A photograph of a human eye; two parabolas superimposed on the eyelids; calculations of the size of the eye using integration – this problem was framed as a pattern-seeking challenge in our 11th and 12th grade math class. This common calculus problem was extended by having students find the volume when the two curves were rotated; with a generic proof to substantiate any claim. The questions of “what patterns exist?” ask student to investigate specific situations and find general solutions for the situation. Will their conjecture hold up under different conditions? Can they prove that the conjecture will hold up? Other math classes present photos or videos and ask students “What is your question?” When students find success in these types of curricular activities, we know that our new math program is gaining traction.
The energetic debate that created the math wars of the last two decades continues with arguments that range from traditional rote memorization to complete reform project based math. At Journeys School, we combine the best of both arguments. We believe that students need to have a strong understanding of core numeracy skills. The mental agility to move numbers in one’s head is critical to long term success in mathematics. Simultaneously we believe that students need to learn how to apply these core skills to novel problems and make generalizations from specific situations. Both the Singapore Math program and the International Baccalaureate curriculum help support these underlying beliefs.
Based on these curricular implementations, the school has a clearly defined philosophy for mathematics curriculum and instruction. These include:1. Students need to value making mistakes in math as a means to learn.2. Students need a strong base of core numeracy skills.3. Students need to experience a mastery based curriculum with a focus on depth over breadth.4. Students need to apply and see math in action – whether through physical demonstrations, investigations, or written work.5. Students need to practice common algorithms so that they become automatic tools in more complex situations.6. Students need to see math as a process where there are multiple valid routes to a single solution.7. Above all, all students should be confident in their mathematical abilities.
At the end point in their math career at Journeys School, we expect that they will come out with strong basic computation skills, excellent number sense, and the courage to solve challenging problems and find success in math in college and beyond. Let’s see how you do on these two problems that our students have solved!
1. (5th grade math) Mrs. Chen made some tarts. She sold 3/5 of them in the morning and ¼ of the remainder on the afternoon. If she sold 200 more tarts in the morning than in the afternoon, how many tarts did she make? (solution: http://www.thedailyriff.com/WordProblems.pdf) 2. (12th grade math) If x0=0, iterate the function f(x) = x2 + c, for values of c = 0, 1, i, -i, -1. Using hand calculations, what happens to these functions as the number of iterations approaches infinity. Does the iterated function approach infinity or reach a constant (or set of constants)? (email nate.mcclennen@journeysschool.org if you would like more information – hint: this describes the Mandelbrot set).
