Jim Greer and his colleagues argued that student modelling is essential to provide adaptive instruction in tutoring systems and showed that effective modelling is possible, despite being enormously challenging. Student modelling plays a prominent role in many intelligent tutoring systems (ITSs) that address problem-solving domains. However,…

Solving word problems is challenging in elementary schools, both for the teacher in teaching students to solve word problems and for the student in learning to solve them. This paper examines how the ideas of learning trajectory and variation pedagogy could be integrated as an instructional principle for teaching this content in the context of…

The goal of this study is to determine the effectiveness of mind games played by secondary school sixth grade students as classroom activities in math and grammar courses on their perceived problem-solving skills and achievements. In the quantitative part of the study, the nonequivalent groups pre-test--post-test control group design from…

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

Although learning from multiple representations has been shown to be effective in a variety of domains, little is known about the mechanisms by which it occurs. We analyzed log data on error-rate, hint-use, and time-spent obtained from two experiments with a Cognitive Tutor for fractions. The goal of the experiments was to compare learning from…

A simple method to introduce the modern periodic table of elements at the high school level as a game of solving a crossword puzzle is presented here. A survey to test the effectiveness of this new method relative to the conventional method, involving use of a wall-mounted chart of the periodic table, was conducted on a convenience sample. This…

Genetics is a unifying theme of biology that poses a major challenge for students across a wide range of post-secondary institutions, because it entails complex problem solving. This article reports a new intelligent learning environment called the Genetics Cognitive Tutor, which supports genetics problem solving. The tutor presents complex,…

The authors' primary aim was to investigate a potential causal relationship between spatial ability and math ability. To do so, they used a pretest-training-posttest experimental design in which children received short-term spatial training and were tested on problem solving in math. They focused on first and second graders because earlier studies…

This paper puts the case for using a pedagogical framework based on the principles of grammatical design in conjunction with conventional creative problem solving strategies in higher education to foster learning for innovation and creativity. It explores the design and delivery of an inaugural creativity and innovation course that used a…

This article deals with evaluating an interactive learning environment (ILE) during the iterative-design process. Various aspects of the system must be assessed and a number of evaluation methods are available. In designing the ILE Ambre-add, several techniques were combined to test and refine the system. In particular, we point out the merits of…

Certain learners are less sensitive to learning environments and can always learn, while others are more sensitive to variations in learning environments and may fail to learn (Cronbach & Snow, 1977). We refer to the former as high learners and the latter as low learners. One important goal of any learning environment is to bring students up…

This study investigated whether instruction that involves comparing the equal sign with other relational symbols is more effective at imparting a relational interpretation of the equal sign than instruction about the equal sign alone. Third- and fourth-grade students in a comparing symbols group learned about the greater than, less than, and equal…

Traditional assessment methods such as tests and essays may not be adequate to evaluate students' ability to solve problems and think critically. I developed a qualitative assessment technique for a junior-level Wildlife Management Techniques course that incorporated written responses in a pre- and post-course reflection exercise. I provided the…

This paper reports on a quasi-experimental study comparing a "productive failure" instructional design (Kapur in Cognition and Instruction 26(3):379-424, 2008) with a traditional "lecture and practice" instructional design for a 2-week curricular unit on rate and speed. Seventy-five, 7th-grade mathematics students from a…

Most students struggle when faced with complex and open-ended tasks because the strategies taught in schools and universities simply require finding and applying the correct formulae or strategy to answer well-structured, algorithmic problems. For students to develop their ability to solve ill-structured problems, they must first believe that…