Question:

I really have the desire to turn my classroom into a hands-on, activities-based classroom, but am still struggling with how to cover it all. I guess I am still not sure how to “get away” from the “drill-and-practice” method. I was curious as to how much homework you assign (on average) and whether or not it was from a textbook or more activity-type problems. I was wondering if you would be able to give me a sort of play-by-play of some of the topics you teach. For example, Graphing Linear Equations. What do you do from day to day and do you ever use the textbook and the traditional problems therein?
Rachel Rosales (Owensboro, KY)

Answer:

In Textbook Free: Kicking the Habit, I give a very detailed synopsis of a textbook-free lesson. My math department at Great Oak High School is known for not following the textbook. We still have students read and do problem sets from the book, but our lessons are not bound to it’s pages. I have been teaching like this for over ten years now, and it has been a wonderfully liberating experience for me, and a productive experience for my students. In short, I can share with you the following.

First off, change your focus. American teachers believe that a day in the classroom revolves around the homework assignment rather than around the lesson. Plan a lesson by asking, “What is the main concept that the students need to understand?” This is different from the tradition of asking, “What do they need to know to get through this problem set tonight?” Then find/create a few problems that address the misunderstanding that students have of that concept. The purpose of the lesson should be to get students to understand what they are doing and not just mimic what you are doing.

Regarding assignments though, I consider “homework” assignments different than “project” assignments. Projects are done about once a week in class, for which the students may go home needing to complete or expand upon. Homework is assigned about 2-3 times a week (never on the weekends), and is usually a handful of questions that expand upon the ideas addressed in class. I usually save the practice/drill problems for the warm-ups the following day (these are also few in number). In my lower level classes, I never assign homework. My school district’s final exam results show that my students are not hindered by sparing them the grief of the drill and kill routine. In fact, my school is our district leader in high school state math scores, and we give the least amount of homework.

In regards to Graphing Linear Equations: I want my students to understand the idea of rate (slope), initial value (y-intercept), what a linear relationship is and how to interept the graph of a linear equation. An example of how I might teach this concept is described below: I usually start with discussing the idea of rate. The lesson centers around the Tic-Tac question:

The following equation represents the relationship of the number of Tic-Tacs eaten, t, to the number of kisses received, k, on a date: k = 2t + 1.

The students are required to describe in writing what the equation says about the scenario. (e.g. “You receive two kisses for every one Tic-Tac you eat, plus you get a guaranteed kiss on the door step at the end of the date.”) They are also required to show a table of values and graph of the scenario. Their homework is to take a new table of values and write an equation and graph relating to the table. Then I take them through Jennifer Sawyer’s “Rising Water” project which has the students generate a variety of linear situations and then compare their equations and graphs to reveal the role of the slope and y-intercept. I follow this up with the “Speeding Ticket Investigation” to reinforce graphing. At this point, we take notes. I usually provide a graphing organizer and take a few days to formalize procedures like writing an equation given slope and a point, given two points, writing equations from graphs, etc. I use the lapboards quite a bit here. I finish with the “Jogging Hare,” by going through the lesson as a class with one set of numbers, then the next day giving the same problem with a new set of values as an assessment. (They may use their notes from the previous run through).  If you teach line of best fit, then I would go one step further with “Cool Shoes.” This usually takes about three weeks, and then I generally spend a couple of days reviewing before the test. (4 weeks total).

Chris Shore, Editor