logo logo European Journal of Educational Research

EU-JER is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.

Subscribe

Publisher (HQ)

Eurasian Society of Educational Research
Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
Eurasian Society of Educational Research
Headquarters
7321 Parkway Drive South, Hanover, MD 21076, USA
algebraic manipulation analogical transformations contextual chemistry problems mathematics problem solving

Using Algebraic Manipulations and Analogical Transformations to Problem-Solving of Contextual Chemistry Problems

Eda Vula , Fatlume Berisha

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts us.

A

Algebraic knowledge transfer is considered an important skill in problem-solving. Using algebraic knowledge transfer, students can connect concepts using common procedural similarities. This quasi-experimental study investigates the influence of algebraic knowledge in solving problems in a chemistry context by using analogical transformations. The impact of structured steps that students need to take during the process of solving stoichiometric problems was explicitly analyzed. A total of 108 eighth-grade students participated in the study. Of the overall number of students, half of them were included in the experimental classes, whereas the other half were part of the control classes. Before and after the intervention, contextual problems were administered twice to all the student participants. The study results indicate that the students of the experimental classes exposed to structured steps in solving algebraic problems and the procedural transformations scored better results in solving problems in mathematics for chemistry compared to their peers who did not receive such instruction. Nevertheless, the result shows that although the intervention was carried out in mathematics classes, its effect was more significant on students' achievements in chemistry. The findings and their practical implications are discussed at the end of the study.

Keywords: Algebraic manipulation, analogical transformations, contextual chemistry problems, mathematics, problem-solving.

cloud_download PDF
Cite
Article Metrics
Views
264
Download
397
Citations
Crossref
0

Scopus
0

References

Baysal, E., & Sevinc, S. (2021). The role of the Singapore bar model in reducing students' errors on algebra word problems. International Journal of Mathematical Education in Science and Technology, 53(2), 289-310. https://doi.org/10.1080/0020739X.2021.1944683

Beigie, D. (2008). Integrating content to create problem-solving opportunities. Mathematics Teaching in the Middle School, 13(6), 352-360. https://doi.org/10.5951/MTMS.13.6.0352

Bodner, G. M., & Herron, D. J. (2002). Problem-solving in chemistry. In J. K. Gilbert, O. De Jong, R. Justi, D. F. Treagust, & J. H. Van Driel, Chemical education: Research-based practice. Kluwer Academic Publishers.

Bopegedera, A. M. R. P. (2019). Preventing mole concepts and stoichiometry from becoming "Gatekeepers" in first year chemistry courses. In S. Kradtap Hartwell, & T. Gupta, Enhancing retention in introductory chemistry courses: Teaching practices and assessments (Vol. 1330, pp. 121-136). American Chemical Society.  https://doi.org/10.1021/bk-2019-1330.ch008 

BouJaoude, S., & Barakat, H. (2003). Students' problem solving strategies in stoichiometry and their relationships to conceptual understanding and learning approaches. Electronic Journal for Research in Science & Mathematics Education, 7(3), 1-42. https://bit.ly/3xNdSno

Bunce, D. M., Gabel, D. L., & Samuel, J. V. (1991). Enhancing chemistry problem solving achievement using problem categorization. Journal of Research in Science Teaching, 28(6), 505-521. https://doi.org/10.1002/tea.3660280605

Bush, S. B., & Krap, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Review, 32(3), 613-632. https://doi.org/10.1016/j.jmathb.2013.07.002

Capraro, M. M., & Joffrin, H. (2006). Algebraic equations: Can middle school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2), 147-164. https://doi.org/10.1080/02702710600642467

Caproro, M. R., Caproro, M. M., & Rupley, H. W. (2012). Reading-enhanced word problem solving: A theoretical model. European Journal of Psychology of Education, 27(1), 91-114. https://doi.org/10.1007/s10212-011-0068-3

Carbonell, J. G. (1983). Learning by analogy: Formulating and generalizing plans from past experience. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.), Machine learning. Symbolic computation. Springer. https://doi.org/10.1016/B978-0-08-051054-5.50009-1

Carlson, E. (2022). Improving student success in stoichiometry via the scale factor method. Journal of Chemical Education, 99(5), 1863-1867. https://doi.org/10.1021/acs.jchemed.1c01155

Chiu, B., Randles, C., & Irby, S. (2022). Analyzing student problem-solving with MAtCH. Frontiers in Education, 6, 769042. https://doi.org/10.3389/feduc.2021.769042

Cook, E., & Cook, R. L. (2005). Cross-proportions: A conceptual method for developing quantitative problem-solving skills. Journal of Chemical Education, 82(8), 1187-1189. https://doi.org/10.1021/ed082p1187

Cresswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approach (2nd ed.). Sage Publications, Inc.

Fuchs, L. S., Fuchs, D., Stuebing, K., Fletcher, J. M., Hamlett, C. L., & Lambert, W. (2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Educational Psychology, 100(1), 30-47. https://doi.org/10.1037/0022-0663.100.1.30

Glynn, S. M. (1989). The teaching with analogies (TWA) model: Explaining concepts in expository text. In K. D. Myth (Ed.), Children's comprehension of narrative and ex-pository text: Research into practice (pp. 185-204). International Reading Association.

Gulacar, O. (2007). An invstigation of successful and unsuccessful students' problem solving in stoichiomethry. Western Michigan University. https://scholarworks.wmich.edu/dissertations

Gulacar, O., Tan, A., Cox, C. T., Bloomquist, J., Jimmy, O., & Cao, N. (2019). Analyzing characteristics of experts in the context of stoichiometric problem-solving. Education Sciences, 9(3), 219-230. https://doi.org/10.3390/educsci9030219

Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395-406. https://doi.org/10.1037/a0017486

Harmon, M. (1993). The role of strategies and knowledge in problem solving: A review of the literature [Paper presentation]. ERIC. https://files.eric.ed.gov/fulltext/ED366640.pdf

Hickendorff, M. (2013). The Language Factor in elementary mathematics assessments: Computational skills and applied problem solving in a multidimensional IRT framework. Applied Measurement in Education, 26, 253-275. https://doi.org/10.1080/08957347.2013.824451

Hodnik Čadež, T., & Manfreda Kolar, V. (2015). Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem. Educational Studies in Mathematics, 89(2), 283-306. https://doi.org/10.1007/s10649-015-9598-y

Huddle, P. A., & Pillay, A. E. (1996). An in‐depth study of misconceptions in stoichiometry and chemical equilibrium at a South African university. Journal of Research in Science Teaching: The Official Journal of the National Association for Research in Science Teaching, 33(1), 65-77. https://doi.org/10.1002/(SICI)1098-2736(199601)33:1<65::AID-TEA4>3.0.CO;2-N

Jonassen, H. D. (2003). Designing research - based instruction for story problems. Educational Psychology Review, 15(3), 267-296. https://doi.org/10.1023/A:1024648217919

Kolar, V. M., & Hodnik, T. (2021). Mathematical literacy from the perspective of solving contextual problems. European Journal of Educational Research, 10(1), 467-483. https://doi.org/10.12973/eu-jer.10.1.467

Korpershoek, H., Kuyper, H., & van der Werf, G. (2014). The relation between students' math and reading ability and their mathematics, physics, and chemistry examination grades in secondary education. International Journal of Science and Mathematics Education, 13(5), 1013-1037. https://doi.org/10.1007/s10763-014-9534-0

Lee, H. S., Betts, S., & Anderson, J. R. (2017). Embellishing problem-solving examples with deep structure information facilitates transfer. The Journal of Experimental Education, 85(2), 309-333. https://doi.org/10.1080/00220973.2016.1180277

Lee, K. L., & Fensham, P. (1996). General strategy for solving high school electrochemistry problems. International Journal of Science Education, 18(5), 543-555. https://doi.org/10.1080/0950069960180504

Lee, K. L., Goh, N. K., Chia, L. S., & Chin, C. (1996). Cognitive variables in problem solving in chemistry: A revisited study. Science Education, 80(6), 691-710. https://doi.org/10.1002/(SICI)1098-237X(199611)80:6<691::AID-SCE4>3.0.CO;2-E

Lythcott, J. (1990). Problem solving and requisite knowledge of chemistry. Journal of Chemical Education, 67(3), 248-252. https://doi.org/10.1021/ed067p248

Mevarech, Z. R., Terkieltaub, S., Vinberger, T., & Nevet, V. (2010). The effects of meta-cognitive instruction on third and sixth graders solving word problems. ZDM Mathematics Education, 42(2), 195-203. https://doi.org/10.1007/s11858-010-0244-y

Ministry of Education, Science, and Technology. (2016a). Korniza Kurrikulare e Arsimit Parauniversitar të Republikës së Kosovës (e rishikuar) [Curriculum Framework of Pre-University Education of the Republic of Kosovo (revised)]. Retrieved May 15, 2019, from Ministria e Arsimit, Shkencës dhe Teknologjisë. https://bit.ly/3zOuqhl

Ministry of Education, Science, and Technology. (2016b). Kurrikula Bërthamë e arsimit të mesëm të ulët të Kosovës (Klasa VI, VII, VIII dhe IX) (e rishikuar) [Core Curriculum of Kosovo Lower Secondary Education (Grades VI, VII, VIII and IX) (revised)]. Retrieved May 15, 2019, from Ministria e Arsimit, Shkencës dhe Teknologjisë. https://bit.ly/3O9veSe

Monroe, E. E., & Orme, M. P. (2002). Developing mathematical vocabulary. Preventing School Failure, 46(3), 139-142. https://doi.org/10.1080/10459880209603359

Nakhleh, M. B. (1993). Are our students conceptual thinkers or algorithmic problem solvers? Identifying conceptual students in general chemistry. Journal of Chemical Education, 70(1), 52-55. https://doi.org/10.1021/ed070p52

Ngu, B. H. (2016). Number and algebra. In G. Hine, R. Reaburn, J. Anderson, L. Galligan, C. Carmichael, M. Cavanagh, B. Ngu, B. White, Teaching secondary mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9781316442814.010

Ngu, B. H., & Phan, H. P. (2020). Learning to solve trigonometry problems that involve algebraic transformation skills via learning by analogy and learning by comparison. Frontiers in Psychology, 11, 2590. https://doi.org/10.3389/fpsyg.2020.558773

Ngu, B. H., & Yeung, A. S. (2012). Fostering analogical transfer: The multiple components approach to algebra word problem solving in a chemistry context. Contemporary Educational Psychology, 37(1), 14-32. https://doi.org/10.1016/j.cedpsych.2011.09.001

Niaz, M. (1995). Relationship between student performance on conceptual and computational problems of chemical equilibrium. International Journal of Science Education, 17(3), 343-355. https://doi.org/10.1080/0950069950170306

Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology Learning Memory and Cognition, 17(3), 398-415. https://doi.org/10.1037/0278-7393.17.3.398

Okanlawon, A. E. (2010). Teaching reaction stoichiometry: Exploring and acknowledging Nigerian chemistry teachers' pedagogical content knowledge. Cypriot Journal of Educational Sciences, 5(2), 107-129. https://www.oalib.com/paper/2751848

Organisation for Economic Co-operation and Development. (2004). Problem solving for tomorrow's world.  https://bit.ly/3zVDpx9

Organisation for Economic Co-operation and Development. (2018). PISA 2015 Results in focus. https://bit.ly/3tLV5rm

Pape, S. J., & Smith, C. (2002). Self-regulating mathematics skills. Theory Into Practice, 41(2), 93-101. https://doi.org/10.1207/s15430421tip4102_5

Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton University Press.

Raviolo, A., Farré, A. S., & Schroh, N. T. (2021). Students' understanding of molar concentration. Chemistry Education Research and Practice, 22(2), 486-497. https://doi.org/10.1039/D0RP00344A

Reeves, L., & Weisberg, R. W. (1994). The role of content and abstract information in analogical transfer. Psychological Bulletin, 115(3), 381-400. https://doi.org/10.1037/0033-2909.115.3.381

Sawrey, B. A. (1990). Concept learning versus problem solving: Revisited. Journal of Chemical Education, 67(3), 253-254. https://doi.org/10.1021/ed067p253

Scherer, R., & Beckmann, J. F. (2014). The acquisition of problem solving competence: Evidence from 41 countries that math and science education matters. Large-scale Assessments in Education, 2(1), 1-22. https://doi.org/10.1186/s40536-014-0010-7

Schmidt, H. J. (1997). An alternate path to stoichiometric problem solving. Research in Science Education, 27(2), 237-249. https://doi.org/10.1007/BF02461319

Schoenfield, A. H. (1985). Mathematical problem solving. Academic Press, Inc.

St Clair-Thompson, H., Overton, T., & Bugler, M. (2012). Mental capacity and working memory in chemistry: Algorithmic versus open-ended problem solving. Chemistry Education Research and Practice, 13(4), 484-489. https://doi.org/10.1039/C2RP20084H

Staver, J. R., & Lumpe, A. T. (1995). Two investigations of students' understanding of the mole concept and its use in problem solving. Journal of Research in Science Teaching, 32(2), 177-193. https://doi.org/10.1002/tea.3660320207

Sumfleth, E. (1988). Knowledge of terms and problem-solving in chemistry. International Journal of Science Education, 10(1), 45-60. https://doi.org/10.1080/0950069880100105

Sunday, E., Ibemenji, K. A., & Alamina, J. I. (2019). Effect of problem-solving teaching technique on students' stoichiometry academic performance in senior secondary school chemistry in Nigeria. Asian Journal of Advanced Research and Reports, 4(3), 1-11. https://doi.org/10.9734/ajarr/2019/v4i330110

Sun-Lin, H. Z., & Chiou, G. F. (2019). Effects of gamified comparison on sixth graders' algebra word problem solving and learning attitude. Educational Technology & Society, 22(1), 120-130. https://bit.ly/39DTPj7

Swanson, H. L., & Fung, W. (2016). Working memory components and problem-solving accuracy: Are there multiple pathways? Journal of Educational Psychology, 108(8), 1153-1168. https://doi.org/10.1037/edu0000116

Tullberg, A., Stromdahl, H., & Lybeck, L. (1994). Students' conceptions of 1 mol and educators' conceptions of how they teach 'the mole'. International Journal of Science Education, 16(2), 145-156. https://doi.org/10.1080/0950069940160204

Vula, E., Avdyli, R., Berisha, V., Saqipi, B., & Elezi, S. (2017). The impact of metacognitive strategies and self-regulation processes of solving math word problems. International Electronic Journal of Elementary Education, 10(1), 49-59. https://doi.org/10.26822/iejee.2017131886

Wong, S. S., Ng, G. J., Tempel, T., & Lim, S. W. (2017). Retrieval practice enhances analogical problem solving. The Journal of Experimental Education, 87(1), 128-138. https://doi.org/10.1080/00220973.2017.1409185

Zoller, U. (1987). The fostering of question-asking capability: A meaningful aspect of problem-solving in chemistry. Journal of Chemical Education, 64(6), 510-513. https://doi.org/10.1021/ed064p510

...