A brick wall provides a fitting description of what happens when teachers try to teach a concept for which students are unprepared. When students are unsuccessful academically, their foundational knowledge may be missing, incomplete, or incorrect. As a result, students "hit a brick wall," and their academic progress stops because they do…

As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to…

Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the "design" of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

This paper presents findings from classroom observations of one teacher (Beth). It focusses on the development of conceptual understanding of fractions with her students, articulated in Kieren's sub-constructs (Kieren, 1980,1988), and Hansen's progressions (Hansen, 2005). The study covers three lessons within a six week unit. Findings from this…

Although an understanding of time is crucial in our society, curriculum documents have an undue emphasis on reading time and little emphasis on core underlying ideas. Given this context, a one-to-one assessment interview, based on a new framework, was developed and administered to investigate students' understanding of core ideas undergirding the…

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK-12 Design and Development project focused on building mathematical…

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and…

There have been many recent policy and program changes in K-12 education across the United States, particularly in area of mathematics. Changes, such as the Common Core State Standards for Mathematics and standards-aligned year-end summative assessments, require an increase in student-centered, cognitively demanding activities in the classroom.…

Previous studies have produced several typologies of teacher questions in mathematics. Probing questions that ask students to explain are often included in the types of questions. However, only rare studies have created subtypes for probing questions or investigated how questioning differs depending on whether technology is used or not. The aims…

The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used…

While the flipped classroom has found much discussion recently, peer tutoring using screencast resources produced by students has not yet. In this paper, we describe student responses to the approach taken at a secondary Catholic school in Melbourne, Australia, where the mathematics teachers used the roll out of tablet PCs to all teachers and…

The introduction of engineering practices within the "Next Generation Science Standards" provides technology educators with opportunities to help STEM educators infuse engineering design within a core curriculum. The introduction of teaching engineering design in early elementary grades also provides opportunities to conduct research…

To help middle school students make better sense of decimals and fraction, the author and an eighth-grade math teacher worked on a 90-minute lesson that focused on representing repeating decimals as fractions. They embedded experimentations and explorations using technology and calculators to help promote students' intuitive and conceptual…