The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

Describes how teachers can use wheels of tricycles, bicycles, and trains to stimulate children with mathematics, relative position, and engineering concepts. Techniques are offered for measuring circumference of a bicycle wheel, gear ratios, and pedal wheel circumferences. Comparative data are given for various sized wheels. (Author/SA)

Model-eliciting activities (MEA), specially designed client-drive, open-ended problems, have been implemented in a first-year engineering course and in secondary schools. The educational goals and settings are different, but the design of an MEA enables it to be versatile. This paper will introduce the reader to the principles that guide MEA…

This publication contains Arizona public schools' academic standards for grade 3. The contents of this document include the following: (1) The Arts Standard 2006--Grade 3; (2) Comprehensive Health Education/Physical Activity Standards 1997--Foundations (Grades 1-3); (3) Foreign and Native Language Standards 1997--Foundations (Grades 1-3); (4)…

This publication contains an updated academic standards of Arizona public schools for grade 5. The contents of this document include the following: (1) The Arts Standard 2006--Grade 5; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Foundations (Grades…

This publication contains an updated academic standards of Arizona public schools for grade 6. The contents of this document include the following: (1) The Arts Standard 2006--Grade 6; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades…

This publication contains the updated academic standards of Arizona for Grade 8. The contents of this document include the following: (1) The Arts Standard 2006--Grade 8; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading…

This publication contains Arizona public schools' updated academic standards for high school. The contents of this document contain: (1) The Arts Standard 2006--High School; (2) Comprehensive Health Education/Physical Activity Standards 1997--Proficiency and Distinction (Grades 9-12); (3) Foreign and Native Language Standards 1997--Proficiency and…

This document contains the Arizona academic standards for Grade 7. The following 11 standards are reviewed: (1) The Arts Standard 2006 --Grade 7; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading Standard Articulated by…

This publication contains Arizona public schools' academic standards for kindergarten. The contents of this document include the following: (1) The Arts Standard 2006--Kindergarten; (2) Comprehensive Health Education/Physical Activity Standards 1997--Readiness (Kindergarten); (3) Foreign and Native Language Standards 1997--Readiness…