Browse > Article
http://dx.doi.org/10.7468/jksmec.2021.24.1.43

The Effects of Leaner-Centered Mathematical Instructions on Students' Reasoning Ability and Achievement  

Cha, So-Jeong (Daegu Dongchun elemantery school)
Kim, Jinho (Daegu National University of Education)
Publication Information
Education of Primary School Mathematics / v.24, no.1, 2021 , pp. 43-69 More about this Journal
Abstract
The purpose of this study is to confirm the influences of learner-centered instruction on learners' achievement and reason ability. In order to accomplish them, the fraction unit and the polygonal unit in the fourth grade were implemented with teaching methods and materials suitable for learner-centered mathematics instruction. Some conclusions could be drawn from the results as follows: First, learner-centered mathematics instruction has a more positive effect on learning of learned knowledge and generating unlearned knowledge in the experimental period than teacher-centered instructions. Second, learner-centered instruction makes an influence of low learning ability on getting achievement positively. Third, as the experimental treatment is repeated, learner-centered instruction has a positive effect on students' reasoning ability. The reasoning ability of students showed a difference in the comparison between the experimental group and the comparative group, and within the experimental group, there was a positive effect of the extension of the positive reasoning ability. Fourth, it can be estimated that the development of students' reasoning ability interchangeably affected their generation test results.
Keywords
learner-centered instruction; reasoning ability; generation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Silver, E. A., & Peterson, R. (1985). Decision systems for inventory management and production planning. Hoboken, NJ: John Wiley & Sons Inc.
2 Skemp, R. R. (1987). The psychology of learning mathematics. London: Penguin Group.
3 Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80.   DOI
4 Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.   DOI
5 NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.
6 von Glasersfeld, E. (1987). The construction of knowledge: Contributions to conceptual semantics. Salinas, CA: Intersystems Publications.
7 Watson, A. & Ohtani, M. (Eds.) (2015). Task design in mathematics education. New York: Springer.
8 Yeh, C., Ellis, M. W., & Hurtado, C., K. (2017). Reimagining the mathematics classroom: Creating and sustaining productive learning environments. Reston, VA: National Council of Teachers of Mathematics Press.
9 Kwon, S. Y. (2003). A study on elementary school students' understanding of fraction. School Mathematics, 5(2), 259-273.
10 Ministry of Education (2015). Elementary mathematics curriculum: Notice 2015-80. Seoul: Ministry of Education.
11 Ministry of Education (2016). Elementary mathematics 4-1 teacher's guide. Seoul: Chunjae Education.
12 Ministry of Education (1997). Elementary mathematics curriculum. Seoul: Author.
13 Kim, M. (2010). An analysis on cognitive obstacles while doing addition and subtraction with fractions. Unpublished Master Thesis at Seoul National University of Education.
14 Kim, M. J. (2007). Understanding of the construct polygons by using teaching aids. Unpublished Master Thesis at Hongik University.
15 Kim, S. M. (2010). The effect of learner-centered lesson on creative problem solving ability in science, academic achievement in science, attitude toward science. Ewha Womans University.
16 Kim, J. H. (2004). Practical Using of Tangram for Inducing Motivation and Improving Creativity.
17 Kim, J. H. (2020a). Tasks with the various entry and exit points for implementing learner-centered instruction in a mixed-ability classroom. Explorations into Future Education, 41(1), 32-45.
18 Kim, J. (2020b). Mathematics classroom where students feel happy: 3rd grade 1st semester addition and subtraction. Gyengki : Gyoyuggwahagsa.
19 Kim, J. H. (2018a). Reexamines some important terminologies for implementing learner-centered instruction. Korean Journal of Educational Research, 39(2), 1-11.
20 Kim, J. H. (2015). Elementary school figure exploration (with GeoGebra): 3rd and 4th graders. Seoul: Gyowoosa.
21 Kim, J. H. (2018b). Mathematics classroom where students feel happy: 1st grade 1st semester operation instructions. Gyengki: Gyoyuggwahag-sa.
22 Kim, J. H. (2020). Implementation of learner-centered instruction: Focused on the open-ended task with several results. Korean Journal of Educational Research, 40(2), 1-10.
23 Kim, J. & Kim, S. M. (2013). Learner-centered mathematics teaching and learning from a constructionist' perspective. In Kim, J., Chang, K., Han, I., and Go, H., Constructivism and Korea mathematics education (pp. 45-64). Seoul : Kyongmoonsa.
24 Kim, J., Lee, S. M., & Kim, S. R. (2010). Achievement of students who have learner-centered instruction for multiplication units. Journal of Elementary Mathematics Education in Korea, 14(1), 136-151.
25 Kim, C. H. (2004). Research for the diagnostic and prescription of fractional addition and subtraction. Gyeongin National University of Education.
26 Nam, H. S. (2002). Developing a program of teaching unlike-denominator fractional operations. Seoul National University of Education.
27 Kim, J. H. (2004). Instructional materials for learner-centered mathematics instruction. 37, 169-185.
28 Roh, Y. A. & Ahn, B. G. (2007). Analysis on error of fourth grade student in geometric domain. Journal of Elementary Mathematics Education in Korea, 11(2), 199-216.
29 Park, K. S. (1996). Some characteristics that can be found in mathematics teaching and learning in elementary schools in Korea. Research in Mathematics Education, 6(2), 99-113.
30 Ryu, H. C. (2004). How to use inquiry type software in mathematics education. The 14th Mathematics Education Seminar, Institute for Mathematics Education, Korea National University of Education, 56-73.
31 Park, S. S. (1993). The effects of elaboration on logical reasoning of 4th grade children. Korea National University of Education.
32 Pang, J. S., Kim, S. H., & Park, K. R. (2006). Development of teaching and learning materials to establish knowledge of elementary school teachers' mathematics and teaching methods. 2005 Subject Joint Research Results Report. KRF-2005-030-B00045, 1943-2029.
33 Oh, S. H. (2000). A study on effectiveness of a fraction operation program using cusenaire rods. Unpublished master thesis, Korea National University of Education.
34 Lee, E. S. (2016). Effects of mathematical instructions based on constructivism on leaners' knowledge generation level and reasoning ability. Unpublished master thesis, Daegu National University of Education
35 Lee, J. E. (2005). Study on transition of teacher knowledge of fractions. Unpublished doctoral dissertation, Korea National University of Education.
36 Lee, H. J. (1999). Constructivism and construction of curriculum. Journal of the Elementary Education Society, 2, 35-61.
37 Lim, Jiye. (2017). An analysis of the examples of triangles and quadrangles generated by elementary school mathematics textbooks, teachers, and students. Unpublished master thesis, Seoul National University of Education.
38 Cho, S. Y. (2011). Effects of mathematical instructions based on constructivism on learners' reasoning ability. Unpublished master thesis, Daegu National University of Education.
39 Jeong, E. S. (2009). An comparative analysis of fraction concept in mathematics textbooks of Korea and Singapore. Mathematics Education, 19(1), 25-43.
40 Jung, H. (2013). Effects of mathematical instructions based on constructivism on learners' reasoning ability. Unpublished master thesis, Daegu National University of Education.
41 Jo, Y. R. (2018). Effects of learner-centered mathematical instructions on learners′mathematical achievement and attitude toward mathematics - Focus on dividing fractions of the 6th Grade. Unpublished master thesis, Daegu National University of Education.
42 Choi, Y. J. (2005). Study on the teaching methods of fractions concept through the analysis of misconcepts of fractions. Unpublished master thesis, Jeon-ju National University of Education
43 Bezuk, N. S., & Bieck, M. (1993). Current research on rational numbers and common fractions: Summary and implications for teachers. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 118-136). New York: Macmillan.
44 Jung, S. Y. (2017). The analysis of influencing on figure conceptual formation and mathematical tendency using GeoGebra in mathematics. Unpublished master thesis, Seoul National University of Education.
45 Jung, E. S. (2005). A scheme of the instruction of geometry concepts through the example and counterexample. Unpublished master thesis, Gyeongin National University Education.
46 Hwang, S. N. (2015). Effects of the leaner-centered mathematical activity on student's mathematical thinking and mathematical learning attitude. Unpublished master thesis, Ewha Womans University
47 Hwang, H. J., Kim, J., Ko, H. K., & Suh, B. E. (2014, Eds). Principles and application learning and teaching of mathematics. Seoul: Kyungmoonsa.
48 Barnett-Clark, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understandings of rational numbers for teaching mathematics in grades 3-5. Reston, VA: NCTM Press.
49 Black, P., Harrison, C., Lee, C., Marshall, B., & William, D. (2003). Assessment for learning: Putting it into practice. New York: Open University Press.
50 Burns, M. (2001). Lessons for introducing fractions to grades 4-5. Sausalito, CA: Math Solutions Publications.
51 Burns, M. (2003). Lessons for extending fractions to grades 5. Sausalito, CA: Math Solutions Publications.
52 Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645.   DOI
53 Chapin, S. H., O'Connor, C. & Anderson, N. C. (2013). Classroom discussions in math: A teacher's guide for using talk moves to support the Common Core and more, Grades K-6: A multimedia professional learning resource (3rd Ed.). Sausalito, CA: Math Solutions Publications.
54 Kim, J., Colen, Y., & Colen, J. (2013). Reform based instruction in Korea. In J. Kim, Han, I., Park, M., & Lee, J. (Eds.), Mathematics education in Korea: Curriculum and teaching and learning practices (pp. 104-129). Singapore: World Scientific Press.
55 Charalambous, C. Y. & Pitta-Pantazi, D. (2015). Perspectives on priority mathematics education: Unpacking and understanding a complex relationship linking teacher knowledge, teaching, and learning. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed.) (pp. 19-59). New York, NY: Routledge.
56 Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.   DOI
57 Kim & Yeo (2019). Teaching practices for all learners in the mathematics classroom. Research in Mathematical Education, 22(2), 123-134.   DOI
58 Levi, L., & Empson, S. B. (2011). Extending children's mathematics: Fractions and decimals. Portsmouth: Heinemann.
59 NCTM (2000). Principles and standards for school mathematics. Reston, VA: Author.
60 Payne, J., Towsley, A., & Huinker, D. (1990). Fractions and decimals. In J. Payne & C. E. Clements (Eds.), Mathematics for the young child (pp. 175-200). Reston, VA: NCTM Press.
61 Rectanus, C. (1994). Math by all means: Geometry grades 3-4. Math Solutions Publications.
62 Reys, R., Lindquist, M., Lambdin, D. V., & Smith, N. L. (2009). Helping children learn mathematics. John Wiley & Sons.
63 Schuster, L. (2009). A month-to-month guide: Fourth-grade math. Sausalito, CA, Math Solutions Publications.