Two weeks ago I had my last week at St. Agnes, and I was sad to leave. Despite some frustrations I had with the adults, the students were almost always gracious, thoughtful, and excited to have me in their classroom. That’s a really great combination to have as a teacher, and I savored it all. In my last week at St. Agnes, I continued to work with 10th-standard students on their statistics, and 9th-standard students on areas and perimeters of circles, arc lengths, and area of sectors.
The 10th-standard students continued to be a real delight in terms of their excitement, though they did get a bit carried away at times and it was certainly more difficult to focus their attention. I think part of it was the subject matter this week. Because they do so much of their math work by hand, they learn a lot of shortcuts and ‘tricks’ that students in the U.S. and other parts of the world rarely come across. So this week, we spent a lot of time on building skills that will help students compute complicated averages more quickly . That meant mostly drilling the students in finding means of random numbers until they got the skill down, and then moving onto word problems that gave them opportunities to show off that new knowledge. Because this was my first time teaching this particular method, I couldn’t come up with any interesting or exciting ways to teach it, so it became mostly about rote memorization and lots of practice. Then again, that’s often the best way to learn a skill, even if it is kind of boring for both student and teacher.
My big project of the week was a lesson for the 9th-standard students on area and perimeter. St. Agnes has a big basketball court in the middle of their school, which rarely gets used for basketball. During recess time, it does get used for a game that resembles an odd mix of soccer, cricket, and dodgeball- no student has been able to explain, or even agree on, the rules, so it’s hard for me to give a real picture of what’s going on. In any case, I was thinking about a project I could do with the students and realized I could have them take measurements and find the area of the school’s basketball court. All of the geometric shapes were basically circles, rectangles, and triangles, so I knew the students had all the necessary math tools to take on the project. I was particularly curious to see if the students would be able to find those shapes on their own, and recognize that some of the more complicated shapes could be found by subtracting the area of a circle from the rectangle surrounding it. I thought it would be a great method to test their knowledge and let them use it in a new way. I centered the 2-day lesson on a hypothetical situation in which the school decided to re-paint the court, but needed help figuring out how much paint to buy. On day 1, I planned to explain the project and answer questions before breaking students into groups and have them take measurements of the court. Day 2 was for students to discuss the problem and find the answer. Both class periods were 45-minutes, so I knew it was a bit ambitious, but I was confident in the students’ skills.
After I passed out the worksheets and divided the students into groups, I gave each team a meter-length of string and had them go down to the court to take the measurements. When we arrived at the court, a few students got cracking right away, but most groups were standing around utterly clueless. A few were completely distressed, and ran to me with questions immediately. Taking a page from my former cooperating teacher in California, I informed my students that they would have to work with each other and talk through their ideas for 5 minutes before anyone could approach me with questions. After they knew I wouldn’t be answering questions, they started talking to each other (imagine!) and trying out their ideas. Before long, almost every group was on the right path and didn’t need to come to me for help. It was a great reminder to me (and one I later shared with them) that they already have lots of skills and resources among their groups, and they don’t need to ask their teachers for guidance on everything. My favorite time in the classroom is always when I can step back and simply observe while students are working with each other. That often gives me the perspective I need to praise strong group or individual work while identifying who might need more support.
Despite their good start, the students still struggled to convert their skills to the task at hand. Instead of simply measuring the diameter of the center-circle and using that measurement to determine the perimeter, students were desperately trying to place their strings along the circle’s boundary. Some never realized that the area of their section could be found by determining the area of a smaller shape within their boundaries, and subtracting it from the larger shape around it. I think part of the problem was in the number of new experiences they were dealing with. Students are rarely asked to work in groups, and these students commented that they had never done “a project like this before”, meaning they hadn’t had a multi-day project that involved numerous steps and lots of lateral thinking.
The students definitely struggled, but I don’t think it was in a bad way, and they all seemed to enjoy the challenge. I had to do more leading than I normally like to do in group projects, but they still demonstrated some good mathematical thinking. One student realized that his group didn’t have to line their string up with the circle in order to calculate the perimeter; they could simply find the diameter and calculate the perimeter and area from that measurement. Another student realized that in order to find out how much white paint would be needed for the lines, his team needed to find the width of the line in addition to the perimeter of each figure on the court. While students struggled overall, there were definite areas of success, and what was most impressive is they didn’t give up. My biggest problem in classrooms back in the States is with students who are convinced that if they don’t understand how to solve a problem immediately, it’s because they don’t know the math or are too stupid to ‘get it’. Even when it was clear that we were running out of time on day 2, almost every student was still working hard to try and figure out the math. I only wish I thought through the lesson more carefully because, as often happens in these hyper-short class periods, we ran out of time.
Before I step back into the classroom, I am currently on a two-week break from schools while I travel with my cousin to other parts of India. He’s visiting from China, where he’s teaching English and perfecting his Mandarin (which sounds pretty perfect to me when he runs into Chinese tourists here). It’s a welcome break and I’ll offer a full travelogue when I return to Kerala.