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…

When making decisions, humans can observe many kinds of information about others' activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others' solutions. Results…

In line with the Common Core and Standards for Mathematical Practice that portray a classroom where students are engaged in problem-solving experiences, and where various tools and arguments are employed to grow their strategic thinking, this article is the story of such a student-initiated problem. A seemingly simple question was posed by…

Some researchers have proposed that video games possess good learning principles and may promote problem solving skills. Empirical research regarding this relationship, however, is limited. The goal of the presented study was to examine whether strategic video game play (i.e., role playing and strategy games) predicted self-reported problem…

The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we…

This article contributes to ongoing discussions related to the nature, scope, and methods of faith-learning integration. The "initiation" approach developed by Tim McDonough (2011) is adapted to faith-learning integration in an attempt to bridge polarizing discussions regarding indoctrination versus rational autonomy and critical…

Today the changing nature of design practice and the role of design within a widening domain indicate that the survival of design as a profession may depend less on traditional design education and more on responding strategically to contemporary changes, influenced by ethical and environmental issues as well as technological advancements. As a…

The web has created new possibilities for collaboration that fit under the terms crowdsourcing and human-based computation. Crowdsourcing applies when a task or problem is outsourced to an undefined public rather than a specific body. Human-based computation refers to ways that humans and computers can work together to solve problems. These two…

We have augmented the Deep Thought logic tutor with a Hint Factory that generates data-driven, contextspecific hints for an existing computer aided instructional tool. We investigate the impact of the Hint Factory's automatically generated hints on educational outcomes in a switching replications experiment that shows that hints help students…

Using the Gap Analysis problem-solving framework (Clark & Estes, 2008), this project examined collaboration around student achievement at the school site leadership level in the Pasadena Unified School District (PUSD). This project is one of three concurrent studies focused on collaboration around student achievement in the PUSD that include…

"Design" can be a noun, or a verb. Six paths for research into engineering design (as verb) are identified, they must be coordinated for internal consistency and plausibility. Design research tries to clarify design processes and their underlying theories--for designing in general, and for particular forms, e.g., design engineering. Theories are a…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

Students develop understanding of mathematics when they translate between and within different mathematical representations. This paper explores a student-generated story and content descriptors from the Australian Curriculum: Mathematics to highlight how primary school students can represent mathematical concepts through exploring the links…

Quek, Tay, Toh, Leong, and Dindyal (2011) proposed that a design-theory-practice troika should always be considered for a designed package to be acceptable to the research users who, in this case, are teachers and schools. This paper describes the fine-tuning to the MProSE problem-solving design made by the teachers in the school after first round…

In a design experiment, the feedback from the teacher-implementer is crucial to the success of the innovation simply because the teacher is finally the one that brings the innovation to life in front of the students. We describe in this paper the feedback made by the teacher-implementer after teaching one cycle of the problem solving module in a…