The Pre-service Elementary Mathematics Teachers’ Views about Proof

Author(s):

Esra Demiray(presenting / submitting)Mine Işıksal

Conference:

ECER 2012

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 11, Mathematical Concepts and Teacher Education 2

Parallel Paper Session

Time:

2012-09-20

17:15-18:45

Room:

ESI 3 - Aula 2

Chair:

Contribution

Reasoning and proof is one of the process standards of National Council of Teachers of Mathematics [NCTM] (2000) and they are seen as central components of mathematics by many researchers. Stylianides (2007) defined proof as “a mathematical argument, a connected sequence of assertions for or against a mathematical claim” (p. 291). As seen from the definition, mathematical argumentation is a fundamental part of mathematics and it has a comprehensive structure. Similarly, Saeed (1996) defined mathematical proof as “a logical sequence of statements leading from a hypothesis to a conclusion using axioms, definitions, previously proved statements and rule of inference” (p. 12). According to Ross (1998), the essence of mathematics lies in proofs. Similarly, Schoenfeld (1994) implied that proof should be in mathematics curriculum at all levels. In other words, students from pre-kindergarten through grade 12 should study mathematical proof.

In the literature, there were studies related to pre-service mathematics teachers’ difficulties regarding reasoning and proof (Baştürk, 2010, Güler, Kar, Öçal and Çiltaş, 2011; Moore, 1994; Sarı, 2008). For example; the study of Riley (2003) showed that pre-service mathematics teachers have weak understanding of truth of a conditional statement and nearly half of the participants couldn’t write a direct mathematical proof. Moralı, Uğurel, Türnüklü and Yeşildere (2006) investigated the views of pre-service mathematics teachers about proof with 182 freshman and 155 senior pre-service mathematics teachers. This study revealed that most of the pre-service mathematics teachers don’t have specific ideas related to proof. As Martin and Harel (1989) stated, teachers’ views and knowledge about proof have an effect on their teaching and students’ conception of proof. Since pre-service elementary mathematics teachers are the future teachers, their views about proof have a critical role in the construction of students’ conception of proof. Thus, in this study, pre-service elementary mathematics teachers’ views about proof were investigated. In other words, with this aim, research questions of the study could be stated as follows.

Is there a significant difference between male and female pre-service elementary mathematics teachers’ views about proof?

Is there a significant difference among freshman, sophomore, junior and senior pre-service elementary mathematics teachers’ views about proof?

Method

To investigate the pre-service elementary mathematics teachers’ views about proof, three state universities in Turkey were selected by using convenience sampling. Data were collected from 659 pre-service elementary mathematics teachers where 123 of them were freshman, 228 of them were sophomore, 143 of them were junior and 165 of them were senior. The number of the female students is 475 and the number of the male students is 184. The proof scale developed by Moralı, Uğurel, Türnüklü and Yeşildere (2006) was used in order to collect data. The proof scale is a five-point Likert-type scale (5=strongly agree, 4=agree, 3=undecided, 2=disagree and 1=strongly disagree) including 20 items. The reliability of the instrument was checked by Cronbach’s alpha which is calculated as 0,837. The instrument was administered to the students at the end of the 2011-2012 fall semester. Data were analyzed through SPSS program. Descriptive statistics and two-way ANOVA was conducted in order to answer research questions.

Expected Outcomes

The assumptions of two-way ANOVA which are level of measurement, independence of observation, normality and homogeneity of variance (Pallant, 2007) were checked. The results revealed that there is not a significant interaction effect between grade level and gender (p=,210) and there is no statistically significant main effect for gender (p=,234). However, there is a statistically significant main effect for grade level (p=,001). In other words, males and females don’t differ in terms of their views about proof but there is a difference in scores of freshman, sophomore, junior and senior pre-service teachers. Post-hoc tests results revealed that the mean score of freshman (M=66,24, SD=10,23) are significantly lower than sophomore (M=69,92, SD=8,89), junior (M=70,06, SD=9,28) and senior pre-service teachers (M=71,28, SD=10,21) respectively. During the implementation of the scale, freshman students took a few courses related to proof. Thus, this could be the reason why freshman students took lower grades compared to the other grade levels. Senior pre-service teachers’ higher scores could also be dedicated to their enrollment and experience in teacher education program. The findings of this study may give valuable interpretations about pre-service elementary mathematics teachers’ views about proof.

References

Baştürk, S. (2010). First-year secondary school mathematics students' conceptions mathematical proofs and proving. Educational Studies, 36(3),283-298. Güler, G., Kar, T., Öçal, M., Çiltaş, A. (2011). Prospective Mathematics Teachers’ Difficulties in Proof. Procedia Social and Behavioral Sciences, 15,336-340. Martin, W. G. and G. Harel (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1)41-51. Moore, R. C. (1994). Making the Transition to Formal Proof. Educational Studies in Mathematics, 27,249-266. Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere, S. (2006). The views of mathematics teachers on proving. Kastamonu Education Journal, 14(1),147-160. National Council of Teachers of Mathematics. (2000). Principles and standarts for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Pallant, J. (2007). SPSS survival manual: A step by step guide to data analysis using SPSS for windows. New York: McGraw-Hill/Open University Press. Riley, K. J. (2003). An investigation of prospective secondary mathematics teachers' conceptions of proof and refutations. (Doctoral dissertation, Montana State University, 2003): Dissertation Abstracts International, UMI # 072699. Ross, K. (1998). Doing and proving: The place of algorithms and proof in school mathematics. American Mathematical Monthly, 3,252-255. Saeed, R. M. (1996). An exploratory study of college students' understanding of mathematical proof and the relationship of this understanding to their attitudes toward mathematics, Ohio University Sarı, M. (2008). Undergraduate students’ difficulties with mathematical proof and proof teaching. Retrieved from http://yess4.ktu.edu.tr/YermePappers/MeltemSari.pdf Schoenfeld, A. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13,55-80. Stylianides, A. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321.

Author Information

Esra Demiray (presenting / submitting)

Middle East Technical University

Elementary Mathematics Education

Zonguldak

Mine Işıksal

Middle East Technical University, Turkey

Search the ECER Programme

Search for keywords and phrases in "Text Search"
Restrict in which part of the abstracts to search in "Where to search"
Search for authors and in the respective field.
For planning your conference attendance you may want to use the conference app, which will be issued some weeks before the conference
If you are a session chair, best look up your chairing duties in the conference system (Conftool) or the app.