In this article, the author describes a lesson he observed involving a function machine. This function machine was a box with a slot at the top of one side and a large cut-out hole at the bottom of the opposite side. A card with a number written on it (the input) was pushed into the slot and the teacher put their hand through the hole of the other…

The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use…

The purpose of this study was to examine graphical feedback, a rarely used method for improving the quality of preschool teaching. Twenty-one lead and assistant teachers participated in the study, although data were analyzed by assessing how much incidental teaching the 10 participating preschoolers with disabilities received. After receiving…

We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)

The authors review the graphical approach to teaching the real business cycle model introduced in Barro. They then look at where this approach cuts corners and suggest refinements. Finally, they compare graphical and exact models by means of impulse-response functions. The graphical models yield reliable qualitative results. Sizable quantitative…

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

This article details the results of a written test designed to reveal how education majors construct and evaluate histograms and frequency polygons. Included is a description of the mistakes made by the students which shows how they tend to confuse histograms with bar diagrams, incorrectly assign data along the Cartesian axes and experience…

This paper describes a teaching method that allows for the fast and early detection of students' conceptions, misconceptions and their development. The empirical study of two examples where the method was applied is reported. The prerequisites for the efficient use of the method are discussed and results of the pilot study of its effectiveness are…

These proceedings contain the papers and posters of the International Conference on e-Learning (EL) 2019, which was organised by the International Association for Development of the Information Society and co-organised by the Instituto Superior de Engenharia do Porto, in Porto, Portugal, July 17-19, 2019. The EL 2019 conference aims to address the…

Teachers need to address global climate change with students in their classrooms as evidence for consequences from these environmental changes mounts. One way to approach global climate change is through examination of authentic data. Mathematics and science may be integrated by interpreting graphs from the professional literature. This study…

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations…

When students understand content deeply, they recognize main concepts and understand the relationships among ideas. But the typical processes students use to study are generally not designed to generate conceptual understandings. Instead, they tend to become passive learners. In this article, the authors present three commonly used classroom…

Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. (Contains 7 figures.)

The ability to visualize student engagement and experience data provides valuable opportunities for learning support and curriculum design. With the rise of the use of learning analytics to provide "actionable intelligence" on students' learning, the challenge is to create visualizations of the data, which are clear and useful to the…