Me While I am Learning Mathematics: Reflections to Elementary School Students’ Drawings
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Oct 13, 2020
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Abstract
Each child will not become senior mathematicians in the future but all children have the right to get learning opportunities which he/she can develop his/her mathematical understanding at school. The success of children in mathematics is closely related to how they are taught mathematics. At this point, the role of teaching mathematics stands out in elementary school since they first encounter mathematics as a subject. Elementary school is the place where students first experience success or failure in mathematics. Therefore, the fundamentals of students' tendencies towards mathematics which will set and affect their future learning life are also laid here. The present study aims to examine the perceptions of elementary school students towards learning mathematics by means of their drawings. Drawings are tools for children to express themselves; they provide information about students' drawings on their classes and their understanding of teaching. In this context, based on the experiences of elementary school students, the phenomenon of learning mathematics was aimed to be defined from their perspective. This research employed phenomenology as a qualitative research design. The study group of the research consisted of 326 elementary school students. The data were collected through the drawings of students on the subject of "me while I am learning mathematics". Content analysis was used in the analysis of the data. According to the research results, it is seen that the math learning environment is usually classroom; people in the learning environment are usually teacher and student(s); materials in the learning environment are general items in the classroom environment; symbols in the learning environment are usually numeral-number-four operation symbols; learning mathematics is usually happy-enjoyable-fun and the process of learning mathematics is usually to do arithmetic.
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TURGUT, Sedat; GÜLŞEN TURGUT, İlknur.
Me While I am Learning Mathematics: Reflections to Elementary School Students’ Drawings.
International Electronic Journal of Elementary Education, [S.l.], v. 13, n. 1, p. 139-154, oct. 2020.
ISSN 1307-9298.
Available at: <https://iejee.com/index.php/IEJEE/article/view/1246>. Date accessed: 27 oct. 2020.
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References
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Anning, A., & Ring, K. (2004). Making sense of children’s drawings. Maidenhead: Open University Press.
Bahr, D. L., & de Garcia, L. A. (2010). Elementary mathematics is anything but elementary. Belmont, CA: Wadsworth.
Barbosa, A., &Vale, I. (2016). Math trails: Meaningful mathematics outside the classroom with pre-service teachers. Journal of the European Teacher Education Network, 11, 63-72.
Biatchford, P. (1996). Pupils’ views on school work and school from 7 to 16 years. Research Papers in Education, 11(3), 263-288. https://doi.org/10.1080/0267152960110305
Borthwick, A. (2011). Children’s perceptions of and attitudes towards their mathematics lessons. In C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 31(1), 37-42. London. Retrieved from https://bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-31-1-07.pdf
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington DC: National Academy Press.
Bunting, C. J. (2006). Interdisciplinary teaching through outdoor education. Champaign, IL: Human Kinetics.
Burns, M., & Silbey, R. (2000). So you have to teach math? Sound advice for K-6 teachers. Sausalito, CA: Math Solutions.
Carey, E., Devine, A., Hill, F., Dowker, A., McLellan, R., & Szucs, D. (2019). Understanding mathematics anxiety: Investigating the experiences of UK primary and secondary school students. Retrieved from https://doi.org/10.17863/CAM.37744
Clements, D. H., & McMillen, S. (1996). Rethinking “concrete” manipulatives. Teaching Children Mathematics, 2(5), 270-279.
Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. New York: Routledge.
Cowan, P. (2006). Teaching mathematics: A handbook for primary and secondary school teachers. New York: Routledge.
Creswell, J. W. (2007). Qualitative inquiry and research design. Choosing among five approaches. Thousand Oaks, CA: Sage Publications, Inc.
Creswell, J. W. (2016). 30 essential skills for the qualitative researcher. Thousand Oaks, California: SAGE Publications Ltd.
Davis, A., Goulding, M., & Suggate, J. (2017). Mathematical knowledge for primary teachers. New York, NY: Routledge.
Department for Education and Employment (DfEE) (1999). The national curriculum: Handbook for primary teachers in England. London: DfEE and QCA.
Donovan, M. S., & Bransford, J. D. (Eds.). (2005). How students learn: History, mathematics, and science in the classroom. Washington, DC: The National Academies Press.
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. https://doi.org/10.1037/0012-1649.43.6.1428
Edwards, S. (2007). Primary mathematics for teaching assistants. USA: Routledge.
Ernst, K., & Ryan, S. (2014). Success from the start: Your first years teaching elementary mathematics. Reston, VA: NCTM.
Eshun, B. A. (2004). Sex-differences in attitude of students towards mathematics in secondary schools. Mathematics Connection, 4(1), 1-13.
Fägerstam, E., & Blom, J. (2013). Learning biology and mathematics outdoors: Effects and attitudes in a Swedish high school context. Journal of Adventure Education and Outdoor Learning, 13(1), 56-75. https://doi.org/10.1080/14729679.2011.647432
Fraser, B. J., & Kahle, J. B. (2007). Classroom, home and peer environment influences on student outcomes in science and mathematics: An analysis of systemic reform data. International journal of Science Education, 29(15), 1891-1909. https://doi.org/10.1080/09500690601167178
Freiman, V., Kadijevich, D., Kuntz, G., Pozdnyakov, S., & Stedøy, I. (2009). Technological environments beyond the classroom. In E. J. Barbeau & P. J. Taylors (Eds.), Challenging mathematics in and beyond the classroom (pp. 97-131). New York, NY: Springer.
Freitag, M. A. (2014). Mathematics for elementary school teachers: A process approach. Belmont, CA: Brooks/Cole.
Fuson, K. C. (1992). Research on learning and teaching addition and subtraction of whole numbers. In G. Leinhardt, R. T. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 53-187). Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.
Goulding, M. (1997). Learning to teach mathematics. London: David Fulton.
Gökçek, T., & Güneş, G. (2011). How students perceive the math teacher? Mehmet Akif Ersoy Üniversitesi Sosyal bilimler Enstitüsü Dergisi, 3(4), 1-9.
Grevholm, B. (2010). Norwegian upper secondary school students’ views of mathematics and images of mathematicians. In K. Kislenko (Ed.), Current state of research on mathematical beliefs XVI. Proceedings of the MAVI-16 Conference (pp. 120-136). Tallin, Estonia: Institute of Mathematics and Natural Sciences, Tallin University.
Hatısaru, V., & Çetinkaya, B. (2012). İlköğretim öğrencilerinin matematik ve matematikçi algılarının incelenmesi [Investigating elementary school students’ perceptions of mathematics and mathematicians]. X. National Congress of Science and Mathematics Education, Niğde University, Niğde.
Haylock, D. (2010). Mathematics explained for primary teachers (4th edition). London: SAGE Publications.
Haylock, D., & Thangata, F. (2007). Key concepts in teaching primary mathematics. London: SAGE Publications.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
Ho, W. K. (2008). Using history of mathematics in the teaching and learning of mathematics in Singapore. Paper presented at the 1st RICE, Singapore: Raffles Junior College.
Holton, D., Cheung, K., Kesianye, S., de Losada, M. F., Leikin, R. Makrides, G., … Yeap, B. (2009). Teacher development and mathematical challenge. In E. J. Barbeau & P. J. Taylors (Eds.), Challenging mathematics in and beyond the classroom (pp. 133-170). New York, NY: Springer.
Julien, H. (2008). Content analysis. In L. M. Given (Ed.), The SAGE encyclopedia of qualitative research methods (pp. 120-122). Thousand Oaks, California: SAGE Publications, Inc.
Kennard, J. (2007). Outdoor mathematics. Mathematics Teaching Incorporating Micromath, 201, 16-18.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Lerman, S. (1998). Research on socio-cultural perspectives of mathematics teaching and learning. In J. Kilpatrick & A. Sierpinska (Eds.), Mathematics education as a research domain: A search for identity. Vol. 1 (pp. 333-350). Dordrecht: Kluwer.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Malchiodi, C. A. (1998). Understanding children's drawings. New York: The Guilford Press.
Masingila, J. O., Davidenko, S., & Prus-Wisniowska, E. (1996). Mathematics learning and practice in and out of school: A framework for connecting these experiences. Educational Studies in Mathematics, 31, 175-200. https://doi.org/10.1007/BF00143931
Merriam, S. B., & Grenier, R. S. (2019). Qualitative research in practice: Examples for discussion and analysis. San Francisco, USA: Jossey-Bass.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: Sage Publications.
Millî Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
Mohamed, L., & Waheed, H. (2011). Secondary students’ attitude towards mathematics in a selected school of Maldives. International Journal of Humanities and Social Science, 1, 277-281.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
National Research Council. (2000). How people learn: Brain, mind, experience, and school. Expanded edition. Washington, DC: The National Academies Press. https://doi.org/10.17226/9853
Neale, D. C. (1969). The role of attitudes in learning mathematics. The Arithmetic Teacher,16(8), 631-640.
Neuman, W. L. (2014). Social research methods: Qualitative and quantitative approaches. Harlow: Pearson.
Nicolaidou, M., & Philippou, G. (2003). Attitudes towards mathematics, self-efficacy and achievement in problem solving. In M. A. Mariotti (Ed.), European research in mathematics education III (pp. 1-11). Pisa: University of Pisa.
Patton, M. Q. (2015). Qualitative research & Evaluation methods: Integrating theory and practice. USA: Sage Publications, Inc.
Picker, S. H., & Berry, J. S. (2000). Investigating pupils' images of mathematicians. Educational Studies in Mathematics, 43, 65-94. https://doi.org/10.1023/A:1017523230758
Punch, S. (2002). Research with children: The same or different from research with adults? Childhood, 9(3), 321-341. https://doi.org/10.1177/0907568202009003005
Reys, R. E., & Nohda, N. (Eds.). (1994). Computational alternatives for the twenty-first century: Cross-cultural perspectives from Japan and the United States. Reston, VA: NCTM.
Richardson, K. M. (2004). Designing math trails for the elementary school. Teaching Children Mathematics, 11(1), 8-14.
Rock, D., & Shaw, J. M. (2000). Exploring children’s thinking about mathematicians and their work. Teaching Children Mathematics, 6(9), 550-555.
Sanchez, K., Zimmerman, L., & Ye, R. (2004). Secondary students’ attitudes toward mathematics. Academic Exchange Quarterly, 8(2), 56-60.
Thanheiser, E., Whitacre, I., & Roy, G. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on whole-number concepts and operations. The Mathematics Enthusiast, 11(2), 217-266.
Toluk Uçar, Z., Pişkin, M., Akkaş, E. N., & Taşçı, D. (2010). İlköğretim öğrencilerinin matematik, matematik öğretmenleri ve matematikçiler hakkındaki inançları. Eğitim ve Bilim, 35(155), 131-144.
Weber, S., & Mitchell, C. (1999). Drawing ourselves into teaching: Studying the images that shape and distort teacher education. Teaching and Teacher Education, 12(3), 303-313. https://doi.org/10.1016/0742-051X(95)00040-Q
Yavuz Mumcu, H. (2020). Ortaokul öğrencilerinin matematik algılarının resmetme yoluyla incelenmesi. Kastamonu Eğitim Dergisi, 28(1), 371-388. https://doi.org/10.24106/kefdergi.3620
Anning, A., & Ring, K. (2004). Making sense of children’s drawings. Maidenhead: Open University Press.
Bahr, D. L., & de Garcia, L. A. (2010). Elementary mathematics is anything but elementary. Belmont, CA: Wadsworth.
Barbosa, A., &Vale, I. (2016). Math trails: Meaningful mathematics outside the classroom with pre-service teachers. Journal of the European Teacher Education Network, 11, 63-72.
Biatchford, P. (1996). Pupils’ views on school work and school from 7 to 16 years. Research Papers in Education, 11(3), 263-288. https://doi.org/10.1080/0267152960110305
Borthwick, A. (2011). Children’s perceptions of and attitudes towards their mathematics lessons. In C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 31(1), 37-42. London. Retrieved from https://bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-31-1-07.pdf
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington DC: National Academy Press.
Bunting, C. J. (2006). Interdisciplinary teaching through outdoor education. Champaign, IL: Human Kinetics.
Burns, M., & Silbey, R. (2000). So you have to teach math? Sound advice for K-6 teachers. Sausalito, CA: Math Solutions.
Carey, E., Devine, A., Hill, F., Dowker, A., McLellan, R., & Szucs, D. (2019). Understanding mathematics anxiety: Investigating the experiences of UK primary and secondary school students. Retrieved from https://doi.org/10.17863/CAM.37744
Clements, D. H., & McMillen, S. (1996). Rethinking “concrete” manipulatives. Teaching Children Mathematics, 2(5), 270-279.
Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. New York: Routledge.
Cowan, P. (2006). Teaching mathematics: A handbook for primary and secondary school teachers. New York: Routledge.
Creswell, J. W. (2007). Qualitative inquiry and research design. Choosing among five approaches. Thousand Oaks, CA: Sage Publications, Inc.
Creswell, J. W. (2016). 30 essential skills for the qualitative researcher. Thousand Oaks, California: SAGE Publications Ltd.
Davis, A., Goulding, M., & Suggate, J. (2017). Mathematical knowledge for primary teachers. New York, NY: Routledge.
Department for Education and Employment (DfEE) (1999). The national curriculum: Handbook for primary teachers in England. London: DfEE and QCA.
Donovan, M. S., & Bransford, J. D. (Eds.). (2005). How students learn: History, mathematics, and science in the classroom. Washington, DC: The National Academies Press.
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. https://doi.org/10.1037/0012-1649.43.6.1428
Edwards, S. (2007). Primary mathematics for teaching assistants. USA: Routledge.
Ernst, K., & Ryan, S. (2014). Success from the start: Your first years teaching elementary mathematics. Reston, VA: NCTM.
Eshun, B. A. (2004). Sex-differences in attitude of students towards mathematics in secondary schools. Mathematics Connection, 4(1), 1-13.
Fägerstam, E., & Blom, J. (2013). Learning biology and mathematics outdoors: Effects and attitudes in a Swedish high school context. Journal of Adventure Education and Outdoor Learning, 13(1), 56-75. https://doi.org/10.1080/14729679.2011.647432
Fraser, B. J., & Kahle, J. B. (2007). Classroom, home and peer environment influences on student outcomes in science and mathematics: An analysis of systemic reform data. International journal of Science Education, 29(15), 1891-1909. https://doi.org/10.1080/09500690601167178
Freiman, V., Kadijevich, D., Kuntz, G., Pozdnyakov, S., & Stedøy, I. (2009). Technological environments beyond the classroom. In E. J. Barbeau & P. J. Taylors (Eds.), Challenging mathematics in and beyond the classroom (pp. 97-131). New York, NY: Springer.
Freitag, M. A. (2014). Mathematics for elementary school teachers: A process approach. Belmont, CA: Brooks/Cole.
Fuson, K. C. (1992). Research on learning and teaching addition and subtraction of whole numbers. In G. Leinhardt, R. T. Putnam, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 53-187). Hillsdale, New Jersey: Lawrence Erlbaum Associates, Inc.
Goulding, M. (1997). Learning to teach mathematics. London: David Fulton.
Gökçek, T., & Güneş, G. (2011). How students perceive the math teacher? Mehmet Akif Ersoy Üniversitesi Sosyal bilimler Enstitüsü Dergisi, 3(4), 1-9.
Grevholm, B. (2010). Norwegian upper secondary school students’ views of mathematics and images of mathematicians. In K. Kislenko (Ed.), Current state of research on mathematical beliefs XVI. Proceedings of the MAVI-16 Conference (pp. 120-136). Tallin, Estonia: Institute of Mathematics and Natural Sciences, Tallin University.
Hatısaru, V., & Çetinkaya, B. (2012). İlköğretim öğrencilerinin matematik ve matematikçi algılarının incelenmesi [Investigating elementary school students’ perceptions of mathematics and mathematicians]. X. National Congress of Science and Mathematics Education, Niğde University, Niğde.
Haylock, D. (2010). Mathematics explained for primary teachers (4th edition). London: SAGE Publications.
Haylock, D., & Thangata, F. (2007). Key concepts in teaching primary mathematics. London: SAGE Publications.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
Ho, W. K. (2008). Using history of mathematics in the teaching and learning of mathematics in Singapore. Paper presented at the 1st RICE, Singapore: Raffles Junior College.
Holton, D., Cheung, K., Kesianye, S., de Losada, M. F., Leikin, R. Makrides, G., … Yeap, B. (2009). Teacher development and mathematical challenge. In E. J. Barbeau & P. J. Taylors (Eds.), Challenging mathematics in and beyond the classroom (pp. 133-170). New York, NY: Springer.
Julien, H. (2008). Content analysis. In L. M. Given (Ed.), The SAGE encyclopedia of qualitative research methods (pp. 120-122). Thousand Oaks, California: SAGE Publications, Inc.
Kennard, J. (2007). Outdoor mathematics. Mathematics Teaching Incorporating Micromath, 201, 16-18.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Lerman, S. (1998). Research on socio-cultural perspectives of mathematics teaching and learning. In J. Kilpatrick & A. Sierpinska (Eds.), Mathematics education as a research domain: A search for identity. Vol. 1 (pp. 333-350). Dordrecht: Kluwer.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Malchiodi, C. A. (1998). Understanding children's drawings. New York: The Guilford Press.
Masingila, J. O., Davidenko, S., & Prus-Wisniowska, E. (1996). Mathematics learning and practice in and out of school: A framework for connecting these experiences. Educational Studies in Mathematics, 31, 175-200. https://doi.org/10.1007/BF00143931
Merriam, S. B., & Grenier, R. S. (2019). Qualitative research in practice: Examples for discussion and analysis. San Francisco, USA: Jossey-Bass.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: Sage Publications.
Millî Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
Mohamed, L., & Waheed, H. (2011). Secondary students’ attitude towards mathematics in a selected school of Maldives. International Journal of Humanities and Social Science, 1, 277-281.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
National Research Council. (2000). How people learn: Brain, mind, experience, and school. Expanded edition. Washington, DC: The National Academies Press. https://doi.org/10.17226/9853
Neale, D. C. (1969). The role of attitudes in learning mathematics. The Arithmetic Teacher,16(8), 631-640.
Neuman, W. L. (2014). Social research methods: Qualitative and quantitative approaches. Harlow: Pearson.
Nicolaidou, M., & Philippou, G. (2003). Attitudes towards mathematics, self-efficacy and achievement in problem solving. In M. A. Mariotti (Ed.), European research in mathematics education III (pp. 1-11). Pisa: University of Pisa.
Patton, M. Q. (2015). Qualitative research & Evaluation methods: Integrating theory and practice. USA: Sage Publications, Inc.
Picker, S. H., & Berry, J. S. (2000). Investigating pupils' images of mathematicians. Educational Studies in Mathematics, 43, 65-94. https://doi.org/10.1023/A:1017523230758
Punch, S. (2002). Research with children: The same or different from research with adults? Childhood, 9(3), 321-341. https://doi.org/10.1177/0907568202009003005
Reys, R. E., & Nohda, N. (Eds.). (1994). Computational alternatives for the twenty-first century: Cross-cultural perspectives from Japan and the United States. Reston, VA: NCTM.
Richardson, K. M. (2004). Designing math trails for the elementary school. Teaching Children Mathematics, 11(1), 8-14.
Rock, D., & Shaw, J. M. (2000). Exploring children’s thinking about mathematicians and their work. Teaching Children Mathematics, 6(9), 550-555.
Sanchez, K., Zimmerman, L., & Ye, R. (2004). Secondary students’ attitudes toward mathematics. Academic Exchange Quarterly, 8(2), 56-60.
Thanheiser, E., Whitacre, I., & Roy, G. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on whole-number concepts and operations. The Mathematics Enthusiast, 11(2), 217-266.
Toluk Uçar, Z., Pişkin, M., Akkaş, E. N., & Taşçı, D. (2010). İlköğretim öğrencilerinin matematik, matematik öğretmenleri ve matematikçiler hakkındaki inançları. Eğitim ve Bilim, 35(155), 131-144.
Weber, S., & Mitchell, C. (1999). Drawing ourselves into teaching: Studying the images that shape and distort teacher education. Teaching and Teacher Education, 12(3), 303-313. https://doi.org/10.1016/0742-051X(95)00040-Q
Yavuz Mumcu, H. (2020). Ortaokul öğrencilerinin matematik algılarının resmetme yoluyla incelenmesi. Kastamonu Eğitim Dergisi, 28(1), 371-388. https://doi.org/10.24106/kefdergi.3620