Wood

N. L.

(1993) Sex and ability differences in children's math self-efficacy and prediction accuracy. Learning and Individual Differences, 5, 259–267.

10.

Fennema

Carpenter

T. P.

Franke

M. L.

Levi

Jacobs

V. R.

Empson

(1996) A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.

11.

Fennema

Franke

M. L.

(1992) Teachers' knowledge and its impact. In Grouws

(Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan. Pp. 147–164.

12.

Giwin

K. B.

Stipek

D. L.

Salmon

J. M.

MacGyvers

V. L.

(2001) In the eyes of the beholder: students' and teachers' judgments of students' motivation. Teaching and Teacher Education, 17, 321–331.

13.

Hacker

D. J.

Bol

Horgan

D. D.

Rakow

E. A.

(2000) Test prediction and performance in a classroom context. Journal of Educational Psychology, 92, 160–170.

14.

IEA Third International Mathematics and Science Study. (1995) Mathematics items: released set for population 2 (seventh and eighth grades). Chestnut Hill, MA: Boston College.

15.

Impara

J. C.

Plake

B. S.

(Eds.) (1998) Mental measurements yearbook. (13th ed.) Lincoln, NE: Buros Institute of Mental Measurements.

16.

Jöreskog

Sörbom

(2002) LISREL 8.5: User's reference guide. Chicago, IL: Scientific Software International.

17.

Linn

R. L.

Miller

M. D.

(2005) Measurement and assessment in teaching. (9th ed.) Upper Saddle River, NJ: Prentice-Hall.

18.

Pajares

Graham

(1999) Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124–139.

19.

Pajares

Kranzler

(1995) Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20, 426–443.

20.

Pajares

Miller

M. D.

(1994) Role of self-efficacy and self-concept beliefs in mathematical problem solving: a path analysis. Journal of Educational Psychology, 86, 193–203.

21.

Pajares

Miller

M. D.

(1995) Mathematics self-efficacy and mathematics performances: the need for specificity of assessment. Journal of Counseling Psychology, 42, 190–198.

22.

Pajares

Miller

M. D.

(1997) Mathematics self-efficacy and mathematical problem solving: implications of using different forms of assessment. The Journal of Experimental Education, 65, 213–228.

23.

Peterson

P. L.

Carpenter

Fennema

(1989) Teachers' knowledge of students' knowledge in mathematics problem solving: correlational and case analyses. Journal of Educational Psychology, 81, 558–569.

24.

Schunk

D. H.

(1981) Modeling and attributional effects on children's achievement: a self-efficacy analysis. Journal of Educational Psychology, 75, 848–856.

25.

Schunk

D. H.

(1991) Self-efficacy and academic motivation. Educational Psychologist, 26, 207–231.

26.

Schunk

D. H.

(1998) Teaching elementary students to self-regulate practice of mathematical skills with modeling. In Schunk

Zimmerman

(Eds.), Self-regulated learning from teaching to self-reflective practice. New York: Guilford. Pp. 137–159.

27.

Stage

F. K.

Carter

H. C.

Nora

(2004) Path analysis: an introduction and analysis of a decade of research. Journal of Educational Research, 98, 5–12.

28.

Tabachnik

B. G.

Fidell

L. S.

(2001) Using multivariate statistics. (4th ed.) Needham Heights, MA: Allyn & Bacon.

29.

Zimmerman

B. J.

(1995) Self-efficacy and educational development. In Bandura

(Ed.), Self-efficacy in changing societies. New York: Cambridge Univer. Press. Pp. 202–231.

30.

Zimmerman

B. J.

(2000) Self-efficacy: an essential motive to learn. Contemporary Educational Psychology, 25, 82–91.