Many teachers have shared with us their successes in implementing the 5 Practices for Orchestrating Productive Mathematics Discussions (Smith and Stein, 2018). Starting with Setting Goals and Selecting Tasks, and moving through Anticipating, Monitoring, Selecting, Sequencing, and Connecting, the 5 Practices provide concrete guidelines about
It’s fine to work on any problem, so long as it generates interesting mathematics along the way—even if you don’t solve it at the end of the day. —Andrew Wiles It seems intuitive that students who are genuinely engaged in a mathematical task will learn the mathematics
How do we give our students a present without telling them what it is before they open it? Often when we tell our students what they are going to learn at the beginning of the lesson, I feel that we are telling them what the present
Contrary to all advice educators receive about timely and high quality feedback, I have an alternate hypothesis. Most mistakes children make are the result not of a misconception they have about mathematics but instead the student has a totally coherent conception that is the result
Each fall teachers struggle with how to support parents who are helping their children with math homework. When conducting back-to-school meetings with parents, teachers typically summarize the math curriculum by course content. Sometimes, teachers will hand out a list of resources, study aids, and games
The Japanese Footbridge, by Claude Monet. Public domain, image obtained from Wikimedia Commons at https://commons.wikimedia.org/wiki/File:1920-22_Claude_Monet_The_Japanese_Footbridge_MOMA_NY_anagoria.JPG Modeling with Mathematics Claude Monet was one of the founders of the art movement known as Impressionism. Artwork prior to this period in the late 19th century was primarily representational or narrative;
Over the years I’ve had the chance to work with all sorts of clever mathematicians. Most of them were under age 11. They had great perspective, unique insight, and novel strategies. I only wish that I could always say the same about myself. There was Robert.
For fifteen years I taught in a district that stood firmly on the premise that all teachers were teachers of reading. As a middle school math teacher, I was also given a reading block each day. As is often the case in ELA, my students
I cannot remember a time when teachers were pleased with their school’s record of success with mathematics fluency. Individual teachers may have been pleased, but there was no system in place for school-wide success. Three of the major problems with mathematics fluency can be solved by
One important reason for studying mathematics is to nurture an aptitude for and a confidence in problem solving. To be good at problem solving, one must be able to sort through the unknown, make sense of it, persevere in it, and come away with a