CONCEPTUAL ISSUES IN QUANTIFYING UNUSUALNESS AND CONCEIVING STOCHASTIC EXPERIMENTS: INSIGHTS FROM STUDENTS’ EXPERIENCES IN DESIGNING SAMPLING SIMULATIONS

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students’ abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis testing. This scheme of ideas involves imagining a population and a sample drawn from it, and an image of repeated sampling as a basis for quantifying a sampling outcome’s unusualness in terms of long-run relative frequency under an assumption about the population’s composition. The study highlights challenges that students experienced, and sheds light on aspects of conceiving stochastic experiments and conceiving a sampling outcome’s unusualness as a probabilistic quantity. First published November 2016 at Statistics Education Research Journal Archives

Creating Microworlds for Exploring Mathematical Understandings in the Early Years of School

This article will describe the strategies and interactions of pairs of Year 2 children (average age 7 years 4 months) while they worked on novel tasks in a computer microworld embedded in a mathematics curriculum. The curriculum encouraged the active exploration of ideas in both on and off computer tasks, which complemented each other. Observations of the children supported the notion that the active construction of knowledge in a computer supported collaborative learning context, enabled the children to engage with powerful ideas and use metastrategic strategies. Further their spontaneous comments and persistence with tasks indicated a high level of interest and enthusiasm for these tasks in preference to those that traditionally characterize mathematical activity.

Assessing Virtual Reality's Potential for Teaching Abstract Science

Understanding how to leverage the features of immersive, three-dimensional (3-D) multisensory virtual reality to meet user needs presents a challenge for human factors researchers. This paper describes our approach to evaluating this medium's potential as a tool for teaching abstract science. It describes some of our early research outcomes and discusses an evaluation comparing a 3-D VR microworld to an alternative 2-D computer-based microworld. Both are simulations in which students learn about electrostatics. The outcomes of the comparison study suggest: 1) the immersive 3-D VR microworld facilitated conceptual and three-dimensional learning that the 2-D computer microworld did not, and 2) VR's multisensory information aided students who found the electrostatics concepts challenging. As a whole, our research suggests that VR's immersive representational abilities have promise for teaching and for visualization. It also demonstrates that characteristics of the learning experience such as usability, motivation, and simulator sickness are important part of assessing this medium's potential.

Symbolizing as a Constructive Activity in a Computer Microworld

In the design of computer microworlds as media for children's mathematical action, our basic and guiding principle was to create possible actions children could use to enact their mental operations. These possible actions open pathways for children's mathematical activity that coemerge in the activity. We illustrate this coemergence through a constructivist teaching episode with two children working with the computer microworld TIMA: Bars. During this episode, in which the children took turns to partition a bar into fourths and thirds recursively, the symbolic nature of their partitioning operations became apparent. The children developed their own drawings and numeral systems to further symbolize their symbolic mental operations. The symbolic nature of the children's partitioning operations was crucial in their establishment of more conventional mathematical symbols.

Children's Learning in a Computer Microworld for Transformation Geometry

Twelve middle school students working in pairs used a computer microworld to explore an introductory curriculum in transformation geometry. The microworld linked a symbolic representation (a set of simple Logo commands) with a visual display that showed the effects of each transformation. Worksheets were designed with the objective of encouraging the students to find and express mathematical patterns in the domain. The students were successful in constructing an accurate working understanding of the transformations. There was a tendency for symbolic overgeneralization in some activities, but the students were able to use visual feedback from the microworld and discussions with their partners to correct their own errors.

Computer Presentational Features for Young Children's Preferential Selection and Recall of Information

Preschool children's preferential selection and recall of words presented in a computer microworld was assessed as a function of action and sound. Forty preschoolers, equally distributed by sex, were randomly assigned to one of four versions of a microworld. Within each version, twenty-four sprite objects were randomly assigned properties of action and sound. The design was counterbalanced so that across the four versions, each sprite assumed all possible factorial combinations of action and sound. As expected, children preferentially selected and later recalled more words presented with action than words presented without action. Although children selected sounds, sounds interfered with children's recall of linguistic information. Results support an action superiority hypothesis and an auditory interference hypothesis. The practical application is to use action as an integral component of educational computer software designed for young children.