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Ibrahim Burak Ölmez; Andrew Izsák – Journal of Mathematics Teacher Education, 2024
In prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial…
Descriptors: Fractions, Mathematics Teachers, Mathematical Logic, Arithmetic
Liu, Qiushan; Braithwaite, David – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2023
Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…
Descriptors: Fractions, Arithmetic, Mathematical Concepts, Affordances
Joung, Eunmi; Kim, Young Rae – International Journal of Education in Mathematics, Science and Technology, 2022
The purposes of this study are to report current Preservice Teachers' (PTs) decimal abilities regarding the types of error patterns that they commit and to analyze characteristics of the errors in the problems posed for multiplication and division in decimals. We have determined common concept- and procedure-based errors made by the PTs. 37 PTs in…
Descriptors: Preservice Teachers, Mathematics Skills, Arithmetic, Fractions
Roan, Elizabeth; Czocher, Jennifer – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…
Descriptors: Mathematics Instruction, Task Analysis, Mathematical Models, STEM Education
Morano, Stephanie; Riccomini, Paul J. – Teacher Education and Special Education, 2020
To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The…
Descriptors: Preservice Teachers, Mathematics Instruction, Pedagogical Content Knowledge, Fractions
Bentley, Brianna; Bossé, Michael J. – International Electronic Journal of Mathematics Education, 2018
This study investigates college students' understanding of arithmetic fraction operations as defined by the Common Core State Standards in grades three through six Mathematics. This study is meant to extend upon an extensive body of research regarding elementary and middle grades students' understanding of fraction operations and see if recognized…
Descriptors: College Students, Mathematics Skills, Fractions, Arithmetic
Jarry-Shore, Michael; Kobiela, Marta – Elementary School Journal, 2020
In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…
Descriptors: Preservice Teachers, Elementary School Teachers, Learning Strategies, Problem Solving
Jarry-Shore, Michael; Kobiela, Marta – Elementary School Journal, 2020
In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…
Descriptors: Preservice Teachers, Elementary School Teachers, Learning Strategies, Problem Solving
Feldman, Ziv; Roscoe, Matt B. – Mathematics Teacher Educator, 2018
The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to…
Descriptors: Mathematics Instruction, Mathematics Teachers, Preservice Teachers, Elementary School Teachers
Kontorovich, Igor' – For the Learning of Mathematics, 2018
How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Arithmetic
Ganor-Stern, Dana – Journal of Learning Disabilities, 2017
The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…
Descriptors: Learning Disabilities, Arithmetic, Mathematics Skills, Computation
Aparicio Landa, Eddie; Sosa Moguel, Landy; Cabañas-Sánchez, Guadalupe – International Journal of Education in Mathematics, Science and Technology, 2021
This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…
Descriptors: Mathematical Concepts, Mathematics Instruction, Geometry, Algebra
Schüler-Meyer, Alexander – International Journal of Research in Undergraduate Mathematics Education, 2019
In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses…
Descriptors: Learning Processes, Arithmetic, College Mathematics, Secondary School Mathematics
Wittmann, Michael C.; Black, Katrina E. – Physical Review Special Topics - Physics Education Research, 2015
Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in "separation" include "division" or "multiplication" after properly "grouping" terms in an equation, "moving" terms (again, at times grouped) from…
Descriptors: Mathematics, Calculus, Problem Solving, Mechanics (Physics)
Ameis, Jerry A. – Mathematics Teaching in the Middle School, 2011
When learning the order of operations, students are instructed to adhere to a directive when determining the numerical value of an arithmetic expression. A more typical approach is the use of a popular mnemonic called PEDMAS (parentheses, exponents, division, multiplication, addition, subtraction). The literature is scant on conceptual approaches…
Descriptors: Mathematics Instruction, Arithmetic, Mnemonics, Multiplication
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