What makes a good challenge? - How to write challenges that engage students and help them become better mathematical thinkers
Developing 'function sense' - building up intuitions about the settings in which linear, quadratic, exponential and periodic functions are useful in modeling the world around us. The role of conjecture - learning to explore and generalize, the importance of proof and disproof
The many uses of the equal sign - The equal sign has different meanings in formulas, definitions, equations, relations and identities. An essay designed to clarify the differences between comparison and assignment. There are planes and there are planes! - A cautionary tale - The meaning of translation, dilation, reflection and rotation of functions that map from a domain of quantity to a range of quantity Formulating Measures - toward modeling in the K-12 science and math curriculum - an examination of the nature of the measures that are related to one anther when we form quantitative models Functions - objects & actions - an attempt to reformulate the secondary school mathematics of analysis and geometry in terms of the dual role of function as both object and action
Semantic Aspects of Quantity is a multi-part essay on the nature of mathematics taught in the elementary grades.
Some Thoughts on Modeling Word Problems Graphically - alternative equivalent graphical representations of two simultaneous linear equations are presented and analyzed. What Do Yo Do with a Broken Calculator ? - arithmetic operations as tools; a strategy for developing facility with this toolkit On Problem Posing & Making Conjectures - an extended argument for the importance of the making and exploring of conjectures in mathematics education On the Need For A Bridging Language for Mathematical Modeling - some examples of the power of qualitative graphical thinking for the development of deep understanding On Assessment in Mathematics - link to the Balanced Assessment in Mathematics task archive Intellectual Mirrors: a step in the direction of making schools knowledge-making places - a link to a 1989 Harvard Educational Review article on the power of exploratory environments for stimulating student (and teacher) creativity in mathematics Models, Simulations & Exploratory Environments - a paper exploring differences and similarities among the three kinds of computer environments. The paper was presented at a
seminar in the Faculty of Science & Technology at The New University of
Lisbon, Portugal, in June 2002 model is to data as chicken is to egg - This essay
was originally written for a science education project designed for
middle school teachers with little to no background in science. It
addresses the central issue of the fugue between model and data in the
process of formulating a model. Growing Pains - variations on an old tale - an essay examining the difference between defining a function globally as a mapping from domain to range and defining a functions iteratively by specifying a value and a differential increment
A Physicist's Lament - link to an essay written for the The Teaching & Learning Mathematics blog of the American Mathematical Society. Tyranny, Discipline, Freedom & License: thoughts on computer use in education - on the use of a
genre of software, not always fashionable, that is characterized
neither by tyranny nor license, but rather by discipline and freedom.
Judah L. Schwartz
 mathMINDhabits by Judah L. Schwartz is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |