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Using Thinking Blocks to Encourage the Use of Higher Order Thinking Skills among Students When Solving Problems on Fractions

Authors: Abdul Halim Abdullah, Nur Liyana Zainal Abidin, Mahani Mokhtar

Abstract:

Problem-solving is an activity which can encourage students to use Higher Order Thinking Skills (HOTS). Learning fractions can be challenging for students since empirical evidence shows that students experience difficulties in solving the fraction problems. However, visual methods can help students to overcome the difficulties since the methods help students to make meaningful visual representations and link abstract concepts in Mathematics. Therefore, the purpose of this study was to investigate whether there were any changes in students’ HOTS at the four highest levels when learning the fractions by using Thinking Blocks. 54 students participated in a quasi-experiment using pre-tests and post-tests. Students were divided into two groups. The experimental group (n=32) received a treatment to improve the students’ HOTS and the other group acted as the control group (n=22) which used a traditional method. Data were analysed by using Mann-Whitney test. The results indicated that during post-test, students who used Thinking Blocks showed significant improvement in their HOTS level (p=0.000). In addition, the results of post-test also showed that the students’ performance improved significantly at the four highest levels of HOTS; namely, application (p=0.001), analyse (p=0.000), evaluate (p=0.000), and create (p=0.000). Therefore, it can be concluded that Thinking Blocks can effectively encourage students to use the four highest levels of HOTS which consequently enable them to solve fractions problems successfully.

Keywords: Thinking blocks, higher order thinking skills, fractions, problem solving.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1339872

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References:


[1] Zakiah Salleh, Norhapidah Mohd Saad, Mohamad Nizam Arshad, Hazaka Yunus & Effandi Zakaria, “Analisis jenis kesilapan dalam operasi penambahan dan penolakan pecahan,” Jurnal Pendidikan Matematik, 2013, vol 1, pp. 1–10.
[2] R. Misquitta, “A Review of the Literature: Fraction Instruction for Struggling Learners in Mathematics, Learning Disabilities Research & Practice,” 2011, vol. 26, pp. 109–119. doi:10.1111/j.1540-5826.2011.00330.
[3] Azlina Ahmad, Siti Salwah Salim, & Roziati Zainuddin. “A Study on Students’ Performance in Solving Word Problems Involving Fractions : Towards the Development of a Cognitive Tool. In International Conference on Computers in Education. Melbourne, Australia, 2004, pp. 833–838.
[4] F. M. Butler, S. P. Miller, K. Crehan, B. Babbitt, and T. Pierce, “Fraction Instruction for Students with Mathematics Disabilities: Comparing Two Teaching Sequences, ” Learning Disabilities Research and Practice, 2003, vol. 18, pp. 99–111. doi:10.1111/1540-5826.00066.
[5] Aida Suraya, Analisis Kesilapan Masalah - Masalah Berkaitan Nombor Perpuluhan dan Pecahan Bagi Pelajaran - Pelajaran Tahun Lima Sekolah Rendah. Jurnal Pendidik Dan Pendidikan, 1994, pp. 15–32.
[6] G. J. Aubrecht, Helping Students Come to Grips with the Meaning of Division. School Science and Mathematics, 2004, vol. 104, pp. 313-321.
[7] T. S., Sean, Penerokaan terhadap kepekaan pecahan dikalangan pelajar tingkatan satu. UTM: Unpublished master dissertation, 2005.
[8] T. Watanabe, Representations in Teaching and Learning Fraction, Teaching Children Mathematics, 2002, vol. 8, pp. 457-464.
[9] Norazrena Abu Samah, Nor Affandy Yahaya and Mohamad Bilal Ali. Personalized Learning Website On Topic of Fraction for Lower Secondary Students, Journal of Edupres, 2011, vol. 1, pp. 135–144. Retrieved from http://eprints.utm.my/15935/.
[10] N. K. Mack, Learning fractions with understanding: Building on informal knowledge. Journal for research in mathematics education, 1990, vol. 21, pp. 16-32.
[11] Malaysian Examination Board, Pentaksiran Kemahiran Berfikir Aras Tinggi (p. 168). Putrajaya: Kementerian Pendidikan Malaysia, 2013.
[12] I.V.S. Mullis, M. O. Martin, P. Foy, and A. Arora, Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Retrieved fromhttp://timss.bc.edu/timss2011/downloads/T11_IR_Mathematics_FullBook.pdf, 2012.
[13] Syafiah Sothir, "Kemahiran berfikir aras tinggi dalam topik garis dan satah dalam tiga dimensi tingkatan empat," UTM: Unpublished degree dissertation, 2013.
[14] Siti Marlina Sabran, "Kemahiran berfikir aras tinggi (KBAT) pelajar tingkatan 5 dalam penyelesaian masalah matematik," UTM: Unpublished master dissertation, 2013.
[15] C. Y. Charalambous, D. Pitta-Pantazi, D. "Revisiting a theoretical model on fractions: Implications for teaching and research," In H. L. Chick & J. L. Vincent (Eds), Proceedings of the 29th PME International Conference, 2005, vol. 2, pp. 233–240.
[16] Naiser, E. A., Wright, W. E., & Capraro, R. M. Teaching fractions: Strategies used for teaching fractions to middle grades students, 2003, Journal of research in childhood education, 18(3), pp. 193-198.
[17] C. D. Bruce, J. Ross, "Conditions for Effective Use of Interactive On-line Learning Objects: The case of a fractions computer- based learning sequence," The Electronic Journal of Mathematics and Technology, 2009, vol. 3, pp. 13–29.
[18] A. Sadi, "Misconceptions in numbers," UGRU journal, 2007, vol. 5, pp. 1-7.
[19] S.Y. Ho, T. Lowrie, T.,"The model method: Students’ performance and its effectiveness," The Journal of Mathematical Behavior, 2014, vol. 35, pp. 87–100. doi:10.1016/j.jmathb.2014.06.002.
[20] K. Mahoney, "Effects Of Singapore’ S Model Method On Elementary Student Problem-Solving Performance: Single Case Research," Doctor Philosophy, Northeastern University Boston, Massachusetts, 2012.
[21] S. F. Ng, K. Lee, "The model method: Singapore children’s tool for representing and solving algebraic word problems," Journal of Research in Mathematics Education, 2009, vol. 40, pp. 282-313.
[22] J. Hoven, B. Garelick, B. " Singapore Math: Simple or Complex?," Educational Leadership, 2007, vol. 65.
[23] P. S. Moyer-packenham, L. A. Ulmer, and K. L. Anderson, "Examining Pictorial Models and Virtual Manipulatives for Third-Grade Fraction Instruction," Journal of Interactive Online Learning, 2012, vol. 11, pp. 103–120.
[24] Y. Cheong, "The Model Method in Singapore," The Mathematics Educator, 2002 vol. 6, pp. 47–64. Retrieved from http://math.nie.edu.sg/ame/matheduc/tme/tmeV6_2/05-Yan KC Final version.pdf
[25] S. Y. Ho, "Seeing the value of visualization," SingTeach (E-Magazine), 2010, Retrieved from http://singteach.nie.edu.sg/math-ed/190.html.
[26] S. C. Kong, " An evaluation study of the use of a cognitive tool in a one-to-one classroom for promoting classroom-based dialogic interaction," Computers & Education, 2011, vol. 57, pp. 1851–1864. doi:10.1016/j.compedu.2011.04.008.
[27] R. N. Carney, J. R. Levin, "Pictorial illustrations still improve students' learning from text," Educational psychology review, 2002, vol 14, pp. 5-26.
[28] Y. B. Har, "Bar Modelling. Singapore: Marshall Cavendish Education," 2010.
[29] C. Looi, K. Lim, K. "From bar diagrams to letter-symbolic algebra: A technology- enabled bridging," Journal of Computer Assisted Learning, 2009, vol. 25, 358-374. doi:10.1111/j.
[30] V. Schwarz, "Exploring Word Problems with Singapore Bar Models," 2008 Retrived Jun 14, 2014, from http://teachers.yale.edu/pdfs/ocg/ocg12.pdf.
[31] C. Y. Piaw, " Kaedah Penyelidikan (2nd ed.," 2009 p. 109). Malaysia: Mc Graw Hill.
[32] J. W. Creswell,. "Educational research: Planning, conducting, and evaluating quantitative and qualitative research (5th ed.)". Boston, MA: Pearson.
[33] N. Malhotra, "Marketing Research: An applied orientation’" New Jersey: Pearson Education, 2010.
[34] P. Y. Foong, "Review of research on mathematical problem solving in Singapore," In W. K. Yoong, L. P. Yee, B. Kaur, F. P. Yee & S. N. Fong (Eds.), Mathematics education: The Singapore journey, 2009, pp. 263-297). Singapore: World Scientific.
[35] S. Y. Ho, "Visualization in primary school mathematics: Its roles and processes in mathematical problem solving," (Unpublished doctoral dissertation). Singapore: National Institute of Education, Nanyang Technological University, 2009.
[36] L. W. Anderson, D. R. Krathwohl, (Eds.). "A taxonomy for learning, teaching and assessing: A revision of Bloom's Taxonomy of educational objectives," 2001: Complete edition, New York: Longman.
[37] van Garderen, D., & Montague, M. Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities: Research & Practice, 2003, 18(4), pp. 246–254.
[38] S. N. Alias, F. Ibrahim, F. " The Level of Mastering Forces in Equilibrium Topics by Thinking Skills," International Journal of Multicultural and Multireligious Understanding, 2015, vol. 2, pp. 18-24.
[39] Rohani Ahmad Tarmizi. "Visualizing Student’s Difficulties in Learning Calculus. Procedia - Social and Behavioral Sciences," 2010, vol. 8, pp. 377–383. Retrieved May 4, 2014 from http://linkinghub.elsevier.com/retrieve/pii/S1877042810021580.
[40] K. R. Woleck, K., "Listen to their pictures: An investigation of children’s mathematical drawings," In A. A. Cuoco & F. R. Curcio (Eds.), 2001 Yearbook: The roles of representation in school mathematics, 2001, pp. 215-227. Reston, VA: NCTM.
[41] Nasarudin Abdullah, Effandi Zakaria, and Lilia Halim, "The Effect of a Thinking Strategy Approach through Visual Representation on Achievement and Conceptual Understanding in Solving Mathematical Word Problems," Asian Social Science, 2012, vol 8. doi:10.5539/ass.v8n16p30.
[42] K. Serpil, K. Cihan, I. Sabri, I. Ahmet, "The role of visualization approach on student’s conceptual learning. Retrieved May 14, 2014, from http://www.clmt.plymouth.ac.uk/journal/konyalionglu.pdf, 2005.
[43] S. A. McLeod, "Bruner. Retrieved January 1, 2015, from http://www.simplypsychology.org/bruner.html, 2008.
[44] B. Bottge, X. Ma, L. Gassaway, M. Butler, and M. Toland, "Detecting and correcting fractions computation error patterns. Exceptional Children, 2013, vol. 80, pp. 237–255. Retrieved May 4, 2014, from http://cec.metapress.com/index/R0150535U02525P1.pdf, 2013.