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Kyeong Hah Roh; Yong Hah Lee – PRIMUS, 2024
This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying…
Descriptors: Undergraduate Students, Mathematics Instruction, Mathematical Logic, Logical Thinking
Kaitlyn Stephens Serbin; Megan Wawro – International Journal of Research in Undergraduate Mathematics Education, 2024
Reasoning with mathematics plays an important role in university students' learning throughout their courses in the scientific disciplines, such as physics. In addition to understanding mathematical concepts and procedures, physics students often must mathematize physical constructs in terms of their associated mathematical structures and…
Descriptors: Mathematical Logic, Logical Thinking, College Students, Quantum Mechanics
Michael D. Hicks – PRIMUS, 2024
Analogy has played an important role in developing modern mathematics. However, it is unclear to what extent students are granted opportunities to productively reason by analogy. This article proposes a set of lessons for introducing topics in ring theory that allow students to engage with the process of reasoning by analogy while exploring new…
Descriptors: Mathematics Instruction, Mathematical Logic, Logical Thinking, Algebra
Theresa Büchter; Andreas Eichler; Katharina Böcherer-Linder; Markus Vogel; Karin Binder; Stefan Krauss; Nicole Steib – Educational Studies in Mathematics, 2024
Previous studies on Bayesian situations, in which probabilistic information is used to update the probability of a hypothesis, have often focused on the calculation of a posterior probability. We argue that for an in-depth understanding of Bayesian situations, it is (apart from mere calculation) also necessary to be able to evaluate the effect of…
Descriptors: Bayesian Statistics, Logical Thinking, Elementary School Teachers, Secondary School Teachers
Paul Christian Dawkins; Kyeong Hah Roh – Journal for Research in Mathematics Education, 2024
This article offers the construct "unitizing predicates" to name mental actions important for students' reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and…
Descriptors: Thinking Skills, Logical Thinking, Mathematical Logic, Validity
Gabrielle Oslington; Joanne Mulligan; Penny Van Bergen – Mathematics Education Research Journal, 2024
In this exploratory descriptive study, changes in one cohort's responses to an authentic statistical investigation at the commencement of years 3 and 4 were analysed. Forty-four students made predictions by interpreting a data table of historical monthly temperatures, represented these data and explained their reasoning. An Awareness of…
Descriptors: Mathematics Instruction, Mathematical Logic, Tables (Data), Prediction
Fangli Xia; Mitchell J. Nathan; Kelsey E. Schenck; Michael I. Swart – Cognitive Science, 2025
Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…
Descriptors: Undergraduate Students, Geometry, Mathematical Concepts, Mathematics Instruction
Paul Mayer; Rich Baraniuk – ACM Transactions on Computing Education, 2025
It is argued that logic, and in particular mathematical logic, should play a key role in the undergraduate curriculum for students in the computing fields, which include electrical engineering (EE), computer engineering (CE), and computer science (CS). This is based on (1) the history of the field of computing and its close ties with logic, (2)…
Descriptors: Teaching Methods, Logical Thinking, Computer Science Education, Engineering Education
Per Haavold; Jan Roksvold; Bharath Sriraman – Investigations in Mathematics Learning, 2024
Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers'…
Descriptors: Preservice Teachers, Student Attitudes, Teacher Education Programs, Validity
Joseph Antonides; Anderson Norton; Rachel Arnold – For the Learning of Mathematics, 2024
This theoretical article explores the affordances and challenges of Euler diagrams as tools for supporting undergraduate introduction-to-proof students to make sense of, and reason about, logical implications. To theoretically frame students' meaning making with Euler diagrams, we introduce the notion of logico-spatial linked structuring (or…
Descriptors: Mathematical Concepts, Visual Aids, Relationship, Schematic Studies
Mehmet Demir; Yilmaz Zengin – Digital Experiences in Mathematics Education, 2024
The aim of this study is to explore how structural and process aspects of secondary school students' mathematical reasoning support each other in a collaborative learning environment through the integration of "GeoGebra" software and the ACODESA method. The study involved four eighth-grade secondary school students, who participated in…
Descriptors: Mathematics Skills, Thinking Skills, Computer Software, Mathematics Instruction
Cathy Marks Krpan; Gurpreet Sahmbi – International Journal of Education in Mathematics, Science and Technology, 2024
This study investigates teachers' perspectives on the use of a mathematical argumentation teaching strategy in elementary mathematics in which students disprove mathematical statements they already know to be false. Mathematical argumentation is a process through which students develop an argument about a mathematical concept and rationalize its…
Descriptors: Elementary School Teachers, Teacher Attitudes, Mathematics Instruction, Teaching Methods
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
Michelle Lo; Teresa K. Dunleavy – Mathematics Teacher: Learning and Teaching PK-12, 2025
The mathematics classroom is particularly vulnerable to these judgments of perfectionism, with endless evidence of students and teachers believing that mathematics is based on an ultimate truth or a single, objective, unique answer. School mathematics still favors students' participation in rote procedures, memorization, and using only a few…
Descriptors: High School Students, High School Teachers, Mathematics Instruction, Standards