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
Bender, T.A. (1980). Processing multiple choice and recall test questions. Paper presented at the Annual Meeting of the American Educational Research Association. Boston, MA. Retrieved from http://www.eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED189160
Berlak, H. (1985). Testing in a democracy. Educational Leadership, 43(2), 16-17.
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 Education, 17(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 International, 49(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
Elias, J. L., & Merriam, S. B. (2005). Philosophical foundations of adult education (3rd ed.). Malabar, FL: Krieger Publishing Company.
Ennis, R. (1985). Large scale assessment of critical thinking in the fourth grade. Paper presented at Issues in the Development of a Large-Scale Assessment of Critical Thinking Skills. The American Educational Research Association Annual Meeting. Chicago, Illinois.
Frederiksen, N. (1984). The real test bias, American Psychologist, 39(1), 1-10.
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.
National Education Association (2015). An educator’s guide to the “four Cs”. Retrieved from http://www.nea.org/assets/docs/A-Guide-to-Four-Cs.pdf
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 Teacher, 104(4), 290-295.
Ray, W. (1978). Writing multiple-choice questions: The problem and a proposed solution. The History Teacher, 11(2), 211-218.
Resnick, L.B. (1987). Education and learning to think. Washington, DC: National Academy Press.
Ribbens, E. (2007). Why I like personal response systems. Journal of College Science Teaching, 37(2), 60-62.
Romberg, T.A, Zarinnia, E.A., Collis, K.F. (1990). A new world view of assessment in mathematics. In G. Kulm (Ed.), Assessing Higher Order Thinking in Mathematics (pp. 21-38). Washington, DC: American Association for the Advancement of Science.
Teaching Effectiveness Program. (2014). Writing multiple choice items that demand critical thinking. University of Oregon. Retrieved from http://tep.uoregon.edu/resources/assessment/ multiplechoicequestions/sometechniques.html#problemsolution
Standards (2012). Retrieved from: www.corestandards.org/ October 30, 2012.
Sternberg and Baron. (1985). A triarchic approach to measuring critical thinking skills: a psychological view. Paper presented at symposium, Issues in the development of a Large-Scale Assessment of Critical Thinking Skills. The American Educational Research Association annual Meeting. Chicago, Illinois.
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 Education, 6(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
Wayne, W. (1982). Relative effectiveness of single and double multiple-choice questions in educational measurement. The Journal of Experimental Education, 51(1), 46-50.
|View Abstract References Full text PDF|
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.
|View Abstract References Full text PDF|
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
Acar, N. (2010). The effect of fraction rulers on the addition and subtraction of fraction abilities of 6th grade students of elementary school (Master’s Thesis). Available from Council of Higher Education Thesis Center Database in Turkey. (Thesis No. 251433).
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 Research, 18(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 Teaching, 24(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 Learning, 3(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).
|View Abstract References Full text PDF|
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
2014 Progress Report of the Arbitration Court of the Kirov region. (2014). Reference Form № 1. from http://kirov.arbitr.ru
Biryukov, B. V. (1974). Cybernetics and science methodology. Moscow: Nauka.
Bluvshtejn, J. D. (1981). Criminological statistics. Minsk.
Cochran, W. (1976). Sampling techniques. Moscow: Statistika
Ermolaev, O. J. (2006). Mathematical statistics for psychologists: the textbook. Moscow: Flint.
Ganieva, Y. N., Azitova, G. S., Chernova, Y. A., Yakovleva, I. G., Shaidullina, A. R., Sadovaya, V. V. (2014). Model of High School Students Professional Education. Life Science Journal, 11(8s), 1097-8135.
Glantz, S. (1998). Biomedical statistics. Moscow: Practice
Glass, J. & Stanly, J. (1976). Statistical methods in pedagogy and psychology. Moscow: Progress.
Gmurman, V. E. (2003). The theory of probability and mathematical statistics: a manual for schools. Moscow: Higher School.
Grabar, M. & Krasnyanskaya K. A. (1977). Application of mathematical statistics in educational research. Non-parametric methods. Moscow: Pedagogika.
Granichina, O. (2012). Mathematical and statistical methods of psychological and educational research: study guide. St. Petersburg, St. Petersburg.: Publishing house of VVM.
Hollender, M. & Wolfe, D. (1983). Nonparametric Statistical Methods. Moscow: Finance and Statistics.
Kabanova-Meller, E.N. (1981). Training activities and developmental teaching. Moscow: Knowledge.
Krajewski, V. V. (1977). Problems of scientific substantiation of training (Methodological Analysis). Moscow: Pedagogika.
Krutetskiy, V. A. (1972). Fundamentals of educational psychology. Moscow: Prosvescheniye
Landa, L. N. (1966). Algorithmization in training. Moscow.
Leontiev, A. N. (1959). Problems of the mental development. Moscow: APS RSFSR.
Lerner, I. J. (1981). Didactic fundamentals of training methods. Moscow: Pedagogika
Litvak, K. B. (1985). Information capacity scope of communal reviews in the territorial census reports as part of households types study. Mathematical methods and computers in the historical research. Moscow.
Masalimova, A. R. & Nigmatov, Z. G. (2015). Structural-Functional Model for Corporate Training of Specialists in Carrying Out Mentoring. Review of European Studies, 7(4), 39-48.
Mikheev, V. (1987). Modeling and measurement theory methods in pedagogy: scientific-methodical manual for teachers and researchers, mathematicians, scientists and graduate students involved in educational research methodology. Moscow: Higher School
Nikolaev, A. G. & Degtyarev, M. P. (2013). Identification of text files by statistical methods (conventional cases).Radioelektronni kopm'yuterni i sistemi, 4 (63), 55-59.
Novikov, D. A. & Novochadov, V. V. (2005). Statistical Methods in Experimental Medicine and Biology (conventional cases).Volgograd: Publishing house of VSMU.
Novikov, D. A. (2004). Statistical methods in educational research (typically). Moscow: MZ-Press
Orlov, A. I. (2001). Development of Methodology of Statistical Methods. Statistical methods of assessment and hypothesis testing. Interuniversity collection of scientific papers. Perm, Perm: Publishing house of the PSU.
Platonov, A. E. (2000). Statistical analysis in medicine and biology: the problem, terminology, logic, computer methods. Moscow, M.: Publishing House of the Academy of Medical Sciences.
Polonsky, V. M. (1987). Assessment of the quality of scientific and pedagogical research. Moscow: Pedagogika.
Professional education. (1999). Dictionary. Key concepts, terminology, relevant vocabulary. Moscow: NMC ACT.
Rosenberg, N. M. (1979). The challenges of measurement in didactics. Kiev.
Shilova, Z. V. (2014) Statistical Methods of Processing Research Results. PhD Thesis. Kirov.
Urbach, V. J (1975). Statistical analysis in biological and medical research. Moscow: Nauka.
Vygotsky, L. S. (1965/1986). Psychology of Art. Moscow: Art.
Vygotsky, L. S. (1982/2012). Problems of general psychology. Moscow: Publishing house "Kniga po trebovaniju."
Zaripova, I. M., Shaidullina, A. R., Upshinskaya, A. Y., Sayfutdinova, G. B., Drovnikov, A. S. (2014). Modeling of Petroleum Engineers Design-Technological Competence Forming in Physical-Mathematical Disciplines Studying Process. American Journal of Applied Sciences, 11(7), 1049-1053.
|View Abstract References Full text PDF|
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
|View Abstract References Full text PDF|
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
Allison, L. (1995). The status of computer technology in classrooms using the integrated thematic instructional model. International Journal of Instructional Media, 22(1), 33 – 43.
Bielefeld, T.G. (2002). On dynamic geometry software in the regular classroom. Zentralblattfür Didaktikder Mathematik, 34(3), 85-92.
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
Gomoll, M. (1999). Choosing Contingency Planning Software. The Ease-Of-Use Issue in Software Selection. Disaster Recovery Journal. Vol. 5, 4.
Göktaş, Y, Küçük, S., Aydemir, M., Telli, E., Arpacık, Ö., Yıldırım & G., Reisoğlu, İ. (2012). Educational Technology Research Trends in Turkey: A Content Analysis of the 2000-2009 Decade. Educational Sciences: Theory & Practice - 12(1), 191-196, Educational Consultancy and Research Center
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.
Kortenkamp, U., & Dohrmann, C. (2010). User interface design for dynamic geometry software. Acta Didactica Napocensia, 3(2), 59–66.
Isiksal, M. & Askar, P. (2005): The effect of spreadsheet and dynamic geometry software on the achievement and self-efficacy of 7th-grade students. Educational Research, 47:3, 333-350
Mackrell, K. (2011a). Design decisions in interactive geometry software. ZDM Mathematics Education, 43:373–387 DOI 10.1007/s11858-011-0327-4
Mackrell, K. (2011b). Finding the area of a circle: Affordances and design issues with different IGS programs. Proceedings of the Second North American GeoGebra Conference: Where Mathematics, Education and Technology Meet? University of Toronto, Toronto, ON June 17-18, 2011.
Oldknow, A. (2001). Special group 2: DGS — Dynamic Geometry Software. In M. Borovcnik & H. Kautschitsch (Ed.): Electronic Proceedings of the Fifth International Conference on Technology in Mathematics Teaching. August, 6-9, 2001 — University of Klagenfurt, Austria.http://wwwg.uniklu.ac.at/stochastik.schule/ICTMT_5/ICTMT_5_CD/Special%20groups/CD_Special2.htm#b9
Oldknow, A. & Tetlow, L. (2008). Using dynamic geometry software to encourage 3D visualisation and modelling. Electronic Journal of Mathematics and Technology.1933-2823 Volume: 2 Source Issue: 1
Petrovici, A. & Sava, A.T. (2010).CABRI 3D-the instrument to make the didactic approach more efficient. Anale. Seria Informatica. Vol 8, 2.
Roberts, D.L. & Stephens, L.J. (1999).The effect of the frequency of usage of computer software in high school geometry. The Journal of Computers in Mathematics and Science Teaching, 18(1), 23-30.
Sträßer, R. (2002). Research on Dynamic Geometry Software (DGS) - an introduction ZDM, Vol. 34 (3).
Stols, G. & Kriek, J.(2011). Why don't all maths teachers use dynamic geometry software in their classrooms? Australasian Journal of Educational Technology, 27(1), 137-151.
Weigand, H.-G. & Weth, T. (2002). Computer im Mathematikunterricht: Neue Wegezualten Zielen. Spektrum, AkademischerVerlag, Heidelberg, Berlin.
|View Abstract References Full text PDF|
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
American Association of Colleges for Teacher Education & Stanford Center for Assessment, Learning, and Equity. (2015).edTPA. Retrieved from http://edtpa.aacte.org/
Ball, D. L. (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. Santa Monica, CA: RAND.
Beijaard, D. (1995). Teachers’ prior experiences and actual perceptions of professional identity. Teachers and Teaching:Theory and Practice, 1(2), 281-294. doi: 10.1080/1354060950010209
Beijaard, D., Meijer, P. C., & Verloop, N. (2004). Reconsidering research on teachers’ professional identity. Teaching and Teacher Education, 20, 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 Education, 36(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 education: The report of the AERA Panel on Research and Teacher Education (pp. 309-424). Mahwah, NJ: Erlbaum.
Common Core State Standards Writing Team. (2011). Progression for the Common Core State Standards for Mathematics (Draft), K–5, Measurement and data. Retrieved from http://commoncoretools.files.wordpress.com/2011/06/ccss_progression_md_k5_2011_06_20.pdf
Confrey, J., Maloney, A. P., Nguyen, K. H., Mojica, G., & Myers, M. (2012). TurnOnCCMath.net: Learning trajectories for the K-8 Common Core math standards. Retrieved from https://www.turnonccmath.net
Council on Undergraduate Research. (2015). Student events. Retrieved from http://www.cur.org/conferences_and_events/student_events/
Dewey, J. (1933). How we think: A restatement of the relation of reflective thinking to the educative process. Boston: Heath.
Educational Testing Service. (2015). The Praxis performance assessment for teachers. Retrieved from http://www.ets.org/ppa/
Ellemor-Collins, D. L., & Wright, R. J. (2008). Student thinking about arithmetic: Videotaped interviews. Teaching Children Mathematics, 15, 106-111.
Ferrini-Mundy, J. (2011). Dear colleague letter: Opportunity for Research Experiences for Undergraduates (REU) sites focusing on STEM education research. Arlington, VA: National Science Foundation. Retrieved from http://www.nsf.gov/pubs/2011/nsf11076/nsf11076.jsp
Forbes, C. T., & Davis, E. A. (2008). The development of pre-service elementary teachers’ curricular role identity for science teaching. Science Education, 92, 909-940. doi: 10.1002/sce.20265
Girod, M., & Pardales, M. (2001, April). “Who am I becoming?” Identity development in becoming a teacher-researcher.Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, WA.
Harrison, R. L. (2008). Scaling the ivory tower: Engaging emergent identity as a researcher. Canadian Journal of Counselling,42(4), 237-248.
Hu, S., Scheuch, K., Schwartz, R., Gaston-Gayles, J., & Li, S. (2008). Reinventing undergraduate education: Engaging college students in research and creative activities. ASHE Higher Education Report, 33(4), 1-103.
Hunter, A. -B., Laursen, S. L., & Seymour, E. (2006). Becoming a scientist: The role of undergraduate research in students’ cognitive, personal, and professional development. Science Education, 91(1), 36-74. doi: 10.1002/sce.20173
Ingersoll, R. M., & Perda, D. (2010). Is the supply of mathematics and science teachers sufficient? American Educational Research Journal, 47, 563-594. doi: 10.3102/0002831210370711
Jenkins, O. F. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13, 141-154. doi: 10.1007/s10857-009-9129-9
Kilpatrick, J., Swafford, J. and Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
McDonough, A., Clarke, B., & Clarke, D. M. (2002). Understanding, assessing and developing children’s mathematical thinking: The power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices. International Journal of Educational Research, 37, 211-226. doi:10.1016/S0883-0355(02)00061-7
Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., Phillips, E. D. (2009). Connected mathematics project 2. Boston: Pearson.
Learn NC & Wheatley, G. (2001). Problem centered math. Retrieved from http://www.learnnc.org/lp/editions/pcmath/cover
National Governors Association for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/
Pillen, M., Beijaard, D., & den Brok, P. (2013). Tensions in beginning teachers’ professional identity development, accompanying feelings and coping strategies. European Journal of Education, 36(3), 240-260. doi: 10.1080/02619768.2012.696192
Ponte, J. P., & Chapman, O. (2008). Preservice mathematics teachers’ knowledge and development. In L.D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 223-261). New York: Routledge.
Reys, B. J., & Reys, R. E. (2004). Recruiting mathematics teachers: Strategies to consider. Mathematics Teacher, 97, 92-95.
Reys, R. E., Reys, B., & Estapa, A. (2013). An update on jobs for doctorates in mathematics education at institutions of higher education in the United States. Notices of the AMS, 60, 470-473.
Ricks, T. E. (2011). Process reflection during Japanese Lesson Study experiences by prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 14, 251-267. doi: 10.1007/s10857-010-9155-7
Russell, S. H., Hancock, M. P., & McCullough, J. (2007). Benefits of undergraduate research experiences. Science, 316, 548-549. doi: 10.1126/science.1140384
Sammons, P., Day, C., Kington, A., Gu, Q., Stobart, G., & Smees, R. (2007). Exploring variations in teachers’ work, lives and their effects on pupils: Key findings and implications from a longitudinal mixed-methods study. British Educational Research Journal, 33, 681-701. doi: 10.1080/01411920701582264
Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.
Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14-22. doi: 10.3102/0013189X034004014
Stigler, J. W., & Hiebert, J. (1999). The teaching gap. New York, NY: Free Press.
Weiland, I. S., Hudson, R. A., & Amador, J. M. (2014). Preservice formative assessment interviews: The development of competent questioning. International Journal of Science and Mathematics Education, 12, 329-352.
Wenger, E. (1999). Communities of practice: Learning meaning and identity. Cambridge: Cambridge University Press.
|View Abstract References Full text PDF|
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
Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245–274. doi: 10.1023/A:1022103903080
Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal,17(2), 39-68. doi: 10.1007/BF03217415
Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127-147. doi: 10.1007/s10649-011-9333-2
Blömeke, S. & Kaiser, G. (2015). Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective. In B. Pepin & B. Roesken-Winter (Eds.), From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions (pp. 227-243). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4_11
Buchberger, B. (2002). Computer algebra: the end of mathematics? ACM SIGSAM Bulletin, 36(1), 3-9.
Carter, G. & Norwood, K.S. (1997). The relationship between teacher and student beliefs about mathematics. School Science and Mathematics, 97(2), 62-67. doi: 10.1111/j.1949-8594.1997.tb17344.x
Cooney, T.J., Shealy, B.E. & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29(3), 306-333.
De Guzman, M., Hodgson, B.R., Robert, A. & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. In Proceedings of the International Congress of Mathematicians (pp. 747-762). Berlin: Documenta mathematica.
Dogan, M. (2007). Mathematics trainee teachers’ attitudes to computers. In M. Joubert (Ed.), Proceedings of the British Society for Research into Learning Mathematics 28(2), (pp. 19-24). United Kingdom: BSRLM.
Dreyfus, T. (1994) The role of cognitive tools in mathematics education. In R. Biehler, R.W. Scholz, R. Sträßer & B. Winkelmann (Eds.), Didactics of Mathematics as a Scientific Discipline (pp. 201–211). Dordrecht: Kluwer. doi: 10.1007/0-306-47204-X
Drijvers, P., Doorman, M., Boon, P., Reed, H. & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213-234. doi: 10.1007/s10649-010-9254-5
Erens, R. & Eichler, A. (2015). The use of technology in calculus classrooms – beliefs of high school teachers. In C. Bernack-Schüler, R. Erens, T. Leuders & A. Eichler (Eds.), Views and Beliefs in Mathematics Education. Results of the 19th MAVI Conference (pp. 133-144). Germany: Springer. doi: 10.1007/978-3-658-09614-4_11
Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics Teaching: The State of the Art (pp. 249-254). New York: Falmer.
Fleener, M.J. (1995). The relationship between experience and philosophical orientation: a comparison of preservice and practicing teachers’ beliefs about calculators. Journal of Computers in Mathematics and Science Teaching, 14(3), 359-376.
Forgasz, H.J. (2002). Teachers and computers for secondary mathematics. Education and Information Technologies, 7(2), 111-125. doi: 10.1023/A:1020301626170
Furinghetti, F. & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G.C. Leder, E. Pehkonen and G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39-57). Dordrecht: Kluwer. doi: 10.1007/0-306-47958-3_3
Fullan, M.G. (1991). The New Meaning of Educational Change. New York: Teachers College Press
Gill, M.G., Ashton, P.T. & Algina, J. (2004). Changing preservice teachers’ epistemological beliefs about teaching and learning in mathematics: An intervention study. Contemporary Educational Psychology, 29(2), 164-185. doi: 10.1016/j.cedpsych.2004.01.003
Georgsen, M., Fougt, S.S., Mikkelsen, S.L.S. & Lorentzen, R.F. (2014). Interventionsdesign i demonstrationsskoleprojektet IT-fagdidaktik og lærerkompetencer i et organisatorisk perspektiv. Retrieved from: http://auuc.demonstrationsskoler.dk/ sites/default/ files/IT-fagdidaktik/interventionsdesign_i_demonstrationsskoleprojektet.pdf
Green, T.F. (1971). The Activities of Teaching. New York: McGraw-Hill.
Goos, M. (2014). Technology integration in secondary school mathematics: the development of teachers’ professional identities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), The Mathematics Teacher in the Digital Era. An International Perspective on Technology Focused Professional Development (pp. 139-161). Dordrecht: Springer. doi: 10.1007/978-94-007-4638-1_7
Hanzsek-Brill, M.B. (1997). The relationships among components of elementary teachers’ mathematics education knowledge and their uses of technology in the mathematics classroom. Unpublished doctoral dissertation. Athens, Georgia: University of Georgia.
Jankvist, U.T. (2015). Changing students’ images of “mathematics as a discipline”. The Journal of Mathematical Behavior,38, 41-56. doi: 10.1016/j.jmathb.2015.02.002
Jankvist, U.T., Misfeldt, M. & Iversen, S.M. (preprint). When students are subject to various teachers’ varying policies: A bricolage framework for the case of CAS in teaching.
Kuhs, T. M., & Ball, D. L. (1986). Approaches to teaching mathematics: mapping the domains of knowledge, skills, and disposition (Research Memo). Lansing, MI: Michigan State University, Center on Teacher Education.
Kvale, S. (1996). Interviews : an introduction to qualitative research interviewing. Thousand Oaks, Calif.: Sage Publications.
Lagrange, J. (2005). Using symbolic calculators to study mathematics: the case of tasks and techniques. The case of tasks and techniques. In D. Guin, K. Ruthven & L. Trouche (Eds.), The Didactical Challenge of Symbolic Calculators. Turning a Computational Device into a Mathematical Instrument (pp. 113-135). New York: Springer. doi: 10.1007/0-387-23435-7_6
Lavicza, Z. (2010). Integrating technology into mathematics teaching at the university level. ZDM, 42(1), 105-119. doi: 10.1007/s11858-009-0225-1
Leatham, K.R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Journal of Mathematics Teacher Education, 9(1), 91-102. doi: 10.1007/s10857-006-9006-8
Leatham, K.R. (2007). Pre-service secondary mathematics teachers’ beliefs about the nature of technology in the classroom. Canadian Journal of Science, Mathematics and Technology, 7(2/3), 183-207. doi: 10.1080/14926150709556726
Leder, G.C. (2015). Foreword. In B. Pepin & B. Roesken-Winter (Eds.), From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions (pp. v-x). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4
Liljedahl, P. (2009). Teachers’ insights into the relationship between beliefs and practice. In J. Maaß & W. Schlöglmann (Eds.), Beliefs and Attitudes in Mathematics Education. New Research Results (pp. 33-44). Rotterdam: Sense Publishers.
McCulloch, A.W. (2011). Affect and graphing calculator use. The Journal of Mathematical Behavior, 30(2), 166-179. doi: 10.1016/j.jmathb.2011.02.002
Nabb, K.A. (2010). CAS as a restructuring tool in mathematics education. Proceedings of the 22nd International Conference on Technology in Collegiate Mathematics. Chicago, IL.
Op’t Eynde, P., de Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 13–37). Dordrecht: Kluwer Academic Publishers (Chapter 2).
Pajares, M.F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. doi: 10.3102/00346543062003307
Partnership For 21st Century Skills (2011). Outcomes for P21 Math Skills Map. Washington, DC: Author. Retrieved from http://www.p21.org/storage/documents/ P21_Math_Map.pdf
Partnership For 21st Century Skills (2004). ICT Literacy Map. Tuczon, Az: Author. Retrieved from http://21ctlearning.pbworks.com/f/ictmap_math.pdf
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F.K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 257-315). Charlotte, NC: Information Age Publishing.
Rokeach, M. (1960). The open and closed mind. New York: Basic Books.
Schmidt, M.E. (1999). Middle grade teachers’ beliefs about calculator use: pre-project and two years later. Focus on Learning Problems in Mathematics, 21(1), 18-34.
Schoenfeld, A.H. (2007). Method. In F.K. Lester, Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 69-107). Charlotte, NC: Information Age Publishing.
Skott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), From Beliefs to Dynamic Affect Systems in Mathematics Education. Exploring a Mosaic of Relationships and Interactions (pp. 3-23). Switzerland: Springer. doi: 10.1007/978-3-319-06808-4_1
Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: a design research study. Journal of Mathematics Teacher Education, 10(4), 217-237. doi: 10.1007/s10857-007-9038-8
Tharp, M.L., Fitzsimmons, J.A. & Ayers, R.L.B. (1997). Negotiating a technological shift: teacher perception of the implementation of graphic calculators. Journal of Computers in Mathematics and Science Teaching, 16(4), 551-575.
Thomas, M.O.J. & Palmer, J.M. (2014). Teaching with digital technology: obstacles and opportunities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), The Mathematics Teacher in the Digital Era. An International Perspective on Technology Focused Professional Development (pp. 71-89). Dordrecht: Springer. doi: 10.1007/978-94-007-4638-1_4
Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127-146). New York: Macmillan.
Van Zoest, L.R., Jones, G.A., & Thornton, C.A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program. Mathematics Education Research Journal, 6(1), 37-55. doi: 10.1007/BF03217261
Walen, S.B., Williams, S.R. & Garner, B.E. (2003). Pre-service teachers learning mathematics using calculators: a failure to connect current and future practice. Teaching and Teacher Education, 19(4), 445-462. doi: 10.1016/S0742-051X(03)00028-3
Wilkins, J.L.M & Brand, B.R. (2004). Change in preservice teachers’ beliefs: an evaluation of a mathematics methods course. School Science and Mathematics, 104(5), 226-232. doi: 10.1111/j.1949-8594.2004.tb18245.x
Winsløw, C. (2003). Semiotic and discursive variables in CAS-based didactical engineering. Educational Studies in Mathematics, 52(3), 271-288. doi: 10.1023/A:1024201714126
|View Abstract References Full text PDF|
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
|View Abstract References Full text PDF|
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
Arikunto, S. (2009). Dasar-dasar evaluasi Pendidikan. Jakarta: Bumi Aksara.
Blanco, L. J., Barona, E. G. & Carrasco, A. C. (2013). Cognition and affect in mathematics problem solving with prospective teachers. The Mathematics Enthusiast, 10 (1 & 2), 335-364.
Chua, Y.P. (2006). Kaedah dan statistik pendidikan, buku 1 Kaedah Kajian. Kuala Lumpur: McGraw Hill.
Dochy, F. (2001). A New assessment era: different needs, new challenges. Learning and Instruction. 10 (1), 11-20.
Ennys, R.H. (2005). A Taxonomy of critical thinking dispositions and abilities in J.B. Baronand R.J. Sternberg Eds., Teaching thinking skills: Theory and practice, new york, w.h. freeman, in evaluating critical thinking skills: Two conceptualizations, Journal of distance education, 20(2),1-20.
Hannula, M.S., Maijala, H. & Pehkonen, E. (2004). development of understanding and self-confidence in mathematics; grades 5–8. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education.
Haryani, D. (2012). Profil proses berpikir kritis siswa SMA dengan gaya kognitif field independen dan berjenis kelamin laki-laki dalam memecahkan masalah matematika, Prosiding SNPM Universitas Sebelas Maret.
Heidari, F. & Bahrami, Z. (2012). The Relationship between thinking styles and metacognitive awareness among Iranian EFL learners. International Journal of Linguistic, 4 (3).
In’am, A. (2003). Geometry euclid, Malang: Bayu Media.
In’am, A. (2012). A Metacognitive approach to solving algebra problem. International Journal of Independent Research and Studies–IJIRS 1(4).
In’am, A. (2015). Menguak penyelesaian masalah matematika: analisis pendekatan metakognitif dan model Polya. Yogyakarta: Aditya Media.
Keichi, S. (2000). Metacognition in mathematics education in Japan. Japan: JSME.
Khoiriyah, (2013). Analisis tingkat berpikir siswa berdasarkan teori van hiele pada materi dimensi tiga ditinjau dari gaya kognitif field dependent dan field independent. Jurnal Pendidikan Matematika Solusi, 1(1).
Komariah, K. (2011). Penerapan metode pembelajaran problem solving model polya untuk meningkatkan kemampuan memecahkan masalah bagi siswa kelas IX J di SMPN 3 Cimahi. Prosiding Seminar Nasional Penelitian, Pendidikan dan Penerapan MIPA, Fakultas MIPA, Universitas Negeri Yogyakarta, 14 Mei 2011.
Kosiak, J.J. (2004). Using a synchronous discussion to facilitate collaborative problem solving in college algebra. Montana State University. Doctoral Dissertation
Larmar, S. & Lodge, J. (2014). Making sense of how i learn; metacognitive capital and the first year university student. The International Journal of the First Year in Higher Education, 5(1), 93-105.
Lerch, C. (2004). Control Decisions and Personal Beliefs: Their Effect on Solving Mathematical Problems. Journal of Mathematical Behavior, 23, 21-36.
Mardzellah, M. (2007). Sains pemikiran dan etika. Kualalumpur: PTS Profesional.
McMillan, J.H. & Schumacher, S.(2001). Reseacrh in Education, New York: Longman.
Memnun, D. S., Hart, L. C. & Akkaya, R. (2012). A Research on the mathematics problem solving belief of mathematics, science and elementary pre service training in Turkey in term of Different Variables. International Journal of Humanities and Social Sciences, 2(24).
Merriam (1988). Case study research in education: A Qualitative approach. Michigan: Jossey-Bass
Murdanu (2004). Analisis kesulitan siswa SLTP dalam menyelesaikan persoalan geometri, Tesis PPS Universitas Negeri Surabaya.
Novotna, J. (2014). Problem solving in school mathematics based on heuristic strategies, Journal on Efficiency and Responsibility in Education and Science, 7(1), 1-6.
Nurdin (2007). Model pembelajaran matematika untuk menumbuhkan kemampuan metakognitif (Model PMKM). Disertasi S-3 Pendidikan Matematika, Universitas Negeri Surabaya.
O’Neil, H. F. & Abedi, J. (1996). Reliability & validity of state metacognitive inventory: potential for alternative assessment. Journal of Educational Research, 89, 234-245
Perkins, C. & Murphy, E. (2006). Identifying and measuring individual engagement in critical thinking in online discussions: an exploratory study. Educational Technology & Society, 9(1), 298-307.
Polya, G. (1971). How to solve it: a new aspect of mathematics method. New Jersey: Princeton University Press
Ruseffendi E.T. (2006). Pengantar kepada membantu guru mengembangkan kompetensinya dalam pengajaran matematika untuk meningkatkan CBSA, Bandung: Tarsito.
Saad, N. (2004). Perlakuan metakognitif pelajar tingkatan empat aliran sains dalam penyelesaian masalah matematik tambahan. Kajian Jabatan Matematik, Fakulti Sains dan Teknologi Universiti Pendidikan Sultan Idris.
Subanji (2007). Proses berpikir penalaran kovariasional pseudo dalam meng-konstruksi grafik fungsi kejadian dinamik berkebalikan. Disertasi S-3 Pendidikan Matematika, Universitas Negeri Surabaya.
Wahyudin (2010). Peranan problem solving dalam matematika, Bandung: FPMIPA UPI
Yang, Y-T.C., Newby, T.J. & Bill, R.L. (2005). Using socratic questioning to promote critical thinking skills in a synchronous discussion forum in distance learning environments. American Journal of Distance Education, 19(3), 163-181.
Yin, R.K. (1989). Case study research design and methods. Washington: Cosmos Corporation.
|View Abstract References Full text PDF|