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…

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…

Organic chemistry is a cognitively demanding subject with persistently low student achievement. This review aimed to identify instructional strategies and educational technologies used to improve learning outcomes in organic chemistry across educational levels and learning environments. A systematic review of 40 experimental studies (2014-2023)…

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…

"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…

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…

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.

Secondary schools in Maine and New Hampshire have been involved in a citizen science program called "All About Arsenic" aimed at addressing arsenic contamination of well water, one of the most pressing public health issues in both states. Nearly half of the population of Maine and New Hampshire derive their drinking water from private…

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…

Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down a local quarter-mile drag strip. The driver, a family member, provided the spectators with time and distance-traveled data from his time slip and asked "Can you calculate how many seconds it took me to go from 0 to 60…

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

When designing lessons and units of study, teachers prepare problems that will make learning accessible, challenging, and targeted to goals. Experienced teachers often can predict classroom dialogue. This sense of déjà vu is even stronger when they teach the same course several times a day. The questions from the students are familiar and almost…