This monograph provides an epistemological rational for the design of an advanced novel analysis metric. The metric is designed to analyze the outcomes of the Tri-Squared Test. This methodology is referred to as: "Tri-Squared Mean Cross Comparative Analysis" (given the acronym TSMCCA). Tri-Squared Mean Cross Comparative Analysis involves…

Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of "post-normal" science -- it is urgent, complex and involves a…

On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…

The modern era of professional baseball playoffs began in 1903, when the champions of the American League and the National League played the first World Series. Except for one year, 1904, this playoff system was maintained until 1969. Beginning in 1969, each of the two leagues in Major League Baseball (MLB) was divided into two divisions to…

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

As two teacher educators, we conducted a collegial action research study and investigated how collaborative lesson preparation and reflection that focused on prospective teachers' thinking supported our perspectives on teaching and learning. We conducted this action research to provide more equal education opportunities to the prospective teachers…

In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13-14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in…

Background: Since students' success in their first-semester college mathematics course is a key factor in their success in engineering, many summer bridge programs for underrepresented students focus on their preparation in mathematics. However, research on the design and efficacy of such programs is limited. We examine the design and…

Lorraine Day provides us with a great range of statistical investigations using various resources such as maths300 and TinkerPlots. Each of the investigations link mathematics to students' lives and provide engaging and meaningful contexts for mathematical inquiry.

Helping students develop an understanding of how to interpret experimental data trends is an important part of the introductory physics laboratory. Unfortunately, many of my colleagues have lamented that too many of their students do this poorly. This is a common refrain, and past research has already revealed student difficulties with…

This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or minimum…

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

This paper explores alternative assessment methods from the perspective of categorizations. It addresses the technologies that support assessment. It discusses initial, formative, and summative assessment, as well as objective and subjective assessment, and formal and informal assessment. It approaches each category of assessment from the…

This study investigates the relationship between students ability to answer reduced language dependency mathematical questions with their overall numeracy level. It investigates whether a student's success at reduced language mathematical questions translates into better overall numeracy scores. It was found, students have up to two years…