This article evaluates the plausibility of synthesizing theory of knowledge objectification (Radford, 2003) with equity research on mathematics education. I suggest the cognitive phenomenon of mathematical inference as a promising locus for investigating the types of agency that equity-driven scholars often care for. In particular, I conceptualize…

We unveiled our plans to revolutionize the students' spatial conception development through the challenge and support of a cooperative learning of practice, the development of the profession as a whole and through sharing innovation and expertise. This encompasses cognitive consultancy, curriculum integration, solutions architecture, management…

As much as ever before, mathematics teachers are searching for ways to connect mathematics to real-life scenarios within STEM contexts. As students develop skill in proportional reasoning, they examine graphical representations of linear functions, learn to associate "slope" with "steepness" and rate of change, and develop…

Proportional reasoning is both complex and layered, making it challenging to define. Lamon (1999) identified characteristics of proportional thinkers, such as being able to understand covariance of quantities; distinguish between proportional and nonproportional relationships; use a variety of strategies flexibly, most of which are nonalgorithmic,…

Recent research efforts (Schmidt et al. in "The preparation gap: teacher education for middle school mathematics in six countries," MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical…

Social development, the progress of technology, and changing economic forces certainly affect the development of the current educational system. One of the main problems of today's school system is how to maintain focus, concentration, and interest among students with regards to the learning that takes place during classes. An important feature of…

In many domains, problem solving involves the application of general domain principles to specific problem representations. In 3 classroom studies with an intelligent tutoring system, we examined the impact of (learner-generated) interactions and (tutor-provided) visual cues designed to facilitate rule-diagram mapping (where students connect…

In the field of mathematics education, understanding teachers' content knowledge (Grossman, 1995; Hill, Sleep, Lewis, & Ball, 2007; Munby, Russell, & Martin, 2001) and studying the relationship between content knowledge and instructional decisions (Fennema & Franke, 1992; Raymond, 1997) are both crucial. Teachers need a robust…

This study investigated how gender shapes the relationships between classroom environment, achievement goals and maths performance. Seventh-grade students ("N"?=?498) from five urban secondary schools filled in achievement goal orientations and classroom environment scales at the beginning of the second semester. Maths performance was…

Increased access to algebra was a focal point of the National Mathematics Advisory Panel's 2008 report on improving mathematics learning in the United States. Past research found positive effects for early access to algebra, but the focus on average effects may mask important variation across student subgroups. The author addresses whether these…

Despite the availability of and pressures to incorporate educational technology into secondary curriculum, schools have not shown that technology is being adequately used by educators or that students in fact know how to use them. In particular, many teachers are not using technology such as graphing calculators as an instructional mathematics…

Many students in the United States are graduating from high school without the math skills they need to be considered college ready. For many of these graduates, who find themselves starting their higher education at a community college, remedial math can become an insurmountable barrier that ends their aspirations for a degree or certificate.…

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

This paper presents a framework for examining the Pedagogical Content Knowledge (PCK) required of mathematics teacher "educators" as they endeavour to build the PCK for teaching mathematics that is required of the pre-service teachers with whom they work. The framework builds on existing research into PCK, and provides a series of…