“Stand up if you have a cell phone with you today,” I announced last Wednesday in my algebra class. The excitement was visible. “Sit down if your phone does not have a camera,” I continued. Their disappointment was manifested in groans of various pitches and duration. I quickly paired them up – over half the class had phones with cameras – and sent them on their way. Their mission: to find as many examples of circles and take pictures of each one. They had ten minutes to complete the job, and they were not to disturb other classes.
“I got 56 pictures Mrs. Stahlhut!” one student exclaimed as he returned to class. “Well I got a picture of Serniak’s watch!” countered another. The class shared their findings for approximately five minutes with an amazing zealousness. While they were taking photos, I had set out examples of circular objects (more than ten items) I had gathered from my kitchen that morning. I also handed out a piece of string and a CSAP ruler (they are paper and therefore bend) on each desk. Students were in a circle (pun intended), and they were told to make a table of measurements, in millimeters, of the diameter and the circumference of each circular item. They passed the item to the right when they had finished measuring. They eagerly explained to each other what a millimeter was and helped each other find the circumference by holding the string around some of the objects. Another ten minutes passed.
Equipped with a table of values, our discussion progressed to which value depended on which value. “Does the length of the circumference depend on the length of the diameter, or does the length of the diameter depend on the length of the circumference?” I questioned. They agreed upon the first choice. “Therefore,” I explained, “the vertical axis should be labeled circumference, and the horizontal axis should be labeled diameter.” They drew their axes and plotted their points.
“Who knows what ‘a line of best fit’ is?” I asked and waited. No response. “OK, it has to pass through at least two points and the remaining points should be equally distributed above the line and below the line. Use your ruler to make the line straight!” I clarified. After they drew their line of best fit I went on to talk about the slope of a line. When we looked at everyone’s slope, it was easy to see if they had made a mistake. Most had a slope near 3.14 (pi). We then used this to write an equation (C = 3.14 D where C=length of circumference and D=length of diameter) and make predictions about other circles.
When class was over, I thought about what was important. Did they understand slope? Did they understand ‘line of best fit’? No, not fully. But I had hooked them by using the cell phones and a concrete example of linear data. What surprised me was the fact that this was my all male class. When my all female class began, the very next period, I was asked “Do we get to use our cell phones in class today?” I was not expecting this activity to be something that both genders would get excited about, but it was!
The next day we did squares. We took pictures, and collected data by drawing and measuring five different squares and their diagonals on graph paper. The equation we came up with was D = 1.41 S where D=length of the diagonal and S=length of the side. Again we talked of slope and lines of best fit.
Next, we will be using the cell phone as a stop watch. Each pair of students will be given a short and a long tongue twister. They will collect data by timing each other saying the tongue twister once, twice, three times, etc. They will plot the data (both lines on the same set of axes) and calculate the slope of both lines. Also, they will write the equation for each line and use the equation to make predictions.
My plan is to follow up with a discussion about y-intercepts. All the examples thus far have passed through the origin. To create an example where the y-intercept is not zero, I plan to find an advertisement about the price of CDs and DVDs. I will tell them they have been given $50 as a birthday present, and they must spend it all on CDs and DVDs. The question is how many of each can they purchase? After exploring this question, we will follow up with linear inequalities, where the solution is the half-plane of points above or below the line.
As a seasoned mathematics teacher, I recognize none of these activities are new. What is new is the fact that I am using these activities. Also, the fact that I am willing to post this on a blog is new. I am the shy introvert who usually prefers to journal my reflections instead of putting them out to the “flat” world. Well, I have now emerged from my cocoon and spread my wings, thanks to encouragement from my colleagues.
Update 11-2-06: I had a request to explain my reference to the all male class and the all female class, so here goes…
Arapahoe High School began offering single-gender classes in swimming, personal survival (health class), and algebra during second semester of the 2003-2004 school year. They were in addition to co-ed classes; they did not replace co-ed classes. The teachers who taught the single-gender classes, administrators, and other interested staff met monthly to share their observations. They also discussed research pertaining to gender-specific education. Students were surveyed about their experience in a single-gender class, and it was favorable. Likewise, the teachers enjoyed the experience although at times found it challenging.
Language Arts, Science, and Social Studies began offering single-gender sections in addition to co-ed sections during the 2004-2005 school year. We have expanded our offerings each year. Students (and their parents) choose whether they want to be in a single-gender section, although we do end up asking some additional students to sign up to "fill" the sections. For the most part, the response has been favorable (hence the expanded offerings each year), but it's still a small portion of our classes (for example, we have 16 sections of co-ed Algebra, 1 male section, 1 female section). Our students have a fair amount of choice in their schedules and this gives them one more option. Teachers, administrators, and interested parents continue to meet regularly and have many discussions about what has worked and what hasn’t in the single-gender classes. They also share their opinions on published articles about single-gender education.
One of our goals this year is to gather data to support our decision to offer single-gender classes. Professor Susan Harter from the University of Denver (DU) and doctoral candidate Shauna Riecks are going to pretest and posttest our classes in an attempt to measure the academic success and affective attitude of our students. We also have implemented the Measure of Academic Progress (MAP testing) for freshmen and sophomores in reading and mathematics. This will facilitate gathering documentation of what we already believe to be true: single-gender classes provide the opportunity for some students to be more successful than in co-ed classes.