| Proposal Type: | Individual Thematic Poster |
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| Domain: | Teaching and Teacher Education |
| SIG: | Teaching and Teacher Education |
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| Title | Activities, Apreciation, and Abstraction: Secondary School Mathematics Teachers' Beliefs about Teaching and Learning Geometry | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Abstract | This poster focuses on my journey through my doctoral research: investigating high school mathematics teachers' beliefs about teaching and learning geometry. Data was collected through 520 questionnaires distributed to teachers from four countries. Factor analysis revealed a three component model similar to the three dimensions of Ernest’s model (1991). Three philosophies of mathematics occur in mathematics teaching (Ernest 1989). They are instrumentalist, Platonist, and problem solving view of mathematics. The factors extracted in this analysis have correspondingly been named: a disposition towards appreciation of geometry, a disposition towards abstraction and a disposition towards activities. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Summary | Introduction The following research questions emerged from a pilot questionnaire distributed to high school mathematics teachers during the 2003-2004 school year. · What are high school mathematics teachers’ beliefs about the role of geometry in the high school curriculum? · What are high school mathematics teachers’ beliefs about the role manipulatives play in the geometry classroom? · What are high school mathematics teachers’ beliefs about the use of dynamic geometry software in high school? What are high school mathematics teachers’ beliefs about the role of proof in high school geometry? Theoretical framework: Studying teachers’ beliefs is important for understanding mathematics teachers’ behaviors in the classroom. (Cooney, Shealy, & Arvold,1998;Ernest,1989;Raymond, 1997; Thompson,1992). I have adopted the characterization of knowledge and beliefs suggested by Furinghetti and Pehkonen (2002) that consider two types of knowledge: objective and subjective. Objective knowledge has to be true whether proved by experiment and/or socially accepted; subjective knowledge is knowledge constructed by an individual. Therefore belief is taken as subjective knowledge. Methodology: I used a questionnaire that included 48 Likert type statements and three open ended reponses.
Responses to the Likert statements were numerically coded from 1-6 with 1 being strongly disagree and 6 being strongly agree. SPSS was used to look at the frequencies of the descriptive data and crosstabs between variables. Chi-squared analysis was performed on the crosstabs. This poster focuses on the results when factor analysis was performed on the data.
Findings I have used factor analysis to enhance my understanding of the part of my data set that is composed of 48 Likert type statements. I chose was principal component analysis with orthogonal (varimax) rotation The first three components extracted from every rotation that I tried were what I call "The Triple A": Activities Appreciation Abstractions The only changes were the order in which they occurred and that more variables loaded on each of the components as I decreased their number. For instance, for the default extraction of components with eigenvalues having absolute value greater than 1, variables about manipulatives loaded on the first component and variables about dynamic geometry loaded on a later variable. As the number of components decreased these variables loaded on the same component. We can interpret the components in terms of teachers’ dispositions: A disposition towards doing activities A disposition towards appreciation of geometry A disposition towards abstraction I saved the component scores as variables for each respondent (N=386 using listwise deletion). These scores allow me to identify each respondent’s disposition. If a respondent scores high on all 3 components we can probably conclude that (s)he is involved with doing geometric activities, discussing applications, and doing proofs. If a respondent scores high on all 3 components we can probably conclude that (s)he is involved with doing geometric activities, discussing applications, and doing proofs. Table 1 lists all eight groups in which a respondent could belong to depending on combinations of component scores in terms of whether they are positive or negative.
Table 1: Component score profiles I wanted to explore whether there was a relationship between groups and gender, membership in professional organizations, attendance at professional meetings, undergraduate major (first degree), having a graduate degree, years of teaching experience, type of school, taking geometry courses, and taking methods courses. My results are found in Table 2. Gender was found to be independent with respect to the eight groups. Other significant relationships were between the groups and whether teachers had a graduate degree, took geometry courses, methods courses and whether geometry was taught as a full year course. Significantly more teachers who have graduate degrees are in group one and significantly less are in group eight. Similarly with teachers who have taken geometry and methods courses and who have taught geometry for a full year.
Table 2: The relationship between the eight groups and other covariates There were no significant relationships between the groups and attendance at professional meetings, undergraduate major, experience, type of school, and when geometry is taught as a topic in an integrated curriculum. |
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| Keywords | Beliefs Mathematics education |
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| Authors | ||||||
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| Name | Surname | Institution | Country | EARLI Number | Presenting | |
| Brenda | Strassfeld | NYU/University of Plymouth | United States | bs49@nyu.edu | * | |
