This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

In this article, the history of the golden ratio is discussed to demonstrate how exploring this ratio would be of value in a secondary mathematics classroom. Following this, a mathematical activity related to the golden ratio that is suitable for students from Year 7 to Year 12 is outlined.

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics…

Off You Go is a PK-12 mathematical routine that leverages children's home resources and assets to help students take a concept with which they have initial or informal understanding and explore and test its boundaries to support defining or estimating with precision. The authors provide a guide for how to adapt this routine to engage students at…

We present a model for describing the growth of students' understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important…

The study aims to evaluate the computerized, and non-computerized activities in the new Palestinian mathematics textbook for 8th grade according to the point of view of teachers who taught with the book during the last semester and who have long years of experience in teaching mathematics. The researcher developed a new framework from a literature…

Today it is critical to excite young people about mathematics in our high-tech STEM world we live in. Math teachers today need to embolden students to be confident in their ability to solve problems, to think and use their imaginations, to understand mathematical concepts, to be creative, and to see math as a human endeavor. The author feels that…

The way in which mathematics is communicated and represented in schools (including the written language, symbols and diagrams of mathematics textbooks and the verbal/spoken classroom interaction itself) constructs particular views of the nature of mathematics and expectations about students' participation in mathematical activity. In a previous…

Technology integration in K-12 mathematics has received increased attention in the last decade as new mathematical technologies have been developed and implemented more often. There is a need for further research on these technologies and for effective implementation practices of technology in mathematics education in general. in practice,…

This study explores the relationships among students' perceived learning opportunities in school mathematics, their perceptions of self in mathematics, and their desire to learn more mathematics in the future. Data included student survey responses from eighth and tenth grade students from a state in the Southeast region of the United States.…

Rational number interpretations can include part-whole, measure, ratio, quotient, and operator. These are all subconstructs of partitioning (Barnett-Clarke et al. 2010; Behr et al. 1980; Clarke, Roche, and Mitchell 2008; Flores, Samson, and Yanik 2006). Each of these subconstructs uses different cognitive skills (Driscoll 1984), so it is important…

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers…

To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical…