This analysis of a problem that is frequently posed at professional development workshops, in print, and on the Web--the coffee-milk mixture riddle--illustrates the timeless advice of George Pólya's masterpiece on problem solving in mathematics, "How to Solve It." In his book, Pólya recommends that problems previously solved and put…

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

This paper reports findings from the efforts of a university-based research team as they worked with middle school educators within formal school structures to infuse computer science principles and computational thinking practices. Despite the need to integrate these skills within regular classroom practices to allow all students the opportunity…

This study aims to demonstrate how the average speed of a light-emitting toy car may be determined using a smartphone's light sensor. The freely available Android smartphone application, "AndroSensor," was used for the experiment. The classroom experiment combines complementary physics knowledge of optics and kinematics to find the…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

Who will make a better estimate concerning the number of jelly beans in a jar, a single person or a group of people? On one side of the debate is the notion that a person would make a better decision because he or she uses unique knowledge that the group may not possess. On the opposite side of the argument is the claim that because of their…

This study, a sub-study of a National Science Foundation (NSF) funded research project, applies a modified strategy of the U[superscript 2]MC for an eight-week afterschool robotics curriculum to promote upper elementary students' computational thinking in the second grade. Twenty-one students in second grade participated in a Life on Mars project…

Computing in some form touches nearly every aspect of day to day life and is reflected in the ubiquitous use of cell phones, the expansion of automation into many industries, and the vast amounts of data that are routinely gathered about people's health, education, and buying habits. Computing is now a part of nearly every occupation, not only…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…

The integration of computational thinking (CT) and computer science (CS) into formal K-12 learning experiences are critical for students to be competent 21st Century problem solvers. Building student competency with these areas is dependent upon educators who have the pedagogical content expertise to integrate CT and CS within their disciplines…

Fitness trackers can provide primary students with exciting opportunities to calculate, measure time and distance, graph, make sense of data, and improve their activity levels. This article suggests ways to use fitness trackers in the classroom.

Russian higher education institutions' tradition of teaching large-enrolled classes is impairing student striving for individual prominence, one-upmanship, and hopes for originality. Intending to converting these drawbacks into benefits, a Project-Centred Education Model (PCEM) has been introduced to deliver Computational Mathematics and…

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. "Solving for x" in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…