Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
Ana M. Martín-Caraballo & Ángel F. Tenorio-Villalón
pp. 53-65 | Article Number: mathedu.2015.004
This paper exemplifies the potential of GeoGebra as didactic resource for teaching Mathematics not only in High School but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative) methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position) method and the tangent (or Newton-Raphson) method, this last as example of fixed-point methods.
Keywords: college mathematics, mathematics activities, numerical algebra, mathematics instruction, computer-assisted instruction
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The effect of Concept Cartoons to Academic Achievement in Instruction on the Topics of Divisibility
Abdullah Kaplan & Mesut Öztürk
pp. 67-76 | Article Number: mathedu.2015.005
The purpose of this study was compared to the effect of academic achievement of concept cartoons and activity based instruction in instruction on the topics of divisibility rules and prime number. The matching- only design, which is quasi experimental design, is used in this study. It is applied sixth grade (N=42) students at a middle school in Gümüşhane in autumn term in academic year 2012- 2013. Different two groups participate for this study. One of the groups is selected control group, which is used activity based teaching, and another group is experimental group, which is used instruction by concept cartoon. SPSS 16.0 packet program is used in the analysis of the data in this study. The first the test of the normality, within pretest and posttest, is applied and was founded that the data is suitable the normality. Then t- test is applied between pretest data for reveal whether different significant or not. ANCOVA is applied covariate pretest results to post test data. The study reveal that there was a significant difference in academic achievement between those students taught with the two methods in favor of concept cartoon which means those students taught by concept cartoon performed better than those taught with activity based instruction. The finding also shows that concept cartoon method is an effective method of teaching topics of divisibility rules and prime numbers.
Keywords: concept cartoons, divisibility rules, prime number, activity based instruction, mathematics education
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How Prospective Teachers Conceptualized Mathematics: Implications for Teaching
pp. 77-95 | Article Number: mathedu.2015.006
What is mathematics? The difficulty of having a precise, universal definition of mathematics has led prospective teachers to define the term in ways that make sense to them. This paper is part of a larger research project conducted in 2000 in an Ontarian university, Canada. The objectives were to identify and discuss conceptualizations of mathematics that prospective teachers brought to their preparation program and to explore the implications of such conceptualizations in terms of teaching and learning. It was believed that both the identification tools and understandings of prospective teachers’ conceptualizations of mathematics were significant for designing an effective pedagogy in accordance with mathematics reform-based perspectives. The research sample consisted of ten prospective teachers enrolled in a one-year bachelor of education program at an Ontarian university. The research used mathematics autobiographies of the respondents and semi-structured interviews of them as sources of data. Guided by the theory of personal construct for analysis of the data, the results showed that the respondents conceptualized mathematics in terms of metaphor, metonymy and combination of the two. The conclusion explores implications of such conceptualizations for mathematics teaching, learning and assessment.
Keywords: conceptions of mathematics, language, metaphoric, metonymic, pre-service teachers, teachers’ math autobiographies
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Gender Differences in Achievement in an Inquiry-Based Learning Precalculus Course
Thomas E. Cooper, Brad Bailey & Karen S. Briggs
pp. 97-110 | Article Number: mathedu.2015.007
The authors conducted a two-semester quasi-experimental study in which each author taught a traditional lecture-based section of precalculus and a section using an inquiry-based approach called a Modified Moore Method in which the students worked through and presented the course material. A common final exam was used to compare student achievement. The results were compared for the overall population and by each instructor. Gender proved to be an important variable with the females performing significantly better in the Modified Moore Method sections than their counterparts in the traditional sections while there were no significant differences for the males.
Keywords: precalculus, inquiry-based learning, gender differences
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A Written Instrument for Assessing Students’ Units Coordination Structures
Anderson Norton, Steven Boyce, Nathan Phillips, Tessa Anwyll, Catherine Ulrich & Jesse L. M. Wilkins
pp. 111-136 | Article Number: mathedu.2015.008
Units coordination refers to students’ abilities to create units and maintain their relationships with other units that they contain or constitute. In recent research, units coordination has arisen as a key construct that mediates opportunities for student learning across several domains of mathematics, including fractions knowledge and algebraic reasoning. To date, assessments of students’ stages of units coordinating ability have relied upon clinical interviews or teaching experiments whose time-intensive nature precludes opportunities for conducting large-scale studies. We introduce a written instrument that teachers and researchers can use with large populations of students. We report on the reliability and validity of assessments based on the instrument.
Keywords: assessment; fractions; multiplicative reasoning; units coordination; written instrument
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