625
Views
3
CrossRef citations to date
0
Altmetric
Articles

Implementing theoretical intervention principles in teaching mathematics to struggling students to promote problem-solving skills

Pages 4-28 | Received 12 Nov 2020, Published online: 30 Jun 2021

References

  • Artino, A. R., Jr. (2008). Cognitive load theory and the role of learner experience: An abbreviated review for educational practitioners. AACE Journal, 16(4), 425–439.
  • Bahadir, M. E., & Ottway, J. R. (2013). Authentic teaching and learning through extra-curricular activities. Technology Interface International Journal, 13(2), 87–95.
  • Bass, H. (2011). A vignette of doing mathematics: A meta-cognitive tour of the production of some elementary mathematics. Montana Mathematics Enthusiast, 8(1/2), 3.
  • Bassok, M., & Holyoak, K. J. (1993). Pragmatic knowledge and conceptual structure: Determinants of transfer between quantitative domains. In D. K. Detterman, & R. J. Sternberg (Eds.), Transfer on trial: Intelligence, cognition, and instruction (pp. 68–98). Ablex Publishing.
  • Bokosmaty, S., Sweller, J., & Kalyuga, S. (2015). Learning geometry problem solving by studying worked examples: Effects of learner guidance and expertise. American Educational Research Journal, 52(2), 307–333. https://doi.org/10.3102/0002831214549450
  • Bouck, E. C., & Cosby, M. D. (2019). Response to intervention in high school mathematics: One school's implementation. Preventing School Failure: Alternative Education for Children and Youth, 63(1), 32–42. https://doi.org/10.1080/1045988X.2018.1469463
  • Brown, R. (2017). Using collective argumentation to engage students in a primary mathematics classroom. Mathematics Education Research Journal, 29(2), 183–199. https://doi.org/10.1007/s13394-017-0198-2
  • Chazan, D. (1996). Algebra for all students? The algebra policy debate. Journal of Mathematical Behavior, 15(4), 455–477. https://doi.org/10.1016/S0732-3123(96)90030-9
  • Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. Teachers College Press.
  • Chazan, D., Callis, S., & Lehman, M. (2008). Embracing reason: Egalitarian ideals and teaching of high school mathematics. Routledge.
  • Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self- explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13(2), 145–182. https://doi.org/10.1207/s15516709cog1302_1
  • Cobb, P., & Jackson, K. (2011). Assessing the quality of the common core state standards for mathematics. Educational Researcher, 40(4), 183–185. https://doi.org/10.3102/0013189X11409928
  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1–2), 113–163. https://doi.org/10.1207/S15327809JLS10-1-2_6
  • Cobb, P., Yackel, E., & Wood, T. (2011). Young children's emotional acts while engaged in mathematical problem solving. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education research – insights from the work of Paul Cobb (pp. 41–71). Springer. https://doi.org/10.1007/978-90-481-9729-3_5. (Original work published 1989)
  • Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114.
  • de Jong, T. (2010). Cognitive load theory, educational research, and instructional design: Some food for thought. Instructional Science, 38(2), 105–134. https://doi.org/10.1007/s11251-009-9110-0
  • de Jong, T., & Ferguson-Hessler, M. G. (1986). Cognitive structures of good and poor novice problem solvers in physics. Journal of Educational Psychology, 78(4), 279–288. https://doi.org/10.1037/0022-0663.78.4.279
  • Desoete, A., Roeyers, H., & De Clercq, A. (2002). The measurement of individual metacognitive differences in mathematical problem solving. In M. Valcke, D. Gombeir, & W. C. Smith (Eds.), Learning styles: Reliability and validity. Proceedings of the 7th annual ELSIN conference (pp. 93–102). Academia Press.
  • Detterman, D. K., & Sternberg, R. J. (eds.). (1993). Transfer on trial: Intelligence, cognition, and instruction. Ablex Publishing Corporation.
  • Dixon, R. A., & Brown, R. A. (2012). Transfer of learning: Connecting concepts during problem solving. Journal of Technology Education, 24(1), 2–17. https://doi.org/10.21061/jte.v24i1.a.1
  • Finn, C. E., Jr., Julian, L., & Petrilli, M. J. (2006). The state of state standards, 2006. Thomas B. Fordham Foundation & Institute.
  • Fischbein, E. (1987). Intuition in science and mathematics. D. Reidel.
  • Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A., … Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude treatment interaction. Journal of Educational Psychology, 106, 499–514.
  • Geary, D. C. (2003). Arithmetical development: Commentary and future directions. In A. Baroody, & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 453–464). Erlbaum.
  • Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15. https://doi.org/10.1177/00222194040370010201
  • Geary, D. C. (2005). Role of cognitive theory in the study of learning disability in mathematics. Journal of Learning Disabilities, 38(4), 305–307.
  • Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice and speed-of processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27(3), 398–406. https://doi.org/10.1037/0012-1649.27.3.398
  • Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74(3), 213–239. https://doi.org/10.1006/jecp.1999.2515
  • Geary, D. C., & Widaman, K. F. (1992). Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16(1), 47–80. https://doi.org/10.1016/0160-2896(92)90025-M
  • Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170. https://doi.org/10.1207/s15516709cog0702_3
  • Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12(3), 306–355. https://doi.org/10.1016/0010-0285(80)90013-4
  • Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15(1), 1–38. https://doi.org/10.1016/0010-0285(83)90002-6
  • Gick, M. L., & Holyoak, K. J. (1987). The cognitive basis of knowledge transfer. In S. M. Cormier, & J. D. Hagman (Eds.), Transfer of learning: Contemporary research and applications (pp. 9–46). Academic Press.
  • Gourdeau, F. (2019). Problem solving as a subject and as a pedagogical approach, and the ongoing dialogue between mathematics and mathematics education. In P. Felmer, P. Liljedahl, & B. Koichu (Eds.), Problem solving in mathematics instruction and teacher professional development. Springer, Cham: Research in Mathematics Education. https://doi-org.mgs.oranim.ac.il/10.1007/978-3-030-29215-7_2
  • Jaeggi, M., Buschkuehl, M., Jonides, J., & Perrig, W. (2008). Improving fluid intelligence with training on working memory. PNAS, 105(19), 6829–6833. https://doi.org/10.1073/pnas.0801268105
  • Jaeggi, S. M., Buschkuehl, M., Etienne, A., Ozdoba, C., Perrig, W. J., & Nirkko, A. C. (2007). On how high performers keep cool brains in situations of cognitive overload. Cognitive, Affective & Behavioral Neuroscience, 7(2), 75–89. https://doi.org/10.3758/CABN.7.2.75
  • 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(2), 114–136.
  • Kamiski, J., Sloutsky, V. M., & Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320(5875), 454–455. https://doi.org/10.1126/science.1154659
  • Kirschner, P., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1
  • Koichu, B. (2003). Junior high school students’ heuristic behaviors in mathematical problem solving [Doctoral dissertation]. Technion, Haifa.
  • Koichu, B. (2015). Towards a confluence framework of problem solving in educational contexts. In K. Krainer, & N. Vondrová (Eds.), CERME9: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 2668–2674). Charles University in Prague.
  • Koichu, B., Berman, A., & Moore, M. (2007a). Heuristic literacy development and its relation to mathematical achievements of middle school students. Instructional Science, 35(2), 99–139. https://doi.org/10.1007/s11251-006-9004-3
  • Koichu, B., Berman, A., & Moore, M. (2007b). The effect of promoting heuristic literacy on the mathematic aptitude of middle-school students. International Journal of Mathematical Education in Science and Technology, 38(1), 1–17. https://doi.org/10.1080/00207390600861161
  • Kollar, I., Ufer, S., Reichersdorfer, E., Vogel, F., Fischer, F., & Reiss, K. (2014). Effects of collaboration scripts and heuristic worked examples on the acquisition of mathematical argumentation skills of teacher students with different levels of prior achievement. Learning and Instruction, 32, 22–36. https://doi.org/10.1016/j.learninstruc.2014.01.003
  • Kribbs, E. E., & Rogowsky, B. A. (2016). A review of the effects of visual-spatial representations and heuristics on word problem solving in middle school mathematics. International Journal of Research in Education and Science, 2(1), 65–74. https://doi.org/10.21890/ijres.59172
  • Kuo, E., Hull, M. M., Gupta, A., & Elby, A. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problems. Science Education, 97(1), 32–57. https://doi.org/10.1002/sce.21043
  • LeFevre, J. A., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3(1), l–30. https://doi.org/10.1207/s1532690xci0301_1
  • Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher, 32(1), 17–20. https://doi.org/10.3102/0013189X032001017
  • Mason, J. (2008). Being mathematical with & in front of learners: Attention, awareness, and attitude as sources of differences between teacher educators, teachers & learners. In T. Wood (Series Ed.), & B. Jaworski (Vol. Ed.), International handbook of mathematics teacher education: Vol. 4. The mathematics teacher educator as a developing professional (pp. 31–56). Sense Publishers.
  • Mason J. (2019). Pre-parative and post-parative play as key components of mathematical problem solving. In P. Felmer, P. Liljedahl, & B. Koichu (Eds.), Problem solving in mathematics instruction and teacher professional development. Springer, Cham: Research in Mathematics Education. https://doi-org.mgs.oranim.ac.il/10.1007/978-3-030-29215-7_5
  • Mayer, R. E. (1998a). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1-2), 49–63. https://doi.org/10.1023/A:1003088013286
  • Mayer, R. E. (1998b). Thinking, problem solving, cognition (2nd ed.). W. H. Freeman.
  • Mayer, R. E. (2004). Should there be a three-strikes rule against pure discovery learning? American Psychologist, 59(1), 14–19. https://doi.org/10.1037/0003-066X.59.1.14
  • Mevarech, Z. R., & Kramarski, B. (2003). The effects of metacognitive training vs. worked-out examples on students’ mathematical reasoning. British Journal of Educational Psychology, 73(4), 449–471. https://doi.org/10.1348/000709903322591181
  • Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, 81–97.
  • Mousel, S. (2006). Bad medicine: Homework or headache? Responsibility and accountability for middle level mathematics students. Action Research Projects, 51, University of Nebraska-Lincoln.
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
  • Nelson, B. C. (2007). Exploring the use of individualized, reflective guidance in an educational multi-user virtual environment. Journal of Science Education and Technology, 16(1), 83–97. https://doi.org/10.1007/s10956-006-9039-x
  • Nunokawa, K. (2006). Using drawings and generating information in mathematical problem solving. Eurasia Journal of Mathematics, Science and Technology Education, 2(3), 33–54. https://doi.org/10.12973/ejmste/75463
  • Ovadiya, T. (2017). Constructing similarity connections between mathematics problems: The case of “weak” high school students. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st conference of the International group for the Psychology of mathematics education (Vol. 2, pp. 71). PME.
  • Pehkonen, E. (2019). An Alternative method to promote pupils’ mathematical understanding via problem solving. In P. Felmer, P. Liljedahl, & B. Koichu (Eds.), Problem solving in mathematics instruction and teacher professional development. Springer, Cham: Research in Mathematics Education. https://doi-org.mgs.oranim.ac.il/10.1007/978-3-030-29215-7_6
  • Pirolli, P. L., & Anderson, J. R. (1985). The role of practice in fact retrieval. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11(1), 136–153. https://doi.org/10.1037/0278-7393.11.1.136
  • Reed, S. K. (1993). A schema-based theory of transfer. In D. K. Detterman, & R. J. Sternberg (Eds.), Transfer on trial: Intelligence, cognition, and instruction (pp. 39–67). Ablex.
  • Robins, S., & Mayer, R. E. (1993). Schema training in analogical reasoning. Journal of Educational Psychology, 85(3), 529–538. https://doi.org/10.1037/0022-0663.85.3.529
  • Rogoff, B. (1990). Explanations of cognitive development through social interaction: Vygotsky and Piaget. In B. Rogoff (Ed.), Apprenticeship in thinking: Cognitive development in social context (pp. 137–150). Oxford University Press.
  • Roorda, G., Vos, P., & Goedhart, M. J. (2015). An actor-oriented transfer perspective on high school students’ development of the use of procedures to solve problems on “rate of change”. International Journal of Science and Mathematics Education, 13(4), 863–889. https://doi.org/10.1007/s10763-013-9501-1
  • Rossow, M. P. (2005). Theoretical basis for learning statics by studying worked examples. http://www.ce.siue.edu/examples/Worked_examples_Internet_text-only/Home_page/Theoretical_basis.pdf.
  • Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4
  • Sweller, J. (2005). The redundancy principle in multimedia learning. In R. E. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 159–167). Cambridge University Press.
  • Sweller, J. (2015a). In academe, what is learned, and how is it learned? Current Directions in Psychological Science, 24(3), 190–194. https://doi.org/10.1177/0963721415569570
  • Sweller, J. (2015b). Working memory, long-term memory, and instructional design. Journal of Applied Research in Memory and Cognition, 5(4), 360–367.
  • Sweller, J. (2016). Working memory, long-term memory, and instructional design. Journal of Applied Research in Memory and Cognition, 5(4), 360–367. https://doi.org/10.1016/j.jarmac.2015.12.002
  • Sweller, J., Ayres, P., & Kalyuga, S. (2011). Measuring cognitive load. In Cognitive load theory. Explorations in the learning sciences, instructional systems and performance technologies, vol 1. New York, NY: Springer. https://doi-org.mgs.oranim.ac.il/10.1007/978-1-4419-8126-4_6
  • Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. https://doi.org/10.1207/s1532690xci0201_3
  • Sweller, J., van Merriënboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296. https://doi.org/10.1023/A:1022193728205
  • Sweller, J., van Merriënboer, J., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
  • Tachie, S. A., & Molepo, J. M. (2019). Exploring teachers’ meta-cognitive skills in mathematics classes in selected rural primary schools in Eastern Cape, South Africa. Africa Education Review, 16(2), 143–161. https://doi.org/10.1080/18146627.2017.1384700
  • van Gog, T., & Paas, F. (2008). Instructional efficiency: Revisiting the original construct in educational research. Educational Psychologist, 43(1), 16–26. https://doi.org/10.1080/00461520701756248
  • van Gog, T., Paas, F., & van Merriënboer, J. J. G. (2008). Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency. Learning and Instruction, 18(3), 211–222. https://doi.org/10.1016/j.learninstruc.2007.03.003
  • Watson, A. (2001). Low attainers exhibiting higher-order mathematical thinking. Support for Learning, 16(4), 179–183. https://doi.org/10.1111/1467-9604.00215
  • Watson, S. M. R., & Gable, R. A. (2012). Unraveling the complex nature of mathematics learning disability: Implications for research and practice. Learning Disability Quarterly, 36(3), 178–187. https://doi.org/10.1177/0731948712461489
  • Yakuel, G. (2007). Mathematics, cumulative structure, for students taking 3–4 study units: Questionnaire 035003 (revised edition). Mishbetzet (Hebrew).
  • Yakuel, G. (2008). Mathematics, cumulative structure, for students taking 3–4 study units: Questionnairè 035002 (revised edition). Mishbetzet (Hebrew).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.