Pushing Math boundaries at The Harbour School
Karim Arditi, Math mentor for Full Steam Ahead program, and Learning Extension @THS
When The Harbour School first discussed collaboration with Mathemagic, the idea was to support the school’s learning extension program as well as offer mentorship to students enrolled in John Hopkins CTY, Northwestern CTD, or Art of Problem Solving classes. The fact that THS gives its students opportunities to pursue advanced courses like these, at their own pace, regardless of age, was something I found inspiring. I’ve always felt that the phrase ‘stages not ages’ should be the generalized approach to education, rather than the ‘one size fits all’ model. In my experience, students learn at different speeds, so this does make sense. A student who already mastered a topic will become bored and disengaged when the classroom teacher is reviewing it for the fifth time. The opposite is also true for students who are behind and are desperately trying their best to figure out what the teacher is explaining; they get flustered and sadly lose confidence because they simply don’t understand. Another point to consider is that every learner has his or her own strengths and abilities so a child who may be ahead of the curve in art may lag behind in mathematics. Hence, there is a critical need for individualization in order to optimize learning for each student. Each case and child is most definitely unique.
I remember when I first landed at Sussex University to pursue a degree in Math. I was a village boy from the South of France who was there on a ‘free ride’ based on my passion for the subject. I arrived in a room full of ‘geniuses’, and felt like the dumbest person there. One kid knew how to count super fast, another was studying third-year materials, and overall the whole department was full of talent. I was quite intimidated. However, throughout my degree, I realized hard work had great value. I may not have been the fastest, or most naturally talented. I was decent at research and deep thought processes. I had grit and tenacity, and I didn’t like giving up. I was shocked when the math department asked me to represent the school for the QAA panel review (UK Quality Assurance Agency). This panel ranks universities and some of the students meet with panel members to share their experiences as students. I was one of five selected to represent the School of Mathematics. Looking back I see why they selected me now, I had scored 100% in my mathematical methods course and was deeply passionate about the subject. Sussex was recognized as the second-best university that year, with a score of 23/24, besting even Cambridge University’s talent. I like to think I played a fractional part in that result. The value of this experience for me is that we can all focus on ourselves, and do our best, and we will land exactly where we are supposed to. Strive to push yourself, grow and develop, work with passion and tenacity. The stars may just align for you. Fortune favors the brave! It sounds cliché, but hard work does pay off.
I was genuinely excited to have access to a pool of high-ability students at THS. My goal was to advance their understanding of Mathematics to a deeper level. I’ve observed that these students like to go fast, and sometimes get bogged down by questions that require them to think in more detail or perform several hard steps to get to a tricky answer. My mission here was to ensure they have both the knowledge and the structure required to tackle these multi-step questions. These questions require formulas, wittiness, little tricks, and speed. The rabbit hole of problem-solving runs deep.
I love mathematics and calculus but have a soft spot for problem-solving. I find it incredibly ingenious because there is no preset solution for questions. You have to think on your feet, sometimes use a geometric formula to resolve an algebraic problem. You have to be knowledgeable, sequential, open-minded, resourceful and most importantly, willing to investigate. Not all students will have the same mathematical tool kits. Some may have great computational speed, while others have strong insights in terms of choosing correct strategies. The key is to recognize their strengths and work with them in developing areas of improvement. It could be the interview question asked at Google or Facebook, it is the curveball you are not prepared for. Typically, you’ll look at a question from the AMC’s (American Math Contest) and you’ll think, “Wow I absolutely can’t do this!” Then you start poking and prodding… small possibilities appear. You try, you fail. You try something else, get a small glimpse of a result, and suddenly get the big reveal!
I live for the reveal, the epiphany.
As parents, we can encourage our children to challenge themselves in Mathematics every day in little ways. Whether it’s discussions about prices at the supermarket, discounts, talking about your actual work and what happens at the office, explaining stocks or sciences, kilobytes or kilograms, profit, and loss or entrepreneurship, or even looking through some interesting age-old math conundrums – these are all ways that we can keep engaging our children in adopting the language of all sciences. It will serve them well in their future as everyone benefits from a strong, confident foundation in Math.
Working with high-ability and twice-exceptional students for more than ten years now, my life’s work is really about mentoring and supporting their personal growth. I can share my nerdy jokes with them, some math riddles, teach number theory so kids can count faster, and present thought-provoking questions for rousing discussions.
So we’ve been doing exactly that. The students and I have shared special moments – from polite, mathematical debates to slightly more passionate moments where we need to regulate the room a little. It all comes from a place of enthusiasm and interest. We’ve had collaborative projects during Math Week where they designed robots and measured surface areas then coated the robot with (imaginary) Osmium–the world’s densest precious metal–and calculated the cost of their project. We’ve done Caribou Contests and AMC walk-throughs and Growth Mindset-type work. We’ve looked at accelerated number systems, factor theorems, classical techniques needed to offer insight into what happens ‘behind the scenes’; breaking numbers down to skin and bones. Opening the floor up for discussion and engaging students to think more deeply are a couple of ways to keep pushing the boundaries.
We have had a great start but there’s still a lot to do. The challenge is always how to take this wonderful, natural talent -the fast ‘CPUs’ – and develop a great work ethic, an investigative mind, great presentation skills, and perhaps most importantly, a desire to never give up.