This article shows how Yup'ik cosmology, epistemology, and everyday practice have implications for the teaching of school mathematics. Math in a Cultural Context (MCC) has a long-term collaborative relationship with Yup'ik elders and experienced Yup'ik teachers. Because of this long-term ethnographically-oriented relationship, the authors--both…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the…

In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel's from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by…

This research investigates similarities and differences in young children's early numeracy skills related to age, nationality and gender. The participants were five- to seven-year-old children from Finland and Iran. Early numeracy was investigated by using tasks measuring number-related relational skills (e.g. comparison, one-to-one…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…

Two people take turns selecting from an even number of items. Their relative preferences over the items can be described as a permutation, then tools from algebraic combinatorics can be used to answer various questions. We describe each person's optimal selection strategies including how each could make use of knowing the other's preferences. We…

In recent times considerable attention has been devoted to the performance of schools and in particular, of students in literacy and numeracy. As part of a national agenda addressing what is portrayed as a crisis in numeracy, and hence mathematics education, governments have introduced a wide range of reform initiatives to improve performance.…

In this paper, we focus on Finnish pre-service elementary teachers' (N = 269) and upper secondary students' (N = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: "We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6…

Numeric magnitudes often bias adults' spatial performance. Partly because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that the orientation of spatial-numeric associations is a late development, tied to reading practice or schooling. Challenging this assumption, we found that preschoolers…

Because number is an abstract quality of a set, the way in which a number is externally represented does not change its quantitative meaning. In this study, we examined the development of the brain regions that support format-independent representation of numerical magnitude. We asked children and adults to perform both symbolic (Hindu-Arabic…

In this article, we use a particular example to illustrate a thematic approach to the teaching and learning of mathematics. Our theme, suitable for undergraduates and able sixth-form students, is the enumeration of mathematical objects associated with the prime factorizations of integers. It is shown in detail how this gives rise to some beautiful…

Speakers are known to make subject-verb agreement errors both when a number-mismatching noun intervenes between the head of the subject phrase and the verb (e.g., "*The key to the cabinets are on the table") and in configurations in which there is a number-mismatching noun that does not intervene (e.g., "*The cabinets that the key open are on the…

Developmental dyscalculia is a learning disability that affects the acquisition of knowledge about numbers and arithmetic. It is widely assumed that numeracy is rooted on the "number sense", a core ability to grasp numerical quantities that humans share with other animals and deploy spontaneously at birth. To probe the links between number sense…