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http://dx.doi.org/10.7468/mathedu.2019.58.3.459

Analyzing seventh graders' statistical thinking through statistical processes by phases and instructional settings  

Kim, Ga Young (Graduate School, Ewha Womans University)
Kim, Rae Young (Ewha Womans University)
Publication Information
The Mathematical Education / v.58, no.3, 2019 , pp. 459-481 More about this Journal
Abstract
This study aims to investigate students' statistical thinking through statistical processes in different instructional settings: Teacher-centered instruction vs. student-centered learning. We first developed instructional materials that allowed students to experience all the processes of statistics, including data collection, data analysis, data representation, and interpretation of the results. Using the instructional materials for four classes, we collected and analyzed the data from 57 seventh graders' discourse and artifacts from two different instructional settings using the analytic framework generated on the basis of literature review. The results showed that students felt difficulty particularly in the process of data collection and graph representations. In addition, even though data description has been heavily emphasized for data analysis in statistics education, it is surprisingly discovered that students had a hard time to understand the relationship between data and representations. Also, there were relationships between students' statistical thinking and instructional settings. Even though both groups of students showed difficulty in data collection and graph representations of the data, there were significant differences between the groups in terms of their performance. Whereas students from student-centered learning class outperformed in making decisions considering verification and justification, students from teacher-centered lecture class did better in problems requiring accuracy than the counterpart. The results from the study provide meaningful implications on developing curriculum and instructional methods for statistics education.
Keywords
Statistical process; Statistical thinking; Instructional methods; Statistics for middle schools;
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Times Cited By KSCI : 5  (Citation Analysis)
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1 Cho, G. E., & Cho, M. S. (2009). A study on the statistical thinking levels of middle school students based on the data-handling process. Korean Journal of Teacher Education, 25(1), 205-225.
2 Cho, Y. N. (2008). Comparative research on the instructional design model of constructivism and objectivism. Secondary Education Research, 56(3), 67-92.
3 Choi, B. H. (2014). An effect of digital storytelling on mathematical disposition, attitude, and achievement in mathematics instruction for sixth graders (Doctoral dissertation). Korea National University of Education, Chungcheong.
4 Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801-823.   DOI
5 Fleiss, J. L. (1971). Measuring normal scale agreement among many raters. Psychological Bulletin, 76(5), 378-382.   DOI
6 Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report pre-K-12. Alexandria, VA: American Statistical Association.
7 Gal, I., & Garfield, J. B. (1997). Curricular goals and assessment challenges in statistics education. In I. gal & J. B. Garfield (Eds.), The Assessment Challenge in Statistical Education (pp. 1-15). Amsterdam, The Netherlands: IOS Press.
8 Garfield, J., & Ben-Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31, 72-77.   DOI
9 Gelman, A., & Nolan, D. (2002). Teaching Statistics: A Bag of Tricks. New York, NY: Oxford University Press.
10 Go, E. S., & Lee, K. H. (2011). Study on levels of thinking of elementary and middle school students on the task of explaining and dealing with variability. Journal of Educational Research in Mathematics, 21(2), 201-220.
11 Go, S. M., Kim, M. S., Jung, J. K., & Cho, W. Y. (2017). Analysis of the problems in statistics units of middle school textbooks for the 3rd grade in terms of statistical literacy. School Mathematics, 19(4), 731-749.
12 Jang, A. R. (2016). A comparative analysis on statistical reasoning questions in textbooks (Master's thesis). Chonnam National University, Kwangju.
13 Jeon, H. J. (2016). An analysis of features of statistical thinking on storytelling-based mathematical institution of the 3rd grade (Master's thesis). Seoul National University of Education. Seoul.
14 Kang, H. Y. (2012). Study of the educational meaning of statistical literacy. Journal for History of Mathematics, 25(4), 121-137.
15 Jeong, M. H. (2014). Influence of the problem-posing activity on the 7th grade students' mathematical achievement and learning attitude (Master's thesis). Korea National University of Education, Chungcheong.
16 Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A framework for characterizing children's statistical thinking. Mathematical Thinking and Learning, 2(4), 269-307.   DOI
17 Jung, H. S., & Kim, J. H. (2013). Effects of mathematical instructions based on constructivism on learners' reasoning ability - with focus on the area of multiplication for 2nd graders. Journal of the Korean School Mathematics Society, 16(1), 31-61.
18 Kim, K. B. (2017). A study on collaborative learning methods for the cultivation of statistical thinking in elementary mathematics (Master's thesis). Korea National University of Education, Chungcheong.
19 Kim, J. H. (2007). 1st graders' achievements who have experienced learning and teaching practices in learner-centered classroom during first school year. Journal of Elementary Mathematics Education in Korea, 11(1), 23-42.   DOI
20 Kim, J. H., Lee, S. M., & Kim, S. L. (2010). Achievement of students who have learner-centered instruction for multiplication units. Journal of Elementary Mathematics Education in Korea, 14(1), 136-151.
21 Kim, M. K., & Kim, H. W. (2011). A study on children's statistical thinking based on survey activities. School Mathematics 13(1), 207-227.
22 Kim, S. H. & Lee, B. J. (2016). The effects of teaching based on a learning-communities approach to mathematics in middle school. Journal of the Korean School Mathematics Society, 19(4), 417-439.
23 Lee, E. S., & Kim, J. H. (2016). Effect of mathematics instruction based on constructivism on learners' knowledge generation level and reasoning ability - focusing on 4th grade fraction. Education of Primary School Mathematics, 19(1), 79-112.   DOI
24 Kim, S. L. (2009). A study on statistical thinking and developing statistical thoughts. Education of Primary School Mathematics, 12(1), 31-38.
25 Kim, T. H., & Kim, J. H. (2010). Effects of math lessons based on constructivism ideas on learners' achievements - with focus on the area of fractions for 4th graders. Education of Primary School Mathematics, 13(2), 67-84.
26 Kwon, N. W. (2001). Characteristics and theory of learner-centered education. Journal of Learner-Centered curriculum and Instruction, 1(1), 29-40.
27 Lee, Y. K. (2009). The effect of Project classes on statistical teaching for first-year middle school students (Master's thesis). Korea National University of Education, Chungcheong.
28 Lee, H. J., & Ko, H. K. (2015). The effect of cooperative learning and peer tutoring program on cognitive domain and affective domain: a meta-analysis. Journal of Educational Research in Mathematics, 25(1), 113-137.
29 Lee, J. H., & Kim, W. K. (2011). Effects of spreadsheet-used instruction on statistical thinking and attitude. The Mathematical Education, 50(2), 185-212.   DOI
30 Lee, S. D., & Kwean, H. J. (2007). The development of teaching-learning materials based on real life and the investigation of students's cognition change about mathematics class using developed materials Journal of the Korean School Mathematics Society, 10(1), 45-69.
31 Lee, Y. K. (2013). The effects of small group cooperative learning and peer mentoring learning on academic achievement and self-efficacy in mathematics (Master's thesis). Sogang University, Seoul.
32 Mooney, E, S. (2002). A framework for characterizing middle school students' statistical thinking. Mathematical Thinking and Learning, 4(1), 23-63. doi: 10.1207/S15327833MTL0401_2   DOI
33 Mascolo, M. F. (2009). Beyond student-centered and teacher-centered pedagogy: Teaching and learning as guided participation. Pedagogy and the Human Sciences, 1(1), 3-27.
34 Ministry of Education (2017). Mathematics curriculum (Ministry of Education No. 2015-74). Sejong, Korea: Author.
35 Mok, Y. H. (2003). Constructivism and the 7th national curriculum. The Korean Journal of Philosophy of Education, 29, 27-43.
36 Mvududu, N. (2005). Constructivism in the statistics classroom: from theory to practice. Teaching Statistics, 27(2), 49-54.   DOI
37 Park, K. M., Lee, H. C., Park, S. H., Kwon, J. R., Yun, S. H., Kang, H. Y., ..., Jeon, I. T. (2015). A study on 2015 revised mathematics curriculum development. Korea Foundation for the Advancement of Science & Creativity.
38 Na, M. Y., Lee, C. S., Lee, J. Y., Yoon, S. J., Oh, Y. R., & Kwon, O. N. (2015). Comparison of achievement standards of Korea 2009 revised curriculum and US CCSSM. Journal of Learner-Centered Curriculum and Instruction, 15(11), 327-347.
39 Oh, Y. Y., & Lee, M. Y. (2008). Exploring directions for improving elementary statistics education. The Journal of Korea Elementary Education, 19(1), 1-13.   DOI
40 Paek, S. Y. (2015). Development and application of statistics project based learning resources for free semester system (Master's thesis). Korea National University of Education, Chungcheong.
41 Park, S. H. (2015). The effects of storytelling instruction on mathematics concept formation and learning attitude (Master's thesis). Kangwon National University, Kangwon.
42 Watson, J. (1997). Assessing statistical thinking using the media. In I. gal & J. B. Garfield (Eds.), The Assessment Challenge in Statistical Education (pp. 107-121). Amsterdam, The Netherlands: IOS Press.
43 Roseth, C., Garfield, J., & Ben-Zvi, D. (2008). Collaboration in learning and teaching statistics. Journal of Statistics Education, 16(1). doi: 10.1080/10691898.2008.11889557   DOI
44 Slavin, R. E. (1989). Research on cooperative learning: an international perspective. Scandinavian Journal of Educational Research, 33(4), 231-243.   DOI
45 Tak, B. J., & Lee, K. H. (2017). An analysis of research trends on statistics education in Korea from 2000 to 2016. Journal of Educational Research in Mathematics, 27(2), 269-289.
46 Bae, H. J., & Lee, D. H. (2016). An analysis on statistical units of elementary school mathematics textbook. Journal of Elementary Mathematics Education in Korea, 20(1), 55-69.
47 Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248.   DOI
48 Woo, J. H. (2000). An exploration of the reform direction of teaching statistics. School Mathematics, 2(1), 1-27.
49 Yang, J. I. (2017). A development of the project learning materials for improving statistical thinking (Master's thesis). Gyeongin National University of Education, Gyeonggi.
50 Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., Raths, J., & Wittrock, M. C. (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives. New York, NY: Addison Wesley Longmann.
51 Biggs, J., & Collis, K. F. (1991). Multimodal learning and the quality of intelligent behavior. In H. A. H. Rowe (Eds.), Intelligence; Reconceptualisation and Measurement (pp. 57-76). Hillsdale, N. J.: Lawrence Erlbaum.
52 Bae, I. S. (2004). The effect of cooperative learning on academic achievement and internal motivation (Master's thesis). Ajou University. Gyeonggi.
53 Baek, S. S., & Kim, W. K. (1999). The analysis of the effects of the problem centered instruction and explanatory instruction. Communications of Mathematical Education, 8, 107-119.
54 Bakker, A. (2004). Design Research in Statistics Education: On Symbolizing and Computer Tools. Utrecht, the Netherlands: CD Beta Press.
55 Ben-Zvi, D., & Garfield, J. (2004). The Challenge of Developing Statistical Literacy, Reasoning and Thinking. Dordrecht, the Netherlands: Kluwer Academic Publishers.
56 Ben-Zvi, D., & Garfield, J. (2008). Introducing the emerging discipline of statistics education. School Science and Mathematics, 108(8), 355-361. Retrieved from https://search.proquest.com/docview/61874708?accountid=10785   DOI
57 Chae, M. R. (2007). The effects of project-based statistics learning on elementary school students' statistical thinking (Master's thesis). Seoul National University of Education. Seoul.
58 Chall, J. S. (2002). The Academic Achievement Challenge: What really Works in the Classroom? New York, NY: Guilford.