Meaningful learning requires deep engagement with ideas. Deep engagement is supported by the critical thinking skill of argumentation. Learning to argue represents an important way of thinking that facilitates conceptual change and is essential for problem solving. In order to appropriately apply argumentation practices to learning, we first…

This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load.…

Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three- to four-year-olds and 24 four- to five-year-olds judged commutativity and associativity principles and solved two-term problems involving number words…

This article describes the collaborative inquiry activity of a group of high school mathematics teachers interested in increasing student engagement and problem solving in the classroom. Specific findings related to the nature of the teacher interactions and subsequent impacts on practice are discussed. The findings focus on (a) the nature of the…

This article describes how actuarial methods can supplant discrepancy models and augment problem solving and Response to Intervention (RTI) efforts by guiding the process of identifying specific learning disabilities (SLD). Actuarial methods use routinized selection and execution of formulas derived from empirically established relationships to…

Learning to program is known to be difficult for novices. High attrition and high failure rates in foundation-level programming courses undertaken at tertiary level in Computer Science programs, are commonly reported. A common approach to evaluating novice programming ability is through a combination of formative and summative assessments, with…

Children and their families and teachers use video-sharing websites for new types of learning and information sharing. With the expansion of the World Wide Web, the ability to freely exchange pattern-based information has grown exponentially. As noted by Alexander, "pattern language development" is a process in which communities freely share…

As the U.S. economy begins to show signs of improvement, executives say they need a workforce fully equipped with skills beyond just the basics of reading, writing, and arithmetic (the three Rs). Skills such as critical thinking and problem solving, communication, collaboration, and creativity and innovation (the four Cs) will become even more…

Problem-solving instruction facilitates children in becoming successful real-world problem solvers. Research that incorporates problem-solving instruction has been limited for students with mild and moderate intellectual disabilities. However, this population of students needs increased opportunities to learn the skills of problem solving. Using a…

Students at the junior high school (JHS) level often cannot use their knowledge of physics for explaining and predicting phenomena. We claim that this difficulty stems from the fact that explanations are multi-step reasoning tasks, and students often lack the qualitative problem-solving strategies needed to guide them. This article describes a new…

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

This study examined how literal symbols affect students' understanding of algebraic expressions. Middle school students (N = 322) were randomly assigned to 1 of 3 conditions in which they were asked to interpret an expression (e.g., 4c + 3b) in a story problem. Each literal symbol represented the price of an item. In the c-and-b condition, the…

We describe the effects of an intervention designed to develop the mathematical word problem solving of low-achievers. The eight students participating in the intervention were selected from 429 10-year-olds on the basis of their difficulties in word problem solving. In the intervention, we combined intensive, systematic, and explicit teacher…

Recently, the importance of ill-structured problem-solving in real-world contexts has become a focus of educational research. Particularly, the hypothesis-development process has been examined as one of the keys to developing a high-quality solution in a problem context. The authors of this study examined predictive relations between young…

Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…