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Norton, Anderson; Boyce, Steven – Journal of Mathematical Behavior, 2013

The purpose of this paper is to illustrate cognitive challenges introduced by Common Core State Standards for Mathematics (2010) with regard to conceptualizing fractions. We focus on a strand of standards that appear across grades three through five, which is best represented in grade four, by standard 4.NF.4a: "[Students should] understand a…

Descriptors: State Standards, Mathematics Skills, Mathematics Achievement, Grade 6

Modestou, Modestina; Gagatsis, Athanasios – Journal of Mathematical Behavior, 2013

The aim of this study was to propose a didactical situation for the confrontation of the epistemological obstacle of linearity (routine proportionality) and consequently for the enhancement of meta-analogical awareness. Errors caused by students' spontaneous tendency to apply linear functions in various situations are strong, persistent and do not…

Descriptors: Student Attitudes, Mathematical Concepts, Epistemology, Error Patterns

Schulman, Steven M. – Journal of Mathematical Behavior, 2013

In this article, the author allows Robert B. Davis to state for himself his own Principles concerning how children learn, and how teachers can best teach them. These principles are put forward in Davis' own words along with detailed documentation. The author goes on compare Davis' words with his practices. A single Davis video (Towers of Hanoi) is…

Descriptors: Video Technology, Films, Mathematics Instruction, Mathematical Concepts

Palha, Sonia; Dekker, Rijkje; Gravemeijer, Koeno; van Hout-Wolters, Bernadette – Journal of Mathematical Behavior, 2013

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

Descriptors: Teaching Methods, Learning Processes, Education, Mathematics Instruction

Ngu, Bing Hiong; Yeung, Alexander Seeshing – Journal of Mathematical Behavior, 2013

Text editing directs students' attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three…

Descriptors: Chemistry, Algebra, Word Processing, Equations (Mathematics)

Stephens, Ana C.; Knuth, Eric J.; Blanton, Maria L.; Isler, Isil; Gardiner, Angela Murphy; Marum, Tim – Journal of Mathematical Behavior, 2013

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students' responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of…

Descriptors: Algebra, Equations (Mathematics), Elementary School Students, Grade 5

Kinda, Shigehiro – Journal of Mathematical Behavior, 2013

Students are presented with problems involving three scenario types of addition and subtraction in elementary mathematics: one dynamic ("Change") and two static ("Combine, Compare"). Previous studies have indicated that the dynamic type is easier for school children, whereas the static types are more difficult and comprehended only gradually…

Descriptors: Subtraction, Mathematics Education, Addition, Foreign Countries

Sack, Jacqueline J. – Journal of Mathematical Behavior, 2013

This article explicates the development of top-view numeric coding of 3-D cube structures within a design research project focused on 3-D visualization skills for elementary grades children. It describes children's conceptual development of 3-D cube structures using concrete models, conventional 2-D pictures and abstract top-view numeric…

Descriptors: Educational Technology, Computer Uses in Education, Research Projects, Computer Interfaces

Wilson, P. Holt; Mojica, Gemma F.; Confrey, Jere – Journal of Mathematical Behavior, 2013

Recent work by researchers has focused on synthesizing and elaborating knowledge of students' thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning…

Descriptors: Mathematics Instruction, Elementary School Teachers, Elementary School Mathematics, Mathematical Logic

Jones, Steven R. – Journal of Mathematical Behavior, 2013

Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

Descriptors: Physics, Calculus, Mathematics Instruction, Mathematical Concepts

Dubinsky, Ed; Wilson, Robin T. – Journal of Mathematical Behavior, 2013

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students' learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented…

Descriptors: High School Students, Disproportionate Representation, Mathematics Instruction, Experimental Teaching

Ding, Meixia; Li, Xiaobao; Capraro, Mary M. – Journal of Mathematical Behavior, 2013

This study examines preservice elementary teachers' (PTs) knowledge for teaching the associative property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to…

Descriptors: Preservice Teachers, Elementary School Teachers, Multiplication, Elementary School Mathematics

Mamona-Downs, Joanna K.; Megalou, Foteini J. – Journal of Mathematical Behavior, 2013

The aim of this paper is to examine students' understanding of the limiting behavior of a function from [set of real numbers][superscript 2] to [set of real numbers] at a point "P." This understanding depends on which definition is used for a limit. Several definitions are considered; two of these concern the notion of a neighborhood of "P", while…

Descriptors: Mathematics, Numbers, Comprehension, College Students

Ko, Yi-Yin; Knuth, Eric J. – Journal of Mathematical Behavior, 2013

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory--the domains…

Descriptors: Mathematical Logic, Validity, Majors (Students), Undergraduate Students

Devichi, Claude; Munier, Valerie – Journal of Mathematical Behavior, 2013

This paper reports classroom research dealing with the difficulties encountered by schoolchildren in the acquisition of angle concept. Two obstacles were pointed out in previous studies: the side-length obstacle and the salience of the prototypical right angle. The first aim of the present study is to determine the extent to which a teaching…

Descriptors: Geometric Concepts, Elementary School Mathematics, Misconceptions, Elementary School Students