4 Grouping skills for mastery
When I was earning my teacher education degree, I took a class on planning and implementing a thematic unit. I loved preparing that unit because it excited me to see connections between the content we were teaching and applications to real life. Upon entering the "real life" of a teacher, I realized that the hours I had spent pouring into a unit might be better spent catching up on grading, making parent contacts or supporting the kids in their after school activities. I became distracted by the hundreds of other tasks that demanded my attention. In the tyranny of the urgent, I forgot the most important thing — creating and teaching quality lessons.
As I started to reconsider the idea of creating and implementing a thematic unit, I realized that I needed to be able to produce quality material. Fortunately, the first thematic unit I created was done during the summer when I was more relaxed and could focus on how and where to find information. I painfully became hung up on little things and had trouble focusing on the big idea. But after my initial struggle, I found a planning process that helped me stay focused on the skills and allowed me to creatively connect the mathematical objectives to real life problems in shorter gaps of time.
Planning a thematic unit
To begin my thematic planning, I start off with a brainstorming session. I generate a list of all the goals and objectives I want to teach within a segmented time. Then, I generate ideas about topics that would connect to these goals and objectives. For example, I decided to teach a pre-algebra unit on functions. The kids had relatively limited knowledge regarding functions and I wanted to show them how functions were used in every day life.
After listing my goals and objectives (finding the slope, y-intercept, determining the type of trend line, graphing scatter plots, etc.), I tried to think of some situations that they might face where a knowledge of functions would be useful. During my brainstorming time, I came up with a few different ideas. Using a current almanac, I found a listing of gas prices over the past few decades. On the Web, I found a couple of different cell phone plans that some of the kids wanted to buy, offering different monthly amounts due to the number of minutes used. I heard some of the kids talking about going to the movies and how the prices would change based on the number of tickets bought. With these ideas in mind, I tried to find a central theme that could tie these ideas together. I decided on the theme "A Day in the Life of a Teenager."
With the central theme in mind, I decided to teach each skill through its real life application. In this situation, I determined that graphing a scatter plot was the most basic skill and should therefore be taught first. Together, the students and I plotted the year and the average gas price for that year, as listed in the almanac. We drew a trend line through the data and discussed different types of trends. This also generated a conversation of some practical examples of data that would produce positive, negative and "no correlation" graphs.
Next, I determined that learning how to find the slope and y-intercept were crucial. We looked at the relationship between the number of movie tickets and the cost of all those tickets. As we plotted these points, we found that the rate of change between each point stayed the same, leading them to discover slope. In addition, we determined when we had bought 0 tickets, we had paid a fee of $0, leading them to the concept of the y-intercept.
To build on this knowledge of slope and the y-intercept, we moved to a more advanced application of these skills. Using a few different cell phone companies rates, we determined the cost of each plan at 100, 200, 300, etc. minutes of talk time while reinforcing the slope and y-intercept. Then we compared which plan was better based on different needs. I created two "customers" that were searching for the perfect cell phone plan to fit to each individual lifestyle. Not knowing which of the two customers I was going to be in the role play, they had to be ready to sell me the plan that best fit my individual needs. I was amazed at the understanding that my students displayed.
I teach students a wide range of students — from individuals that are re-taking pre-algebra, average students and students that are experiencing their first time in a regular mainstream classroom, due to behavioral or learning disability-type issues. Despite their backgrounds, my students bought into this theme because it was presented to them in a manner they viewed relevant to their own lives. They were motivated to figure out the answers.
Thinking outside the book
In my quest to create thematic units, I have found some non-traditional ways to group skills into units. When I planned my first thematic units, I tended to group skills in the same manner that textbooks usually follow. For example, skills that show number sense can often be grouped together. However, the longer I have explored and practiced the idea of thematic planning, the more dissatisfied I have become with the traditional grouping of skills. In fact, I have taken all the skills involving fractions (comparing fractions, adding/subtracting fractions, multiplying/dividing fractions, and so on) and put them into different units throughout the year. Then, I added the skills involving decimals (comparing decimals, adding/subtracting decimals, multiplying/dividing decimals, and so on) and matched them up with the fractions skills, combining the skills around the operation instead of the topic "fractions" or "decimals." I followed this same procedure with all the basic skills necessary for advancement to the next course. I have found that the kids tend to remember the rules for using these skills better when they are practiced frequently and consistently through the year. I don’t usually hear, "When did we do the unit on fractions?" or "We haven’t studied decimals since the beginning of the year!"
This type of "circular" curriculum, in which many skills are taught throughout the year, has several benefits:
- It helps students who transfer in and out of the schools. These students haven’t missed out on an entire concept (or chapter) since a portion of each of the concepts is taught through each unit.
- It becomes easier to plan and teach units that correspond with the other curriculum areas whether core or elective. Being able to connect the mathematical experience to an experience in another class or outside of school enhances student learning and motivation. It has also been my experience that thematic planning promotes positive teacher collaboration with those in other subject areas.
- We don’t have the "end of the year rush" to cover skills that haven’t been taught yet. The end of the year can be spent on deepening knowledge of the content areas and practicing the reasoning skills needed to solve problems effectively.
- I can more easily plan units that hold the kids’ attention and relate directly to their interests. Even though it takes the kids about a month to get used to this method of grouping skills, they tend to prefer it by the year’s end.
As this year has wrapped up, I’ve asked some of my students what they think about the way I present math. Some of my favorite comments have been, "You always show us how we can use it." "It seems like we were reviewing all year long." And for my loyal students who come back to visit, the first question out of their mouths is, "What unit are you on?"