Kentucky has been a leader in the movement to more rigorous college and career ready standards to support their students' success in the 21st century. Kentucky was the first state to adopt new college and career ready standards (CCRS)--termed the Kentucky Core Academic Standards. Many of Kentucky's districts have moved proactively and…

This five-year evaluation examined the effectiveness of a promising middle-school mathematics intervention funded through an Investing in Innovation (i3) development grant. Evaluation objectives were to: (1) study the impact of an intervention aimed at increasing the academic achievement of students in Algebra I--a gate-keeping course--as measured…

This study characterizes teaching practices that involve students' funds of knowledge ([FoK], Gonzalez, 1995; Moll, 1992; Moll, Amanti, Neff, & Gonzalez, 1992). FoK may be defined as bodies of knowledge, skills, language, and experiences found in students' homes and communities for potential use in formal learning. I investigated how high…

This book's 28 chapters are adapted and updated from articles published in NCTM's "Journal for Research in Mathematics Education" between 2000 and 2010. The authors have rewritten and revised their work to make it clear, understandable, and--most of all--useful for mathematics teachers today. To help teachers even more, these articles…

The formation of the Common Core State Standards can be regarded as the predecessor of a national curriculum. This research addresses how the proposed national math curriculum compares to the math curricula of a sample of peer-nations (Singapore, Netherlands, Germany, and Japan) with high student achievement rates in math, while relating the math…

In this work we investigated the problem solving behaviors of 3 high school students as each solved four common non-routine problems with the goal to trace performance constancy across different subject areas and problem types. Additionally, we aimed to identify possible factors that influenced children's choices of heuristics in different problem…

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers' mathematical and pedagogical knowledge. The analysis of teachers' reflections on their learning explored teachers' understanding of mathematical connections and…

Proportional reasoning has been recognised as a crucial focus of mathematics in the middle years and also as a frequent source of difficulty for students (Lamon, 2007). Proportional reasoning concerns the equivalence of pairs of quantities that are related multiplicatively; that is, equivalent ratios including those expressed as fractions and…

I argue for the inclusion of topics in high school mathematics curricula that are traditionally reserved for high achieving students preparing for mathematical contests. These include the arithmetic mean--geometric mean inequality which has many practical applications in mathematical modelling. The problem of extremalising functions of more than…

The study reported in this article sought to explore and observe how grade 9 learners solve real-wor(l)d problems (a) without real context and (b) without real meaning. Learners' abilities to make sense of the decontextualised word problems set in the real world were investigated with regard to learners' use of common sense in relation to problem…

This paper is based on the concept that lively and interactive math classes are possible by incorporating rich tasks to meet the needs of students operating at different levels in the classrooms. A study was carried out to find out the impact on learning and motivation of using rich tasks at secondary level in the maths class by incorporating…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

Although the use of dynamic software in high school mathematics in the United States has emerged as a research topic, little research has been conducted on how teachers integrate new software in relation to at-home technology networks. Interviews with eight mathematics teachers from four North Carolina counties participating in 1:1 laptop…

The purpose of this study was to explore middle grade mathematics students' uses of scaffolding and its effectiveness in helping students solve non-routine problems. Students were given two different types of scaffolds to support their learning of sixth grade geometry concepts. First, students solved a math task by using a four square graphic…

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…