Traditional school laboratory exercises on a system of moving objects connected by strings involve deriving expressions for the system acceleration, a = (?F)/m, and sketching a graph of acceleration vs. force. While being in the form of rational functions, these expressions present great opportunities for broadening the scope of the analysis by…

System Dynamics is a required course offered to junior Mechanical Engineering students at Penn State Erie, the Behrend College. It addresses the intercoupling dynamics of a wide range of dynamic systems: including mechanical, electrical, fluid, hydraulic, electromechanical, and biomedical systems. This course is challenging for students due to the…

This article documents the classroom mathematical practices observed in a collegiate level teacher education course related to the circle topic. The course, which was prepared as design research, utilized a dynamic geometry environment which influenced the type and nature of the evolved mathematical practices. The study uses emergent perspective…

Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…

This article describes a two-day optics laboratory activity that investigates the scientific phenomenon of reflection, which students are generally familiar with but usually have not studied in depth. This investigation can be used on its own or as part of a larger unit on optics. This lesson encourages students to think critically and…

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

The literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments…

In this article, educators at University Primary School in Champaign, Illinois, share examples and understandings of the ways The Project Approach challenges young children to think critically about topics of importance in their world. Project investigations that provoke academic and social challenges for individuals and classroom communities of…

Fractions constitute a stumbling block in mathematics education. To improve children's understanding of fractions, we designed an intervention based on learning-by-doing activities, which focused on the representation of the magnitude of fractions. Participants were 292 Grade 4 and 5 children. Half of the classes received experimental instruction,…

The propose of this study is to study Physics Learning Achievement, projectile motion, using the Mathematica program of Faculty of Science and Technology Phetchabun Rajabhat University students, comparing with Faculty of Science and Technology Phetchabun Rajabhat University students who study the projectile motion experiment set. The samples are…

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

I present a witty solution in this article about how we may obtain data simply and cheaply from physical experiments, with which we can do counting, as well. To this interdisciplinary task I turn to Delphi for help, in which we can program a digital video as a multimedia element. I show an example from the programming of plain multimedia elements…

This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they…