The role of probability in curricula for children has fluctuated greatly over the past several decades. Recently, some countries have removed probability from their preschool and primary curricula, and others have retained it. One reason for such lack of agreement is that theory about early probability learning is still relatively new and under…

Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…

The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

According to the author, the "Australian Curriculum: Mathematics (AC:M) requires primary school students to measure the attributes of angle, time, temperature, length, area, capacity and mass. This article outlines some misconceptions held by primary school students which appear to stem from them not understanding terminology concerning the…

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…

This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

While a wide range of approaches and tools have been used to study children's creativity in school contexts, less emphasis has been placed on revealing students' creativity at university level. The present paper is focused on defining a tool that provides information about mathematical creativity of prospective mathematics teachers in…

The Louisiana mathematics standards were created by over one hundred Louisiana educators with input by thousands of parents and teachers from across the state. Educators envisioned what mathematically proficient students should know and be able to do to compete in our society and focused their efforts on creating standards that would allow them to…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

The most recent Kindergarten Common Core Mathematics State Standards include an emphasis on teaching geometry skills, such as recognizing, describing, naming, and composing shapes. This article provides five effective ideas for teachers of young children as they introduce and teach shapes.