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.…

One of the major benefits of the face-to-face teaching environment is that social interaction opportunities are a natural part of the course: Learners meet in the same room for the same allotted period of time each week. This social opportunity is not organic to online courses; therefore, to have this social interaction as a part of online classes…

While there is widespread agreement that "all" learners of the 21st century need to be numerate and literate, reforming pedagogical practices to achieve such an outcome is challenging for many teachers. This is a report of one aspect of a project which aims to integrate a culturally responsive pedagogical mathematics practice within…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Math Teachers' Circles (MTCs) bring math teachers and university mathematicians together to engage in collaborative mathematical activity. Currently there are over 110 MTCs across 40 states. A key claim is that MTCs are "communities of practice." However, to date there has been no research to substantiate this claim. In this paper, we…

Lesson study is a professional development activity that increases teachers' attention to student thinking. However, coordinating teachers' live observations of a lesson can be challenging. Using the framework of "distributed cognition," we investigate whether technology supports teachers' examination of student thinking and aids the…

This column presents ideas and techniques to enhance your science teaching. This month's issue shares information about a unit promoting scientific literacy and the engineering design process. The integration of engineering with scientific practices in K-12 education can promote creativity, hands-on learning, and an improvement in students'…

This study reports upon design-based research that enacted mobile mathematics learning for preservice teachers across classroom, community, and online settings. The integration of mobile learning within mathematics teacher education is understudied, and it is necessary to better understand mobile technology affordances when locating disciplinary…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

This article describes a teacher's Maths lesson that focuses on numeracy in health and physical education learning area. In the lesson, the students were learning about Directed Numbers, something they often struggle with and a topic where the teacher finds it hard to explain using real life situations when using addition and subtraction. The…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

Recognizing meaning in students' mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student's non-traditional strategy for dividing fractions. Six categories of…

Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

The 2007 Trends in International Mathematics and Science Survey highlighted how attitudes to mathematics had declined sharply for students in many of the high attaining countries in the survey, England being no exception. There is a notable drop in positive attitudes to mathematics between 9 and 14, as well as a remarkable decline for 14 year olds…