Proof is a foundational mathematical activity that has been underrepresented in school mathematics. The recently adopted Common Core State Standards in Mathematics includes eight process standards, several of which promote the inclusion of reasoning and proof across all grades, courses, and students. If students are to reach the expectations…

This research studied the role of mathematics as a roadblock to college completion for community college-bound students in California. Using longitudinal quantitative analysis, I observed the educational pipeline between high school and community college and analyzed how different high school mathematics histories predicted readiness, or…

As part of a longitudinal case study on engagement in middle years mathematics, 20 students attending their first year of secondary school in Western Sydney were asked to provide views on their experiences of the transition to secondary school in relation to mathematics teaching and learning. Differences in teacher-student relationships caused the…

Three mathematics textbooks of different grade levels, compared with Chinese math textbooks of the same grades, were selected that were used in some of the middle schools in Clark County Schools District (CCSD). Systematical review of the three textbooks were made grade by grade in order to figure out "Are Our Math Textbooks a Mile Wide and…

The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers' perceptions of students' ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From…

There is a dearth of research on the mechanisms for preservice teachers' development of the pedagogical knowledge necessary for effective use of such technologies. We explored the emergent Technological Pedagogical and Content Knowledge (TPACK) (Niess 2005, 2006, 2007) of a group of secondary mathematics preservice teachers in a methods course as…

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications,…

The purpose of this study is to examine the ICT usage and academic achievement of Turkish students in PISA 2006 data. The sample of the study included 4942 students from 160 schools. Frequencies, independent samples t-tests, ANOVAs, pearson correlation coefficients, exploratory factor analysis, and regression analysis were used. A high percentage…

These proceedings contain the papers of the 18th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2021), held virtually, due to an exceptional situation caused by the COVID-19 pandemic, from October 13-15, 2021, and organized by the International Association for Development of the Information Society…

The problem of creating lamp shades to specific design parameters allows rich and interesting explorations in the mathematics of circles and triangles. This interactive project helps students build their spatial reasoning and is especially appropriate during a unit on either the Pythagorean theorem or similar triangles. (Contains 7 figures and 1…

We introduce the sociomathematical norm of "speaking with meaning" and describe its emergence in a professional learning community (PLC) of secondary mathematics and science teachers. We use "speaking with meaning" to reference specific attributes of individual communication that have been revealed to improve the quality of discourse among…

Upper secondary students' task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a…

To create an environment in which all students have opportunities to notice, describe, and wonder about variability, this article takes a context familiar to many teacher--sampling colored chips from a jar--and shows how this context was used to explicitly focus on variation in the classroom. The sampling activity includes physical as well as…

This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.)