Proportional thinking in my classroom

With my students, they are introduced to ratios, rates, and proportions. My favorite problem that I pose to them is about a car I bought.

Here is the prompt they would get for this problem. I was in the market to get a new car. After test driving several different cars, I decided on getting 2001 Buick Century. While driving around after I bought it, I noticed that the gas gauge stays at full until I have about a gallon of gas left and then it goes to empty. So, I went to my mechanic and asked him about it. He told me it would be around $500 to fix it. I did not want to spend the money to fix it so I came up with a solution. What did I do so I would not have to spend the money to fix it?

At this point, students are asked to brainstorm ideas on what to do. Some students say that they would just fix it, but I remind them that I don't want to spend the money. We talk about what information do you know and what type of information could you find out. We eventually get to the gas tank itself and we could find out the mileage that the car gets. So, I give them that I went 300 miles on 15 gallons of gas. I pose this question, how does this help us?

Students point out that we now know how many miles per gallon get. The students will point out that we can find how many gallons the tank is from the owner's manual which is 17 gallons. Then the students set up a proportion to find 340 miles. At this point, I ask the students what does that 340 miles mean. Some students see that this is how far you can go on a tank of gas, but many students still do not see what this information means.

After discussing this problem, we look at how the unit rate could change. I tell the students that I check it once a month and ask why? After discussing that it could change, we talk about what types of things could change the rate.

Many of these students really enjoy this problem. They like that you can come up with a solution to this without spending the money. Some of the students actually have come across this problem with a car they have already encountered. I like this problem for my students because they get to look at different concepts like unit rates and proportions. It's also an excellent real-life example that students may encounter or already have encountered.

Gradual Release

When we discussed Gradual Release in class on Wednesday, I had really only heard of it. It was one of those buzz words in education that I had heard and knew what it generally meant. Though I knew that it was about have students get more control of learning in the classroom, I did not know how the actually process worked. When looking at the handout of Gradual Release, I was actually quite suprised. It was basically the same process that I use in my classroom. When talking about most concepts in the classroom, I use a three step approach. Most of the concepts I cover in class are either concepts my students forgot or really did not learn or retention from school. Since they struggle with the concepts, I start talking about the concept either making connections or possibly looking at a problem in general. I will go though the concepts possibly with a sample problem or two. Then I do blur the second part between sharing and guiding the students. Depending on the concepts, I may model the concept. I may guide them through the problem using leading questions. If it is an important concept or a hard concept, I will using modeling first, then guiding them through the problem. Once I have done this, I give the students one or two problems or even an activity for students to do on their own or in groups. I will then walk around and see how students were doing and check their work. By walking around I get to check to see if there is any information that I forgot to explain or general confusion. It also allows me to work with individual students if they are struggling. I can teach them other methods that may work best for them. Overall, my students like this process because they get to see the concepts on the board, but get to try it on their own to see if they understand the problems. I like it because I get to know the students and where the strengths and weaknesses are in their learning.

My classroom situation

For the most part in my classes, I have been given plenty of resources to be successful. For my classes, the students have numerous resources that are available to them. The students have access to an online textbook, online lecture videos, study plans which tracks each individual student's progress, and different ways to get help on problems from their homework. For individual problems, the students have examples, a help me solve this feature, short videos, access to the section of the textbook, and direct e-mail with the instructor for help. As for instructor resources, there are not as many as for the students. All instructors are given access to a faculty guide. The faculty guide gives the instructors an idea of how they should structure the class. For some topics, instructors have submitted ideas or activities that can be used for the class. Mostly, the instructors are left to find things that work best for them. It gives you the freedom to teach things in ways that you want, but you have little ideas to be given. Also the instructors are not given much guidance. As a new instructor, you are not given a mentor instructor. You may be given a name of instructor who can help you, but it is left up to you to determine most things on your own. Most instructors do not get to interact with other instructors on a day to day basis. I occasionally see other instructors throughout the day, but do not get to have much interaction. We generally get to meet twice a quarter, once at the beginning of the quarter and once in the middle of the quarter. These meetings are recommended, but not required therefore not all of the faculty show up to these meetings. The biggest challenge I have in my classroom is with the students. Most of my students are motivated which is a big difference from when I worked with secondary students. My biggest problem is the level of my students. There is a big difference in the levels of my students. Some of my students need just a refresher in mathematics since they have not taken it in years, but some of my students struggle with the basic concepts of adding and subtracting whole numbers. With having these great differences, sometimes it is hard to keep the higher level students engaged while not losing the lower level students to confusion.