## Teaching Strategies

## Strategy #1 - Do it by Themselves

I have found that students retain information better if they do it themselves. Teachers can still provide guidance, and help, but the students who discover a new concept on their own remember it much better, than those who were told. In order for students to figure something out for themselves, they have to make connections with what they already know (constructivism). As students learn to make connections between different ideas, and concepts it becomes easier to tie the learning together.

In addition, students get tired of hearing my voice, and I get tired of talking. Using this strategy puts the students in charge for a while. They become responsible for their own learning, and are therefore more interested, more engaged in the process.

I try to use this teaching strategy as often as possible. I still use it less than I would like. As important as it is for students to develop concepts on their own, it also takes more time. I am still working on balancing time constraints and having students 'do the work.'

The students are often frustrated and complain that I am 'not teaching them' when I use this strategy. Generally, their complaints fade when they realize they did not need me to tell them the answer. The first time I consciously used this teaching strategy, was with graphing and recognizing different functions. (This lesson plan is included in the Lesson Plans section of the portfolio.) In this lesson, students had to graph different functions; constant, linear, quadratic, cubic, and absolute value, and then find the pattern that made them all similar. You can see samples of student work here.

I also employed this strategy for investigating parallel lines. Students graphed different pairs of lines, and then compared both the lines and the functions. By the end of the lesson, students had noticed that all of the pairs of lines were parallel, and that they all had the same slope. This lesson took place on February 23rd and still today students will tell me that parallel lines have the same slope.

## Strategy #2 - Small Group Work

My students love to talk. They can talk for hours without letting up. They can talk to the same person for hours without letting up. I can not believe that they have that much to say to each other all day, everyday.

I finally gave up the battle of getting them to be quiet. Instead I turned the classroom learning situation into one where it was OK, even beneficial to talk to each other. I put them in groups.

I was smart enough to let my high schoolers choose their own groups. This way the groups got along and could work together. I did not have to deal with accidentally placing 'worst enemies' in the same group. The students also naturally differentiated themselves for the most part. The hard working students chose to work with other hard working students, and that left the lazier students stuck with each other. I wound up with a class of students who were all doing work, whether by choice, or neccessity.

Of course groups would get distracted with the latest gossip or rumors going around, but that was why I was there. I could gently steer them back to the mathematical topic at hand.

I also quickly discovered that my students learned a lot more from each other than they did from me. They understand each other, and their explanations ten times better than they do mine.

I typically use groups when they have to 'learn something themselves.' If the students are in groups they don't feel quite so lost. They have their group members to help them figure out what to do and why it is important. I also use groups as a way to review. Each group must make a poster solving and explaining a problem. The posters are then passed around the room so the groups can learn from each other.

## Strategy #3 - Multiple Methods

Not all students learn the same way. Some students need to hear information, others need to read it, others need to move to understand something. However, all students need to reinforce what they have learned.

One way I accommodate different learning styles is by teaching using multiple methods. The different methods reach different students, while at the same time reinforcing what we have learned before. It also gives the students an opportunity to find a method they are comfortable with.

Two situations immediately spring to mind when I think of using multiple methods.

The first is polynomial multiplication. We spent a lot of time with this concept in my Algebra I class. We first approached it by using algebra tiles. This reached the tactile learners, while also giving the rest of the students a pictorial understanding of polynomial multiplication. We also used graph paper to draw algebra tiles. We then went on to talk about FOIL. First. Outer. Inner. Last. This method, for multiplying binomials, worked great for students who learned by hearing, and reading. Finally, we also used the box method to multiple polynomials. This method connected well to the algebra tiles. Both methods used a grid to make the answer.

At the end of the polynomial multiplication unit, students had multiple methods to choose from. All of the students understood and could use, at least one of the methods.

I also used multiple methods when learning how to solve quadratic equations.

We started out with graphing. Graphing was something my students were very comfortable with and confident they knew how to do. Students could look at a graph and determine where it crossed the x-axis to solve the quadratic equation.

Next we moved on to factoring. Factoring had been taught before (again using multiple methods) so they were familiar with the concept. Since students knew how to factor quadratics, all we had to do was discuss how to solve a factored equation.

Next we started with completing the square. This was an entirely new concept for the students and did not work quite as well as I had hoped. It did, for some reason, resonate with some of my students, and even now they use completing the square to solve quadratic equations.

Finally, we learned how to use the quadratic formula. Since students were already familiar with substitution and simplification, many of them liked using the quadratic formula. In fact, the most frequent comment I heard from students about the quadratic formula was, "Its not hard, but it takes a long time."

Again, by the end of the unit, students had a solving quadratics arsenal to choose from.

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