Given math's importance, states are adopting a range of K12 policies to improve math outcomes. As these and other policies unfold, policymakers need to monitor intended outcomes and ultimately gauge impact. They need answers to basic questions: Are more students taking and passing algebra and advanced math? Are performance gaps changing between…

This article reports on an analysis of the process in which "knowledge to be taught" was transposed into "knowledge actually taught," concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical…

Discovery learning has long been a part of mathematics teaching in the elementary and middle grades. Since the 1960s and 1970s, based on the work of Jean Piaget, Jerome Bruner, and others, helping students 'discover' or 'construct' their own understandings of mathematical concepts through well-designed activities facilitated by a competent teacher…

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…

This study is concerned with the reasoning that undergraduates apply when deciding whether a prompt is an example or non-example of the subspace concept. A qualitative analysis of written responses of 438 students revealed five unconventional tacit models that govern their reasoning. The models account for whether a prompt is a subset of a vector…

We present two empirical studies with 241 and 211 pre-service teachers that evaluate the explanatory power of word order matching and static comparison as models for the reversal error. We used tasks consisting of generating an algebraic equation representing a comparison given in a verbal statement. We introduce the types of magnitude involved in…

Even though algebraic ideas are addressed across a number of grades, algebra continues to serve as a gatekeeper to upper mathematics and degree attainment because of the high percentage of students that fail algebra classes and become halted in their educational progress. One reason for this is students not having the opportunity to build on their…

In this report, we present an analysis of two prospective secondary mathematics teachers' generalizing actions in quantitative contexts. Specifically, we draw from a teaching experiment to report how Lydia and Emma engaged in different generalizing processes for the same task. Based on these differences, we found Lydia's generalizing actions…

In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, "Limit Representation Transformation Test" with a reliability of…

This study examined secondary mathematics teachers' content knowledge for teaching the concept of function. Content knowledge, for the purpose of this study, includes the common content knowledge and specialized content knowledge domains of Ball and her colleagues' Mathematical Knowledge for Teaching (MKT) framework. Data were collected through a…

This study was aimed to validate a digital tool for diagnosing mathematical proficiency in the Number and Algebra strand of 1,504 Thai seventh-grade students. Researchers employed a multidimensional approach, an extension of the Rasch model to measure its quality. A design-based research method was adopted to create the diagnostic tool which…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

This study describes how nine university professors managed their teaching when a shift from lecturing to inquiry-based learning was mandated in a large enrollment course, linear algebra for math majors. We describe the tensions that emerged and how they were resolved, in part via the production of worksheets that were used in teaching. We…

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

The researchers conducted a microanalysis of two purposefully sampled sessions of a tutor working with a student with a learning disability (LD) engaging with multi-step equations with and without fractions. During the tutoring sessions, the student experienced quick, independent success on equations without fractions, but struggled considerably…