Michael Strange | Teaching Portfolio

Instruction and Delivery

Meaningful Learning Experience

One of the questions I have heard the most in my student teaching is "when are we going to use this in real life?" Telling them that this is, in fact, their real life doesn't seem to work. What they are trying to ask is "how is this relevent to my life?" I think that question is what I'm trying to answer with most of my lessons. I had a wonderful opportunity, and took advantage of it, when we began to cover systems of linear equations. I don't think any other topic in Algebra I is more applicable to "real" life than systems, so I wrote up a group project for the students to see how to apply what they are learning to solve a real world problem.

Linear Systems Group Project

In this project the students were to choose between two scenarios:

Comparing two cell phone plans based on the monthly cost and the cost per text messaging.

Comparing two new cars based on the purchase price and the cost to drive it every month which is dependent upon the gas mileage and price of fuel.

The students were group in heterogeneous groups and had to assign roles to each group member. The roles were Data Chief, Head Architect, Master Analyst, and Lead Designer. Each member had a task--Data Chief had to research and collect the data, the Head Architect used the data to build a system of linear equations, the Master Analyst solved the the system, and the Lead Designer was responsible for putting together the final presentation and finished product.

I structured the instructions for each piece as a memo to each member within the team and gave the memos out as the previous piece of the project was completed. (I've only included the memos for the car project)

Memo to the Data Chief

Memo to the Head Architect

Memo to the Master Analyst

Memo to the Lead Designer

To complete the project the students had to make a decision on the chosen scenario based on their own work and then explain why.

Although there were some hiccups along the way, for instance group members not completing their tasks on time and lack of communication between the team, I think the project was a success. The learning experience was layered. The first layer was the application of linear systems to a life problem. The majority of the students seemed excited about the project and even added onto the scenario (i.e. choosing cars they found more interesting than the ones selected in the project). The second layer was working on a team. Each member had to rely on another to complete their portion. This handoff of responsibility seemed new to them and provided an excellent opportunity to teach how a team can function and succeed or flounder and fail. Lastly, the students got to experience how the corporate world works. The use of memos designated to a particular team member mimics those that I personally have worked with in previous careers. So even though this project was an exercise in applying mathematics, it offered several life lessons.

In the future I hope to build more elaborate projects that incorporate more than a single topic from the curriculum. What I envision is a semester long project where the pieces of it can't be completed until we have mastered a given unit.

Questioning Strategies

There are two areas that I have tried to develop sound questioning strategies--during class instruction and in a formal assessment (quiz/test).

During class instruction I try to use a variety of questioning techniques. For routine arithmetic and basic algebraic operations which the students should all be familiar with I tend towards chorus responses. I try not to do any mathematical operation on my own but rather rely on student responses even if it requires a wait. I have read that chorus response aren't not preferable but I have found that by using it during simple operations it creates an atmosphere where the students become used to responding to questions so that when we move to more recent material and I begin calling on students directly, the students are more comfortable speaking out even if they are guessing. I use directly calling on students for two reasons. One is as an informal assessment of understanding. In each class there are a handful of students that I use as a barometer of general understanding. These are mid to lower achieving students and by their responses I am able to judge whether the class is ready for more independent work or they need further instruction, perhaps in a different style. I also use direct questioning to bring in kids who have drifted off and are either talking or just not paying attention in general. With these students I tend not to make them answer the question but rather I call on them, wait a few seconds while they fumble with trying to figure out what was asked, and then call on a student that was paying attention. I vary this as well and will sometimes call on students in the direct vicinity of a student not paying attention. This method seems to work quite well and I feel that I have a decent amount of student engagement during questioning.

For a formal assessment I have tried a few different things. In the beginning I used Exam View which is a test generator provided by the school. It has some strengths but it also lacks flexibility. For instance, certain questions cannot be "recalculated" to provide numbers that I would feel are more appropriate. The formatting of the tests is also limited. I have trouble creating a test where there is proper spacing between the questions. The biggest problem for me, though, is control. When creating a quiz or exam I have in mind exactly what I want to assess. The only way to assure that the students are tested on what I want to test them on is to write the questions myself so that I can eliminate any superfluous material. Doing so is time consuming but I have found a piece of software that allows the flexibility of creating my own questions while it takes care of the formatting thus greatly reducing the time it would take to create an assessment.

Expanding a bit on the type of questions I have written for assessments, I don't believe in "tricking" the students. I write questions that are similar in nature to those they have seen in class and in their homework assignments. I try to write fair questions. For instance, many of the students have trouble with negative numbers and with fractions so I make sure that not all of the questions contain negative number and fractions if the test is on solving linear systems. But, I do include some questions of that nature because they are expected to be able to work with them. The point is that I don't want to punish a student for what they don't know, but rather to reward them for what they do know. That brings me to another point which is partial credit. Unlike most of the other teachers in the department I do award partial credit. Again, I believe this is the fairest scenario for the student. If the question is to solve a system using substitution and they perform the procedure correctly but drop a negative sign along the way I don't believe that the student should not receive any credit for that. A minor deduction and move on. For all of the non-multiple choice tests I have given I have developed a rubric to guide me in awarding partial credit and I plan on continuing to do so.

Technology

I enjoy technology and understand it's impact on education. From graphing calculators to sophisticated mathematical software, technology expands the playing field of mathematics education and in doing so expands the accessibility of the curriculum.

As an example of how I use technology in the classroom is an exploration of exponential functions which I wrote using Mathematica. Originally designed as a student lab experience, due to time constraints we had to use the application as class presentation which diminished its effectiveness. I believe that in order for technology to be effective it has to be placed in the students hands.

The lab I wrote allows the students to use sliders to change the two parameters of the exponential function. They immediately see the change in the graph and are able to investigate when the graph (and function) changes from growth to decay and what effect negative numbers have on the graph. Here is a screenshot of the application (PDF) along with the actual working application (Mathematica Notebook). The application requires Mathematica Player to view which is available here.

I intend to use Mathematica to a great extent in my classroom. I plan to develop several labs over the summer in preparation for next Fall.