Dr. Petrosino began class today by giving students approximately 15 minutes to work on a circumference of the earth problem. Approximately half of the class worked in pairs, while the other half worked alone. After time was up, some students shared their work with the class. Many groups approached this problem in the same way, though at least two individuals who worked alone became stuck quickly and were unable to get very far. Another individual observed that she was very engaged at first, but when she realized she was going to get stuck because she had no calculator, her attention wandered.
He asked the students to recall the ten-question quiz they took at the end of the previous class period, and showed them the results. The students did quite well on this quiz, which covered most of the necessary facts they needed to know to solve the circumference problem. A student observed that the hardest part of a problem is the initial deconstruction and planning; when the problem is already broken down into components (as on the quiz) it is easy to supply the information from memory. In other words, it was not the skills that were the problem, but rather when to use those skills.
Dr. Petrosino made the argument that the quiz from Monday was “TAKS-like” in that it mimicked the form and question type of a typical standardized test. It indicated that the students have high algorithmic and factual knowledge. The circumference problem students were given today, however, was something else.
This country is very good at factual knowledge like the quiz; we are good at worksheets and studying facts for a test. Instructionally, teaching factual knowledge is easy and can be done by computer programs, individuals with no training, or anyone who possesses the right series of facts. Teaching factual knowledge doesn’t require insight into cognition, assessment, reasoning, innovation, or creativity.
The back-of-the-envelope problems from Monday and the circumference problems today require more conceptual knowledge and transfer, which is what students typically are not getting in a classroom focused on standardized test performance.
Dr. Petrosino posed the question to the students, “How is it that we are hindered when we think about a problem that someone solved thousands of years ago?” and encouraged the students to think how they want to teach: as they were taught, with high emphasis on facts, or do they want to integrate complexity and creativity?
He added that they should look back at their own education appreciatively and critically and think about the kind of teaching they want to do. How do you move our instruction from being factually based to being conceptual and transfer based?
Sara finished class today by walking students through a sample rubric that would build a rubric around the Eratosthenes problem in order to create a mathematics unit. Students found the idea interesting, but were constrained by the idea that math must be taught in sequence (e.g., algebra, geometry, algebra II, etc).