Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach

Mulugeta Woldemicheal Gebresenbet; Mulugeta Atnafu Ayele

doi:doi:10.11648/j.edu.20170601.12

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Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach

Mulugeta Woldemicheal Gebresenbet, Mulugeta Atnafu Ayele

Published in Education Journal (Volume 6, Issue 1)

Received: 12 October 2016 Accepted: 27 October 2016 Published: 10 January 2017

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Abstract

The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to what extent do students improve their achievement of procedural and conceptual understanding in descriptive statistics using Modeling Instructional Approach. The study was conducted at two secondary schools in urban district in West Oromia Zone, Ethiopia. For comparisons, four grade nine sections with a total of 163 students were selected by purposive sampling technique. Quality Assurance Guide instrument was used to assess students’ models on Model Eliciting Activities (MEA). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. The quantitative data of the study was analyzed using descriptive statistics, and independent t-test. The qualitative data of the study was analyzed using thematic and content analyses. The findings of this study are: though students found MEAs cognitively challenging tasks, they constructed different models working in a team collaboratively. The study showed students more likely can enhance their critical understanding of descriptive statistics and gain modeling experiences working on relevant non-routine tasks like MEAs and doing project on their own themes. Also a statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach.

Published in	Education Journal (Volume 6, Issue 1)
DOI	10.11648/j.edu.20170601.12
Page(s)	5-21
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Descriptive Statistics, Non-Routine Problems, Model-Eliciting Activities, Understanding, Achievement

References

[1]	English, L. D. (2013a). Complex modeling in primary and middle schools years: An interdiscplinary approach. In G. A. Stillman, G. Kasier, & J. P. Werner Blum, Teaching mathematical modelling: Connecting research to practice (pp. 491-503). New York.London: Springer.
[2]	Kaiser, G., & Schwarz, B. (2006). Mathematical modeling as a bridge between school and university mathematics. ZDM, 196-208.
[3]	Stillman, G. A., Kasier, G., Blum, W. & Brown, J. (2013). Teaching mathematical modeling: Connecting research to practice. London: Springer.
[4]	Kaiser, G., Blohomhoj, M., & Siriraman, B. (2006). Towards a didactical theory for mathematical modeling. ZDM, 82-85.
[5]	Chamberlin, S. A., & Coxbill, E. (2012). Using Model-Elicting Activities to introduce upper elementary students to Statistical Reasoning and Mathematical Modeling. In L. H. Mayes, Quantitative reasoning and mathematical modeling: A driver for STEM integrated education and teaching in context. (pp. 169-179). Wyoming: Wyoming Insititute for the Study of Mathematics Education, Laramie, WY.
[6]	English, L. D. (2013b). Surviving an avalanche of data. Teaching Children Mathematics, 364-372.
[7]	Kinnear, V. (2013). Young children statistical reasoning: A tale of two contexts. A dissertation thesis. Queensland Technology University of Technology, Australia.
[8]	Sriraman, B., & English, L. (2010). Theories of Mathematics Education: New Frointers. Springer.
[9]	Cobb, G. W. (2007). One possible framework for thinking about experential learning. International Statistical Review, 336-347.
[10]	Garfield, J., & Ben-Zvi, D. (2008). Developing students' statistsical reasoning: Connecting research and teaching practice. London: Springer.
[11]	Ministry of Education (MoE) (2009a). Education and development, Ministry of Education, Addis Ababa, Ethiopia.
[12]	Ministry of Education (MoE) (2010a). Education Sector Development Program IV (ESDP IV): Program action plan, Federal Ministry of Education, Addis Abeba, Ethiopia.
[13]	Ministry of Education (MoE) (2010b). Mathematics teacher’s guide for Grade 9, Ministry of Education, Addis Ababa Ethiopia.
[14]	Micheal, K. & O'Connell, A. (2014). Statistics Education in Ethiopia: Successes, challenges and opportunities. In K. Makar, B. de Sousa & R. Gould (Eds.) Sustainably in Statistics Education. Proceedings of the ninthth International Conference on Teaching Statistics (ICOTS-9, July, 2014, Flagstaff, Arizona, USA). Voorburg, The Netherlands: International Statistical Institute.
[15]	Kaiser, G. (2010). Introduction: ICTMA and the reaching of modeling and application. In L. Richard, P. L. Galbraith, C. R., Haines, & A. Harford (Eds.), Modeling students' mathematical modeling competencies (PP. 1-2). New York: Springer.
[16]	Lesh, R., & Doerr, H. (Eds.). (2003). Beyond constructivism:Models and Modeling Perspectives on mathematices problem solving , learning and teaching. London: Lawrance Erlbaum Assocciate Publisher. [17] Lesh, R., & Fennewald, T. (2010). The nature of Models and Modeling: Introduction to part I modeling: What is it? why we do it? In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford, Modeling students' mathematical competencies (pp. 5-12). London: Springer.
[17]	Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM, 38(3), 302-310.
[18]	Ferri, R. B., & Lesh, R. (2013). Should interpretation systems considered to be Models if they only function implicitly. In G. A. Stillman, G. Kaiser, & W. Blum, Teaching mathematical modelling: Connecting research and practice (pp. 57-66). New York; London: Springer.
[19]	Lesh, R. (2012). Research on Model and Modeling and implication for common core state curriculum standards. In L. H. Mayes, Quantitative reasoning and mathematical modeling: A driver for STEM integrated education and teaching in context. (pp. 169-179). Wyoming: Wyoming Insititute for the Study of Mathematics Education, Laramie, WY.
[20]	Lesh, R., Yoon, C., & Zawojewski, J. (2007). John Dewey revisited-Making mathematics practical versus making practice mathematical. In R. A. Lesh, E. Hamilton, & J. J. Kaput, Foundations for the future in Mathematics Education (pp. 315-348). Mahwah, NJ London: Lawrance Erlbaum Associate Publisher.
[21]	Glasersfeld, E. v. (2003). Book review: Beyond constructivism, Models and Modeling Perspectives on mathematics problem solving, learning and teaching. ZDM, 325-329.
[22]	Hamilton, E., Lesh, R. Lester, F. & Yoon, C. (2007). The use of reflection tool in building personal models. In R. Lesh, E. Hamilton, & J. J. Kaput (Eds.), Foundations for future in Mathematics Education (pp. 1-6). Mahwha: NJ: Lawrence Erlbaum.
[23]	Magiera, M. T. (2013). An aluminium Bat Activity supports goals of STEM learning by engaging students in resourcful problem solving. Mathematics Teaching in the Middle School, 349-355.
[24]	Diefes-Dux, H., Whittenberg, L., & McKee, R. (2013). Mathematics modeling at the intersection of elementary mathematics, art and engineering Education. In L. D English & J. T Mulligan (Eds.), Reconceptualizing early mathematics learning, advance in Mathematics Education, 309-325. doi:10.1007/978-94-007-6440-8_15
[25]	Mousoulides, N. G., & English, L. D. (2012). Modeling as a bridge between real world problems and school mathematics. The 12th International Congress on Mathematics Education, 1-10.
[26]	Shuman, L. J, Besterfield-Sacre, M. E, Bursic, K. M, Vedic, N. S., & Siewiorek, N. (2012). CCLI. Model-Eliciting Activities, American Society for Engineering Education, 1-12.
[27]	Wild, C., & Pfannkuch, M. (1999). Statistical thinking in emperical enquiry. International Statistical Review , 223-265.
[28]	Doerr, H. M., & English, L. D. (2003). A modeling perspective on students' mathematical reasoning about data. Journal for Research in Mathematics Education, 110-136.
[29]	Garfield, J., delMass, R. C., & Ziefeller, A. (2009). Using Model-Eliciting Activities (MEAs) in statistics classroom. Roundtable Presentation at the Joint Statistical Meetings (pp. 1-7). Washington DC: University of Minnesota.
[30]	Noll, J., Geberesenbet, M., & Glover, E. D. (2012). A Modeling and simulation approach to informal inference:Successes and challenges. The 12th International Congress on Mathematical Education: Teaching and Learning of Statistics (TSG-12) (pp. 141-150). South Korea, Seoul: International Congress on Mathematical Education.
[31]	Hjalmarson, M. A., Moore, T. J., & delMass, R. (2011). Statistical analysis when the data is an image: Elicting student thinking about sampling and variability. Statistics Education Research Journal, 15-34.
[32]	Pearl, D. K., Garfield, J. B., delMas, R., Groth, R. E., Kaplan, J. J., MaGowan, H., & Lee, H. S. (2012). Connecting research to practice in a culture of assessment for introductory college level Statistics. [Online: http:// www.causeweb.org/research/guidelines/ResearchReport_DEC_2012.PDF].
[33]	Schwartz, D. L., Sears, D., & Chang, J. (2007). Reconsidering prior knowledge. In M. Lovett and P. Shah (Eds.), Thinking with data (pp. 319-344). New York: Erlbaum.
[34]	Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research in Mathematics and Science Education (pp. 113–149). Mahwah, NJ: Lawrence Erlbaum and Associates.
[35]	World Bank (2006). Assessing national achievement levels in education. (Eds.) Greaney V. & Kellenghan.
[36]	Ethiopian National Examination Agency (2010). Ethiopian First National Learning Assessment (Grade 10 and 12).
[37]	Ethiopian National Examination Agency (2013). Ethiopian Second National Learning Assessment (Grade 10 and 12).
[38]	Meletiou-Mavrotheris, M. (2007). The Formalist mathematical tradition as an obstacle to stochastical reasoning. In K. Francois, & J. P. V Bandegem (Eds.) Philosophical dimensions in Mathematics Education (PP. 131-155). Springer
[39]	Gouvea, J. S., Sawtelle, V., Geller, B. D., & Turpen, C. (2013). A framework for analyzing interdiscplinary tasks: Implication for student learning and curricular design. CBE- Life Science Education, 187-205.
[40]	Creswell, J. W. (2014). Research design: Quantitative, qualitative, mixed Method (4th ed.). Thousand Oaks, CA: Sage Publication.
[41]	Boaler, J. (2009). When politics took the place of inquiry : A response to the national mathematics advisory panel's review of instructional practice. Educational Researchers, 588-594. doi:10.3102/0013189X08327998
[42]	Campell, D. T., & Stanley, J. C. (1963). Experimental and quasi Experimental designs. USA: Houghton Mifflin Company.
[43]	Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks: Sage Publications.
[44]	Chamberlin, S. A. & Moon, S. M. (2005). Model-Eliciting Activities as a tool to develop and identify creatively gifted mathematicians. The Journal of Secondary Gifted Education, 37-47.
[45]	Freire, P. (1970). Pedagogy of the Oppressed. The Seabury Press. New York.
[46]	Gutstein, E. (2006). Reading and writing the world with mathematics: Towards a pedagogy for social Justice. USA: Routeldge.
[47]	Lesser, L. M., Wall, A. A., Carver, R. H., Pearl, D. K., Martin, N., Kupier, S., . . . Weber, J. J. (2013). Using fun in statistics classroom: An exploratory study of college instructors' hesitation and motivations. Journal of Statistics Education , 1-3.
[48]	Schoenfeld, A. (2004). The math wars. Educational Policy, 256-286.

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Mulugeta Woldemicheal Gebresenbet, Mulugeta Atnafu Ayele. (2017). Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Education Journal, 6(1), 5-21. https://doi.org/10.11648/j.edu.20170601.12

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Mulugeta Woldemicheal Gebresenbet; Mulugeta Atnafu Ayele. Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Educ. J. 2017, 6(1), 5-21. doi: 10.11648/j.edu.20170601.12

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AMA Style

Mulugeta Woldemicheal Gebresenbet, Mulugeta Atnafu Ayele. Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Educ J. 2017;6(1):5-21. doi: 10.11648/j.edu.20170601.12

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@article{10.11648/j.edu.20170601.12,
  author = {Mulugeta Woldemicheal Gebresenbet and Mulugeta Atnafu Ayele},
  title = {Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach},
  journal = {Education Journal},
  volume = {6},
  number = {1},
  pages = {5-21},
  doi = {10.11648/j.edu.20170601.12},
  url = {https://doi.org/10.11648/j.edu.20170601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.edu.20170601.12},
  abstract = {The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to what extent do students improve their achievement of procedural and conceptual understanding in descriptive statistics using Modeling Instructional Approach. The study was conducted at two secondary schools in urban district in West Oromia Zone, Ethiopia. For comparisons, four grade nine sections with a total of 163 students were selected by purposive sampling technique. Quality Assurance Guide instrument was used to assess students’ models on Model Eliciting Activities (MEA). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. The quantitative data of the study was analyzed using descriptive statistics, and independent t-test. The qualitative data of the study was analyzed using thematic and content analyses. The findings of this study are: though students found MEAs cognitively challenging tasks, they constructed different models working in a team collaboratively. The study showed students more likely can enhance their critical understanding of descriptive statistics and gain modeling experiences working on relevant non-routine tasks like MEAs and doing project on their own themes. Also a statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach.},
 year = {2017}
}

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TY  - JOUR
T1  - Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach
AU  - Mulugeta Woldemicheal Gebresenbet
AU  - Mulugeta Atnafu Ayele
Y1  - 2017/01/10
PY  - 2017
N1  - https://doi.org/10.11648/j.edu.20170601.12
DO  - 10.11648/j.edu.20170601.12
T2  - Education Journal
JF  - Education Journal
JO  - Education Journal
SP  - 5
EP  - 21
PB  - Science Publishing Group
SN  - 2327-2619
UR  - https://doi.org/10.11648/j.edu.20170601.12
AB  - The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to what extent do students improve their achievement of procedural and conceptual understanding in descriptive statistics using Modeling Instructional Approach. The study was conducted at two secondary schools in urban district in West Oromia Zone, Ethiopia. For comparisons, four grade nine sections with a total of 163 students were selected by purposive sampling technique. Quality Assurance Guide instrument was used to assess students’ models on Model Eliciting Activities (MEA). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. The quantitative data of the study was analyzed using descriptive statistics, and independent t-test. The qualitative data of the study was analyzed using thematic and content analyses. The findings of this study are: though students found MEAs cognitively challenging tasks, they constructed different models working in a team collaboratively. The study showed students more likely can enhance their critical understanding of descriptive statistics and gain modeling experiences working on relevant non-routine tasks like MEAs and doing project on their own themes. Also a statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach.
VL  - 6
IS  - 1
ER  -

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Author Information

Mulugeta Woldemicheal Gebresenbet

Department of Mathematics, College of Science, Dire Dawa University, Dire Dawa, Ethiopia
Mulugeta Atnafu Ayele

Department of Science & Mathematics Education, Addis Ababa University, Addis Ababa, Ethiopia

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APA Style

Mulugeta Woldemicheal Gebresenbet, Mulugeta Atnafu Ayele. (2017). Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Education Journal, 6(1), 5-21. https://doi.org/10.11648/j.edu.20170601.12

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ACS Style

Mulugeta Woldemicheal Gebresenbet; Mulugeta Atnafu Ayele. Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Educ. J. 2017, 6(1), 5-21. doi: 10.11648/j.edu.20170601.12

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AMA Style

Mulugeta Woldemicheal Gebresenbet, Mulugeta Atnafu Ayele. Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach. Educ J. 2017;6(1):5-21. doi: 10.11648/j.edu.20170601.12

Copy | Download

@article{10.11648/j.edu.20170601.12,
  author = {Mulugeta Woldemicheal Gebresenbet and Mulugeta Atnafu Ayele},
  title = {Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach},
  journal = {Education Journal},
  volume = {6},
  number = {1},
  pages = {5-21},
  doi = {10.11648/j.edu.20170601.12},
  url = {https://doi.org/10.11648/j.edu.20170601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.edu.20170601.12},
  abstract = {The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to what extent do students improve their achievement of procedural and conceptual understanding in descriptive statistics using Modeling Instructional Approach. The study was conducted at two secondary schools in urban district in West Oromia Zone, Ethiopia. For comparisons, four grade nine sections with a total of 163 students were selected by purposive sampling technique. Quality Assurance Guide instrument was used to assess students’ models on Model Eliciting Activities (MEA). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. The quantitative data of the study was analyzed using descriptive statistics, and independent t-test. The qualitative data of the study was analyzed using thematic and content analyses. The findings of this study are: though students found MEAs cognitively challenging tasks, they constructed different models working in a team collaboratively. The study showed students more likely can enhance their critical understanding of descriptive statistics and gain modeling experiences working on relevant non-routine tasks like MEAs and doing project on their own themes. Also a statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Enhancing Secondary School Students’ Understanding of Descriptive Statistics Using a Modeling Instructional Approach
AU  - Mulugeta Woldemicheal Gebresenbet
AU  - Mulugeta Atnafu Ayele
Y1  - 2017/01/10
PY  - 2017
N1  - https://doi.org/10.11648/j.edu.20170601.12
DO  - 10.11648/j.edu.20170601.12
T2  - Education Journal
JF  - Education Journal
JO  - Education Journal
SP  - 5
EP  - 21
PB  - Science Publishing Group
SN  - 2327-2619
UR  - https://doi.org/10.11648/j.edu.20170601.12
AB  - The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to what extent do students improve their achievement of procedural and conceptual understanding in descriptive statistics using Modeling Instructional Approach. The study was conducted at two secondary schools in urban district in West Oromia Zone, Ethiopia. For comparisons, four grade nine sections with a total of 163 students were selected by purposive sampling technique. Quality Assurance Guide instrument was used to assess students’ models on Model Eliciting Activities (MEA). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. The quantitative data of the study was analyzed using descriptive statistics, and independent t-test. The qualitative data of the study was analyzed using thematic and content analyses. The findings of this study are: though students found MEAs cognitively challenging tasks, they constructed different models working in a team collaboratively. The study showed students more likely can enhance their critical understanding of descriptive statistics and gain modeling experiences working on relevant non-routine tasks like MEAs and doing project on their own themes. Also a statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach.
VL  - 6
IS  - 1
ER  -

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