The study described in this paper investigated a unique collaboration among a special education and two general educators that sought to prepare students for success in the general education mathematics curriculum and that consisted of coordinated, reform-based instructional design across classroom and pull-out services provided by the special…

Students who are identified as having a disability, according to the Individuals with Disabilities Education Act (IDEA), are guaranteed a Free Appropriate Public Education (FAPE) that provides them access to the general curriculum (IDEA Regulations, 34 C.F.R. § 300.39 [a][3]liil). NCTM and CEC believe that for students with disabilities,…

This study examined students' experiences of peer feedback practices as related to awareness raising of learning goals, self-monitoring, self-efficacy, anxiety, and enjoyment in teaching English as a foreign language (EFL) and mathematics. Data consisted of student surveys from two data sets related to teaching in lower secondary school (n =…

Research for Action (RFA) in partnership with the University of Texas at Austin is engaged in a five-year mixed-methods study of the reforms associated with California AB 705. Over the course of the study, our team will assess the implementation, impact, and cost effectiveness of reforms associated with the law. This report first offers a…

In this article we critique, disrupt and resist the taken for granted use of the term "fun" in learning; specifically as it is used to justify mathematics education apps that purport to portray maths learning as a fun experience. We accomplish this critique through the creation of a digital artwork called "Arithmomania." This…

In this age of easy access to the internet and to spreadsheets, easy-to-apply numerical methods exist that are vastly superior to Simpson's rule and the (corrected) trapezoidal rule. Gaussian quadrature (GQ) is such a method. What follows tells how enthusiastic Year 9 students with a physics problem provoked a science teacher into re-discovering a…

Let R be an integral domain with quotient field F, let S be a non-empty subset of R and let n = 2 be an integer. If there exists a rational function ?: S [right arrow] F such that ?(a)[superscript n] = a for all a ? S, then S is finite. As a consequence, if F is an ordered field (for instance,[real numbers]) and S is an open interval in F, no such…

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

What is questioned and what is taken for granted when carrying out research into the teaching of a given mathematical topic such as Group Theory? This paper presents two different questioning procedures using the methodological tools provided by the Anthropological Theory of the Didactic (ATD). The first one, leading to an undergraduate…

Observation-based frameworks of instructional quality differ largely in the approach and the purposes of their development, their theoretical underpinnings, the instructional aspects covered, their operationalization and measurement, as well as the existing evidence on reliability and validity. The current paper summarizes and reflects on these…

The continual supply of new items is crucial to maintaining quality for many tests. Automatic item generation (AIG) has the potential to rapidly increase the number of items that are available. However, the efficiency of AIG will be mitigated if the generated items must be submitted to traditional, time-consuming review processes. In two studies,…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

The purpose of this article is to explore the use of didactical phenomenology as an instructional design heuristic. In doing so, I will articulate ways in which didactical phenomenology can be used in conjunction with the guided reinvention and emergent models heuristics to support instructional design. This discussion will be supported by…

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in…