Recently, the Algoma District School Board invited Jon Orr in to work with our applied math teachers. Jon is an Apple Distinguished Educator who works in the Lambton Kent District School Board. There are links to some of his “stuff” at the end this post.
Jon certainly showed us how to use the iPad and some particular apps to effectively engage our students but what truly spoke to me on this day was the desired and necessary change that he made to his instructional practice. He explained this using the context of the plot in a story.
In many math classes that I attended and in many that I taught, the climax occurred way too early in the class period and there was very little build up to that climax. After homework check and take up, definitions and procedures would be defined. We would do a couple of examples and then maybe an extension of those examples where we had to apply some of what we just did. And then homework.
In this model, the teacher does most of the work. In order for most students to be successful, they must follow the step by step procedure to solve the problem. Then, on the test or quiz, they must rely on their recall ability to remember the steps. If the textbook problems don’t look similar to the examples, they may not know where to get started. How many times have we heard, after handing back a test, “We didn’t do an example like that in class”?
The instructional change that Jon spoke of is modelled after Dan Myer‘s approach and the 3 Act Math Problem. The students start with a visual – often times a partial video. They state what they notice about what they watched and then what they wonder about what they watched. The “wonderings” become the math problem that they work on together. Often times the teacher will steer the problem in a certain direction but will eventually answer all of the “wonderings”. Jon has his students develop their solutions on a dry erase surface so changes are easy to make and as a result, they are more likely to take a risk. They will then watch the rest of the video for the answer. If need be, notes would be developed at the end of the cycle and some practice questions may also be assigned. Often the solutions will involve more than one strand from the course and the path to a solution can take on many facets. Through the use of the iPad, Jon takes pictures of the solutions and then shares them with the class for discussion. What makes this approach so effective?
Students do most of the work. The multimedia aspect can be engaging for the students. In fact, as a culminating activity near the end of the course, Jon has the students create their own 3 Act videos. Students learn best when they’re engaged and create their own understanding. By coming up with their own questions, they create ownership in the process and are more likely to follow through. Also, watching the rest of the video to see what happens, can peak the students’ interest to see if their solution is correct.
Students become better problem solvers. When I asked Jon to compare the before and after of this instructional change, this was high on his list. In many cases there may not be an exact answer because of assumptions that must be made about what students see in the videos. Students must do this in order to make sense of why their answer is different than the one in the video. Often, those “What assumptions can you make…” questions are the ones that we don’t assign in the textbook.
Curriculum expectations can be clustered. I have often times disregarded some instructional approaches because it takes up too much time in class. For years, I taught one section after the other in the textbook and each section equalled one class period and one(or 2) specific expectations in the curriculum document. With careful planning, each 3 Act activity could cover more than one expectation. In fact, in “Growing Success” (Ontario policy document on assessment, evaluation and reporting), it states, “…evaluation focuses on students’ achievement of the overall expectations…Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of the overall expectations…”.
A couple of things that Jon didn’t discuss with us because of the nature of his visit are 1) he doesn’t teach in “units” like most textbooks are organized, and 2) his grade 9 and 10 students don’t see any marks except for their midterm and final marks. He “spirals” the coverage of the expectations so students can experience them together in any combination and they can be revisited often during the course. His students’ assessment experience is mainly feedback on how to improve and resubmissions are common place.
Jon and Kyle Pearse have developed a number of these tasks which include a short summary, a complete teacher resource guide and all media files. A complete course of these tasks designed for intermediate math teachers (grades 7-12) can be accessed on iTunes U. The name of the course is, “Curious Math: Foundations of Math”. Also, below I have included more links to Jon’s work.
Thanks for sharing, Jon!