This study used HIMATT (Highly Interactive Model-based Assessment Tools and Technologies) to evaluate the cognitive models of individuals who are solving complex mathematical problems. The goal was to determine the ability of HIMATT to assess learning in mathematics. Research on cognitive and mental models proposes that internal conceptual systems…

A common activity in school mathematics is to derive a function from a table of values. There are two general strategies one might adopt to determine the function f. First, one might try to determine a connection between a particular n and f(n), and then evaluate whether it holds for other values of n. An alternative strategy would be to look for…

This paper is, essentially, the transcription of my conference at the conference CIEAEM 63, promoted by the CIEAEM/Commission for the Study and Improvement of Mathematics Teaching, held in Barcelona, Spain, from 24 to 29 July 2011. The main objective of the CIEAEM, since its foundation, in the fifties, has been to analyze the actual conditions and…

Intuition presents as a crucial component of professional competence for many occupations, including emergency physicians because many of their decisions have to be made quickly. When arriving at the scene of an accident, they promptly have to assess the circumstances and initiate immediate life-saving measures without opportunities for deep…

The recent push for more problem solving in elementary school mathematics classrooms intimidates many teachers. Anyone can look at the arguments--that problem solving deepens knowledge, provides real-world context, allows for multiple entry points, and so on--and see their logic and potential (Lester and Charles 2003). But teachers tend to think…

The purpose of this essay is to draw out key insights from Dewey's important text "Logic: The Theory of Inquiry" to provide theoretical and practical support for the emergent field of teacher research. The specific focal point is the argument in Cochran-Smith and Lytle's "Inside/Outside: Teacher Research and Knowledge" on the significance of…

This dissertation examines two related questions. "How do mixed membership models work?" and "Can mixed membership be used to model how students use multiple strategies to solve problems?". Mixed membership models have been used in thousands of applications from text and image processing to genetic microarray analysis. Yet…

Achieving effective learning via digital media continues to be a major concern in contemporary education. The daily use of all forms of digital media is part of our lives and therefore becomes a key component of education. Educators must consider the process of digital media curriculum as a learning model and form of experience adapted to…

This is an exploratory study into the individual problem-posing characteristics of 480 Grade 9 Singapore students who were novice problem posers working on two geometric tasks. The students were asked to pose a problem for their friends to solve. Analyses of solvable posed problems were based on the problem type, problem information, solution type…

In this paper, we discuss the diffusion (of an innovation) and relate it to our attempt to spread our initial design of a mathematics practical paradigm in the teaching of problem solving.

Preparing health practitioners to respond to the rising burden of disease from climate change is emerging as a priority in health workforce policy and planning. However, this issue is hardly represented in the medical education research. The rapidly evolving wide range of direct and indirect consequences of climate change will require health…

The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry…

Each year, thousands of undergraduates in the science, technology, engineering, and mathematics (STEM) fields conduct research in US university and college laboratories. Such undergraduate research (UR) experiences are common practice in US higher education, with nearly a century of history at research universities and liberal arts colleges.…

This paper presents a study that investigated the process of change in 5-6-year-old children's successful problem-solving approaches when tackling a multiple-step task in elementary arithmetic. Micro-developmental changes in children's successful problem-solving behavior were analyzed using Karmiloff-Smith's model of representational redescription…

Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…