The first of which is Michelle Naidu, who I previously interviewed in my post Flipped Pessimism: What the opponents are saying and the second is Nathan Banting (http://musingmathematically.blogspot.ca/). Every time I have met Nathan, I have been blown away by his thoughtfulness, his love of math and his love of engaging learners! I tried to set up a video interview with Nathan, but that didn't work out. Fortunately, I was still about to get his thoughts regarding flipped teaching, his teaching strategies, his thoughts on technology in math education and his experience with VLCs.
Ryan: I know Flipped Teaching is something you haven't really explored. From what you have heard, what do you think of the concept?
Nathan: Flipped teaching still worries me. I think mathematics education should focus on the broad themes that make it accessible and practical. I am worried that teachers will abuse the videos and then use their class time as a glorified study hall. It is very possible to flip your room, and make no fundamental shift in your teaching. On the other hand, building the atomic skills with good videos would benefit a teacher trying to use class time to work on deeper problems. If we can harness the foundational skills for homework, we can then begin to apply them in meaningful ways with our contact hours. Too often, online videos are used as digital lectures; the Khan academy presents a flagship in this regard. If we can use digital media as a starting point rather than the end-goal, I think assigning a flipped homework package could prove beneficial. There are also the issues of accessibility and student effort. They really have no bearing on the pedagogical issue at the root of the question.
Ryan: You have been doing great work using "Problem-Based Learning" in your secondary math courses. Can you provide a brief summary of how you are employing this method?
Nathan: Problem Based learning (PrBL) is a system where topics are examined within the midst of a larger issue. It can be a situational problem that provides context, or a fabricated one that relies on a base of mathematical skills. In essence, the task is given and curricular math is its underpinning. Good problems force students to make mathematical decisions. They then must understand the consequences of those decisions. Problems range in complexity; a problem may take 30 minutes or 2 classes. Some introduce topics, some cement the learning. Often, they are solved in “think-tanks” of students working to arrive at a solution. PrBL is designed to allow students to chew on a topic without rushing through a pre-set algorithm to arrive at an answer neatly printed in the answer key.
Ryan: Are there certain topics where you have been unable to employ this method? If so, how did you approach those topics?
Nathan: I have developed the entire Workplace [and Apprenticeship] courses (10 & 20) around problems and projects. The practical topics allow for me to choose relevant situations and tasks for the students. I find it tough to implement large scale projects into an abstract course. In my experience, students are intimidated by its unfamiliarity. PrBL does fit nicely into all streams. Presenting a thought provoking entry event can begin to build understanding across the board. Whether it is getting students using graphing software to graph their first quadratic with a TOV [table of values] or asking them to design a data set with given central tendencies, providing an open environment for them to make connections is key. In the higher levels, more direct instruction is given, but anchor problems are a great reference for teacher and students.
Ryan: In your mind, what is the role of homework in a secondary math classroom?
Nathan: I think homework needs to be done to build a toolbox. Every student mathematician needs an angle to approach challenges. Those angles always necessitate a mathematical arsenal. Simple operations may help them pick fair teams where more complicated means (factoring, trigonometry, etc) may open doors to more novel and elegant solutions. Homework exists to practice pieces; the sad part is that most students never get the opportunity to use those pieces in a larger scope.
Ryan: In what ways are you currently using technology in your teaching?
Nathan: In my Workplace PBL classes, students have full access to the internet and all the software it provides. I use it to create individualism and autonomy. It switches the focus of the math class. Students are now expected to create a pathway to a solution; they need to show me that path. The formula and algorithm are not really the focus anymore, because they are all readily available. In other courses, graphing software is used a visualization tools and online centres are set up for group collaboration. Some of the best lessons use simple technologies. A set of dice, a cylindrical can and a utility knife, a magic 8-ball, coloured envelopes, protractors, etc. I think teachers have lost sight of the usefulness of this technology. I have an IWB [interactive white board], but the moving of a metre stick often shows the breadth of angles more efficiently.
Ryan: If you had an unlimited teaching budget, how would you use technology in your teaching?
Nathan: Unlimited budget is a dangerous thing. I think I would have two answers for 2 separate classes. W&A) I would ask for a laptop computer for every student. Accompanied with this would be full licences to Microsoft suite as well as zero administrator passcodes. I want students to be able to search out appropriate software to solve their problem. Mice need to replace trackpads, and even a touch pad where students can write in their thoughts to create a digital portfolio. Technology needs to encourage students to document their process; I find word documents don’t accomplish this feat.
For the other strands, I would ask for a set of tablets. I think the portability of the machines make them attractive. Students could have a variety of apps at their fingertips. Unit converters, calculators, graphers, simulators for dice and other probability games. Conjunction with geogebra would provide a very tangible look to functions. Graphing and posting with ease. I would eliminate graph paper altogether. Students could have an all-in-one collaboration station, but they also work great in isolation. There would have to be one for each student; they log in, use it for the class, and dock it for the night.
Ryan: You are a part of a Virtual Learning Community on Twitter and also as a blogger that discusses math education. How has being a part of that community improved your teaching?
Nathan: Edublogging began as a personal documentation system, and has become so much more. It provides an authentic audience that our students so desperately need. Twitter is the single best decision of my teaching career. It allows me to see what other distinguished educators are doing quickly and effortlessly. It starts the wheels turning, and provides a support system throughout the process of implementation. I cannot stress enough the importance for teachers to be digital citizens. Unless we become one, we will never understand our students as digital agents.
As you can see, Nathan is doing exceptional work and is a leader in Problem Based Learning in our province. I hope you have enjoyed reading his responses and are left feeling inspired that this individual is teaching our youth! He has left me with a few things to chew on and consider as I move forward as an educator and a designer.
Follow Nathan on Twitter
@NatBanting to get updates and links to his work.