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The Opportunities for Mathematical Reasoning Skills That Teachers Provide for Their Students in The Learning Environment

Yıl 2024, Cilt: 11 Sayı: 3, 1 - 21, 02.05.2024
https://doi.org/10.17275/per.24.31.11.3

Öz

The acquisition of mathematical reasoning skills is directly related to the opportunities gained by the students in the learning environment. The complete lack or the rarity of such situations that support mathematical reasoning in the learning environment is an obstacle to conceptual learning. Therefore, it is important to investigate the extent to which different aspects of reasoning are encountered in teachers’ presentations and to convey the reflections of those from the learning environment. The objective of this study is to examine the opportunities for mathematical reasoning skills that teachers give to their students. A holistic case study design was used in the study process as a qualitative research approach. The study was carried out with two teachers working in public schools. Unstructured observations and video recordings conducted by the researchers were used to collect data, and content and descriptive analysis analyse the obtained data. When the teachers were evaluated regarding the opportunities for mathematical reasoning they provided in their classes, it was concluded that although these constitute a variety of opportunities, they present limited opportunities that could fully support mathematical reasoning. It is thought that offering limited opportunities in the learning environment may negatively affect students’ mathematical reasoning skills.

Destekleyen Kurum

no support

Proje Numarası

-

Teşekkür

We are grateful to the teachers who participated in this research.

Kaynakça

  • Altıparmak, K., & Oziş, T. (2005). An investigation upon mathematical proof and development of mathematical reasoning, Ege Journal of Education, 6(1), 25-37.
  • Arnesen, K. K., & Rø, K. (2022). The complexity of supporting reasoning in a mathematics classroom of shared authority. Mathematical Thinking and Learning, 1-26. https://doi.org/10.1080/10986065.2022.2059628.
  • Bahtiyari, A.O. (2010). The awareness in proof and reasoning concepts and their importances in mathematics education of the eight class. (Unpublished master’s dissertation). Atatürk University, Erzurum.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-8 sınıflar). [Teaching mathematics in secondary school (5th-8th grades) (Extended 2th ed.)]. Ankara: Pegem publisher.
  • Bergqvist, T., & Lithner, J. (2012). Mathematical reasoning in teachers’ presentations. The Journal of Mathematical Behavior, 31 (2), 252-269.
  • Birkeland, A. (2019). Pre-service teachers’ mathematical reasoning–how can it be developed?. The Mathematics Enthusiast, 16(1), 579-596.
  • Boaler, J. (2010). The road to reasoning. In K. Brodie (Ed.), Teaching mathematical reasoning in secondary school classrooms (pp. v–vii). New York: Springer.
  • Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89-105.
  • 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. London: Springer Science+Business Media.
  • Creswell, J.W. (2013). (Qualitative Inquiry and Research Design: Choosing Among Five Approaches). (Expanded Second Edition). (Translation Eds. Mesut Bütün & Selçuk Beşir Demir). Ankara: Siyasal Publisher.
  • Dahlan, J. A., & Wibisono, Y. (2021). The effect of hands-on and computer-based learning activities on conceptual understanding and mathematical reasoning. International Journal of Instruction, 14(1), 143-160. https://doi.org/10.29333/iji.2021.1419a
  • Davidson, A., Herbert, S., & Bragg, L. A. (2019). Supporting elementary teachers’ planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17, 1151-1171. https://doi.org/10.1007/s10763-018-9904-0
  • Ellis, A., Özgür, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31, 107-132. https://doi.org/10.1007/s13394-018-0246-6
  • Güler, A., Halıcıoğlu, M. B., & Taşğın, S. (2013). [Qualitative research methods in social sciences]. Ankara: Seçkin Publishing.
  • Herbert, S., & Bragg, L. A. (2021). Factors in a professional learning program to support a teacher’s growth in mathematical reasoning and its pedagogy. Mathematics education research journal, 33(3), 409-433.
  • Herbert, S., Vale, C., White, P., & Bragg, L. A. (2022). Engagement with a formative assessment rubric: A case of mathematical reasoning. International Journal of Educational Research, 111, https://doi.org/10.1016/j.ijer.2021.101899
  • Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review. Education sciences, 10(10), 289. https://doi.org/10.3390/educsci10100289.
  • House, P. (1999). Mathematical reasoning: in the eye of the beholder. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 175-188). Reston, VA: National Council of Teachers of Mathematics.
  • Işık, A. (2007). Görselleştirme ve matematik öğretimi [Visualisation and mathematics teaching]. İlköğretmen Eğitimci Dergisi [İlköğretmen Educator Journal], 7, 18-21.
  • Jäder, J., Sidenvall, J., & Sumpter, L. (2016). Students’ mathematical reasoning and beliefs in non-routine task solving. International Journal of Science and Mathematics Education, 15(4), 759–776. https://doi.org/10.1007/s10763-016-9712-3
  • Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20-32.
  • Karakuş, M., &Yeşilpınar, M. (2016). An analysis of activites and measurment-evalaution process in a sixth grade math lesson: a case study. Pegem Journal of Education and Instruction, 3 (1), 35-54.
  • Kocagül Sağlam, M., & Unal Çoban, G. (2018). Development of scientific reasoning skills test towards ınservice and pre-service science teachers. Elementary Education Online, 17(3).
  • Lannin, J., Ellis, A., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. NCTM.
  • Lithner, J. (2005). A framework for analysing qualities of mathematical reasoning: Version 3. Research Reports in Mathematics Education 3, Department of Mathematics, Umea˚ University.
  • Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning. Research Reports in Mathematics Education, Department of Mathematics, Ume˚a University.
  • Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67 (3), 255–276.
  • Malloy, C. E. (1999). Developing Mathematical Reasoning in the Middle Grades: Recognizing DiversityIn L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 13-22). Reston, VA: National Council of Teachers of Mathematics.
  • Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96, 169–186. https://doi.org/10.1007/s10649-017-9773-4
  • Melhuish, K., Thanheiser, E., & Guyot, L. (2018). Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization. Journal of Mathematics Teacher Education, 1-33.
  • Mevarech, Z. R., & Iddini, V. (2021). Developing young children's mathematics knowledge and reasoning through mathematics e-book activities supported by metacognitive scaffolding. Journal of Cognitive Education and Psychology, 20(2), 179-189.
  • Ministry of National Education, (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim program [ Secondary Mathematics Course (5, 6, 7 and 8th Grades) Curriculum]. Ministry of National Education. National Board of Education Supreme Council of National Education. Ankara, Turkey.
  • Ministry of National Education, (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı.[ Secondary Mathematics Course (5, 6, 7 and 8th Grades) Curriculum]. Ministry of National Education. National Board of Education Supreme Council of National Education. Ankara, Turkey.
  • Mukuka, A., Mutarutinya, V., & Balimuttajjo, S. (2021). Mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Journal on Mathematics Education, 12(1), 73-92. http://doi.org/10.22342/jme.12.1.12508.73-92.
  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1-20. https://doi.org/10.1080/24727466.2014.11790339
  • NCTM (2000). Principles and Standards for School Mathematics. Reston, Va. NCTM.
  • Oliveira, H., & Henriques, A., (2021). Preservice mathematics teachers’ knowledge about the potential of tasks to promote students’ mathematical reasoning. International Journal of Research in Education and Science (IJRES), 7(4), 1300-1319. https://doi.org/10.46328/ijres.2472
  • Olson, J. C. (2007). Developing students’mathematical reasoning through games. Teaching Children Mathematics, 13(9), 464-471.
  • Olsson, J., & Granberg, C. (2022). Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch. Mathematical Thinking and Learning, 1-28.
  • Olsson, J., & Teledahl, A. (2018). Feedback to encourage creative reasoning. In MADIF 11: The eleventh research seminar of the Swedish Society for Research in Mathematics Education, January 23–24, 2018, Karlstad University (pp. 101-110).
  • Oz, T., & Isık, A. (2020). Investigation of The possibilities for mathematical reasoning skills candidate mathematics teachers offer their students. Online Journal of Mathematics, Science and Technology Education, 1(1), 87-100.
  • Putra, A., Fauzi, K.M., & Landong, A. (2020). Differences in the improvement of students' mathematical reasoning ability and self-confidence between metacognitive approaches and realistic mathematical approaches in mts negeri baliğe. Journal of Education and Practice. 11 (36). Doi:10.7176/JEP/11-36-15.
  • Rohana, B. (2015). The enhancement of students’ teacher mathematical reasoning ability through reflective learning. Journal of Education and Practice. 6, (20).
  • Russell, S.J. (1999). Mathematical reasoning in the elementary grades. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 1-13). Reston, VA: National Council of Teachers of Mathematics.
  • Saleh, M., Prahmana, R. C. I., Muhammad, I., & Murni. (2018). Improving the reasoning ability of elementary school students through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. http://dx.doi.org/10.22342/jme.9.1.5049.41-54
  • Smit, R., Hess, K., Taras, A., Bachmann, P., & Dober, H. (2023). The role of interactive dialogue in students’ learning of mathematical reasoning: A quantitative multi-method analysis of feedback episodes. Learning and Instruction, 86, 101777. https://doi.org/10.1016/j.learninstruc.2023.101777
  • Stacey, K. (2006). What is mathematical thinking and why is it important. Progress report of the APEC project: collaborative studies on innovations for teaching and learning mathematics in different cultures (II)—Lesson study focusing on mathematical thinking. Tokyo and Sapporo, Japan.
  • Sukirwan, Darhim & Herman, T. (2018). Analysis of students’ mathematical reasoning. In Journal of Physics: Conference Series. (948, 1) pp. 012036. IOP Publishing.
  • Sumpter, L., & Hedefalk, M. (2018). Teachers' Roles in Preschool Children's Collective Mathematical Reasoning. European Journal of STEM Education, 3(3).
  • Tang, E.P., & Gınsburg, H.P. (1999). Young children’s mathematical reasoning: a psychological view. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 45-62). Reston, VA: National Council of Teachers of Mathematics.
  • Umay, A. (2003). Mathematical reasoning ability. Hacettepe University Journal of Education Faculty, 24, 234-243.
  • Umay, A., & Kaf, Y. (2005). A study on flawed reasoning in mathematics. Hacettepe University Journal of Education Faculty, 28, 188-195.
  • Xin, Y. P., Chiu, M. M., Tzur, R., Ma, X., Park, J. Y., & Yang, X. (2020). Linking teacher–learner discourse with mathematical reasoning of students with learning disabilities: An exploratory study. Learning Disability Quarterly, 43(1), 43-56. https://doi.org/10.1177/0731948719858707
  • Widiartana, I. P. H. (2018). The Effect of Open-Ended Approach Towards Students’ Mathematical Reasoning. In Journal of Physics: Conference Series. 1028 (1). pp. 012134.
  • 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.
  • Yıldırım, A. & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. (8th ed.). Ankara: Seçkin Publishing.
Yıl 2024, Cilt: 11 Sayı: 3, 1 - 21, 02.05.2024
https://doi.org/10.17275/per.24.31.11.3

Öz

Proje Numarası

-

Kaynakça

  • Altıparmak, K., & Oziş, T. (2005). An investigation upon mathematical proof and development of mathematical reasoning, Ege Journal of Education, 6(1), 25-37.
  • Arnesen, K. K., & Rø, K. (2022). The complexity of supporting reasoning in a mathematics classroom of shared authority. Mathematical Thinking and Learning, 1-26. https://doi.org/10.1080/10986065.2022.2059628.
  • Bahtiyari, A.O. (2010). The awareness in proof and reasoning concepts and their importances in mathematics education of the eight class. (Unpublished master’s dissertation). Atatürk University, Erzurum.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-8 sınıflar). [Teaching mathematics in secondary school (5th-8th grades) (Extended 2th ed.)]. Ankara: Pegem publisher.
  • Bergqvist, T., & Lithner, J. (2012). Mathematical reasoning in teachers’ presentations. The Journal of Mathematical Behavior, 31 (2), 252-269.
  • Birkeland, A. (2019). Pre-service teachers’ mathematical reasoning–how can it be developed?. The Mathematics Enthusiast, 16(1), 579-596.
  • Boaler, J. (2010). The road to reasoning. In K. Brodie (Ed.), Teaching mathematical reasoning in secondary school classrooms (pp. v–vii). New York: Springer.
  • Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89-105.
  • 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. London: Springer Science+Business Media.
  • Creswell, J.W. (2013). (Qualitative Inquiry and Research Design: Choosing Among Five Approaches). (Expanded Second Edition). (Translation Eds. Mesut Bütün & Selçuk Beşir Demir). Ankara: Siyasal Publisher.
  • Dahlan, J. A., & Wibisono, Y. (2021). The effect of hands-on and computer-based learning activities on conceptual understanding and mathematical reasoning. International Journal of Instruction, 14(1), 143-160. https://doi.org/10.29333/iji.2021.1419a
  • Davidson, A., Herbert, S., & Bragg, L. A. (2019). Supporting elementary teachers’ planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17, 1151-1171. https://doi.org/10.1007/s10763-018-9904-0
  • Ellis, A., Özgür, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31, 107-132. https://doi.org/10.1007/s13394-018-0246-6
  • Güler, A., Halıcıoğlu, M. B., & Taşğın, S. (2013). [Qualitative research methods in social sciences]. Ankara: Seçkin Publishing.
  • Herbert, S., & Bragg, L. A. (2021). Factors in a professional learning program to support a teacher’s growth in mathematical reasoning and its pedagogy. Mathematics education research journal, 33(3), 409-433.
  • Herbert, S., Vale, C., White, P., & Bragg, L. A. (2022). Engagement with a formative assessment rubric: A case of mathematical reasoning. International Journal of Educational Research, 111, https://doi.org/10.1016/j.ijer.2021.101899
  • Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review. Education sciences, 10(10), 289. https://doi.org/10.3390/educsci10100289.
  • House, P. (1999). Mathematical reasoning: in the eye of the beholder. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 175-188). Reston, VA: National Council of Teachers of Mathematics.
  • Işık, A. (2007). Görselleştirme ve matematik öğretimi [Visualisation and mathematics teaching]. İlköğretmen Eğitimci Dergisi [İlköğretmen Educator Journal], 7, 18-21.
  • Jäder, J., Sidenvall, J., & Sumpter, L. (2016). Students’ mathematical reasoning and beliefs in non-routine task solving. International Journal of Science and Mathematics Education, 15(4), 759–776. https://doi.org/10.1007/s10763-016-9712-3
  • Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20-32.
  • Karakuş, M., &Yeşilpınar, M. (2016). An analysis of activites and measurment-evalaution process in a sixth grade math lesson: a case study. Pegem Journal of Education and Instruction, 3 (1), 35-54.
  • Kocagül Sağlam, M., & Unal Çoban, G. (2018). Development of scientific reasoning skills test towards ınservice and pre-service science teachers. Elementary Education Online, 17(3).
  • Lannin, J., Ellis, A., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. NCTM.
  • Lithner, J. (2005). A framework for analysing qualities of mathematical reasoning: Version 3. Research Reports in Mathematics Education 3, Department of Mathematics, Umea˚ University.
  • Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning. Research Reports in Mathematics Education, Department of Mathematics, Ume˚a University.
  • Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67 (3), 255–276.
  • Malloy, C. E. (1999). Developing Mathematical Reasoning in the Middle Grades: Recognizing DiversityIn L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 13-22). Reston, VA: National Council of Teachers of Mathematics.
  • Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96, 169–186. https://doi.org/10.1007/s10649-017-9773-4
  • Melhuish, K., Thanheiser, E., & Guyot, L. (2018). Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization. Journal of Mathematics Teacher Education, 1-33.
  • Mevarech, Z. R., & Iddini, V. (2021). Developing young children's mathematics knowledge and reasoning through mathematics e-book activities supported by metacognitive scaffolding. Journal of Cognitive Education and Psychology, 20(2), 179-189.
  • Ministry of National Education, (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim program [ Secondary Mathematics Course (5, 6, 7 and 8th Grades) Curriculum]. Ministry of National Education. National Board of Education Supreme Council of National Education. Ankara, Turkey.
  • Ministry of National Education, (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı.[ Secondary Mathematics Course (5, 6, 7 and 8th Grades) Curriculum]. Ministry of National Education. National Board of Education Supreme Council of National Education. Ankara, Turkey.
  • Mukuka, A., Mutarutinya, V., & Balimuttajjo, S. (2021). Mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Journal on Mathematics Education, 12(1), 73-92. http://doi.org/10.22342/jme.12.1.12508.73-92.
  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1-20. https://doi.org/10.1080/24727466.2014.11790339
  • NCTM (2000). Principles and Standards for School Mathematics. Reston, Va. NCTM.
  • Oliveira, H., & Henriques, A., (2021). Preservice mathematics teachers’ knowledge about the potential of tasks to promote students’ mathematical reasoning. International Journal of Research in Education and Science (IJRES), 7(4), 1300-1319. https://doi.org/10.46328/ijres.2472
  • Olson, J. C. (2007). Developing students’mathematical reasoning through games. Teaching Children Mathematics, 13(9), 464-471.
  • Olsson, J., & Granberg, C. (2022). Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch. Mathematical Thinking and Learning, 1-28.
  • Olsson, J., & Teledahl, A. (2018). Feedback to encourage creative reasoning. In MADIF 11: The eleventh research seminar of the Swedish Society for Research in Mathematics Education, January 23–24, 2018, Karlstad University (pp. 101-110).
  • Oz, T., & Isık, A. (2020). Investigation of The possibilities for mathematical reasoning skills candidate mathematics teachers offer their students. Online Journal of Mathematics, Science and Technology Education, 1(1), 87-100.
  • Putra, A., Fauzi, K.M., & Landong, A. (2020). Differences in the improvement of students' mathematical reasoning ability and self-confidence between metacognitive approaches and realistic mathematical approaches in mts negeri baliğe. Journal of Education and Practice. 11 (36). Doi:10.7176/JEP/11-36-15.
  • Rohana, B. (2015). The enhancement of students’ teacher mathematical reasoning ability through reflective learning. Journal of Education and Practice. 6, (20).
  • Russell, S.J. (1999). Mathematical reasoning in the elementary grades. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 1-13). Reston, VA: National Council of Teachers of Mathematics.
  • Saleh, M., Prahmana, R. C. I., Muhammad, I., & Murni. (2018). Improving the reasoning ability of elementary school students through the Indonesian realistic mathematics education. Journal on Mathematics Education, 9(1), 41–54. http://dx.doi.org/10.22342/jme.9.1.5049.41-54
  • Smit, R., Hess, K., Taras, A., Bachmann, P., & Dober, H. (2023). The role of interactive dialogue in students’ learning of mathematical reasoning: A quantitative multi-method analysis of feedback episodes. Learning and Instruction, 86, 101777. https://doi.org/10.1016/j.learninstruc.2023.101777
  • Stacey, K. (2006). What is mathematical thinking and why is it important. Progress report of the APEC project: collaborative studies on innovations for teaching and learning mathematics in different cultures (II)—Lesson study focusing on mathematical thinking. Tokyo and Sapporo, Japan.
  • Sukirwan, Darhim & Herman, T. (2018). Analysis of students’ mathematical reasoning. In Journal of Physics: Conference Series. (948, 1) pp. 012036. IOP Publishing.
  • Sumpter, L., & Hedefalk, M. (2018). Teachers' Roles in Preschool Children's Collective Mathematical Reasoning. European Journal of STEM Education, 3(3).
  • Tang, E.P., & Gınsburg, H.P. (1999). Young children’s mathematical reasoning: a psychological view. In L. V. Stiff and F. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 45-62). Reston, VA: National Council of Teachers of Mathematics.
  • Umay, A. (2003). Mathematical reasoning ability. Hacettepe University Journal of Education Faculty, 24, 234-243.
  • Umay, A., & Kaf, Y. (2005). A study on flawed reasoning in mathematics. Hacettepe University Journal of Education Faculty, 28, 188-195.
  • Xin, Y. P., Chiu, M. M., Tzur, R., Ma, X., Park, J. Y., & Yang, X. (2020). Linking teacher–learner discourse with mathematical reasoning of students with learning disabilities: An exploratory study. Learning Disability Quarterly, 43(1), 43-56. https://doi.org/10.1177/0731948719858707
  • Widiartana, I. P. H. (2018). The Effect of Open-Ended Approach Towards Students’ Mathematical Reasoning. In Journal of Physics: Conference Series. 1028 (1). pp. 012134.
  • 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.
  • Yıldırım, A. & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. (8th ed.). Ankara: Seçkin Publishing.
Toplam 57 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Eğitim Üzerine Çalışmalar (Diğer)
Bölüm Research Articles
Yazarlar

Tuba Öz 0000-0003-0536-9360

Ahmet Işık Bu kişi benim 0000-0002-1055-2330

Proje Numarası -
Erken Görünüm Tarihi 7 Mayıs 2024
Yayımlanma Tarihi 2 Mayıs 2024
Kabul Tarihi 8 Mart 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 11 Sayı: 3

Kaynak Göster

APA Öz, T., & Işık, A. (2024). The Opportunities for Mathematical Reasoning Skills That Teachers Provide for Their Students in The Learning Environment. Participatory Educational Research, 11(3), 1-21. https://doi.org/10.17275/per.24.31.11.3