The ability to effectively problem solve is a highly valued competency expected of university graduates, independent of their area of study. Evaluation of problem-solving skill (PSS) development is hindered by a shortage of available tools for monitoring student progress and by lack of defined instructional strategies for development of these…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

Recently, there has been a growing interest in learning approaches that combine two phases: an initial problem-solving phase followed by an instruction phase (PS-I). Two often cited examples of instructional approaches following the PS-I scheme include Productive Failure and Invention. Despite the growing interest in PS-I approaches, to the best…

Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both…

Using expository text and examples available in 10 college textbooks we identify two conceptions of angles, trigonometric functions, and inverse trigonometric functions that rely on either a static or a dynamic definition of angle. Although the textbooks favor a conception of trigonometric functions that is based on a dynamic conception of angle,…

The concept of fractions is perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity is fractions having five interrelated constructs: part-whole, ratio, operator, quotient, and measure. In this study, we used this framework to investigate the…

"Media Clips" appears in every issue of "Mathematics Teacher," offering readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Based on "In All the Light We Cannot See" (2014), by Anthony Doerr, this article provides a brief trigonometry problem that was solved by…

We consider designs for conceptual learning where students first engage in pre-symbolic problem solving and then articulate their solutions formally. An enduring problem in these designs has been to support students in accessing their pre-conceptual situated process, so that they can reflect on it and couch it in mathematical form. Contemplative…

This paper analyzes the thought process involved in problem solving and its categorization as creative thinking as defined by psychologist R. Weisberg (2006). Additionally, the notion of insight, sometimes present in unconscious creative thinking and often leading to creative ideas, is discussed in the context of geometry problem solving. In…

A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…

Help turn students into problem solvers. With lesson imaging, teachers anticipate how chosen activities will unfold in real time--what solutions, questions, and misconceptions students might have and how teachers can promote deeper reasoning. When lesson imaging occurs before instruction, students achieve lesson objectives more naturally and…

Community violence exposure is associated with increased depressive symptoms in adolescents. This study examined whether coping style moderates this relationship over time. Eighty-four low-income, urban adolescents (M[subscript age] = 13.36, 50% female, 95% African American) participated in two waves of a longitudinal study. Youth reported on…

The Soil Nutrient Relationships course serves juniors and seniors with a major or minor in agronomy at the University of Nebraska-Lincoln. Pre-pandemic enrollment averaged 65 students. In 2021 and 2022, course enrollment was 42 and 55, respectively. The course was adjusted to a flipped design in 2017. Moving into 2021, the Soil Nutrient…

The aim of this study was to develop a student entrepreneurship education model that integrates the design thinking model into the creative problem-solving process and finds solutions to problems through Lean Canvas. The solutions generated can be translated into a unique value proposition substantiated by ownership of a competitive advantage that…

Transitional engineering students are those who are academically ineligible to enter a bachelor's engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor's engineering program. The associate…