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.
| Published in | International Journal of Elementary Education (Volume 8, Issue 1) |
| DOI | 10.11648/j.ijeedu.20190801.13 |
| 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), 2019. Published by Science Publishing Group |
English as a Second Language, Problem Solving, Cognitive Linguistics
| [1] | Xin, Y., Jitendra, A. K., & Deatline-Buchanan, A. (2005). The effects of mathematical word problem-solving on middle school students with learning problems. The Journal of Special Education, 39 (3), 181-192. Retrieved February/March. |
| [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. |
| [17] | Lakoff, G. & Nuñez, R. E. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York: Basic Books. |
| [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. |
| [19] | Wood, M. B. (2010). Not understanding Andy: A metaphorical analysis students’ resistance to learning. For the Learning of Mathematics, 30 (3), 17-22. |
| [20] | Liedtke, W. W., & Sales, J. (2001). Writing tasks that succeed. Mathematics Teaching in the Middle School, 6(6), 350-355. |
| [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. |
| [22] | Ntenza, S. (2006). Investigating forms of children's writing in grade 7 mathematics classrooms. Educational Studies in Mathematics, 61 (3), 321-345. |
| [23] | National Council of Teachers of Mathematics (Ed.) (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics. |
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
ACS 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
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
Share This Article
Twitter
Linked In
Facebook
Copy
Download@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://article.sciencepublishinggroup.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}
}
TY - JOUR T1 - Problem-Solving Among English Language Learners: A Cognitive Linguistic Approach AU - Rod Case AU - Gwendolyn Williams AU - Peter Cobin Y1 - 2019/05/07 PY - 2019 N1 - https://doi.org/10.11648/j.ijeedu.20190801.13 DO - 10.11648/j.ijeedu.20190801.13 T2 - International Journal of Elementary Education JF - International Journal of Elementary Education JO - International Journal of Elementary Education SP - 18 EP - 25 PB - Science Publishing Group SN - 2328-7640 UR - https://doi.org/10.11648/j.ijeedu.20190801.13 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. VL - 8 IS - 1 ER -
Email: