When the Stars Align

con·ver·gence /kənˈvɜrdʒəns/ [kuhn-vur-juhns] noun 1. Also called: convergency the act, degree, or a point of converging 2. concurrence of opinions, results, etc

Yesterday, it was as though the stars aligned and things I have been working on for over twenty years converged and crystallized in my mind.

Years ago when my children were young, I was the public speaking leader for their 4-H club. I taught 4-Hers how to write and deliver interesting and engaging speeches. They learned how to hook the audience by peaking their curiosity, deliver the bulk of the message in the body of the speech, and end in a clever way, usually leaving the audience wanting more.

When I returned to the classroom, I knew the essential elements of a speech also applied to a math lesson. I had to find ways to intrigue my students, engage them in the lesson, and then sum things up at the end. However, I don't believe I have ever seen this done in a more deliberate and creative way than I did while listening to Dan Meyer present on real-world problem solving yesterday.

During our time together, Meyer led us through his version of the "Three Acts" of a math class. He equated these acts to the scenes of a movie. In "Act One" Meyer uses a visual, either picture or video, to peak the students' curiosity. He relates a short story to draw his audience in and with as few words as possible he sets the hook. He lures the students into wanting to know something mathematical.

According to Meyer there are several important aspects of this opening act. The first thing is allowing students to pose all sorts of questions based upon the visual presented. As all the questions are posted, the teacher should ask for a show of hands about other people who had the same question. This is one of the methods Meyer believes helps reluctant students buy-in to the process. After all questions have been posed, each question is addressed by the teacher and then eliminated until one remains. This is the problem that the class will solve.

Another important feature of "Act One", is having students estimate what they think the answer might be. Meyer also requires students to write down a guess they know is too low to be the correct answer and one that is too high to be the correct answer, thereby establishing a range within which a reasonable answer would be found. According to Meyer, "Everyone can hazard a guess, and it only costs you about 7 seconds of class time. This is one way to engage some of your more reluctant math students."

In "Act Two", the teacher asks students to help solve the problem but does not initially supply all the needed information. The participants determine what information they might need in the form of a list and then the teacher addresses each item on the list and supplies only enough information, in a visual format, so the problem can be attacked. The teacher then acts as a facilitator, or guide on the side, as students do the bulk of the work on solving the problem. At no time during "Act Two", does the teacher dictate a strategy that students must use to find their solution. The teacher merely circulates, asks questions about the work, redirects students as necessary, and takes notes on different strategies.

During "Act Three", Meyer believes teachers should ask students to check the reasonableness of their answer; does it fit within the range of numbers that were chosen in act one? The remainder of this act involves leading a summary discussion of the different strategies that were used by various groups of students. The teacher can also use this time to formalize the mathematics. Meyer noted another way to engage students during the summary discussion is to assign them a task at the beginning of the discussion. He asks students to think about which group was the "laziest" and used the most efficient method to solve the problem. At the end of the act, Meyer again returns to a visual method to show the correct answer. He also suggests acknowledging the student with the closest original guess, thereby letting the class know that estimating at the beginning of the lesson was not busy work.

I look at this "Three Act" script as a perfect opportunity for math teachers of all age groups to address most or all of the common core practice standards. It might also lead to students who are more engaged in math and see its usefulness.

In My Spare Time

ar·cane /ɑrˈkeɪn/ –adjective known or understood by very few; mysterious; secret; obscure; esoteric

So....in my spare time, I'm a math teacher... but I really love to write. The right side of my brain has, since childhood, been pretty highly developed. As I child, I was much more adept at creative endeavors than in those scientific. I was a lover of school and all things bookish and I excelled in the areas of language arts and reading. Now don't get me wrong, I was a good student in the areas of math and science too but mostly because I tried really hard; in part due to the fact I did not want to be in trouble. (More later on the parenting style that reminded you on the way out the door...."if you get in trouble at school you will be in twice as much trouble when you get home").

One might think that this love of writing would have led to my choice of careers. Maybe if I had been more courageous in my younger years, I would have worked at being a writer. However, I was really fond of eating and having a roof over my head, and as I mentioned before I had always loved school; so I followed in the family footsteps and got a teaching degree. Then when I graduated from college, every job I was offered was in the area of math. First, I taught math to inmates at a maximum security prison, then to: fifth and sixth graders, adults through a continuing education program at the local community college, seventh and eighth graders, and finally teachers.

I think there is a reason math wasn't my favorite subject while in school and that reason is also the reason I LOVE teaching math today. During my academic career I was taught a lot of arcane procedures, which in most cases, I was able to memorize. However, some of what I memorized never made sense to me, and knowing my capacity for memorization was nearing its limits, I only took as much math as was required. I don't remember ever getting to explore in math class, discovering why the rules and procedures for math really worked.

So as my teaching career progressed, I moved away from teaching the way I had been taught (those arcane procedures) to other methods that built understanding. That meant that I had to study and discover many of the things that had baffled me as a student. As I grew in my understanding of mathematics, I have tried to lead others in developing their conceptual understanding of math as well. I won't lie to you, it is a real high when you see the light bulb come on for someone; whether they are in a first grade classroom or the teacher in a math workshop. So, in my spare time, when I'm not blogging, I'm a math teacher.....