METHODS FOR TEACHING THE NUMBERING OF NON-NEGATIVE WHOLE NUMBERS THROUGH CRITICAL THINKING
Keywords:
Numeration, place value, non-negative whole numbersAbstract
Numeration of non-negative whole numbers is often taught as memorizing number names and applying place-value rules. Such teaching can produce correct reading and writing while leaving fragile reasoning in comparison, the meaning of zero, and answer checking. This thesis proposes a method that embeds critical thinking into numeration lessons: pupils state claims about number structure, test those claims with representations, and revise claims using evidence. The approach is designed for primary classrooms and for pre-service teacher education, emphasizing argumentation, error analysis, and representational coherence as routine instructional elements.
References
Shulman L.S. Those who understand: Knowledge growth in teaching // Educational Researcher. — 1986. — Vol. 15, No. 2. — P. 4–14. — DOI: 10.3102/0013189X015002004.
Ball D.L., Thames M.H., Phelps G. Content knowledge for teaching: What makes it special? // Journal of Teacher Education. — 2008. — Vol. 59, No. 5. — P. 389–407. — DOI: 10.1177/0022487108324554.
National Research Council. Adding It Up: Helping Children Learn Mathematics. — Washington, DC: The National Academies Press, 2001. — DOI: 10.17226/9822.
National Council of Teachers of Mathematics. Principles to Actions: Ensuring Mathematical Success for All. — Reston, VA: NCTM, 2014.
Fuson K.C. Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction, and place value // Cognition and Instruction. — 1990. — Vol. 7, No. 4. — P. 343–403. — DOI: 10.1207/s1532690xci0704_4.
Fuson K.C. Children’s Counting and Concepts of Number. — New York: Springer, 1988. — DOI: 10.1007/978-1-4612-3754-9.
Facione P.A. Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction. Research Findings and Recommendations (The Delphi Report). — Newark, DE: American Philosophical Association, 1990. — (ERIC ED315423).
Ennis R.H. The Nature of Critical Thinking: An Outline of Critical Thinking Dispositions and Abilities. — Urbana, IL: University of Illinois, 2011.
Paul R., Elder L. The Miniature Guide to Critical Thinking Concepts and Tools. — London: Bloomsbury Publishing Plc, 2019. — 48 p. — ISBN 978-1-53813-494-8.
Clements D.H., Sarama J. Learning and Teaching Early Math: The Learning Trajectories Approach. — New York: Routledge, 2009. — DOI: 10.4324/9780203883389.
Pólya G. How to Solve It: A New Aspect of Mathematical Method. — Princeton, NJ: Princeton University Press, 1945.
