In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

The two most popular decision-making processes are tossing a coin and playing rock, paper, scissors. In the activity described in this article, students find the theoretical probabilities of winning a coin toss and a round of the rock, paper, scissors game. They next devise strategies to win and test them out. Students then compare the theoretical…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

This paper describes a relatively new active learning approach--Design Thinking--and its adoption in two comparative politics courses. I draw on my experience using Design Thinking in political science courses to offer instructors another pedagogical tool in the active learning toolkit. I outline the rationale for adopting a Design Thinking…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

Leading by doing takes an unwavering and visible commitment to an intentional, continuous improvement process. Teams at every system level distribute leadership to support effective practice so outcomes improve. Using a practice-based approach to improving mathematics outcomes, the Kentucky Department of Education (KDE) facilitated a continuous…

Inspired by the work of the social and cultural historian Tim Cole, Stuart Farley decided to look again at the way he teaches the Holocaust. He wanted to focus on the geographical concept of place as a way of enabling his Year 9 students to build far more diverse narratives, which took full account of the chronological diversity of people's…

The inclusion of engineering in the Next Generation Science Standards (NGSS) as a key component of K-12 science learning has provided both opportunities and challenges for elementary teachers. One challenge is integrating the design thinking processes that undergird engineering with core science concepts and current issues facing scientists and…

There is a broad consensus that beginning teachers of mathematics need a strong foundation in mathematical knowledge for teaching (MKT), defined as the mathematical knowledge required to recognize, understand, and respond to the mathematical work of teaching one must engage in. One recurrent challenge in teacher education is how to provide support…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Abilities in scientific thinking and reasoning have been emphasized as core areas of initiatives, such as the Next Generation Science Standards or the College Board Standards for College Success in Science, which focus on the skills the future will demand of today's students. Although there is rich literature on studies of how these abilities…