I'll be presenting a session on Geometric Puzzles at the Asilomar meeting of the California Math Council. (Saturday, Dec 2, Sanderling, 1:30pm The printed program says I'm in the middle school, but that is not correct. The app has the location right.). I will include material that I believe is relevant to teachers from kindergarten… Continue reading Geometric Puzzles at Asilomar
Author: hpicciotto
Puzzles for the Classroom
In my last post, I shared some generalities about puzzle creation. Today, I will zero in on the specifics of creating puzzles for the mathematics classroom. I will do this by way of analyzing some examples. Multiple PathsA characteristic of all classrooms is that they are constituted of students whose backgrounds and talents vary widely. … Continue reading Puzzles for the Classroom
Puzzle Creation
John Golden asked whether I had written about my approach to puzzle creation. I've only written a brief post on the subject, five years ago. Yet I believe that my work as a curriculum developer is largely based on my involvement with puzzles: solving them, constructing them, editing them. Of course, puzzling is not the… Continue reading Puzzle Creation
Scissors Congruence!
I attended the San Francisco Math Teachers' Circle last weekend. It was facilitated by Paul Zeitz. The topic: showing two polygons have equal area by cutting one into pieces, and rearranging them to cover the other one with no gaps or overlaps.The assumption was that the area of a rectangle is length times width. The… Continue reading Scissors Congruence!
On NCTM, Part 2
In Part 1, I discussed my relationship with NCTM, its Standards, and its journals, mostly The Mathematics Teacher. In this post, I discuss NCTM conferences, and compare them with other math teacher gatherings.NCTM Conferences vs. Local ConferencesI've had much, much better luck attending great sessions at my local Northern California conference in Asilomar (Pacific Grove,… Continue reading On NCTM, Part 2
On NCTM, Part 1
I've read a few blog posts about the National Council of Teachers of Math (NCTM) in the last few weeks:Three posts by Tina Cardone, which can serve as an introduction to NCTM. NCTM and the Math Forum by Tracy Zager, including links to other posts (including NCTM's response) about the shutting down of the Math Forum.My… Continue reading On NCTM, Part 1
Stumped by Euclidea
I've really enjoyed solving the puzzles in Euclidea, a brilliantly designed app for iOS and Android. The basic format is "given this, construct that". You start with just two tools: a straightedge and a slack compass (i.e. a compass that does not remember the radius it was last set to). As you find useful and… Continue reading Stumped by Euclidea
Transformational Proof
Prior to the publication of the Common Core State Standards for Math (CCSSM), transformational geometry was rarely seen in geometry courses. It certainly was missing from the one I taught. Still, I have always been interested in this topic, and it provided the backbone of my "Geometry 2" class, a post-Algebra 2 elective which I… Continue reading Transformational Proof
More on Geometric Construction
(To search from previous posts on this topic, use the Search box on the right.) I suspect that by far the most common introduction to geometric construction in US classrooms is a presentation by the teacher (or textbook) on various compass and straightedge construction techniques. "This is how you construct a perpendicular bisector. This is… Continue reading More on Geometric Construction
Errata
According to Merriam-Webster, the word errata means "errors" in Latin, but it is used in English to mean corrigenda which in Latin means "corrections". So there you have it: errors can be corrected — student errors, teacher errors, and (ahem) curriculum developer errors.My books, great as they are, do contain errors. Some are small errors… Continue reading Errata
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