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Teaching and Assessing Higher Order Thinking in the Mathematics Classroom with Clickers

Jim Rubin & Manikya Rajakaruna

pp. 37-51  |   DOI:
Published Online: April 04, 2015
Article Views: 2322  |  Article Download: 2261

Abstract

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

References

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Biggs, J.B. & Collis, K. F. (1982). Evaluating the quality of learning: the solo taxonomy. New York: Academic Press.

Caldwell, J. E. (2007). Clickers in the large classroom: Current research and best practice tips. CBE Life Sciences Education, 6(1), 9-20.

Collis, K. F. (1982). The solo taxonomy as a basis of assessing levels of reasoning in mathematical problem solving. Proceedings from the Sixth International Conference for the Psychology of Mathematical Education. Antwerp, Belgium: University of Antwerp.

Collis, K. G., Romberg, T.A., & Jurdak, M. E. (1986). A technique for assessing mathematical  problem-solving ability. Journal for Research in Mathematics Education17(3), 206-221.

Common Core State Standards Initiative (2015). About the common core state standards. Retrieved from http://www.corestandards.org/about-the-standards/

DeBourgh, G. A. (2008). Use of classroom “clickers” to promote acquisition of advanced

reasoning skills. Nurse Education in Practice, 8, 76-87.

Douglas, M., Wilson, J., & Ennis, S. (2012). Multiple-choice question tests: A convenient, flexible and effective learning tool? A case study. Innovations In Education And Teaching International49(2), 111-121.

Dowd, S. B. (1992). Multiple-choice and alternate-choice questions: Description and analysis. Retrieved from http://files.eric.ed.gov/fulltext/ED351376.pdf

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Hansen, J. D., & Dexter, L. (1997). Quality multiple-choice test questions: Item-writing. Journal of Education for Business,73(2), 94.

Hatch, J., Murray, J., & Moore, R. (2005). Manna from heaven or “clickers” from hell: Experiences with an electronic response system. Journal of College Science Teaching, 34(7), 36-39.

Kolikant, Y.B.D., Calkins, S., & Drane, D. (2010). “Clickers” as catalysts for transformation of teachers. College Teaching, 58,127-135.

Lin, S., & Singh, C. (2012). Can multiple-choice questions simulate free-response questions? AIP Conference Proceedings,1413(1), 47-50. doi:10.1063/1.3679990

Lockwood, D.F. (2003). Higher order thinking in teaching senior science. Retrieved from http://members.shaw.ca/donlockwood/mcquestions.htm

Liu, W.C. & Stengel, D. (2011). Improving student retention and performance in quantitative courses using clickers. The International Journal for Technology in Mathematics Education, 18(1), 51-58.

Miller, R. G., Ashar, B. H., & Getz, K. J. (2003). Evaluation of an audience response system for the continuing education of health professionals. The Journal of Continuing Education in the Health Professions, 23(2), 109-115.

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Oermann, M. H., & Gaberson, K. B. (2006). Evaluation and testing in nursing education (2nd ed.). New York: Springer Publishing Company, Inc.

Popelka, S. R. (2010). Now we're really clicking! Mathematics Teacher104(4), 290-295.

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Stuart, S. A. J., Brown, M. I., & Draper, S. W. (2004). Using an electronic voting system in logic lectures: One practitioner’s application. Journal of Computer Assisted Learning, 20, 95-102.

Stupans, I. (2006). Multiple choice questions: Can they examine application of knowledge? Pharmacy Education6(1), 59-63. doi:10.1080/15602210600567916

Torres, C., Lopes, A., Babo, L., & Azevedo, J. (2011). Improving multiple-choice questions. US-China Education Review B1, 1-11.

Uhari, M., Renko, M., & Soini, H. (2003). Experiences of using an interactive audience response system in lectures. BMC Medical Education, 3(12). Retrieved from http://www.biomedcentral.com/ content/pdf/1472-6920-3-12.pdf

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2

The Affective Domain in Mathematics Learning

Nuria Gil Ignacio, Lorenzo J. Blanco Nieto and Eloísa Guerrero Barona

pp. 16-32  |   DOI:
Published Online: October 10, 2006
Article Views: 2280  |  Article Download: 2829

Abstract

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.

References

N/A

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3

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  |   DOI:
Published Online: March 01, 2016
Article Views: 1980  |  Article Download: 1440

Abstract

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

References

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Akın, P. (2009). The effects of problem-based learning on students? Success in the teaching the topic fractions at the 5th grade. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 241307).

Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.). (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Routledge.

Demirdöğen, N. (2007). The effect of realistic mathematics education method to the teaching fraction concept in 6th classes of primary education. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 207129).

Erdağ, S. (2011).  The effect of mathematics teaching supported by concepts cartoons decimal fractions on academic achievement and retention in 5th grade classes of primary schools. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 296499).

Goodwin, K. (2008). The impact of interactive multimedia on kindergarten students’ representations of fractions. Issues in Educational Research18(2), 103-117.

Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Sense publishers.

Kayhan, H. C. (2010). Determining of primary school students? Mental models in the process of converting fractions each other. (Doctoral dissertation). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 279658).

Lee, H.J. & Boyadzhiev, I. (2013). Challenging Common Misconceptions of Fractions through GeoGebra. In R. McBride & M. Searson (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2013 (pp. 2893-2898). Chesapeake, VA: AACE.

Martín-Caraballo, A. M., & Tenorio-Villalón, Á. F. (2015). Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities. Mathematics Education, 10(2), 53-65

McNamara, J., & Shaughnessy, M. M. (2010). Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Grades 3-5. Math Solutions.

Mısral, M. (2009). The effect of the education which is done by the different sub-constructs of fractions on the conceptual and operational knowledge levels of primary school 6th grade students about adding subtraction and multiplication in fraction. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 237470).

Moyer-Packenham, P. S., Ulmer, L. A., & Anderson, K. L. (2012). Examining Pictorial Models and Virtual Manipulatives for Third-Grade Fraction Instruction. Journal of Interactive Online Learning, 11(3),103-120.

Newstead, K. and Murray, H. (1998). Young students’ constructions of fractions. In A. Olivier & K. Newstead (Eds.),Proceedings of the Twenty-second International Conference for the Psychology of Mathematics Education: Vol. 3. (pp. 295-302). Stellenbosch, South Africa.

Pesen, C. (2007). Öğrencilerin kesirlerle ilgili kavram yanılgıları [Students’ Misconceptions About Fractions]. Eğitim ve Bilim,32(143), 79-88.

Pilli, O. (2008). The effects of computer-assisted instruction on the achievement, attitudes and retention of mathematics in 4th grade courses. (Doctoral dissertation). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 27694).

Pitta-Pantazi, D., Gray, E., & Christou, C. (2004). Elementary school students’ mental representations of fractions. InProceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 41-48).

Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study.Journal of Computers in Mathematics and Science Teaching24(1), 5-25.

Sözer, N. (2006). The impact of drama method on fourth class students at mathematics in a primary school regarding success of students, their attitudes and learning retention. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 191047).

Suh, J., Moyer, P. S., & Heo, H. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. Journal of Interactive Online Learning3(4), 1-21.

The National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics.Reston, VA: Author.

Thambi, N., & Eu, L. K. (2013). Effect of Students’ Achievement in Fractions using GeoGebra. SAINSAB. 16. 97-106.

Van de Walle, J.A., Karp, K.S. & Bay-Williams, J.M. (2010). Elementary and middle school mathematics teaching developmentally (Seventh Edition), USA: Pearson Publications.

Yazgan, Y. (2007). An experimental study on fraction understanding of children at the age of 10 and 11. (Doctoral dissertation). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 220989).

Yumuşak, E. Y. (2014). The effects of game-supported mathematics learning unit of fractions of 4. grade achievement and permanence. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 351006).

Yurtsever, N.T. (2012). A study on fifth grade students’ mistakes, difficulties and misconceptions regarding basic fractional concepts and operations. (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 321086).

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4

Selection of Appropriate Statistical Methods for Research Results Processing

Rezeda M. Khusainova, Zoia V. Shilova & Oxana V. Curteva

pp. 303-315  |   DOI:
Published Online: April 10, 2016
Article Views: 1454  |  Article Download: 3299

Abstract

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

References

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5

Teachers’ beliefs about mathematical knowledge for teaching definitions

Reidar Mosvold & Janne Fauskanger

pp. 43-61  |   DOI:
Published Online: November 10, 2013
Article Views: 1106  |  Article Download: 1589

Abstract

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

References

N/A

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6

Pre-Service Math Teachers’ Opinions about Dynamic Geometry Softwares and Their Expectations from Them

Hakan Şandır & Serdar Aztekin

pp. 421-431  |   DOI:
Published Online: April 28, 2016
Article Views: 1076  |  Article Download: 1036

Abstract

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

References

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Daher, W. (2009). Pre-service Teachers' Perceptions of Applets for Solving Mathematical Problems: Need, Difficulties and Functions. Educational Technology & Society, 12 (4), 383–395.

Erbas, A. K. & Yenmez, A. A. (2011).The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons. Computers & Education, 57(4), 2462-2475.http://dx.doi.org/10.1016/j.compedu.2011.07.002

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Guven, B. (2012).Using dynamic geometry software to improve eight grade students’ understanding of transformation geometry. Australian Journal of Educational Technology, 28(2), 364-382

Hull, A. N., & Brovey, A. J. (2004).The impact of the use of dynamic geometry software on student achievement and attitudes towards mathematics. Action Research Exchange, 3(1), 24-37.

Hohenwarter, M. & Fuchs, K. (2004). Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. ZDM classification: R 20, U 70, Retrieved on 10-November-2014, at                                                                                                                            URL: http://archive.geogebra.org/static/publications/pecs_2004.pdf

Hohenwarter, M., & Lavicza, Z. (2007). Mathematics teacher development with ICT: towards an International GeoGebra Institute. In D. Küchemann (Ed.), Proceedings of the British Society for Research into Learning Mathematics. 27(3):49-54. University of Northampton, UK: BSRLM.

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7

Identity Development during Undergraduate Research in Mathematics Education

Randall E. Groth & Jenny McFadden

pp. 357-375  |   DOI:
Published Online: March 01, 2016
Article Views: 1010  |  Article Download: 826

Abstract

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

References

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Beijaard, D. (1995). Teachers’ prior experiences and actual perceptions of professional identity. Teachers and Teaching:Theory and Practice1(2), 281-294. doi: 10.1080/1354060950010209

Beijaard, D., Meijer, P. C., & Verloop, N. (2004). Reconsidering research on teachers’ professional identity. Teaching and Teacher Education20, 107-128. doi:10.1016/j.tate.2003.07.001

Chong, S., Low, E. L., & Goh, K. C. (2011). Emerging professional identity of pre-service teachers. Australian Journal of Teacher Education36(8), 50-64.

Clift, R. T., & Brady, P. (2005). Research on methods courses and field experiences. In M. Cochran-Smith & K.M. Zeichner (Eds.), Studying teacher educationThe report of the AERA Panel on Research and Teacher Education (pp. 309-424). Mahwah, NJ: Erlbaum.

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8

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  |   DOI:
Published Online: March 02, 2016
Article Views: 884  |  Article Download: 1119

Abstract

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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9

Patterns of Metacognitive Behavior During Mathematics Problem-Solving in a Dynamic Geometry Environment

Ana Kuzle

pp. 20-40  |   DOI:
Published Online: February 02, 2013
Article Views: 787  |  Article Download: 859

Abstract

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

References

N/A

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10

The Quality and Criteria of Evaluation of Educational Work at the Universities of Russia at the Contemporary Stage

Lera A. Kamalova & Elena Raykova

pp. 71-79  |   DOI:
Published Online: April 21, 2016
Article Views: 696  |  Article Download: 698

Abstract

The relevance of the research problem is due to the fact that  in modern higher professional education system are not taken into account  some objective trends taking place in the youth environment. Educational work is taking a special importance as an integral part of specialist training in the modern University. Education of youth is one of the priority directions in the sphere of national security, the most important factor of political, economic and spiritual transformation of the Russian society. The main purpose of the educational work is training of creative thinking and harmoniously developed specialists with profound theoretical knowledge, formed professional competence, high moral qualities. The article provides an analytical assessment of the quality and criteria of educational work at the universities of Russia, the peculiarities of educational work in higher educational institutions. In accordance to the issues and the nature of the study we used systemic-structural and comparative analysis methods. Experience, described in the article, can be used in the process of improving of educational work system with students-specialists of primary schools.

Keywords: education, educational work, criteria, quality, training of primary school teachers, improvement of teacher training.

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