Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g. Bialystok, [Bialystok, E., 2001]; Hilchey & Klein, [Hilchey, M.D.,…

Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is…

This study investigates whether number dissimilarities on subject and object DPs facilitate the comprehension of subject- and object-extracted centre-embedded relative clauses in children with Grammatical Specific Language Impairment (G-SLI). We compared the performance of a group of English-speaking children with G-SLI (mean age: 12;11) with that…

We report a multidimensional test that examines middle grades teachers' understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers' and students' reasoning in this content…

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that…

This study was situated in a semester-long classroom teaching experiment examining prospective teachers' understanding of number concepts and operations. The purpose of this paper is to describe the learning goals, tasks, and tools used to cultivate prospective teachers' understanding of addition and subtraction with whole numbers. Research…

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

Some people recognize a palindrome when they see one, however fewer realize that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music. The traditional mathematical curriculum has often left palindromes out of the common vernacular. Where…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…

This article looks at a simple geometry problem that also involves some reasoning about number combinations, and show how it was used in a Year 7 classroom. The problem is accessible to students with a wide range of abilities, and provides scope for stimulating extensive discussion and reasoning in the classroom, as well as an opportunity for…

In this paper two studies are reported in which two contrasting claims concerning the intuitiveness of the law of large numbers are investigated. While Sedlmeier and Gigerenzer ("J Behav Decis Mak" 10:33-51, 1997) claim that people have an intuition that conforms to the law of large numbers, but that they can only employ this intuition…

To examine the relative performance in number sense among low-SES students, new immigrant students, and typical learners in grades 4 through 6, data were collected through a number sense web-based, two-tier test. A total of 628 fourth graders, 535 fifth graders, and 524 sixth graders in Taiwan participated in this study. Results showed that there…

Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students in a ten-session teaching experiment. The students successfully reinvented four basic counting…

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the…