"Bridges in Mathematics," published by the Math Learning Center (MLC), is an elementary school math curriculum covering kindergarten through fifth grade that focuses on problem solving and skill building, and applies a combination of whole-group, small-group, and independent activities. Lessons incorporate visual models, including…

The main goals of this study were to test whether multiple representations, such as diagrams and equations, per se help to acquire conceptual understanding in probability, and to investigate whether learners need instructional support to utilize the potentials of multiple representations. The authors conducted an experimental study with 8…

Intelligent Tutoring Systems (ITSs) that adapt to an individual student's needs have shown significant improvement in achievement over non-adaptive instruction (Murray 1999). This improvement occurs due to the individualized instruction and feedback that an ITS provides. In order to achieve the benefits that ITSs provide, we must find a way to…

Although most online learning environments are predominately text based, researchers have argued that representational support for the conceptual structure of a problem would address problems of coherence and convergence that have been shown to be associated with threaded discussions and more effectively support collaborative knowledge…

The authors describe a Modeling Instruction program that places an emphasis on the construction and application of conceptual models of physical phenomena as a central aspect of learning and doing science. (Contains 1 table.)

Professionally developed and freely accessible through the Internet, scientific data maps have great potential for teaching and learning with data in the science classroom. Solving problems or developing ideas while using data maps of Earth phenomena in the science classroom may help students to understand the nature and process of science. Little…

This research investigated how fourth and fifth grade students spontaneously "unpacked" a word problem when generating a graphic representation to aid in problem solution. Relationships among the type of graphic representation produced, spatial visualization, drawing ability, gender, and problem solving also were examined and described.…

In this paper, we integrate organizational, engineering education, and educational learning literature to develop a model of student learning so as to research how learning style, behavioral tendencies, gender, and race have the potential to act as facilitators or barriers to the learning process. We argue that the gains in higher-order cognitive…

This article focuses on current examples of project or design-based learning at the secondary school level in the context of the increasing importance of creativity and innovative thinking in the twenty-first century. The authors argue that students today learn more effectively in pedagogical practices that emphasise holistic thinking, active…

Children of foreign origin are increasingly failing in mathematics in Swedish compulsory schools. This article analyses the didactics at a school proven very successful in teaching mathematics to all children including the 70% of children of foreign origin. The situation at the studied school is compared to research of the Swedish school system…

These proceedings contain the papers of the 18th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2021), held virtually, due to an exceptional situation caused by the COVID-19 pandemic, from October 13-15, 2021, and organized by the International Association for Development of the Information Society…

Argumentation is a process that occurs often in ill-defined domains and that helps deal with the ill-definedness. Typically a notion of "correctness" for an argument in an ill-defined domain is impossible to define or verify formally because the underlying concepts are open-textured and the quality of the argument may be subject to discussion or…

Current science assessments typically present a series of isolated fact-based questions, poorly representing the complexity of how real-world science is constructed. The National Research Council asserts that this needs to change to reflect a more authentic model of science practice. We strongly concur and suggest that good science assessments…

Technological literacy education involves the teaching of basic engineering principles and problem solving, including elementary electrical circuit analysis, to non-engineering students. Learning materials on circuit analysis typically rely on equations and schematic diagrams, which are often unfamiliar to non-engineering students. The goal of…

This paper presents a qualitative case study of statistical practice in a university-based statistical consulting centre. Naturally occurring conversations and activities in the consulting sessions provided opportunities to observe questions, problems, and decisions related to selecting, using, and reporting statistics and statistical techniques…