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The Use of a Length and Measurement HLT by Pre-Service Kindergarten Teachers' to Notice Children's Mathematical Thinking
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Callejo, M. Luz; Pérez-Tyteca, Patricia; Moreno, Mar; Sánchez-Matamoros, Gloria – International Journal of Science and Mathematics Education, 2022
The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children's mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching…
Descriptors: Preservice Teachers, Preschool Teachers, Sequential Learning, Measurement
Changes in Students' Mental Constructions of Function Transformations through the APOS Framework
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Melike Yigit Koyunkaya; Burcak Boz-Yaman – International Electronic Journal of Mathematics Education, 2023
This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…
Descriptors: Foreign Countries, Mathematics Education, Mathematical Concepts, Learning Processes
Unit Transformation Graphs: A Case Study
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Norton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…
Descriptors: Mathematics Education, Problem Solving, Preservice Teachers, Preservice Teacher Education
Proof Frameworks: A Way to Get Started
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Selden, Annie; Selden, John; Benkhalti, Ahmed – PRIMUS, 2018
Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to…
Descriptors: Undergraduate Students, College Mathematics, Mathematics Education, Mathematical Logic
Does Comparing Informal and Formal Procedures Promote Mathematics Learning? The Benefits of Bridging Depend on Attitudes toward Mathematics
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Hattikudur, Shanta; Sidney, Pooja G.; Alibali, Martha W. – Journal of Problem Solving, 2016
Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined…
Descriptors: Mathematics Education, Problem Solving, Student Attitudes, Mathematics Skills
A Developing Approach to Studying Students' Learning through Their Mathematical Activity
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Simon, Martin; Saldanha, Luis; McClintock, Evan; Akar, Gulseren Karagoz; Watanabe, Tad; Zembat, Ismail Ozgur – Cognition and Instruction, 2010
We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which…
Descriptors: Mathematics Education, Learning Processes, Research Methodology, Mathematics Activities