In my last post, I argued that, as teachers and math education leaders in a school or district, we need to free ourselves from the sequencing preordained by the textbook, and instead pay attention to what actually works with our students. In this post, I will present some general guidelines for sequencing topics, and some… Continue reading Sequencing
Alison Blank makes good points in her interesting presentation: "Math is not linear", where she encourages us to make connections, go on tangents, preview future topics and review past ones. In short, we should not be trapped in the inflexible sequence suggested by textbooks and school culture. In a recent blog post, Jim Tanton makes… Continue reading Mind Maps
In my previous post, I listed questions to use in class discussions, or in conversation with a student or a group of students. Today, I'll discuss how to handle wrong answers. This is complicated and there is no single correct answer for all situations. I'll start by clarifying my goals:broad participation by students in the… Continue reading Handling Wrong Answers
On the first weekend of December, the California Math Council held its annual meeting in Asilomar for the 60th time. (I attended for the 33rd time, and presented roughly the same talk I had presented in 1984.) Over the decades, the "must-attend" presenters have changed. Two of my favorites back in the day were Harold… Continue reading Any Questions?
A PLC is a Professional Learning Community. In an ideal world, every math department is a PLC,but in reality there are some obstacles to that idea:not all schools give teachers time to dedicate to professional learningnot all teachers are interested in professional growthit is not clear what to do in a PLC, even if the… Continue reading Department as PLC
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
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
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
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!
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