The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This report summarizes recommendations from NCTM, NRC, CCSSM, NMAP, and IES to guide early numeracy instruction for elementary age students in general and special education classroom settings. We highlight common threads among general and special education research recommendations and provide a numeracy intervention curriculum model connecting…

The researcher examined the effects of two alternative instructional methods, Programmed Learning Sequenced (PLS) and Interactive Whiteboard (IWB), on the mathematics achievement and attitude of eighth graders. The relationship between specific Dunn & Dunn learning-style elements and the posttest scores after instruction with the PLS and IWB…

The purpose of this study was to evaluate a practical procedure for determining the optimum sequencing of pictorial classification tasks in science using mean difficulty indices generated by a standard sample of grade two students. Acquisition of such skills can affect the learner's performance on subsequent material and the teacher's efforts in…

Engineering students use spatial thinking when examining diagrams or models to study structure design. It is expected that most engineering students have solidified spatial thinking skills during K-12 schooling. However, according to what we know about geometry learning and teaching, spatial thinking probably needs to be explicitly taught within…

This newsletter contains five articles. The first, "Discourse Structure in Reading," by Ron Shook, suggests that reading materials for the beginning ESL (English as a second language) reader often have three defects: (1) profusion of detail as question fodder; (2) an oversimplified syntax; and (3) an artificial construction that violates…