My preferred approach to teaching high school math -- the last twenty minutes

[Dictated to my phone so beware of homonyms]

Note: Though the connection may not be immediately obvious, the following thoughts on teaching will eventually tie in with a larger piece on George Pólya.

Though it varied someone from class to class and situation to situation, my preferred method was to reserve the last part of the class for students to work individually while I went around the room and checked each student's work. Generally, I would give the students a couple of worksheets to be handed in at the end of class. After completing those worksheets, they were instructed to spend the rest of the hour working on their homework. I wasn't always able to get to every student every day, but I came close, and I never let more than a couple of days go by without making sure that I had personally observed a student doing problems in my class.

If a lots of the students were having trouble doing the assignment, I would sometimes interrupt the routine, go back up to the board, and reteach some of the material. That was fairly rare. Most of the time, two or three students would need real help and the rest only needed either a couple of quick suggestions or simply confirmation that they were doing the problems correctly.

The personal help was important, as was the knowledge on the students' part that if they needed help in the future I would be there. This approach also let me make sure that neither the class or any of the students got into a death spiral where confusion and failure started causing a cascading effect. By personally watching students successfully completing assigned problems, I could make sure that everyone was keeping up. Grading was also an important part of that process but for assessment there is no substitute for actually watching how a kid going through a problem.

In some cases, particularly with advanced classes, I might stray from this approach, but if we are talking about at-risk kids in tough environments who need to make up ground academically, I believed then and believed now this is the best way to teach high school math.

If I sound a little over emphatic with that last sentence and perhaps even a little bitter it's because I am more than a little bitter about the direction our schools have headed. I enjoyed that kind of teaching and I got excellent results with it, but if I were to go back into the profession now, there is almost no way I could give that kind of personal attention nor could I take the same level of accountability for students' success. Class sizes have simply gotten too large.

On a completely unrelated note...

Detroit Public Schools EM shifts funds from classroom
By Dr. Thomas C. Pedroni

Many of us are shocked to learn that DPS plans to cut costs in the coming year by further increasing class sizes. Already at an unmanageable target of 38 per classroom in grades 6 through 12, Emergency Manager Jack Martin’s fiscal year 2015 budget allows class sizes in those grades to expand to 43.