Araştırma Makalesi
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EXAMINATION OF DIAGRAMMATIC REPRESENTATION AND VERBAL PROBLEM-SOLVING REPRESENTATIONS OF PRIMARY SCHOOL STUDENTS

Yıl 2023, Cilt: 12 Sayı: 3, 228 - 244, 30.09.2023

Emel Çilingir Altıner Halil Önal

https://doi.org/10.55020/iojpe.1288522

Öz

This study aimed to examine the diagrammatic representation skills and problem-solving performances of students according to their problem-solving representations. A cross-sectional survey design using quantitative methods was used in this study. The sample consisted of 31 second-grade and 41 third-grade students from a public primary school in Turkey. The Diagrammatic Representation Test and Mathematical Operations Test were used in this study. The data were analyzed with descriptive statistical analysis, the chi-square test, the independent samples t-test, discriminant analysis and logistic regression analysis. The findings indicated that while the preferred types of representations for solving verbal problems and problem-solving performance did not vary significantly based on grade level, scores obtained from the diagrammatic representation test exhibited significant differences. It was observed that students' problem-solving performance and diagrammatic skills could predict their preferred types of representations for solving verbal problems. Consequently, students who possess knowledge regarding effective representation preferences, as well as the ability to construct and utilize them, are more likely to generate appropriate and high-quality representations, leading to accurate problem-solving outcomes. This, in turn, enhances their performance in diagrammatic representation tasks.

Anahtar Kelimeler

Diagrammatic representation pictorial representation schematic representation symbolic representation verbal problem solving

Etik Beyan

This study was designed in accordance with ethical rules, and the necessary approvals were obtained, including parent consent forms, school board information forms, and university ethics board report [45346595 – Date: 05/07/2021 No: 131383]. Students were informed that their responses would be kept confidential and used for research purposes only, and they were told that they could withdraw from this study at any time. The authors declare that they have no competing interests.

Destekleyen Kurum

Çukurova University

Proje Numarası

SBA-2021-13633

Teşekkür

We would like to thank Çukurova University BAPSIS unit for supporting this study and also the children and their teachers who voluntarily participated in the study.

Kaynakça

  • Acevedo Nistal, A., Clarebout, G., Elen, J., Van Dooren,W., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM-The International Journal on Mathematics Education, 41, 627-636. https://doi.org/10.1007/s11858-009-0189-1
  • Baltacı, A. (2018). Nitel araştırmalarda örnekleme yöntemleri ve örnek hacmi sorunsalı üzerine kavramsal bir inceleme [A conceptual review of sampling methods and sample size problems in qualitative research]. Bitlis Eren University Social Science Journal, 7(1), 231-274.
  • Beckmann, S. (2004). Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4–6 texts used in Singapore. The Mathematics Educator, 14, 42–46.
  • Blazhenkova, O., & Kozhevnikov, M. (2009). The new object‐spatial‐verbal cognitive style model: Theory and measurement. Applied Cognitive Psychology: The Official Journal of the Society for Applied Research in Memory and Cognition, 23(5), 638-663. https://doi.org/10.1002/acp.1473
  • Boonen, A. J. H., van der Schoot, M., Van Wesel, F., De Vries, M. H. & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001
  • Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van Der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001
  • Booth, J. L., & Koedinger, K. R. (2012). Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving. British Journal of Educational Psychology, 82(3), 492-511. https://doi.org/10.1111/j.2044-8279.2011.02041.x
  • Cheng, P. C. (2004, March). Why diagrams are (sometimes) six times easier than words: benefits beyond locational indexing. In International Conference on Theory and Application of Diagrams (pp. 242-254). Springer, Berlin, Heidelberg.
  • Cooper, J. L., Sidney, P. G., & Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology, 32(1), 24-38. https://doi.org/10.1002/acp.3371
  • Davenport, J. L., Yaron, D., Klahr, D., & Koedinger, K. (2008). When do diagrams enhance learning? A framework for designing relevant representations. In Proceedings of the 8th international conference on International conference for the learning sciences - Volume 1 (ICLS'08). International Society of the Learning Sciences, 191–198. https://doi.org/10.5555/1599812.1599834
  • Diezmann, C., & Lowrie, T. (2009). Primary students' spatial visualization and spatial orientation: an evidence base for instruction. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 417-424). PME, Greece.
  • Ertuna, L., & Uçar, Z. T. (2021). An investigation of elementary school 4-7th grade students' ability to link equivalent fractions' symbolic and graphical representations. Sakarya University Journal of Education, 11(3), 613-631. https://doi.org/10.19126/suje.992377
  • Fraenkel, J. R., & N. E. Wallen. (2003). How to design and evaluate research in education. New York: McGraw Hill.
  • Frick, A., & Newcombe, N. S. (2015). Young children's perception of diagrammatic representations. Spatial Cognition & Computation, 15(4), 227-245. https://doi.org/10.1080/13875868.2015.1046988
  • Galindo-Morales, E. (1994). Visualization in the calculus class: Relationship between cognitive style, gender, and use of technology (Doctoral dissertation), The Ohio State University.
  • Gültekin, S. B., & Altun, T. (2022). Investigating the Impact of Activities Based on Scientific Process Skills on 4th Grade Students' Problem-Solving Skills. International Electronic Journal of Elementary Education, 14(4), 491-500. https://doi.org/10.26822/iiejee.2022.258
  • Hatisaru, V. (2020). Exploring evidence of mathematical tasks and representations in the drawings of middle school students. International Electronic Journal of Mathematics Education, 15(3), em0609. https://doi.org/10.29333/iejme/8482
  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684-689.
  • Johnson-Laird, P. N. (1983). A computational analysis of consciousness. Cognition & Brain Theory, 6(4), 499–508.
  • Kalayc, S. (2005). Multvarate Statstcal Technques wth SPSS. Asl Publsher, Ankara, Turkey
  • Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory & cognition, 33(4), 710-726. https://doi.org/10.3758/BF03195337
  • Krutetskii V. A. (1976). The psychology of mathematical abilities in schoolchildren, University of Chicago Press, Chicago.
  • Lowrie, T. (2020). The utility of diagrams in elementary problem solving. Cognitive Development, 55, 1-12. https://doi.org/10.1016/j.cogdev.2020.100921
  • Lowrie, T., & Clements, M. K. (2001). Visual and nonvisual processes in Grade 6 students' mathematical problem solving. Journal of Research in Childhood Education, 16(1), 77-93. https://doi.org/10.1080/02568540109594976
  • Lowrie, T., & Kay, R. (2001). Relationship between visual and nonvisual solution methods and difficulty in elementary mathematics. Journal of Educational Research, 94(4), 94(4), 248–255. https://doi.org/10.1080/00220670109598758
  • Mayer, R. (2005). Cognitive theory of multimedia learning. In R. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 31–48). Cambridge: Cambridge University Press.
  • Mayer, R. E. (1989). Models for understanding. Review of educational research, 59(1), 43-64. https://doi.org/10.3102/00346543059001043
  • Mayer, R. E., & Massa, L. J. (2003). Three facets of visual and verbal learners: Cognitive ability, cognitive style, and learning preference. Journal of educational psychology, 95(4), 833. https://doi.org/10.1037/0022-0663.95.4.833
  • Metin, M. (2014). Eğitimde bilimsel araştırma yöntemleri [Scientific research methods in education]. Ankara: Pegem Academy Publications.
  • Meyer, J. (2000). Performance with tables and graphs: Effects of training and a visual searchmodel. Ergonomics, 43, 1840 1865. https://doi.org/10.1080/00140130050174509
  • Murata, A. (2004). Paths to learning ten-structured understanding of teen sums: Addition solution methods of Japanese grade 1 students. Cognition and Instruction, 22, 185–218. https://doi.org/10.1207/s1532690xci2202_2
  • Murayama, K. (2003). Learning strategy use and short- and long-term perceived utility. Japanese Journal of Educational Psychology, 51, 130–140. https://doi.org/10.5926/jjep1953.51.2_130
  • National Center for Education Statistics (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Presmeg, N. C. (2006, July). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19-34).
  • Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53-78. https://doi.org/10.1007/s10649-016-9736-1
  • Sevimli, E. (2013). Bilgisayar cebiri sistemi destekli öğretimin farklı düşünme yapısındaki öğrencilerin integral konusundaki temsil dönüşüm süreçlerine etkisi [The effect of a computer algebra system supported teaching on processes of representational transition inintegral topics of students with different types of thinking]. (Unpublished Doctoral dissertation). Marmara University, Turkey.
  • Stenning, K., & Oberlander, J. (1995). A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive science, 19(1), 97-140. https://doi.org/10.1016/0364-0213(95)90005-5
  • Stylianou, D. (2010). Teachers’ conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325-434. https://doi.org/10.1007/s10857-0109143-y
  • Surya, E., Sabandar, J., Kusumah, Y. S., & Darhim, D. (2013). Improving of junior high school visual thinking representation ability ın mathematical problem solving by Ctl. Journal. Math. Edu., 1(4). https://doi.org/10.22342/jme.4.1.568.113-126
  • Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh grade students (Unpublished Doctoral dissertation). Monash University.
  • Taşova, H. İ. (2011). Matematik öğretmen adaylarının modelleme etkinlikleri ve performansı sürecinde düşünme ve görselleme becerilerinin incelenmesi [Investigating thinking and visualisation skills of preservice mathematics teachers in modelling activities and performance]. (UnpublishedDoctoral dissertation). Marmara University, Turkey.
  • Tian, F., Hou, Y., Zhu, W., Dietrich, A., Zhang, Q., Yang, W., ... & Cao, G. (2017). Getting the joke: insight during humor comprehension–evidence from an fMRI study. Frontiers in psychology, 8, 1835. https://doi.org/10.3389/fpsyg.2017.01835
  • Tytler, R., Prain, V., Kirk, M. et al. (2023) Characterising a representation construction pedagogy for ıntegrating science and mathematics in the primary school. Int J of Sci and Math Educ 21, 1153–1175. https://doi.org/10.1007/s10763-022-10284-4
  • Uesaka, Y., & Manalo, E. (2012). Task‐related factors that influence the spontaneous use of diagrams in math word problems. Applied Cognitive Psychology, 26(2), 251-260. https://doi.org/10.1002/acp.1816
  • Uesaka, Y., Manalo, E., & Ichikawa, S. I. (2010, August). The effects of perception of efficacy and diagram construction skills on students’ spontaneous use of diagrams when solving math word problems. In International Conference on Theory and Application of Diagrams (pp. 197-211). Springer, Berlin, Heidelberg.
  • Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of learning disabilities, 40(6), 540-553. https://doi.org/10.1177/00222194070400060501
  • Van Garderen, D., & Montague, M. (2003). Visual‐spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246-254. https://doi.org/10.1111/1540-5826.00079
  • Van Garderen, D., Scheuermann, A., & Jackson, C. (2012). Developing representational ability in mathematics for students with learning disabilities: A content analysis of grades 6 and 7 textbooks. In Learning Disability Quarterly, 35(1), 24-38. https://doi.org/10.1177/0731948711429726
  • Van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Disability Quarterly, 36(3), 145–160. https://doi.org/10.1177/0731948712438558
  • Zahner, D., & Corter, J. E. (2010). The process of probability problem solving: Use of external visual representations. Mathematical Thinking and Learning, 12(2), 177-204. https://doi.org/10.1080/10986061003654240

Yıl 2023, Cilt: 12 Sayı: 3, 228 - 244, 30.09.2023

Emel Çilingir Altıner Halil Önal

https://doi.org/10.55020/iojpe.1288522

Öz

Proje Numarası

SBA-2021-13633

Kaynakça

  • Acevedo Nistal, A., Clarebout, G., Elen, J., Van Dooren,W., & Verschaffel, L. (2009). Conceptualising, investigating and stimulating representational flexibility in mathematical problem solving and learning: A critical review. ZDM-The International Journal on Mathematics Education, 41, 627-636. https://doi.org/10.1007/s11858-009-0189-1
  • Baltacı, A. (2018). Nitel araştırmalarda örnekleme yöntemleri ve örnek hacmi sorunsalı üzerine kavramsal bir inceleme [A conceptual review of sampling methods and sample size problems in qualitative research]. Bitlis Eren University Social Science Journal, 7(1), 231-274.
  • Beckmann, S. (2004). Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4–6 texts used in Singapore. The Mathematics Educator, 14, 42–46.
  • Blazhenkova, O., & Kozhevnikov, M. (2009). The new object‐spatial‐verbal cognitive style model: Theory and measurement. Applied Cognitive Psychology: The Official Journal of the Society for Applied Research in Memory and Cognition, 23(5), 638-663. https://doi.org/10.1002/acp.1473
  • Boonen, A. J. H., van der Schoot, M., Van Wesel, F., De Vries, M. H. & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001
  • Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van Der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001
  • Booth, J. L., & Koedinger, K. R. (2012). Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving. British Journal of Educational Psychology, 82(3), 492-511. https://doi.org/10.1111/j.2044-8279.2011.02041.x
  • Cheng, P. C. (2004, March). Why diagrams are (sometimes) six times easier than words: benefits beyond locational indexing. In International Conference on Theory and Application of Diagrams (pp. 242-254). Springer, Berlin, Heidelberg.
  • Cooper, J. L., Sidney, P. G., & Alibali, M. W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology, 32(1), 24-38. https://doi.org/10.1002/acp.3371
  • Davenport, J. L., Yaron, D., Klahr, D., & Koedinger, K. (2008). When do diagrams enhance learning? A framework for designing relevant representations. In Proceedings of the 8th international conference on International conference for the learning sciences - Volume 1 (ICLS'08). International Society of the Learning Sciences, 191–198. https://doi.org/10.5555/1599812.1599834
  • Diezmann, C., & Lowrie, T. (2009). Primary students' spatial visualization and spatial orientation: an evidence base for instruction. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 417-424). PME, Greece.
  • Ertuna, L., & Uçar, Z. T. (2021). An investigation of elementary school 4-7th grade students' ability to link equivalent fractions' symbolic and graphical representations. Sakarya University Journal of Education, 11(3), 613-631. https://doi.org/10.19126/suje.992377
  • Fraenkel, J. R., & N. E. Wallen. (2003). How to design and evaluate research in education. New York: McGraw Hill.
  • Frick, A., & Newcombe, N. S. (2015). Young children's perception of diagrammatic representations. Spatial Cognition & Computation, 15(4), 227-245. https://doi.org/10.1080/13875868.2015.1046988
  • Galindo-Morales, E. (1994). Visualization in the calculus class: Relationship between cognitive style, gender, and use of technology (Doctoral dissertation), The Ohio State University.
  • Gültekin, S. B., & Altun, T. (2022). Investigating the Impact of Activities Based on Scientific Process Skills on 4th Grade Students' Problem-Solving Skills. International Electronic Journal of Elementary Education, 14(4), 491-500. https://doi.org/10.26822/iiejee.2022.258
  • Hatisaru, V. (2020). Exploring evidence of mathematical tasks and representations in the drawings of middle school students. International Electronic Journal of Mathematics Education, 15(3), em0609. https://doi.org/10.29333/iejme/8482
  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684-689.
  • Johnson-Laird, P. N. (1983). A computational analysis of consciousness. Cognition & Brain Theory, 6(4), 499–508.
  • Kalayc, S. (2005). Multvarate Statstcal Technques wth SPSS. Asl Publsher, Ankara, Turkey
  • Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory & cognition, 33(4), 710-726. https://doi.org/10.3758/BF03195337
  • Krutetskii V. A. (1976). The psychology of mathematical abilities in schoolchildren, University of Chicago Press, Chicago.
  • Lowrie, T. (2020). The utility of diagrams in elementary problem solving. Cognitive Development, 55, 1-12. https://doi.org/10.1016/j.cogdev.2020.100921
  • Lowrie, T., & Clements, M. K. (2001). Visual and nonvisual processes in Grade 6 students' mathematical problem solving. Journal of Research in Childhood Education, 16(1), 77-93. https://doi.org/10.1080/02568540109594976
  • Lowrie, T., & Kay, R. (2001). Relationship between visual and nonvisual solution methods and difficulty in elementary mathematics. Journal of Educational Research, 94(4), 94(4), 248–255. https://doi.org/10.1080/00220670109598758
  • Mayer, R. (2005). Cognitive theory of multimedia learning. In R. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 31–48). Cambridge: Cambridge University Press.
  • Mayer, R. E. (1989). Models for understanding. Review of educational research, 59(1), 43-64. https://doi.org/10.3102/00346543059001043
  • Mayer, R. E., & Massa, L. J. (2003). Three facets of visual and verbal learners: Cognitive ability, cognitive style, and learning preference. Journal of educational psychology, 95(4), 833. https://doi.org/10.1037/0022-0663.95.4.833
  • Metin, M. (2014). Eğitimde bilimsel araştırma yöntemleri [Scientific research methods in education]. Ankara: Pegem Academy Publications.
  • Meyer, J. (2000). Performance with tables and graphs: Effects of training and a visual searchmodel. Ergonomics, 43, 1840 1865. https://doi.org/10.1080/00140130050174509
  • Murata, A. (2004). Paths to learning ten-structured understanding of teen sums: Addition solution methods of Japanese grade 1 students. Cognition and Instruction, 22, 185–218. https://doi.org/10.1207/s1532690xci2202_2
  • Murayama, K. (2003). Learning strategy use and short- and long-term perceived utility. Japanese Journal of Educational Psychology, 51, 130–140. https://doi.org/10.5926/jjep1953.51.2_130
  • National Center for Education Statistics (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Presmeg, N. C. (2006, July). A semiotic view of the role of imagery and inscriptions in mathematics teaching and learning. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19-34).
  • Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53-78. https://doi.org/10.1007/s10649-016-9736-1
  • Sevimli, E. (2013). Bilgisayar cebiri sistemi destekli öğretimin farklı düşünme yapısındaki öğrencilerin integral konusundaki temsil dönüşüm süreçlerine etkisi [The effect of a computer algebra system supported teaching on processes of representational transition inintegral topics of students with different types of thinking]. (Unpublished Doctoral dissertation). Marmara University, Turkey.
  • Stenning, K., & Oberlander, J. (1995). A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive science, 19(1), 97-140. https://doi.org/10.1016/0364-0213(95)90005-5
  • Stylianou, D. (2010). Teachers’ conceptions of representation in middle school mathematics. Journal of Mathematics Teacher Education, 13(4), 325-434. https://doi.org/10.1007/s10857-0109143-y
  • Surya, E., Sabandar, J., Kusumah, Y. S., & Darhim, D. (2013). Improving of junior high school visual thinking representation ability ın mathematical problem solving by Ctl. Journal. Math. Edu., 1(4). https://doi.org/10.22342/jme.4.1.568.113-126
  • Suwarsono, S. (1982). Visual imagery in the mathematical thinking of seventh grade students (Unpublished Doctoral dissertation). Monash University.
  • Taşova, H. İ. (2011). Matematik öğretmen adaylarının modelleme etkinlikleri ve performansı sürecinde düşünme ve görselleme becerilerinin incelenmesi [Investigating thinking and visualisation skills of preservice mathematics teachers in modelling activities and performance]. (UnpublishedDoctoral dissertation). Marmara University, Turkey.
  • Tian, F., Hou, Y., Zhu, W., Dietrich, A., Zhang, Q., Yang, W., ... & Cao, G. (2017). Getting the joke: insight during humor comprehension–evidence from an fMRI study. Frontiers in psychology, 8, 1835. https://doi.org/10.3389/fpsyg.2017.01835
  • Tytler, R., Prain, V., Kirk, M. et al. (2023) Characterising a representation construction pedagogy for ıntegrating science and mathematics in the primary school. Int J of Sci and Math Educ 21, 1153–1175. https://doi.org/10.1007/s10763-022-10284-4
  • Uesaka, Y., & Manalo, E. (2012). Task‐related factors that influence the spontaneous use of diagrams in math word problems. Applied Cognitive Psychology, 26(2), 251-260. https://doi.org/10.1002/acp.1816
  • Uesaka, Y., Manalo, E., & Ichikawa, S. I. (2010, August). The effects of perception of efficacy and diagram construction skills on students’ spontaneous use of diagrams when solving math word problems. In International Conference on Theory and Application of Diagrams (pp. 197-211). Springer, Berlin, Heidelberg.
  • Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of learning disabilities, 40(6), 540-553. https://doi.org/10.1177/00222194070400060501
  • Van Garderen, D., & Montague, M. (2003). Visual‐spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246-254. https://doi.org/10.1111/1540-5826.00079
  • Van Garderen, D., Scheuermann, A., & Jackson, C. (2012). Developing representational ability in mathematics for students with learning disabilities: A content analysis of grades 6 and 7 textbooks. In Learning Disability Quarterly, 35(1), 24-38. https://doi.org/10.1177/0731948711429726
  • Van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Disability Quarterly, 36(3), 145–160. https://doi.org/10.1177/0731948712438558
  • Zahner, D., & Corter, J. E. (2010). The process of probability problem solving: Use of external visual representations. Mathematical Thinking and Learning, 12(2), 177-204. https://doi.org/10.1080/10986061003654240
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Sınıf Eğitimi, Alan Eğitimleri
Bölüm Research Articles
Yazarlar

Emel Çilingir Altıner 0000-0002-8085-553X

Halil Önal 0000-0001-6983-3842

Proje Numarası SBA-2021-13633
Yayımlanma Tarihi 30 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 12 Sayı: 3

Kaynak Göster

APA Çilingir Altıner, E., & Önal, H. (2023). EXAMINATION OF DIAGRAMMATIC REPRESENTATION AND VERBAL PROBLEM-SOLVING REPRESENTATIONS OF PRIMARY SCHOOL STUDENTS. International Online Journal of Primary Education, 12(3), 228-244. https://doi.org/10.55020/iojpe.1288522
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