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Erik Tillema; Joseph Antonides – Investigations in Mathematics Learning, 2024
The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…
Descriptors: Multiplication, Mathematical Logic, Mathematics Instruction, Problem Solving
Fetiye Aydeniz Temizer – Journal of Mathematics Teacher Education, 2024
A 12-episode constructivist teaching experiment with two pairs of elementary preservice teachers was conducted to examine how they reason distributively and proportionally. Specifically, I studied how prospective teachers reason with ratios as multiplicative comparisons. Prospective teachers solved different problems in one specific context (Step…
Descriptors: Constructivism (Learning), Elementary School Teachers, Preservice Teachers, Mathematical Logic
Jaehong Shin; Soo Jin Lee – Investigations in Mathematics Learning, 2024
In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…
Descriptors: Mathematics Instruction, Multiplication, Middle School Students, Mathematical Logic
Brandon McMillan – Investigations in Mathematics Learning, 2025
Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…
Descriptors: Mathematics Skills, Thinking Skills, Mathematical Logic, Multiplication
Carney, Michele; Paulding, Katie; Champion, Joe – Applied Measurement in Education, 2022
Teachers need ways to efficiently assess students' cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process…
Descriptors: Middle School Students, Logical Thinking, Mathematical Logic, Problem Solving
Erickson, Sarah A.; Lockwood, Elise – International Journal of Research in Undergraduate Mathematics Education, 2021
Combinatorial proof is an important topic both for combinatorics education and proof education researchers, but relatively little has been studied about the teaching and learning of combinatorial proof. In this paper, we focus on one specific phenomenon that emerged during interviews with mathematicians and students who were experienced provers as…
Descriptors: Mathematics Skills, Mathematical Logic, Mathematics Instruction, Multiplication
Vanluydt, Elien; Verschaffel, Lieven; Van Dooren, Wim – Educational Studies in Mathematics, 2022
Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…
Descriptors: Preferences, Word Problems (Mathematics), Problem Solving, Error Patterns
Nicholas Shaver; Anna DeJarnette – The Mathematics Educator, 2024
This study was guided by the question, how do we understand the multiplicative reasoning of upper high school students and use that to give insight to their performance on a standardized test? After administering a partial ACT assessment to a class of high school students, we identified students to make comparisons between low and high scoring…
Descriptors: High School Students, Mathematical Logic, Standardized Tests, Scores
Gündogdu, Nida Sultan; Piskin Tunç, Mutlu – Journal of Pedagogical Research, 2022
The aim of this study was to examine the proportional reasoning skills of seventh-grade students before and after the implementation of STEM activities involving proportional and non-proportional relationships. Case study, one of the qualitative study methods, was used in the research. The data for the study was obtained from eight students. Seven…
Descriptors: Grade 7, Middle School Students, Logical Thinking, Thinking Skills
Sawatzki, Carly; Downton, Ann; Cheeseman, Jill – Mathematics Education Research Journal, 2019
What could two people stand to gain from sharing a taxi ride? We aimed to explore the extent to which this challenging yet accessible financial context might stimulate students' mathematical exploration of multiplicative thinking and proportional reasoning. Through teaching experiment methodology, data were collected from 37 Year 5 and 6 students…
Descriptors: Mathematics Instruction, Mathematical Logic, Mathematical Concepts, Teaching Methods
Izsák, Andrew; Kulow, Torrey; Beckmann, Sybilla; Stevenson, Dean; Ölmez, Ibrahim Burak – Mathematics Teacher Educator, 2019
We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as…
Descriptors: Mathematics Instruction, Multiplication, Division, Mathematical Concepts
Askew, Mike – Curriculum Journal, 2018
This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…
Descriptors: Mathematics Education, Multiplication, Mathematical Logic, Mathematical Concepts
Stevenson, Dean L.; Beckmann, Sybilla; Johnson, Sheri E.; Kang, Rui – North American Chapter of the International Group for the Psychology of Mathematics Education, 2018
We have extended two perspectives of proportional reasoning to solve problems based in probability. Four future middle grade teachers were enrolled in a mathematics content course that emphasized reasoning about multiplication with quantities. The course expected future teachers to generate and explain methods for solving proportions. Probability…
Descriptors: Problem Solving, Probability, Middle School Teachers, Preservice Teachers
Xin, Yan Ping; Chiu, Ming Ming; Tzur, Ron; Ma, Xiaojun; Park, Joo Young; Yang, Xuan – Learning Disability Quarterly, 2020
Informed by a constructivist-based, student-adaptive pedagogical approach, this study explores the benefits of teacher-learner discourse moves for the mathematics learning of students with learning disabilities (LD). During a constructivist teaching experiment for nurturing the multiplicative reasoning and problem solving of five third-grade…
Descriptors: Teacher Student Relationship, Mathematical Logic, Students with Disabilities, Learning Disabilities
Hickendorff, Marian – European Journal of Psychology of Education, 2018
Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…
Descriptors: Foreign Countries, Grade 6, Problem Solving, Mathematics Skills