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Richard Cornwall has been very successful at devising integrated learning strategies. As his students participate in simulations and projects, they learn the skills and applications of mathematics, and integrate math with all their other studies. Richard recently set up a "stock market" unit, which involves all 180 Grade 8 students at Sir Ernest MacMillan School in Scarborough, Ontario. He has also modified and led a unit in which students built bridges out of pasta.
Richard has coached mathematics students in competitions and served as mentor to many of his students. One of his students writes: "Over my two years with Mr. Cornwall as my teacher, math grew to be my favourite, as well as my best, subject. It's hard to believe that I struggled in Grade 6 with a subject that will be my major at university." Richard has also been recognized by the local school board as being an example for other teachers, has published books on teaching and contributed to the professional development of his colleagues.
"I see integrated teaching in our school as 'bridging the gap' between old-style teaching and contemporary education."
As I have become more experienced in the classroom, my role as teacher has changed. I now encourage students to find the patterns, connections and contexts in knowledge and in life situations. I show students how to evaluate experience — the reasonableness of things.
My technique for teaching students as whole people is "integrated learning." Both the stock market and bridge-building simulations are the result of going through the Common Curriculum and extrapolating the outcomes in the various subject areas. My colleagues and I then create innovative ways to reach the required outcomes by building on the students' interests and strengths. Consequently, the simulations we have developed are integrated across the curriculum.
The next step is to track students when they move into high school, and to make more connections up and down the school system.
Although some of our projects may seem overwhelmingly large, they began quite simply. The stock market simulation, for example, snowballed from a relatively simple exercise for one class to become an event that involved the whole school.
For two hours every Friday afternoon for one term, 180 Grade 8 students and their teachers participated in a "stock market" in the school's cafeteria. There were two parts to the unit: each student was given an imaginary $10 000 to invest in the Toronto Stock Exchange, and groups of four to five students used $200 000 in startup capital to form companies to buy and sell stock. We made sure each group included a mix of boys and girls, as well as students of varying abilities.
At first, we gave the students play money, but they lost or misplaced it easily. Later, all transactions were done by "cheque," and students had to update their balance sheets each week.
Each session started with 10 to 15 mental math warm-up questions, followed by calculator questions related to math and business. The teachers wrote these at first. Later in the unit, the students themselves devised the questions. Each company could give one answer for each question, and got a $50 credit for each correct answer.
Then the buying and selling began. Each week, a different student in each company would be designated as the group's presenter, and would have 20 minutes to entice other students to buy the company's stock. It was as loud and chaotic as a real stock exchange.
We used a combination of dice and value cards to make stocks rise and fall. A black "½" card combined with a roll of 12, for instance, would make a particular stock rise by $6. Another set of cards based on world events could also affect stocks. When the World Basketball Championships were held in Toronto, for example, sporting goods stocks rose by $25.
During the last half hour of each Friday session, the students made business cards, flyers and stock certificates for their businesses.
My math students became enthusiastic. They brought in newspapers and started comparing stock prices over lunch. The companies they formed, which included clothing companies, airlines and an amusement park, started to advertise. Their firms purchased "air time" on the school's public address system. Posters appeared on the cafeteria walls. Disputed claims were taken to a mock court.
Supplying the resources students needed to make the project grow was important. We bought a video from the Toronto Stock Exchange and used a teaching unit produced by the Exchange and the Toronto Star. Additional help came from parents and community members. Parents brought in copies of magazines such as Fortune and Business Week, which students used to get ideas for their own companies. A stockbroker, a loan manager and an advertising salesperson came to speak to individual classes.
At the end of the unit, we posted a list of the companies that had made the most money. In the future, we would like to have some sort of awards ceremony.
The unit was particularly successful with students who normally dislike math. The strong real-life component made it more relevant to ESL students and others. And, because the unit is both cooperative and competitive, it teaches the students to be responsible for their own learning.