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Cuhadar, Ismail – Measurement: Interdisciplinary Research and Perspectives, 2022
In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT.…
Descriptors: Sample Size, Item Response Theory, Test Items, Mathematical Models
Brian John Winkel – International Journal of Mathematical Education in Science and Technology, 2024
We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…
Descriptors: Calculus, Learner Engagement, Video Technology, Mathematical Concepts
State of the Art on the Leonardo Sequence: An Evolutionary Study of the Epistemic-Mathematical Field
Milena Carolina dos Santos Mangueira; Francisco Regis Vieira Alves; Paula Maria Machado Cruz Catarino; Elen Viviani Pereira Spreafico – Pedagogical Research, 2024
This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…
Descriptors: Mathematics Instruction, Teaching Methods, Doctoral Students, Mathematics
Megan H. Wickstrom; Hyunyi Jung – Journal for Research in Mathematics Education, 2024
A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…
Descriptors: Teaching Methods, Mathematics Instruction, Mathematical Models, Preservice Teachers
Alison G. Lynch; Elise Lockwood; Amy B. Ellis – Research in Mathematics Education, 2024
In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…
Descriptors: College Faculty, Mathematical Concepts, Mathematics Education, Mathematics Instruction
Hyunyi Jung; Corey Brady – Mathematical Thinking and Learning: An International Journal, 2025
In this article, we investigated how a class engaged in whole-class discussions of modeling solutions, across two different types of modeling tasks: a Model Eliciting Activity (MEA) and a Three-Act Task. We analyzed whole-class discourse as small groups presented and responded to each other's solutions to a MEA and a Three-Act Task. We have also…
Descriptors: Mathematical Models, Discussion (Teaching Technique), Class Activities, Simulation
Karina Nuñez-Gutierrez; Camilo Andrés Rodríguez-Nieto; Lisseth Correa-Sandoval; Vicenç Font Moll – International Electronic Journal of Mathematics Education, 2025
The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…
Descriptors: High School Students, Thinking Skills, Mathematics Instruction, Task Analysis
Pickering, Jayne; Adelman, James S.; Inglis, Matthew – Journal of Numerical Cognition, 2023
Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…
Descriptors: Number Concepts, Multiplication, Symbols (Mathematics), Mathematics Skills
Wilkie, Karina J.; Roche, Anne – Journal of Mathematics Teacher Education, 2023
When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for…
Descriptors: Elementary School Teachers, Mathematics Teachers, Mathematics Instruction, Teaching Methods
Braun, Thorsten; Stierle, Rolf; Fischer, Matthias; Gross, Joachim – Chemical Engineering Education, 2023
Contributing to a competency model for engineering thermodynamics, we investigate the empirical competency structure of our exams in an attempt to answer the question: Do we test the competencies we want to convey to our students? We demonstrate that thermodynamic modeling and mathematical solution emerge as significant dimensions of thermodynamic…
Descriptors: Thermodynamics, Consciousness Raising, Engineering Education, Test Format
Linda Parish – Australian Primary Mathematics Classroom, 2023
Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…
Descriptors: Mathematical Models, Teaching Methods, Mathematics Instruction, Elementary School Students
Chenchen Ma; Jing Ouyang; Gongjun Xu – Grantee Submission, 2023
Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain…
Descriptors: Psychological Evaluation, Clinical Diagnosis, Item Analysis, Algorithms
Greefrath, Gilbert; Siller, Hans-Stefan; Klock, Heiner; Wess, Raphael – Educational Studies in Mathematics, 2022
The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help of a test developed for this purpose from a conceptual model, we examine whether this pedagogical content knowledge can be promoted in its different facets--especially knowledge about…
Descriptors: Preservice Teachers, Secondary School Teachers, Mathematics Teachers, Pedagogical Content Knowledge
Rost, Marvin; Knuuttila, Tarja – Education Sciences, 2022
Models are at the core of scientific reasoning and science education. They are especially crucial in scientific and educational contexts where the primary objects of study are unobservables. While empirical science education researchers apply philosophical arguments in their discussions of models and modeling, we in turn look at exemplary…
Descriptors: Mathematical Models, Mathematical Logic, Science Process Skills, Science Education
Turner, Erin E.; Roth McDuffie, Amy; Bennett, Amy Been; Aguirre, Julia; Chen, Mei-Kuang; Foote, Mary Q.; Smith, James E. – International Journal of Science and Mathematics Education, 2022
Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics,…
Descriptors: Mathematical Models, Elementary School Science, Mathematics Skills, Holistic Approach