Gems of maths understanding or ‘ah-ha’ moments are often similar for teachers regardless of their location
Over the past 25 years, I have been very fortunate that my business has given me the opportunity to travel and work in several countries. During this time, I have delivered thousands of hours of professional learning to help educators in their mission to teach math conceptually. During these sessions, there are always a number of little “Ah ha” moments for teachers, regardless of their location in the world. These are the moments that make my job rewarding. So it’s no coincidence that I call these moments little “gems”. They are little treasures for the learner and for me.
My youngest child Gemma was born on my birthday. She is my little Gem. Gemma has always had a keen interest in mathematics and in her dad’s business. For many years, she has shared in my passion and watched the business grow. Gemma also has an exceptional aptitude for card games. She is efficient at calculating scores in her head, and she has an innate ability to see patterns and sequences within numbers. Unfortunately for the rest of the family, this gives her a distinct advantage when we play games like Rummikub or Five Crowns.
After one particular game of Uno, Gemma was left with a large handful of cards for which she had to calculate the total and deduct it from her score. It struck me that Gemma calculated her total points particularly quickly. I asked if she remembered being taught that strategy at school. Sadly, she answered that she had just taught herself. Many questions quickly popped in my head. Why wasn’t Gemma taught this strategy in Year 2? Why didn’t I take the time to share this strategy with her? How many other students are not aware of this strategy? Prompted by feelings of failure as a father and as a maths teacher, I suggested that she should teach other children her method. Gemma’s eyes lit up and she decided she would teach the idea using videos.
Gemma has never been shy. She likes to steal the limelight and dominate the conversation, so the idea of having her own YouTube channel was exciting. She started work immediately and had her first two videos recorded and edited within a couple of hours. You can view these here.
The first video focuses on making tens and uses real playing cards to give students a meaningful reason to learn the strategy.
The second video focuses more on the symbols and emphasises the fact that numbers can be added in any order.
After those first videos were made, I started working more closely with Gemma, sharing a few lightbulb moments that teachers have experienced in my professional learning sessions. I figured if teachers benefitted from these moments, then parents and students would too. It was during one of these sessions that Gemma had her own “Ah ha” moment. She excitedly announced, “Let’s call these videos GemStones!” I thought it was brilliant: Gem for Gemma and the notion of precious moments of learning, and Stones referring to our maths program Stepping Stones.
I think you’ll agree that Gemma is a natural in front of the camera and at explaining those “Ah ha” moments. She has also explored representations for odd/even numbers, and multiplication as an array. Eventually, she made a video showcasing an efficient method for teaching the fives multiplication facts.
All too often we use skip counting, which is highly inefficient but does not easily allow us to see the turnaround fact. In the video, Gemma uses arrays to help the viewer see how to leverage a tens fact they should know to figure out a fives fact. For example, if we know 10 x 8 = 80, then we should also know that 5 x 8 is half of 80, which is 40. Using this method, the viewer can efficiently calculate the total in one or two steps, and they can also see the turnaround fact¾that 5 x 8 is the same as 8 x 5. Gemma is now doing all the editing herself and has added a challenge at the end of each video which gives the viewer an opportunity to practice what they have just learned.
The greatest “Ah ha moment that teachers have in my sessions is when I am demonstrating how to use a conceptual approach to teach basic addition facts. This particular idea makes use of cubes or counters to help see numbers as quantities. Watch what Gemma does with the cubes in this video.
If you are like 99% of teachers who learned facts by memorisation, then I fully expect your eyes will open wide and I will hear pennies drop all over the country. For this video, we discussed the need to create a printable page that viewers can use at school or at home to practice the strategy. With a little help, Gemma has used PowerPoint to make a useful addition to the activity. Since then, she has also added links for printable activities to pre-existing GemStones videos.
It amazes me that Gemma is using social media to share little gems of maths understanding with teachers, parents, and young learners all around the world. She is helping to share all the “Ah ha” moments experienced in my professional learning sessions. I hope you enjoy the videos and have your own moments of revelation!
Watch Gemma’s Latest Videos.
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