In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…

Multimedia engineers develop digital content in a wide range of fields that require them to acquire skills in the development of web solutions for those fields. In this study, we evaluated the level of didactic knowledge of mathematics that Multimedia Engineering degree students possess. The aim was to determine whether they are prepared to…

Research on learning through serious games has been gaining importance in recent years. We develop the serious game "Tempoly," concerning the learning of the four arithmetic operations on polynomials. A quasi-experimental study was carried out with 95 students of 8th grade, to evaluate the reactions of the students to the game, the…

It has been shown in multiple studies that expert-created on-demand assistance, such as hint messages, improves student learning in online learning environments. However, there are also evident that certain types of assistance may be detrimental to student learning. In addition, creating and maintaining on-demand assistance are hard and…

Mathematics education scholars have generally classified students' conception of the equal sign as either operational or relational. Adding to these conceptions, Jones (2008) introduced the idea of substitutional conception. Building off these scholars, I introduce a form of understanding the equal sign that includes a transformative equivalence…

In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…

The addressed question from the interface between theory and teaching practice of constructivism is discussed at the background of whereabouts of the Common Core (CCSS-M) constructivist-based mathematics curriculum. It concerns the formulation of constructivist methodology of teaching, whose existence is called in doubts by US constructivist…

There is a broad consensus that beginning teachers of mathematics need a strong foundation in mathematical knowledge for teaching (MKT), defined as the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching one must engage in. One recurrent challenge in teacher education is how to provide support…

Using state-representative surveys, we investigated how familiar Texas, Ohio, Kentucky, and Massachusetts principals are with their state's K-12 standards, as well as the strength of their policy environments, using a policy attribute theory. We found relatively high levels of buy-in toward the idea of standards but only a general familiarity with…

Mathematics courses should prepare students to use mathematics in a range of contexts, including science. However, students often struggle in applying mathematics in physics courses, even when they understand the mathematical content (Rebello et al., 2007). Often the root of this struggle is attributed to the "student" or the…

A key topic throughout school geometry is measurement--namely, distance, area, and volume. This article focuses on one key idea for finding and justifying the area of two-dimensional (2D) shapes: area-preserving transformations. Although especially pertinent to geometry teachers, this article highlights a vertical connection of ideas progressing…

Children experience joy in well-designed mathematics classrooms. This article describes five research-based practices for bringing joy into PreK-Grade 2 math lessons.

This article describes an example of differentiating instruction (DI) involving middle school students from a five-year project funded by the National Science Foundation. In one phase of the project, a classroom teacher and the research team differentiated instruction for a class of 18 seventh-grade students during a 26-day unit on proportional…

This article discusses funky protractor tasks, which are designed to provide opportunities for students to reason about protractors and angle measure. These tasks afforded opportunities for students to think critically about angular measurement tools, which supported the teachers with valuable insights into students' developing conceptions of…

Holistic assessment is an evaluative approach in which assessors work backwards from an overall appraisal of work to determine the criteria relevant to individual student responses. One of the strongest proponents of this approach in higher education is Royce Sadler, whose theoretical contributions over recent decades provide a strong conceptual…