Research Article
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Improving Mathematical Reasoning and Mathematics Attitude of Disadvantaged Children in Rural Regions

Year 2019, Volume: 7 Issue: 14, 673 - 697, 29.10.2019
https://doi.org/10.18009/jcer.628742

Abstract

This
study aims at examining the effects of an enriched learning environment on
improving Mathematical Reasoning (MR) and Mathematics Attitude (MA) of
disadvantaged children (11-and 12-year-olds). The participants were 5th
graders (N = 17) and 6th graders (N = 18) who were studying in a
rural school in a province of Turkey. The data were obtained via Mathematical
Reasoning Test (MRT), Mathematics Attitude Scale (MAS), and groups
argumentation. A Wilcoxon Signed Rank test was used to reveal the pre/post-test differences. Statistical
comparisons of the MR and MA were also made by using the tests’ mean scores.
There is evidence from the environment that the MR of both groups was
significantly developed but grade/age did not have a significant effect
on MR. The study found that the MA of both groups improved after the
intervention, but these improvements were not statistically significant. No
significant effect was determined regarding age on the improvement of MA. This
research has shown that the MR and MA of children of such disadvantaged rural
regions can improve when rich learning environments are designed.

Supporting Institution

Adıyaman University

Project Number

EFMAP/2017-0001

Thanks

Adıyaman University Scientific Research Project Department

References

  • Baloğlu, M., & Koçak, R. (2006). A multivariate investigation of the differences in mathematics anxiety. Personality and Individual Differences, 40(7), 1325-1335.
  • Behr, M. J., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landau (Eds.), Acquisitions of mathematics concepts and processes (pp. 92–126). New York: Academic Press.
  • Bragg, L. A., Herbert, S., Loong, E. Y. K., Vale, C., & Widjaja, W. (2016). Primary teachers notice the impact of language on children’s mathematical reasoning. Mathematics Education Research Journal, 28(4), 523-544.
  • Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York: Springer.
  • Clarkson, P. C. (2004). Researching the language for rational explanations in mathematics teaching and learning. In Australian Association for Research in Education Conference, Melbourne, Australia.
  • Çiftçi, Ş. K., & Cin, F. M. (2018). What matters for rural teachers and communities? Educational challenges in rural Turkey. Compare: A Journal of Comparative and International Education, 48(5), 686-701.
  • DeLay, D., Laursen, B., Kiuru, N., Poikkeus, A. M., Aunola, K., & Nurmi, J. E. (2015). Stable same-sex friendships with higher achieving partners promote mathematical reasoning in lower achieving primary school children. British Journal of Developmental Psychology, 33(4), 519-532.
  • Ellis, A., Özgür, Z., & Reiten, L. (2018). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, https://doi.org/10.1007/s13394-018-0246-6
  • Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills (MA Thesis). Adıyaman University, Turkey
  • Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude (Doctoral dissertation). Ataturk University, Turkey.
  • Erdem, E. (2017). A current study on grade/age-and gender-related change in math anxiety. European Journal of Education Studies, 3(6), 396-413.
  • Erdem, E., & Soylu, Y. (2017). Age-and gender-related change in mathematical reasoning ability and some educational suggestions. Journal of Education and Practice, 8(7), 116-127.
  • Erdem, E., & Soylu, Y. (2019). The effect of a learning environment designed using different teaching ways on mathematical reasoning and mathematics attitude. Kastamonu Education Journal, 27(3), 1273-1290.
  • Fan, X., & Chen, M. (1999). Academic achievement of rural school students: A multi-year comparison with their peers in suburban and urban schools. Journal of Research in Rural Education, 15, 31-46.
  • Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33(1), 18-28.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
  • 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.
  • Holyoak, K. J. & Morrison, R. G. (2005). Thinking and reasoning: A reader’s guide. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 1–9). New York, NY: Cambridge University Press.
  • Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 31–39). Brisbane: MERGA.
  • Hunter, R. (2012). Coming to ‘know’ mathematics through being scaffolded to ‘talk and do’ mathematics. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal/hunter2.pdf
  • Hunter, J. (2014). Developing learning environments which support early algebraic reasoning: A case from a New Zealand primary classroom. Mathematics Education Research Journal, 26(4), 659-682.
  • Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16.
  • Jimerson, S., Egeland, B., & Teo, A. (1999). A longitudinal study of achievement trajectories: Factors associated with change. Journal of Educational Psychoogy, 91(1), 116–126.
  • Judge, S., & Watson, S. M. (2011). Longitudinal outcomes for mathematics achievement for students with learning disabilities. The Journal of Educational Research, 104(3), 147-157.
  • Kramarski, B. & Zeichner, O. (2001). Using technology to enhance mathematical reasoning: Effects of feedback and self-regulation learning. Educational Media International, 38(2-3), 77-82.
  • Kuhn, D., Shaw, V., & Felton, M. (1997). Effects of dyadic interaction on argumentative reasoning. Cognition and Instruction, 15, 287–315.
  • Lithner, J. (2000a). Mathematical reasoning and familiar procedures. International Journal of Mathematical Education in Science and Technology, 31(1), 83-95.
  • Lithner, J. (2000b). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41, 165-190.
  • Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.
  • Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937-949.
  • Mason, J. (2001). Questions about mathematical reasoning and proof in schools. Opening address to QCA Conference, UK.
  • McCrone, S. (2005). The development of mathematical discussions: an investigation of a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.
  • Moss, J. & Case, R. (1999). Developing children’s understanding of the rational numbers: a new model and experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122 – 147.
  • Ministry of National Education [MoNE]. (2013). Middle school mathematics 5-8. Classes teaching program. Ankara: Head Council of Education and Morality.
  • Mutodi, P., & Ngirande, H. (2014). Exploring mathematics anxiety: mathematics students' experiences. Mediterranean Journal of Social Sciences, 5(1), 283-294.
  • National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, Virginia.
  • Nisbet, S. (2006). Mathematics without attitude. Keynote address to the Annual Conference of the Queensland Association of Mathematics Teachers, Brisbane.
  • Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15-30.
  • Olson, J. (2007). Developing students’ mathematical reasoning through games. Teaching Children Mathematics, 13(9), 464-471.
  • Öğdül, H. G. (2010). Urban and rural definitions in regional context: A case study on Turkey. European Planning Studies, 18(9), 1519-1541.
  • Pape, S. J., Bell. C. V., & Yetkin, I. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics 53, 179-202.
  • Randolph, T. D. (1997). An assessment of mathematics anxiety in students from grades four through eight. Unpublished doctoral dissertation, Southern Illinois University at Carbondale, United States-Illinois.
  • Schliemann, A. D. & Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review, 22(2), 242-266.
  • Staples, M. E., & Truxaw, M. P. (2012). An initial framework for the language of higher-order thinking mathematics practices. Mathematics Education Research Journal, 24(3), 257-281.
  • Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99-120.
  • Şengül, S. & Dereli, M. (2013). The effect of learning integers using cartoons on 7th grade students’ attitude to mathematics. Educational Sciences: Theory & Practice, 13(4), 2509-2534.
  • Uğurel, I. & Moralı, S. (2006). Cartoons and their use in mathematics. National Education, 170, 32-47.
  • Vygotsky, L. S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press.
  • Williams, J. H. (2005). Cross-national variations in rural mathematics achievement. Journal of Research in Rural Education, 20(5)
  • Yackel, E. Cobb, P., & Wood, T. (1999). The interactive constitution of mathematical meaning in one second grade classroom: An illustrative example. Journal of Mathematical Behavior, 17(4), 469-488.
  • Yackel, E. & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, G. Martin and D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 227–236). Reston, VA: National Council of Teachers of Mathematics.
  • Yankelewitz, D., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. The Journal of Mathematical Behavior, 29, 76-85.

Improving Mathematical Reasoning and Mathematics Attitude of Disadvantaged Children in Rural Regions

Year 2019, Volume: 7 Issue: 14, 673 - 697, 29.10.2019
https://doi.org/10.18009/jcer.628742

Abstract

This
study aims at examining the effects of an enriched learning environment on
improving Mathematical Reasoning (MR) and Mathematics Attitude (MA) of
disadvantaged children (11-and 12-year-olds). The participants were 5th
graders (N = 17) and 6th graders (N = 18) who were studying in a
rural school in a province of Turkey. The data were obtained via Mathematical
Reasoning Test (MRT), Mathematics Attitude Scale (MAS), and groups
argumentation. A Wilcoxon Signed Rank test was used to reveal the pre/post-test differences. Statistical
comparisons of the MR and MA were also made by using the tests’ mean scores.
There is evidence from the environment that the MR of both groups was
significantly developed but grade/age did not have a significant effect
on MR. The study found that the MA of both groups improved after the
intervention, but these improvements were not statistically significant. No
significant effect was determined regarding age on the improvement of MA. This
research has shown that the MR and MA of children of such disadvantaged rural
regions can improve when rich learning environments are designed.

Project Number

EFMAP/2017-0001

References

  • Baloğlu, M., & Koçak, R. (2006). A multivariate investigation of the differences in mathematics anxiety. Personality and Individual Differences, 40(7), 1325-1335.
  • Behr, M. J., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landau (Eds.), Acquisitions of mathematics concepts and processes (pp. 92–126). New York: Academic Press.
  • Bragg, L. A., Herbert, S., Loong, E. Y. K., Vale, C., & Widjaja, W. (2016). Primary teachers notice the impact of language on children’s mathematical reasoning. Mathematics Education Research Journal, 28(4), 523-544.
  • Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York: Springer.
  • Clarkson, P. C. (2004). Researching the language for rational explanations in mathematics teaching and learning. In Australian Association for Research in Education Conference, Melbourne, Australia.
  • Çiftçi, Ş. K., & Cin, F. M. (2018). What matters for rural teachers and communities? Educational challenges in rural Turkey. Compare: A Journal of Comparative and International Education, 48(5), 686-701.
  • DeLay, D., Laursen, B., Kiuru, N., Poikkeus, A. M., Aunola, K., & Nurmi, J. E. (2015). Stable same-sex friendships with higher achieving partners promote mathematical reasoning in lower achieving primary school children. British Journal of Developmental Psychology, 33(4), 519-532.
  • Ellis, A., Özgür, Z., & Reiten, L. (2018). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, https://doi.org/10.1007/s13394-018-0246-6
  • Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills (MA Thesis). Adıyaman University, Turkey
  • Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude (Doctoral dissertation). Ataturk University, Turkey.
  • Erdem, E. (2017). A current study on grade/age-and gender-related change in math anxiety. European Journal of Education Studies, 3(6), 396-413.
  • Erdem, E., & Soylu, Y. (2017). Age-and gender-related change in mathematical reasoning ability and some educational suggestions. Journal of Education and Practice, 8(7), 116-127.
  • Erdem, E., & Soylu, Y. (2019). The effect of a learning environment designed using different teaching ways on mathematical reasoning and mathematics attitude. Kastamonu Education Journal, 27(3), 1273-1290.
  • Fan, X., & Chen, M. (1999). Academic achievement of rural school students: A multi-year comparison with their peers in suburban and urban schools. Journal of Research in Rural Education, 15, 31-46.
  • Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. The Journal of Special Education, 33(1), 18-28.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
  • 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.
  • Holyoak, K. J. & Morrison, R. G. (2005). Thinking and reasoning: A reader’s guide. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 1–9). New York, NY: Cambridge University Press.
  • Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 31–39). Brisbane: MERGA.
  • Hunter, R. (2012). Coming to ‘know’ mathematics through being scaffolded to ‘talk and do’ mathematics. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal/hunter2.pdf
  • Hunter, J. (2014). Developing learning environments which support early algebraic reasoning: A case from a New Zealand primary classroom. Mathematics Education Research Journal, 26(4), 659-682.
  • Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16.
  • Jimerson, S., Egeland, B., & Teo, A. (1999). A longitudinal study of achievement trajectories: Factors associated with change. Journal of Educational Psychoogy, 91(1), 116–126.
  • Judge, S., & Watson, S. M. (2011). Longitudinal outcomes for mathematics achievement for students with learning disabilities. The Journal of Educational Research, 104(3), 147-157.
  • Kramarski, B. & Zeichner, O. (2001). Using technology to enhance mathematical reasoning: Effects of feedback and self-regulation learning. Educational Media International, 38(2-3), 77-82.
  • Kuhn, D., Shaw, V., & Felton, M. (1997). Effects of dyadic interaction on argumentative reasoning. Cognition and Instruction, 15, 287–315.
  • Lithner, J. (2000a). Mathematical reasoning and familiar procedures. International Journal of Mathematical Education in Science and Technology, 31(1), 83-95.
  • Lithner, J. (2000b). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41, 165-190.
  • Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.
  • Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937-949.
  • Mason, J. (2001). Questions about mathematical reasoning and proof in schools. Opening address to QCA Conference, UK.
  • McCrone, S. (2005). The development of mathematical discussions: an investigation of a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.
  • Moss, J. & Case, R. (1999). Developing children’s understanding of the rational numbers: a new model and experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122 – 147.
  • Ministry of National Education [MoNE]. (2013). Middle school mathematics 5-8. Classes teaching program. Ankara: Head Council of Education and Morality.
  • Mutodi, P., & Ngirande, H. (2014). Exploring mathematics anxiety: mathematics students' experiences. Mediterranean Journal of Social Sciences, 5(1), 283-294.
  • National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, Virginia.
  • Nisbet, S. (2006). Mathematics without attitude. Keynote address to the Annual Conference of the Queensland Association of Mathematics Teachers, Brisbane.
  • Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15-30.
  • Olson, J. (2007). Developing students’ mathematical reasoning through games. Teaching Children Mathematics, 13(9), 464-471.
  • Öğdül, H. G. (2010). Urban and rural definitions in regional context: A case study on Turkey. European Planning Studies, 18(9), 1519-1541.
  • Pape, S. J., Bell. C. V., & Yetkin, I. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics 53, 179-202.
  • Randolph, T. D. (1997). An assessment of mathematics anxiety in students from grades four through eight. Unpublished doctoral dissertation, Southern Illinois University at Carbondale, United States-Illinois.
  • Schliemann, A. D. & Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review, 22(2), 242-266.
  • Staples, M. E., & Truxaw, M. P. (2012). An initial framework for the language of higher-order thinking mathematics practices. Mathematics Education Research Journal, 24(3), 257-281.
  • Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99-120.
  • Şengül, S. & Dereli, M. (2013). The effect of learning integers using cartoons on 7th grade students’ attitude to mathematics. Educational Sciences: Theory & Practice, 13(4), 2509-2534.
  • Uğurel, I. & Moralı, S. (2006). Cartoons and their use in mathematics. National Education, 170, 32-47.
  • Vygotsky, L. S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press.
  • Williams, J. H. (2005). Cross-national variations in rural mathematics achievement. Journal of Research in Rural Education, 20(5)
  • Yackel, E. Cobb, P., & Wood, T. (1999). The interactive constitution of mathematical meaning in one second grade classroom: An illustrative example. Journal of Mathematical Behavior, 17(4), 469-488.
  • Yackel, E. & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, G. Martin and D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 227–236). Reston, VA: National Council of Teachers of Mathematics.
  • Yankelewitz, D., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. The Journal of Mathematical Behavior, 29, 76-85.
There are 52 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Emrullah Erdem 0000-0002-6588-5431

Tahsin Fırat 0000-0002-3577-7907

Ramazan Gürbüz 0000-0002-2412-5882

Project Number EFMAP/2017-0001
Publication Date October 29, 2019
Submission Date October 3, 2019
Acceptance Date October 25, 2019
Published in Issue Year 2019 Volume: 7 Issue: 14

Cite

APA Erdem, E., Fırat, T., & Gürbüz, R. (2019). Improving Mathematical Reasoning and Mathematics Attitude of Disadvantaged Children in Rural Regions. Journal of Computer and Education Research, 7(14), 673-697. https://doi.org/10.18009/jcer.628742

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