Teaching and Assessing Higher Order Thinking in the Mathematics Classroom with Clickers
Jim Rubin & Manikya Rajakaruna
pp. 37-51 |
Many schools have invested in clicker technology, due to the capacity of the software to track formative assessment and the increased motivation that students show for incorporating technology in the classroom. As with any adoption of new software that demands amending pedagogy and learning applications, the extent to which clickers are living up to expectations has not yet become apparent. The present study sought to explore the potential of using clickers to teach the reasoning processes behind solving higher order thinking word problems in a mathematics class. A pilot study was conducted with a college algebra class to refine questions used in the coursework and field test a survey to measure student attitudes towards the teaching methodology. The main study took place over the fall semester with a college algebra class (N=21). Results showed increased student motivation and acumen for using the technology and higher test scores, but frustration on the part of both the teacher and students when trying to apply the pedagogy for the purpose of learning higher order thinking reasoning processes. The potential for the technology to offer an alternative for formative assessment was a strong positive element.
Keywords: clickers, college algebra, higher order thinking, mathematics
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The Affective Domain in Mathematics Learning
Nuria Gil Ignacio, Lorenzo J. Blanco Nieto and Eloísa Guerrero Barona
pp. 16-32 |
The present work set out to analyze the beliefs, attitudes, and emotional reactions that students experience in the process of learning mathematics. The aim was to be able to demonstrate that the existence of positive attributes, beliefs, and attitudes about themselves as learners are a source of motivation and expectations of success in dealing with this subject. We used a sample of 346 students of the second cycle of Obligatory Secondary Education (ESO) of high schools in Badajoz. The participants responded to a questionnaire on beliefs and attitudes about mathematics. It was found that neither the students' gender nor their year of studies influenced their beliefs about their self-concept of mathematics.
Keywords: Beliefs, Attitudes, Emotions, Mathematics Self-Concept, Secondary Education And Mathematics Learning.
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The Effects of GeoGebra On Third Grade Primary Students’ Academic Achievement in Fractions
Mehmet Bulut, Hanife Ünlütürk Akçakın, Gürcan Kaya & Veysel Akçakın
pp. 347-255 |
The aim of this study is to examine the effects of GeoGebra on third grade primary students’ academic achievement in fractions concept. This study was conducted with 40 students in two intact classes in Ankara. One of the classes was randomly selected as an experimental group and other for control group. There were 19 students in the experimental group, while 21 students in control group. The matching- only posttest- only control group quasi-experimental design was employed. As a pretest, student’s first term mathematics scores were used. Data were collected with post-test about fractions. The post-test consisted of 22 short ended questions. Thanks to the scores weren’t violated the normality, independent t test was employed. The findings of the study showed that there were significant differences in favor of the experimental group. According to findings of this study, it was recommended that GeoGebra supporting teaching methods can be used on teaching fractions in third grade.
Keywords: third grade, fractions, geogebra, achievement
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Selection of Appropriate Statistical Methods for Research Results Processing
Rezeda M. Khusainova, Zoia V. Shilova & Oxana V. Curteva
pp. 303-315 |
The purpose of the article is to provide an algorithm that allows choosing a valid method of statistical data processing and development of a model for acquiring knowledge about statistical methods and mastering skills of competent knowledge application in various research activities. Modelling method is a leading approach to the study of this problem. It allows us to consider this issue as a targeted and organized process of application of the author’s methodology for the selection of appropriate statistical method for the efficient processing of the research results. The article showcases an algorithm that allows to choose an appropriate method of statistical data processing: general algorithm of statistical methods application in scientific research, statistical problems systematization based on which there have been outlined conditions for specific research methods application. To make a final decision concerning the statistical method at the stage of data received and statistical tasks of the research defined, it is proposed to use an author’s algorithm that allows to competently select the method of processing the research results.
Keywords: statistical processing of the research results, statistical methods, research, statistical criteria, algorithm
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Teachers’ beliefs about mathematical knowledge for teaching definitions
Reidar Mosvold & Janne Fauskanger
pp. 43-61 |
Previous research indicates the importance of teachers’ knowledge of mathematical definitions—as well as their beliefs. Much remains unknown, however, about the specific knowledge required doing the mathematical task of teaching involving definitions and the related teacher beliefs. In this article, we analyze focus-group interviews that were conducted in a Norwegian context to examine the adaptability of the U.S. developed measures of mathematical knowledge for teaching. Qualitative content analysis was applied in order to learn more about the teachers’ beliefs about mathematical knowledge for teaching definitions. The results indicate that teachers believe knowledge of mathematical definitions is an important aspect of mathematical knowledge for teaching, but they do not regard it as important to actually know the mathematical definitions themselves.
Keywords: mathematical knowledge for teaching, teacher beliefs, mathematical definitions
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Teachers’ Beliefs about the Discipline of Mathematics and the Use of Technology in the Classroom
Morten Misfeldt, Uffe Thomas Jankvist & Mario Sánchez Aguilar
pp. 395-419 |
In the article, three Danish secondary level mathematics teachers’ beliefs about the use of technological tools in the teaching of mathematics and their beliefs about mathematics as a scientific discipline are identified and classified - and the process also aspects of their beliefs about the teaching and learning of mathematics. The potential relationships between these sets of beliefs are also explored. Results show that the teachers not only manifest different beliefs about the use of technology and mathematics as a discipline, but that one set of beliefs can influence the other set of beliefs. The article concludes with a discussion of the research findings and their validity as well as their implications for both practice and research in mathematics education.
Keywords: mathematics teachers’ beliefs, beliefs about mathematics as a discipline, beliefs about use of technology, lever potential, blackboxing
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Identity Development during Undergraduate Research in Mathematics Education
Randall E. Groth & Jenny McFadden
pp. 357-375 |
We describe a model that leverages natural connections between undergraduate research and mathematics teacher preparation. The model integrates teaching and research by prompting undergraduates to continuously reflect on classroom data from lessons they have taught. It is designed to help undergraduates build identities as teachers who base decisions on empirical data, and also to build identities as future graduate students in mathematics education. The identities that undergraduates participating in the first year of the project developed pertaining to these roles are described. Undergraduates generally identified with a problem-based approach to teaching and saw themselves as future graduate students in various fields, including mathematics education. Suggestions for improving and adapting the model for use in other settings are also provided.
Keywords: classroom research, formative assessment, identity, reflection, undergraduate research
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Pre-Service Math Teachers’ Opinions about Dynamic Geometry Softwares and Their Expectations from Them
Hakan Şandır & Serdar Aztekin
pp. 421-431 |
This study was designed to determine the pre-service teachers’ opinions about three dynamic geometry software (Cabri II Plus, the Geometer's Sketchpad, GeoGebra) and influences of gender and academic achievement to these opinions. The researchers also investigated the most important properties that the pre-service teachers expect from a dynamic geometry software. The study was conducted in the 2011-2012 academic year with 64 prospective teachers who had taken a course about math education software during a year in the university. Results revealed that pre-service teachers found Geometers’ Sketchpad more effective than others in the positive development of the students' attitudes and in teaching high level geometry. However, they think that GeoGebra is easier than Cabri II Plus to use and has wide area of use. According to the pre-service teachers; using a native language, screen clarity, a detailed user manual and the ease of use are the most important properties of a dynamic geometry software.
Keywords: Dynamic Geometry Software, Pre-service Teachers’ Expectations, Cabri II Plus, the Geometer's Sketchpad, GeoGebra
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Patterns of Metacognitive Behavior During Mathematics Problem-Solving in a Dynamic Geometry Environment
pp. 20-40 |
This paper describes the problem solving behavior of two preservice teachers as they worked individually on three nonroutine geometry problems. A dynamic tool software, namely the Geometer’s Sketchpad, was used as a tool to facilitate inquiry in order to uncover and investigate the patterns of metacognitive processes. Schoenfeld’s (1981) model of episodes and executive decisions in mathematics problem solving was used to identify patterns of metacognitive processes in a dynamic geometry environment. During the reading, understanding, and analysis episodes, the participants engaged in monitoring behaviors such as sense making, drawing a diagram, and allocating potential resources and approaches that helped make productive decisions. During the exploring, planning, implementation, and verification episodes, the participants made decisions to access and consider knowledge and strategies, make and test conjectures, monitor the progress, and assess the productivity of activities and strategies and the correctness of an answer. Cognitive problem-solving actions not accompanied by appropriate metacognitive monitoring actions appeared to lead to unproductive efforts. Redirection and reorganizing of thinking in productive directions occurred when metacognitive actions guided the thinking and when affective behaviors were controlled.
Keywords: problem solving, metacognition, nonroutine geometry problems, preservice teachers, dynamic geometry software
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Euclidean Geometry's Problem Solving Based on Metacognitive in Aspect of Awareness
pp. 2319-2331 |
Solving mathematical problems, as the main subject, is intended to improve one’s ability in mathematics. The approach adopted in this present research was a qualitative one with the subject of the second semester students of mathematics in mathematics department. Six students consisting of two students under high, two middle, and two low ability categories were involved in this research. The data were obtained through four problems in the geometry subject test. The validity test employed was the item validity and the four exersices showed the coefficients of 0.79; 0.75; 0.70, and 0.82, respectively, meaning that the four exersices fulfilled the problem validity, meanwhile the test of reliability showed the coefficient of 0.78, namely the problems also met the reliability requirement. The results of the research showed that students were aware of what to plan and to do in the problem solving. The respondents realized them by writing the aspects they knew and the problems they intended to solve. In terms of the learning results, the two groups, high and middle, possessed some awareness in problem solving, but the students under the low category may be said to have less awareness of what to do in problem solving.
Keywords: Awareness, metacognitive, problem solving
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