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Cheng, Chen; Kibbe, Melissa M. – Cognitive Science, 2023
Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like…
Descriptors: Young Children, Mathematics Skills, Arithmetic, Problem Solving
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
Wong, Harris; Odic, Darko – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2021
Research over the past 20 years has suggested that our intuitive sense of number--the Approximate Number System (ANS)--is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the…
Descriptors: Number Systems, Symbols (Mathematics), Equations (Mathematics), Problem Solving
Abd-Elhameed, W. M.; Zeyada, N. A. – International Journal of Mathematical Education in Science and Technology, 2017
This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…
Descriptors: Generalization, Numbers, Number Concepts, Number Systems
Aksoy, Nuri Can; Yazlik, Derya Ozlem – Journal of Education and Training Studies, 2017
In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method,…
Descriptors: Fractions, Error Patterns, Grade 6, Grade 5
McDowell, Eric L. – Mathematics Teacher, 2016
By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…
Descriptors: Fractions, Number Systems, Number Concepts, Numbers
Hurst, Chris; Hurrell, Derek – Mathematics Education Research Group of Australasia, 2016
Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…
Descriptors: Multiplication, Number Systems, Teaching Methods, Number Concepts
Carney, Michele B.; Smith, Everett; Hughes, Gwyneth R.; Brendefur, Jonathan L.; Crawford, Angela – Mathematics Education Research Journal, 2016
Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…
Descriptors: Cognitive Style, Learning Strategies, Problem Solving, Mathematical Aptitude
Steinke, Dorothea A. – Journal of Adult Education, 2015
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
Descriptors: Community Colleges, Number Concepts, Number Systems, Numbers
Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2015
The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A threeweek long solution process by a pair of ninth-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…
Descriptors: Attention, Grade 9, Attention Control, Educational Theories
Morris, Bradley J.; Masnick, Amy M. – Cognitive Science, 2015
Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…
Descriptors: Comparative Analysis, Number Concepts, Thinking Skills, Critical Thinking
Lin, Yung-Chi; Yang, Der-Ching; Li, Mao-Neng – EURASIA Journal of Mathematics, Science & Technology Education, 2016
A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…
Descriptors: Misconceptions, Number Concepts, Numbers, Number Systems
Tira, Michael D.; Tagliabue, Mariaelena; Vidotto, Giulio – Psicologica: International Journal of Methodology and Experimental Psychology, 2014
In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…
Descriptors: Number Concepts, Number Systems, Numbers, Science Experiments
Jorgensen, Theresa A.; Shipman, Barbara A. – PRIMUS, 2012
This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…
Descriptors: Majors (Students), Liberal Arts, Class Activities, Learning Activities
Hirsch, Jenna – MathAMATYC Educator, 2012
A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…
Descriptors: Mathematics Education, Number Concepts, Number Systems, Numbers