Learning from Mr. Ahern

I so much enjoyed observing Mr. Ahern’s class.  One thing that stood out to me was the way Mr. Ahern was able to gently guide students towards understanding a math concept without actually telling them how to do it: he facilitated students discovering it on their own.  It was amazing to watch.  One of the biggest “ah-ha” moments I had while watching was the way he used the students’ own interest and ideas to create math problems for his lesson.  It was so engaging! Almost all of the students in the class were raising their hands to participate, which meant a much higher likelihood of students understanding these new concepts.  Let me give you some examples:

• Purposing the lesson. Mr. Ahern was teaching a lesson on adding and subtracting negative numbers.  The first thing he did in the lesson was put up the Essential Question for the day and ask students to consider it.
   I didn’t get the EQ written down, but the discussion about it framed the lesson and got kids thinking about what they were going to be learning that day.
• Guiding discovery. This one is hard to explain because there seemed to be so many subtle steps involved, but I’m going to try because I think it’s really valuable.  Mr. Ahern had clearly picked the problems he was going to review ahead of time.  He picked problems that would lead students to their own conclusion about how adding and subtracting negative numbers works.  So each time a student would answer a problem correctly, he would say something like “So, you’re saying that (insert mathematical principle here),” and imply that the student came up with the idea.  The problem is that my explanation isn’t doing it justice at all, because the students actually were generating the knowledge and stumbling onto discoveries just because of the sequence of questions Mr. Ahern chose.
• Scaffolding. Mr. Ahern reviewed some problems from the homework assignment.  As he was talking about adding and subtracting negative numbers he used multiple visuals.  He had a SmartNotebook document that had images so that students could essentially count-out the problems, he also had an image of a number line to visually represent moving in positive or negative directions.
• Real-world examples.  Sometimes the students would get confused.  One question was: “What is -3 - 1?”  When a student answered “2,” Mr. Ahern said, “Ok, let’s think about this.  If you borrow $3 from me for lunch money today, and you borrow another $1 from me tomorrow, how much do you owe me?”  The student had no problem coming up with $4, and this helped her cement the concept.  Mr. Ahern threw in these real-world examples all the time.

Making learning personal. After scaffolding the students through a couple of problems, Mr. Ahern asked “Ok! Who has a problem for me?”  The students got such a kick out of writing their own math problems.  Mr. Ahern then invited the students to solve the problems they wrote in front of the class with support and encouragement from him as they talked through it.