International Journal of Elementary Education

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Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach

Received: 21 December 2018    Accepted: 12 February 2019    Published: 07 May 2019
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Abstract

New mathematics standards ask teachers to strengthen mathematics instruction while still building upon communication skills. In today's classroom, this is complicated by the growing number of English language learners (ELLs) across the country who because they are still learning English struggle with the language of mathematics. Researchers who have addressed the question of problem-solving among ELLs have explored schema-based instruction or the use of math journals. Of these two approaches, a discussion of the ELL population is not included in research on math journals and problem solving. Within the research on schema-based instruction, research limit their findings to ELLs with math difficulties (MD). This study addresses the gap in the research on problem-solving among ELLs. A writing structure referred to as Source, Path, Goal (SPG) was used as a linguistic scaffold and type of schema-based instruction. Instruction was set in an elementary ELL classroom. Each group received a different level of scaffolded instruction: 1) instruction only treatment group, 2) instruction plus practice treatment group. Three non-parametric sign tests were conducted (one for each group) to compare pre- and post-test results and indicated strong support for the use of scaffolding plus practice. An analysis of the students’ written explanations of how they solved their math problems only indicated an increase in problem-solving skills for instruction only treatment group, but both treatment groups increased in the depth of their mathematical thinking. Implications for practice and future research are shared.

DOI 10.11648/j.ijeedu.20190801.13
Published in International Journal of Elementary Education (Volume 8, Issue 1, March 2019)
Page(s) 18-25
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

English as a Second Language, Problem Solving, Cognitive Linguistics

References
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[2] Parmar, R. S., Cawley, J. F., & Frazita, R. R. (1996). Word problem-solving by students with and without mild disabilities. Exceptional Children, 62, 415–429.
[3] Jitendra, A. K., Star, J. R., Dupuis, D. N., & Rodriguez, M. C. (2013). Effectiveness of schema-based instruction for improving seventh-grade students’ proportional reasoning: A randomized experiment. Journal of Research on Educational Effectiveness, 6, 114–136. http://dx.doi.org/ 10.1080/19345747.2012.725804.
[4] Jitendra, A. K., Harwell, M. R., Dupuis, D. N., Karl, S. R., Lein, A. E., Simonson, G., & Slater, S. C. (2015). Effects of a research-based mathematics intervention to improve seventh-grade students’ proportional problem solving: A cluster randomized trial. Journal of Educational Psychology, 107, 1019–1034. doi: 10.1037/edu0000039.
[5] Driver, M. K. & Powell, S., (2017). Culturally and linguistically responsive schema intervention: Improving word problem solving for English language learners with mathematics difficulty. Learning Disability Quarterly, 40 (1) 41-45.
[6] English Learners in Public Schools (2018). The Condition of Education. National Center for Educational Statistics. Retrieved from https://nces.ed.gov/programs/coe/indicator_cgf.asp.
[7] Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly: Overcoming Learning Difficulties, 23:2, 139-159. doi: 10.1080/10573560601158461.
[8] Lowrie, T., Diezmann, C. M. & Logan, T. (2011). Understanding graphicacy: Students’ making sense of graphics in mathematics assessment tasks. International Journal for Mathematics Teaching and Learning, 12, 3. Retrieved from http://www.cimt.org.uk/journal/index.htm.
[9] Jitendra, A. K., Harwell, M. R., Dupuis, D. N., Karl, S. R., (2017). A randomized trial of the effects of schema-based instruction on proportional problem-solving for students with mathematics problem-solving difficulties. Journal of Learning Disabilities, 50 (3) 322–336.
[10] Jitendra, A. K., Star, J. R., Rodriguez, M., Lindell, M., & Someki, F. (2011). Improving students’ proportional thinking using schema-based instruction. Learning and Instruction, 21 (6), 731–745. doi: 10.1016/j.learninstruc.2011.04.002.
[11] Jitendra, A. K., Harwell, M. R., Dupuis, D. N., Karl, S. R., Lein, A. E., Simonson, G., & Slater, S. C. (2015). Effects of a research-based mathematics intervention to improve seventh-grade students’ proportional problem solving: A cluster randomized trial. Journal of Educational Psychology, 107, 1019–1034. doi: 10.1037/edu0000039.
[12] [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. doi: 10.1111/1540-5826.00079.
[13] Kalyuga, S. (2006) Assessment of learners' organised knowledge structures in adaptive learning environments. Applied Cognitive Psychology, 20(3), 311-320. doi: 10.1002/acp.1247.
[14] Kostos, K., & Shin, E. (2010). Using math journals to enhance second graders’ communication of mathematical thinking. Early Childhood Education Journal, 38 (3), 223-231. doi: 10.1007/s10643-010-0390-4.
[15] Martin, C. & Polly, D. (2016). Examining the impact of writing and literacy connections on mathematics learning. Investigations in Mathematics Learning, 8 (3), 59-74. doi: 10.1080/24727466.2016.11790354.
[16] Martin, C. L. (2015). Writing as a tool to demonstrate mathematical understanding. School Science & Mathematics, 115 (6), 302-313. doi: 10.1111/ssm.12131.
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[18] Font, V., Godino, J. D., Planas, N., & Acevedo, J. I. (2010). The object metaphor and synecdoche in mathematics classroom discourse. For the Learning of Mathematics, 30 (1), 15-19.
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[21] Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners. The Journal of Mathematical Behavior, 40, 43-62. doi: 10.1016/j.jmathb.2015.01.005.
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Author Information
  • Department of Languages, Literacy and Culture, University of Nevada, Reno, USA

  • Department of Curriculum and Teaching, Auburn University, Auburn, USA

  • Loder Elementary School, Washoe County Schools, Reno, USA

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  • APA Style

    Rod Case, Gwendolyn Williams, Peter Cobin. (2019). Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach. International Journal of Elementary Education, 8(1), 18-25. https://doi.org/10.11648/j.ijeedu.20190801.13

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    Rod Case; Gwendolyn Williams; Peter Cobin. Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach. Int. J. Elem. Educ. 2019, 8(1), 18-25. doi: 10.11648/j.ijeedu.20190801.13

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    AMA Style

    Rod Case, Gwendolyn Williams, Peter Cobin. Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach. Int J Elem Educ. 2019;8(1):18-25. doi: 10.11648/j.ijeedu.20190801.13

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  • @article{10.11648/j.ijeedu.20190801.13,
      author = {Rod Case and Gwendolyn Williams and Peter Cobin},
      title = {Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach},
      journal = {International Journal of Elementary Education},
      volume = {8},
      number = {1},
      pages = {18-25},
      doi = {10.11648/j.ijeedu.20190801.13},
      url = {https://doi.org/10.11648/j.ijeedu.20190801.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijeedu.20190801.13},
      abstract = {New mathematics standards ask teachers to strengthen mathematics instruction while still building upon communication skills. In today's classroom, this is complicated by the growing number of English language learners (ELLs) across the country who because they are still learning English struggle with the language of mathematics. Researchers who have addressed the question of problem-solving among ELLs have explored schema-based instruction or the use of math journals. Of these two approaches, a discussion of the ELL population is not included in research on math journals and problem solving. Within the research on schema-based instruction, research limit their findings to ELLs with math difficulties (MD). This study addresses the gap in the research on problem-solving among ELLs. A writing structure referred to as Source, Path, Goal (SPG) was used as a linguistic scaffold and type of schema-based instruction. Instruction was set in an elementary ELL classroom. Each group received a different level of scaffolded instruction: 1) instruction only treatment group, 2) instruction plus practice treatment group. Three non-parametric sign tests were conducted (one for each group) to compare pre- and post-test results and indicated strong support for the use of scaffolding plus practice. An analysis of the students’ written explanations of how they solved their math problems only indicated an increase in problem-solving skills for instruction only treatment group, but both treatment groups increased in the depth of their mathematical thinking. Implications for practice and future research are shared.},
     year = {2019}
    }
    

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    AB  - New mathematics standards ask teachers to strengthen mathematics instruction while still building upon communication skills. In today's classroom, this is complicated by the growing number of English language learners (ELLs) across the country who because they are still learning English struggle with the language of mathematics. Researchers who have addressed the question of problem-solving among ELLs have explored schema-based instruction or the use of math journals. Of these two approaches, a discussion of the ELL population is not included in research on math journals and problem solving. Within the research on schema-based instruction, research limit their findings to ELLs with math difficulties (MD). This study addresses the gap in the research on problem-solving among ELLs. A writing structure referred to as Source, Path, Goal (SPG) was used as a linguistic scaffold and type of schema-based instruction. Instruction was set in an elementary ELL classroom. Each group received a different level of scaffolded instruction: 1) instruction only treatment group, 2) instruction plus practice treatment group. Three non-parametric sign tests were conducted (one for each group) to compare pre- and post-test results and indicated strong support for the use of scaffolding plus practice. An analysis of the students’ written explanations of how they solved their math problems only indicated an increase in problem-solving skills for instruction only treatment group, but both treatment groups increased in the depth of their mathematical thinking. Implications for practice and future research are shared.
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