Michael Strange | Teaching Portfolio

Teaching Preparation

Learning Experience

I opened the very first lesson that I gave during my student teaching with a discussion of what mathematicians actually do. The students who responded to the question "what do mathematicians do?" all thought that they sat around solving equations. I explained that math is actually a science and professional mathematicians perform research in the attempt to make discoveries. So I told the class that we were to be mathematicians and search for our own discoveries. This was met with skeptical comments and rolling eyes. But I was not perturbed.

It is my belief that children are curious by nature and if we can harness that curiosity then we can guide them to discoveries that they need to learn. Whether this is by demonstrating a hole in their knowledge, using a novel situational problem, or challenging them, we can set them up to begin to ask questions and hopefully see what is coming next.

As an example I will use a lesson I did on parallel and perpendicular lines (relevant section highlighted). In this lesson I began by asking the students what parallel lines were. Many of them said "lines that don't intersect". I then asked if there was a way we could tell if lines were parallel using what algebra we knew. Silence. So I drew parallel lines according to their definition and added a coordinate plane. Quickly they responded with "ahhh...they have the same slope." They had discovered the algebraic definition of parallel lines with just a touch of guidance.

What was most interesting about this lesson was happened after the discovery. While working with the the slopes a few students began to question what would happen if.... I was simply ecstatic. They began to ask the fundamental question to inquiry based instruction....what if. Since that first lesson I have encouraged them to ask hypothetical and it has had mixed results. Sometimes they go down false roads and sometimes they figure out what is coming next. In either case I always encourage their questions and then help them figure out which path is valid. Even with incorrect hypotheses we take a minute or two to investigate and see what happens. I think that through this process they internalize a deeper understanding of what is being taught and why it is the truth.

Lesson Design

While designing a lesson I try to focus on student activity with as little lecture as possible. If I write out a lesson and see that I'm talking for more than twenty minutes I know that the plan may need a rewrite. One thing that I've learned is to break the lesson into pieces. For instance, in the lesson on parallel lines I broke the lesson into two parts to limit the amount of information being covered and to offer the students practice and investigation on one thing at a time. Not only does this reduce the amount of time that I'm talking in a given shot, but offers a break in the lesson so the students don't become turned off.

I also try to vary the type of independent work from day to day. One day we may have small group work to turn in and the next will be pairs working on individual assignments for grades. Occasionally, particularly when the students are struggling with a topic, we have true independent practice which allows me to offer one on one instruction. I have also tried to incorporate "games" and competitions into lessons when appropriate. One game that I've found quite effective is to break the class into three or four large groups and then have a member of each group go to the board to compete against the other groups solving a problem. While they are solving at the board the other group members work the same problem and offer coaching from their desks. The first group to finish gets two points and any group with a correct answer gets one. At the end of the class I collect all of the work as an assessment. The results have been very good. The competitive nature of the game creates a motivation for the students at their desks to not only solve the given problem but also to see where their partner at the board has gone right or wrong. I think the real learning is going on when the students are at their desks and that is the reason for the assessment being over their individual work and not on the board work.