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Nicole M. Wessman-Enzinger – Mathematics Teacher: Learning and Teaching PK-12, 2023
What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…
Descriptors: Mathematics Instruction, Construction (Process), Number Systems, Grade 5
Patrick K. Kirkland; Claire Guang; Chineme Otuonye; Nicole M. McNeil – Journal of Numerical Cognition, 2024
Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…
Descriptors: Number Concepts, Thinking Skills, Mathematical Concepts, Multiple Choice Tests
Ling Zhang; Naiqing Song; Guowei Wu; Jinfa Cai – Educational Studies in Mathematics, 2025
This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…
Descriptors: Cognitive Processes, Mathematics Skills, Problem Solving, Eye Movements
Utomo, Dwi Priyo – Journal of Research and Advances in Mathematics Education, 2020
Relational understanding constitutes students' awareness of appropriate procedures to solve problems along with logical reasoning. It is pivotal to help students solve problems in mathematics. It is necessary that the teaching of mathematics be directed to achieve relational understanding. Accordingly, students are capable of solving complicated…
Descriptors: Numbers, Problem Solving, Elementary School Students, Grade 5
Shuyuan Yu – ProQuest LLC, 2022
Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…
Descriptors: Logical Thinking, Mathematical Logic, Mathematics Instruction, Visual Aids
Cramer, Kathleen; Monson, Debra; Ahrendt, Susan; Wyberg, Terry; Pettis, Christy; Fagerlund, Chelsey – Investigations in Mathematics Learning, 2019
This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…
Descriptors: Grade 4, Fractions, Numbers, Elementary School Mathematics
Abdullah Terzi; Tugrul Kar – Education 3-13, 2024
The present study aimed to test the effect of the problem-posing instruction experimentally based on the extended active learning framework on the development of Turkish middle school sixth-grade students' (N = 19) problem-posing and -solving skills with whole-number operations. The training programme was completed in 13 lessons over a seven-week…
Descriptors: Foreign Countries, Grade 6, Elementary School Students, Problem Solving
Roche, Anne; Clarke, Doug; Sexton, Matt – Australian Primary Mathematics Classroom, 2023
The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…
Descriptors: Mathematics Instruction, Grade 5, Grade 6, Elementary School Students
Fouryza, Darin; Amin, Siti Maghfirotun; Ekawati, Rooselyna – International Journal of Evaluation and Research in Education, 2019
This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the…
Descriptors: Lesson Plans, Numbers, Mathematics Instruction, Teaching Methods
Poloczek, Sebastian; Hammerstein, Svenja; Büttner, Gerhard – Journal of Numerical Cognition, 2022
Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…
Descriptors: Children, Learning Strategies, Mathematics Skills, Computation
Jacobson, Erik; Liu, Jinqing; Bharaj, Pavneet Kaur; Savich, Theodore – North American Chapter of the International Group for the Psychology of Mathematics Education, 2021
There have been many efforts to measure pedagogical content knowledge with multiple-choice survey instruments, but little is known about how different types of items contribute. In this study, we examined interviews with 9 Grade 4 teachers to develop a deeper understanding of how teachers select pedagogical representations in the context of a…
Descriptors: Pedagogical Content Knowledge, Elementary School Mathematics, Elementary School Teachers, Grade 4
Barbieri, Christina Areizaga; Booth, Julie L.; Chawla, Kamal – Educational Psychology, 2023
The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…
Descriptors: Fractions, Mathematics Instruction, Teaching Methods, Algebra
Can, Derya; Yetkin Özdemir, I. Elif – International Journal of Science and Mathematics Education, 2020
Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students' number sense. The aim of this study was to examine fourth-grade elementary school students' number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and…
Descriptors: Elementary School Students, Grade 4, Numeracy, Number Concepts
Harris, Danielle; Lowrie, Tom; Logan, Tracy; Hegarty, Mary – British Journal of Educational Psychology, 2021
Background: The role of gender in both spatial and mathematics performance has been extensively studied separately, with a male advantage often found in spatial tasks and mathematics from adolescence. Spatial reasoning is consistently linked to mathematics proficiency, yet despite this, little research has investigated the role of spatial…
Descriptors: Spatial Ability, Problem Solving, Mathematics Achievement, Number Concepts
McMullen, Jake; Hannula-Sormunen, Minna M.; Lehtinen, Erno; Siegler, Robert S. – British Journal of Educational Psychology, 2022
Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and…
Descriptors: Elementary School Students, Middle School Students, Grade 6, Grade 7