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…

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

Authoring tools for Intelligent Tutoring System (ITS) have been shown to decrease the amount of time that it takes to develop an ITS. However, most of these tools currently do not extend to collaborative ITSs. In this paper, we illustrate an extension to the Cognitive Tutor Authoring Tools (CTAT) to allow for development of collaborative ITSs that…

Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving…

Jeannette Wing's influential article on computational thinking 6 years ago argued for adding this new competency to every child's analytical ability as a vital ingredient of science, technology, engineering, and mathematics (STEM) learning. What is computational thinking? Why did this article resonate with so many and serve as a rallying cry for…

This article is based on a systematic review of educational research, policy and professional literature relating to creative environments for learning in schools. Despite the search yielding 210 documents, comparatively few empirical studies were published between 2005 and 2011 that addressed the review objectives. Only 18 studies included in the…

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…

"Success stories," i.e., cases in which mathematical problems posed in a controlled setting are perceived by the problem posers or other individuals as interesting, cognitively demanding, or surprising, are essential for understanding the nature of problem posing. This paper analyzes two success stories that occurred with individuals of different…