Keywords
online collaborative discourse
mathematical reasoning
difficulties in learning mathematics
students with learning difficulties
How to Cite
Abstract
The present research study was carried out in an online learning environment in a small group of eighth-grade students. The research proposes a learning framework that relies on collaborative mathematical discourse with the intention to promote the reasoning ability of students with difficulties in mathematics. The aim of mathematical discourse is the reciprocal building of the ability of the learner with difficulties to provide explanations during the discourse between the learner and his peers and between the learner and the teacher. This type of learning was found to be effective, and the communicational continuum between the learner and the material and between the learner and the group is preserved. The learning process built on authentic mathematical tasks strengthened the learners’ ability to create communication among themselves. The discourse encouraged the development of mathematical thinking abilities among the learners with difficulties, such as posing arguments and drawing conclusions while explaining and justifying these arguments. The mathematical discourse also encouraged students to choose and to monitor the form and processes of their thinking and increased their problem-solving ability.
References
Ben-Yehuda T., Licht P., Implementation of a Model for Tailored Intervention: Teaching Groupsn of Learners with Difficulties in Mathematics Who Are Integrated in Regular Education, [in:] Inclusion: Learners with Disabilities in the Education System, Eds. G. Avisar, S. Reiter, Achva Press, Haifa 2013. (Hebrew)
Boyd M.P., Markarian W.C., Dialogic Teaching: Talk in Service of a Dialogic Stance, Language & Education: An International Journal, 2011, 25(6).
Brody C.M., Davidson N., Professional Development for Cooperative Learning: Issues and Approaches, State University of New York Press Albany, New York 1998.
Buzu-Shwartz M., Banya Y., Learning in Small Groups: Learning to Talk and Talking to Learn, Echo of Education, 2013 August, 88(07). (Hebrew)
Chen C.H., Law V., Scaffolding Individual and Collaborative Game-Based Learning in Learning Performance and Intrinsic Motivation, Computers in Human Behavior, 2016 February, 55.
Cohen E.G., Restructuring the Classroom: Conditions for Productive Small Groups, Review of Educational Research, 1994, 64(1).
Common Core State Standards Initiative, Common Core State Standards for Mathematics (CCSSM). Washington DC: The National Governors Association Center for Best Practices and Council of Chief State School Officers. http://www.corestandards.org/wpcontent/uploads/Math_Standards1.pdf [1.07.2020].
Cooke L.B., Adams V.M., Encouraging “Math Talk” in the Classroom, Middle School Journal, 1998, 29(5).
Denvir B., Stolz C., Brown M., Low Attainers in Mathematics, Policies and Practices in Schools, Schools Council Working Paper, 1982, 72, 5-16, Methuen Educational, London.
Drigas A., Kokkalia G., Lytras M.D., ICT and Collaborative Co-Learning in Preschool Children Who Face Memory Difficulties, Computers in Human Behavior, 2015 October, 51.
Dunleavy M., Dexter S., Heinecke W., What Added Value Does a 1:1 Student to Laptop Ratio Bring to Technology-Supported Teaching and Learning? Journal of Computer Assisted Learning, 2007, 23.
Erdem, E., Gürbüz R., An Analysis of Seventh-Grade Students’ Mathematical Reasoning, Cukurova University Faculty of Education Journal, 2015, 44.
Franke M.L., Turrou A.C., Webb N.M., Ing M., Wong J., Shin N., Fernandez C., Student Engagement with Others’ Mathematical Ideas: The Role of Teacher Education and Support Moves, The Elementary School Journal, 2015, 116.
Friedman Y., Measurement and Assessment of Social and Educational Programs, Henrietta Szold Institute 2005. (Hebrew)
Gardner H., Multiple Intelligences: Theory and Practice, Branco Weiss Institute for the Cultivation of Thinking & Department of Curricula, Ministry of Education, Culture, & Sport, Israel 1996. (Hebrew)
Geary D.C., Mathematics and Learning Disabilities, Journal of Learning Disabilities, 2004, 37.
Geary D.C. The Origin of Mind: Evolution of Brain, Cognition, and General Intelligence, American Psychological Association, Washington DC, US 2005 http://dx.doi.org/10.1037/10871-000
Geary D.C., Hoard M.K., Byrd-Craven J. et al., Cognitive Mechanisms Underlying Achievement Deficits in Children with Mathematical Learning Disability, Child Development, 2007, 78.
Goldman S.R., Strategy Instruction in Mathematics, Learning Disabilities Quarterly, 1989, 12.
Hativa N., Teaching Processes in the Classroom, Academic Press for the Development of Teaching Faculty in the Classroom, Tel Aviv 2003. (Hebrew)
Haylock D., Teaching Mathematics to Low Attainers, Paul Chapman Publishing, London 1991.
Heggart K.R., Yoo J., Getting the Most from Google Classroom: A Pedagogical Framework for Tertiary Educators, Australian Journal of Teacher Education, 2018, 43(3).
Horizon Report, Higher Education Edition, 2017.
Hsu P.S., Examining Current Beliefs, Practices and Barriers about Technology Integration: A Case Study, TechTrends: Linking Research and Practice to Improve Learning, 2016, 60(1).
Ilam G., The Philosophy and Psychology of Vygotsky: From Cultural Instruments to Psychological Instruments, [in:] Lev Vygotsky – Thought and Culture, Eds. A. Kozulin, G. Ilam, Branco Weiss Institute, Jerusalem 2003. (Hebrew)
Imbeau M.B., Tomlinson C.A., Leading and Managing a Differentiated Classroom, ASCD, Alexandria, VA 2010.
Jonassen D.H., Chad C., Hsiu-Ping Y., Computers as mindtools for engaging learners in critical thinking, TechTrends, 1998, 43.
Jordan N.C., Levine S.C., Socio-Economic Variation, Number Competence, and Mathematics Learning Difficulties in Young Children, Developmental Disabilities Research Reviews, 2009, 15.
Katz J., Developing Mathematical Thinking: A Guide to Rethinking the Mathematics Classroom, Rowman & Littlefield Publishers, Lanham, Maryland 2014.
Keshet-Meor J., Differential Teaching in the 21st Century, [in:] Equals: School Support of Equality of Opportunity, Ed. J. Mandel-Levy, Avney Rosha Institute, Jerusalem 2017. (Hebrew)
Kidron R., Difficulties in Learning Arithmetic, Otsar Hamore, Tel Aviv 1985. (Hebrew)
Linchevsky L., Tuval H., The Role of the Models as an Auxiliary Means for Those with Difficulties in Arithmetic: Analysis of the Concept of the Fraction, Trends, 1993, 35. (Hebrew)
Mason J., Burton L., Stacey K., Thinking Mathematically, Pearson Education Limited, Inggris 2010.
Mayer R.E. (Ed.), The Cambridge Handbook of Multimedia Learning, Cambridge University Press, New York 2005.
Mayer R.E., Multimedia Learning, Cambridge University Press, New York 2009.
McDonnell J., Mathot-Buckner C., Thorson N., Fister S., Supporting the Inclusion of Students with Moderate and Severe Disabilities in Junior High School General Education Classes:
The Effects of Classwide Peer Tutoring, Multi-Element Curriculum, and Accommodations, Education and Treatment of Children, 2001 May, 24(2), https://www.jstor.org/stable/42899651 [date of access: 1.07.2020]
Ministry of Education, Director General Circular 1995: Tests and Assessment in the Elementary School: National Feedback and School Feedback, 1996. (Hebrew)
Ministry of Education, Integrated Instruments: Guide to Work in the Individualized Hour, Department of Secondary Education, Pedagogical Administration, Ministry of Education, State of Israel, 2009: http://meyda.education.gov.il/files/ChinuchMukar/4.pdf [date of access: 1.07.2020]. (Hebrew)
Ministry of Education, Opportunities in Teaching and Learning in a Small Group, Department of Elementary Education, Pedagogical Administration, Ministry of Education, State of Israel, 2009. (Hebrew)
Mintz R., Nachmias R., Teaching Science and Technology in the Era of Knowledge, Computers in Education, 1998, (Hebrew)
National Council of Teachers of Mathematics (NCTM), Executive Summary Principles and Standards for School Mathematics, 2000. https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf [date of access: 1.07.2020]
Niss M., Mathematical Competence and PISA, [in:] Assessing Mathematical Literacy: The PISA Experience, The Foundations of PISA Mathematics, Eds. K. Stacey, R. Turner, Springer International Publishing Switzerland 2015.
O’Donnell A.M., Kelly J., Learning from Peers: Beyond the Rhetoric of Positive Results, Educational Psychology Review, 1994, 6.
OECD (2018). PISA 2021 Mathematics Framework (Draft) – November. https://pisa-2021-maths.oecd.org/files/PISA%202021%20Mathematics%20Framework%20Draft.
pdf [date of access: 1.07.2020].
Pace M.H., Ortiz E., Get the GOOF! Teaching Children Mathematics, 2016, 23(3).
Papert S., Introduction: Computers for Children; Computers and Computers Cultures, [in:] Mind-Storms. Children, Computers, and Powerful Ideas, Ed. S. Papert, Basic Books Inc., New York 1980.
Rawding M.R., Wills T., Discourse: Simple Moves that Work, Mathematics Teaching in the Middle School, 2012, 18(1).
Regev H., Shimoni S., The Mathematical Discourse One or More Discourse? Pamphlet for the Teacher of Mathematics, 2005, 34. (Hebrew)
Rimor R., Decentralized Learning: From the Search for Information to the Construction of Knowledge – Processes of Organization and Construction of Knowledge in Computerized Environments of Databases, Ph.D. Dissertation, Ben Gurion University of the Negev 2002. (Hebrew)
Rutherford S., Collaborative Learning: Theory, Strategies, and Educational Benefits, Nova Science Publishers, Inc., New York 2014.
Salomon G., Communication: Concepts in the Educational Discussion, Sifriat Poalim 1981. (Hebrew)
Salomon G., Technology and Education in the Information Era, Haifa University – Zmora-Betan Press, Tel Aviv 2000. (Hebrew)
Schoenfeld A., Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics, Journal of Education, 2016, 196(2).
Sfard A., Thinking as Communicating: Human Development, Development of Discourses, and Mathematizing, Cambridge University Press, New York 2008.
Sfard A., Lavie I., Objects from Talk: How Small Children Create Numbers in Conversation, Research and Study in Mathematical Education, 2016 November, 4. (Hebrew)
Stacey K., What Is Mathematical Thinking and Why Is It Important? Paper Presented in APEC Symposium: Innovative Teaching Mathematics through Lesson Study II, 2006 December, 3-4.
Stake R.E., Case studies, [in:] Handbook of Qualitative Research (2nd Ed.), Eds. N.K. Denzin, S.L. Lincoln, Sage Publications, London 2000.
Stanford P., Crowe M.W., Hollie F., Differentiating with Technology, Teaching Exceptional Children Plus, 2010 April, 6, 4.
Tam M., Constructivism, Instructional Design, and Technology: Implications for Transforming Distance Learning, Educational Technology and Society, 2000, 3(2).
Tomlinson C.A., How to Differentiate Instruction in Mixed-Ability Classrooms, Association for Supervision and Curriculum Development, Alexandria VA 1995.
Tomlinson C.A., The Differentiated Classroom: Responding to the Needs of All Learners, Pearson, Upper Saddle River, New York 2005.
Vansteensel M.J., Bleichner M.G., Freudenburg Z.V., Hermes D., Aarnoutse E.J., Leijten F.S., ... Ramsey N.F., Spatiotemporal characteristics of electrocortical brain activity during mental calculation, Human Brain Mapping, 2014, 35(12).
Vygotsky L.S., Mind in Society: The Development of Higher Mental Process, Harvard University Press, Cambridge 1978.
Wagganer E.L., Creating Math Talk Communities, Teaching Children Mathematics, 2015, 22(4).
Weiss D., Pedagogical Sympathy to Technological Instruments, Echo of Education Journal, 2010. (Hebrew)
Wenger-Trayner E., Wenger-Trayner B., Introduction to Communities of Practice, 2015, https://wenger-trayner.com/introduction-to-communities-of-practice/GoogleScholar [date of access: 1.07.2020].
Yagi S.S., An Exploration of First Grade Students’ Engagement in Mathematical Processes during Whole Group Discussions, [in:] Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Eds. M.B. Wood, E.E. Turner, M. Civil, J.A. Eli, The University of Arizona, Tucson, AZ 2016.
Zevenbergen R., Dole S., Wright R., Teaching Mathematics in Primary Schools, Allen & Unwin, Australia 2004.