How do spies encrypt messages so they can’t be easily decoded? How can I measure the height of an object using knowledge of angles and trigonometry? Is it possible to use knowledge of mathematics to create art? How many months does it take to pay off $1,345 of credit card debt if I make a monthly payment of $200 and my annual interest rate is 23%? What is the most efficient way to mill a log into usable timber?
Ask five different OA students and you will find at least five different ways of thinking about each of these problems and perhaps even more methods of finding a reasonable answer. These are the sorts of questions our students are chewing on in addition to learning traditional math concepts like long division of polynomialsor graphing trigonometric functions.
Academics at The Outdoor Academy emphasize teaching students how to think critically and deeply about the subject matter. In mathematics this means more than simply learning a new concept and “checking the box” so we don’t “fall behind” other schools and students. It also means grappling with complex problems and trying to apply our clean and precise mathematical concepts to the messy world around us. We do, however, have a duty to meet the diverse curriculum needs of our students’ sending schools. This is accomplished by coordinating with our students’ math teachers and by individually tailoring our instruction to meet those needs. In addition to teaching the required math concepts we also have a duty to prepare our students to face the difficult problems of the future—problems that often involve both quantification and out-of-the-box thinking.
To address this two-sided coin we use a simple tool in all math courses at the Outdoor Academy—a math journal. Throughout the semester students are given journal prompts where they are asked to address complex problems and articulate their process of problem solving. After an initial attempt, students are given formal feedback from their teacher and informal feedback from peers. The feedback helps students to identify valid lines or reasoning and thinking and, more importantly, where a different line of reasoning or thinking could be used to find a more correct answer. Students are not graded simply on whether or not their answer is correct, but how mathematically sound their approach is and how well they have articulated that process on paper using words, numbers, diagrams, graphs, and tables.
The goal of our math journal is to provide a space for students to not only grapple with challenging problems but also feel comfortable with making mistakes and growing from failure. Over the course of the semester students push themselves to identify complexities or inaccuracies, explore unanswered or unanswerable questions, and even challenge their teacher. While this process can be frustrating for students, it often leads to deep understandings of the topic at hand and a sense of satisfaction when things do finally fall into place.
It is not enough, however, to just hear about it from the math teacher; below I have collected a few opinions from current Semester 46 students on their math journals:
“It can be a little challenging but they provoke a deeper level of thought than presented in typical classes… sometimes they are really confusing but when they click it’s really satisfying”
“[Our teachers] have very high expectations for our math journals which is shown by how harshly they grade them but I feel the grading does reflect the amount of time I put into it…I liked the last one where we had to write our own word problems and scenarios to pay off credit card debt because it was cool to see how it applied to real life situations.”
“Sometimes they’re fun because often in math they don’t tell you how you actually use it but other times they’re sort of annoying because they take a lot of time and some entries ask me to do something different than the way my brain would usually work.”
“Math journals are a great way to engage with math in a way you wouldn’t with the curriculum in your sending school. They also teach you about things like credit cards that force you to apply your math to the real world instead of textbook scenarios…They can also take a looong time.”
“You learn a lot about stuff you would simply not hear anywhere else.”