Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby…

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…

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

This report summarises the research activities and findings from the TLRI-funded project entitled "Visualising Chance: Learning Probability Through Modelling." This exploratory study was a 2-year collaboration among two researchers, two conceptual software developers/interactive graphics experts, three university lecturers/practitioners,…

Promoting and sustaining effective discussion--that which contributes to learning--is a skill that eludes many instructors (Darling-Hammond, 2008; Ge, Yamashiro, & Lee, 2000). This study explored the role and strategies of an expert instructor in an online advanced instructional design (ID) course that utilized a case-based learning (CBL)…

This study explores how structured reflective practice by teachers in a Reform congregational school contributes to relational growth and the development of an inquiry stance in teaching. Analysis of teachers' responses to weekly prompts about their classroom experiences reveals three prominent themes: classroom management as inquiry, the tension…

The ability to self-regulate learning (SRL) is a skill theorized to transfer across learning environments. Students with this ability can consider a learning task, identify a goal, develop a plan to achieve it, execute that plan, and monitor and adapt learning until the goal is met. This paper examines the educational implications of developing…

Project-based learning (PBL) in the science classroom provides an opportunity for students to investigate socioscientific issues that are current, authentic, and relevant. In a typical PBL unit, the teacher designs a narrative plan and acts as a facilitator who helps gather and organize student ideas. The framework of the Next Generation Science…

Summary writing is an important skill that students use throughout their academic careers, writing supports reading and vocabulary skills as well as the acquisition of content knowledge. This exploratory and development-oriented investigation appraises the recently released online writing system, "Graphical Interface of Knowledge…

A teacher educator and college librarian collaboratively designed and taught teacher education workshops about finding and evaluating what works in teaching. This study investigated interactions of self-efficacy for information literacy, self-efficacy for solving problems with evidence-based practices, skills of searching for and citing sources,…

Purpose: The construction of learning scenarios is a way to plan for teaching activities, promoting the development of skills related to problem solving, collaboration, critical thinking and creativity. Using learning scenarios as a lesson planning strategy becomes a powerful tool in initial teacher education. On the one hand, it mobilizes…

Developing optimum solutions to engineering problems typically relies on structured and complex thought processes that require evaluation, interpretation and opinion. Well-developed critical thinking (CT) skills are essential for dealing with the multi-dimensional nature of these problems. CT in an engineering context is well reported in teaching…

What if you could challenge your 11th graders to figure out the best response to a partial meltdown at a nuclear reactor in fictional Gammatown, USA? With this volume in the "STEM Road Map Curriculum Series," you can! "Radioactivity" outlines a journey that will steer your students toward authentic problem solving while…

This report follows up on the book "Leapfrogging Inequality: Remaking Education to Help Young People Thrive," published in 2018 by the Center for Universal Education (CUE) at the Brookings Institution. The book argued the importance of education leapfrogging--creating transformative shifts rather than incremental evolution by harnessing…