The Effect Of Teaching Experience On The Geometric Reasoning Stages Of In-Service Elementary School Teachers

Author(s):

ERDOĞAN HALAT

Conference:

ECER 2008

Network:

27. Didactics - Learning and Teaching

Format:

Paper

Session Information

27 SES 10C, Learning and Teaching in the MST

Paper Session

Time:

2008-09-12

14:45-16:15

Room:

B3 333

Chair:

Bernard Schneuwly

Contribution

Over the past few decades, research has indicated that many students encounter difficulties and show poor performance in geometry classrooms (e.g., Fuys, Geddes, & Tischler, 1988; Gutierrez, Jaime, & Fortuny, 1991; Halat, 2006/2007). For instance, Usiskin (1982) claims that many students fail to grasp key concepts in geometry, and leave the geometry classes without learning basic terminology. Moreover, research shows a decline in students’ motivation toward mathematics courses (c.f., Gottfried, Fleming & Gottfried, 2001). According to Billstein & Williamson (2003), there was a decline in students’ motivation toward mathematics. In fact, there is a linear correlation between student achievement and motivation in mathematics (Ryan & Pintrich, 1997; Dev, 1998). There are many factors, such as perception of cognitive competence, perception of parental support, teaching experience, environment, task difficulty, peer-support, gender and curriculum appearing to play prominent roles on student achievement and motivation in the mathematics classroom (e.g., Driscoll, 1994; Reeve, 1996; Wentzel, 1997; Middleton, 1999; Alderman, 1999; Chappell, 2003; Young-Loveridge, 2005). It is clear that all of these variables have effects on student learning but teaching experience has the greatest effects among others on students’ motivation and mathematics learning because of the fact that it shapes teachers’ teaching approach and enhances teachers’ content knowledge. This affects students’ success and attitudes toward mathematics. Besides, according to Stipek (1998), both teachers and students spend most of their times at schools. In other words, pedagogical and content knowledge of teachers play vital roles on students’ accomplishments in the classrooms. Since the mid 1980s there has been a growing interest in the area of teaching and learning geometry (e.g., Crowley, 1987; Gutierrez, Jaime, & Fortuny, 1991; Clements & Battista, 1990; Mason, 1997; Lappan, Fey, Fitzgerald, Friel, & Phillips, 1996). The National Council of Teacher of Mathematics (NCTM) (2000) recommends that new ideas, strategies, and research findings be utilized in teaching in order to help students overcome their difficulties in learning mathematics. Knowing theoretical principles provides an opportunity to devise practices that have a greater possibility of succeeding (e.g., Swafford, Jones, & Thornton, 1997). The van Hiele model of thinking that was structured and developed by Pierre van Hiele and Dina van Hiele-Geldof between 1957 and 1986 focuses on geometry. This current study examined the in-service elementary school teachers’ geometric reasoning stages and the effects of teaching experience on the geometric thinking levels of the in-service elementary school teachers. The following question guided the study: Is teaching experience as a variable playing prominent role on the in-service elementary school teachers’ reasoning stages in geometry?

Method

Participants There were a total of 104 in-service elementary school teachers involved in this study that included 61 (59%) male and 43 (41%) female. The in-service elementary school teachers had different years of teaching experience from 1 to 21 years at public schools. The participants were divided into three groups shown in table-1 below based on years of teaching experience. This study took place in a city located in the west part of Anatolia in Turkey. The data was collected during spring -2006. The in-service elementary school teachers took the VHGT at their work places during the school day. Table 1 Frequency Table for Years of Teaching Experience Groups N A-Elementary School Teachers: 1-4 years B-Elementary School Teachers: 5-10 years C-Elementary School Teachers: 11-up years Total 37 34 33 104 Data Sources The researchers gave the in-service elementary school teachers a geometry test called Van Hiele Geometry Test (VHGT) that consists of 25 multiple-choice geometry questions. The VHGT was administered to the participants by the researchers. The VHGT was taken from the study of Usiskin (1982). The VHGT is designed to measure one’s van Hiele level in geometry. Test Scoring Guide In this study, the I-V scheme was used for the levels. This scheme allows the researchers to use level-0 (pre-recognition) for students who do not function at what the van Hieles named the ground or basic level (Clements & Battista, 1990). It is also consistent with Pierre van Hiele’s numbering of the levels. For this report, all references and all results from research studies using the 0-IV scale have been changed to the I-V scheme. All participants’ answer sheets from VHGT were read and scored by the investigator. All participants got a score referring to a van Hiele level from the VHGT guided by Usiskin’s grading system. Analysis of Data The data were responses from the in-service elementary school teachers’ answer sheets. In the process of the assessment of participants’ van Hiele levels, the criterion for success at any given level was four out of five correct responses. At the beginning of the analysis, the investigators constructed a frequency table to acquire information about the participants’ van Hiele level distributions. And then, the One-way ANOVA with α = .05 was used to compare the geometric thinking levels of the three groups.

Expected Outcomes

The study showed that although the participants showed all van Hiele levels except level-V in different percentiles, the mean scores of the in-service elementary school teachers’ geometric reasoning stages in all three groups A, B, and C were between levels-I (Visualization) and -II (Analysis). The study revealed that after four years of teaching, it can be seen a decrease in the elementary school teachers’ geometric reasoning stages. Similarly, after ten years of teaching, the decrease was getting larger in the elementary school teachers’ van Hiele levels in geometry. In other words, the study implies that the more years the in-service elementary school teachers teach mathematics or geometry, the lower van Hiele levels they attain. There might be several points that can explain this result. On one hand, the more you teach, the more you are expected to increase your pedagogical and content knowledge in mathematics or in other areas. On the other hand, you might probably forget some of the topics or formulas in any area if you can not update your pedagogical and content knowledge. Therefore, the in-service elementary school teachers who taught 11 or more years may forget some of the formulas about geometry or may haven’t revised their content knowledge. As a conclusion, according to the finding of this study, it is apparent that having years of teaching experience was an important factor on the in-service elementary school teachers’ geometric thinking levels. But, it was not linear with the reasoning stages.

References

REFERENCES Alderman, K. M. (1999). Motivation for achievement. Possibilities for teaching and learning. Mahwah, NJ: Lawrence Erlbaum Associates. Billstein, R., & Williamson, J. (2003). Middle grades MATH Thematics: The STEM project. In S. L. Senk & D. R. Thompson (Eds.), Standards-based school mathematics curricula. What are they? What do students learn? (pp. 251-284). Lawrence Erlbaum Associates: NJ. Chappell, M.F. (2003). Keeping mathematics front and center: Reaction to middle-grades curriculum projects research. In S. L. Senk & D. R. Thompson (Eds.), Standards-based school mathematics curricula. What are they? What do students learn? (pp. 285-298). Lawrence Erlbaum Associates: NJ. Clements, D., & Battista, M. (1990). The effects of logo on children’s conceptualizations of angle and polygons. Journal for Research in Mathematics Education, 21(5), 356-371. Crowley, M. (1987). The van Hiele model of development of geometric thought. In M. M. Lindquist, (Ed.), Learning and teaching geometry, K-12 (pp.1-16). Reston, VA: NCTM. Driscoll, M.P. (1994). Psychology of learning for instruction. Boston, MA: Allyn & Bacon Publishers. Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education: Monograph Number 3. Gottfried, A. E., Fleming, J. S., & Gottfried, A. W. (2001). Continuity of academic intrinsic motivation from childhood through late adolescence: A longitudinal study. Journal of Educational Psychology, 93(1), 3-13. Gutierrez, A., Jaime, A., & Fortuny, J. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22, 237-251. Halat, E. (2006). Sex-related differences in the acquisition of the van Hiele levels and motivation in learning geometry. Asia Pacific Education Review, vol 7(2), 173-183. Halat, E. (2007). Reform-based curriculum & acquisition of the levels. Eurasia Journal of Mathematics, Science and Technology Education.vol.3(1):41-49. Lappan, G, Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (1996). Shapes and design. Two-dimensional geometry. Palo Alto, CA: Dale Seymour Publications. Mason, M. M. (1997). The van Hiele model of geometric understanding and mathematically talented students. Journal for the Education of the Gifted, 21(1), 39-53. Middleton, J. A. (1999). Curricular influences on the motivational beliefs and practice of two middle school mathematics teachers: A follow-up study. Journal for Research in Mathematics Education, 30(3), 349-358. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Reeve, J. (1996). Motivating others: Nurturing inner motivational resources. Needham Heights, MA: Allyn & Bacon. Stipek, D. (1998). Motivation to learn from theory to practice. (3rded.). Needham Heights, MA: Allyn & Bacon A Viacom Company. Swafford, O. J., Jones, G. A., & Thornton, C. A. (1997). Increased knowledge in geometry and instructional practice. Journal for Research in Mathematics Education, 28(4), 467-483. Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. (Final report of the Cognitive Development and Achievement in Secondary School Geometry Project.) Chicago: University of Chicago. (ERIC Document Reproduction Service No. ED220288). Young-Loveridge, J. (2005). The impact of mathematics education reform in New Zealand: Taking children’s views into account. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, A. Roche (Eds), Proceedings of MERGA28. (Vol.1, pp. 18-33). Sydney, Australia. Wentzel, K. R. (1997). Students motivation in middle school: The role of perceived pedagogical caring. Journal of Educational Psychology, 89(3), 411-419.

Author Information

ERDOĞAN HALAT

Kocatepe University

College of Education

AFYONKARAHİSAR

212

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