In this case study, we investigate one teacher's implementation of DNR-based combinatorics curriculum in their high school discrete mathematics class. By examining the teacher's practices in whole-class discussions of two counting problems, we study how they advanced a variety of ways of thinking to support the development of a set-oriented way of…

Literacy scholars have called for writing instruction to promote civic engagement, student agency, and multimodal composing. This study addressed this call by describing a research-practice partnership to reimagine writing instruction in a high school English course by incorporating human-centered design challenges. Using case study methods, we…

In the modern era, Geographic Information Systems (GIS) have revolutionized diverse fields yet a deficiency in geographical education lingers in the U.S. educational system. This dissertation offers a thorough analysis of this gap, focusing on the potential of the GIS as an innovative solution for enriching geographical education. The Geospatial…

Although there have been calls for secondary mathematics education in the U.S. to incorporate problem-solving and creativity, the lion's share of instruction is designed to train students to accurately use procedures or understand concepts made by mathematicians in the past (National Research Council, 1999; Watson, 2008). This disconnect…

Computational thinking--a set of mental and cognitive tools applied to problem solving--is a fundamental skill that all of us (and not just computer scientists) draw on. Educators have found that computational thinking enhances learning across a range of subjects and reinforces students' abilities in reading, writing, and arithmetic. This book…

This paper describes a high school or introductory university course in scientific programming that introduces the computer revolution into the physics curriculum at the beginning. In the first one-hour lecture, Euler's method is presented and used to compute a solution to the analytically unsolvable two-body problem. In the remainder of the…

Almost twenty years ago, the National Council of Teachers of Mathematics (NCTM) published "Principles and Standards for School Mathematics" (2000), which recommended that teachers should incorporate more writing into their math lessons, claiming that writing helps students "consolidate their thinking" (p. 402) by causing them…

Increasing and decreasing functions can be combined into a quadratic to explore the competing demands of number of sales, price points and profit (or loss). An interesting application of taxation rates is also explored.

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

"Preparing Teachers for Deeper Learning" answers an urgent call for teachers who educate children from diverse backgrounds to meet the demands of a changing world. In today's knowledge economy, teachers must prioritize problem-solving ability, adaptability, critical thinking, and the development of interpersonal and collaborative skills…

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

"Designing backwards" is presented here as a means to utilize human-centered processes in diverse educational settings to help teachers and students learn to formulate and operate design processes to achieve three sequential and interrelated goals. The first entails teaching them to effectively and empathetically identify, frame and…

A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinised teaching approaches and…

The aim of this study is to analyze and document the extent to which high school teachers rely on a set of technology affordances to articulate epistemological and cognitive actions in problem solving approaches. Participants were encouraged to construct dynamic representations of tasks and always to look for different ways to identify and support…

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…