Join the Dots - its as easy as 1,2,4,8

I have always felt that there are many components to what we call "learning" that in a structured educational system are often sequenced into progressive hierarchies. Certain concepts and skills are linked, and definitely need foundations. Yet some of these sequences, or progressions  don't always reflect our capacity, or readiness to develop them. Curiosity shouldn't be phased out at 6, anymore than logical thinking should wait until your 16.

This is a story of 7 year old, that reminded me of this.

During February 2017, I was honored to be given the role of Visiting Scholar - at Petrosains - a major science centre based in Kuala Lumpur (KL) Malaysia. I worked with them near 15 years ago, soon after they were established, to help them manage and develop their capacity around exhibitions, and exhibit production. Now, 15 years on, we have both - progressed and matured ( well... they have). They now run a very strong mix, of a destination science centre attraction ( in KL), a series of significant regional centres, and one that is continuing to expand, and a growing range of educational programs, targeting a diverse range of topics and audiences.

One of the projects I was able to run while visiting, was a series of hands on teacher development sessions, both In KL and Kota Kinabalu (KK)  - in Sabah - Borneo. Participants in these workshops where educators working in primary and secondary schools, but also included educational leaders, and philanthropists keen to support development of underprivileged communities, through education, and innovation. These workshops were to advocate for and introduce teachers to hands on enquiry activities using the most simple of materials. We used colour, and pendulums, light and chemistry as topics  around which to enquiry, but we did also include activities that challenge and develop logic, critical thinking, and problem solving.



While all the participants enjoyed the activities, and reported that they were keen to incorporate these into their teaching, a high percentage were extraordinarily motivated - requiring threats of physical violence to get them to stop one activity so we could move onto the next.

It was one of these teachers, that was bubbling with enthusiasm, and driving her group ( and others groups) enquiry through a hail of questions, that made the day of working with secondary teachers especially memorable.

She came up and was very apologetic, letting me know she had to leave just before the end of the session to pick up her son. It was of course fine, she had clearly been energized and taken a lot from the activities, as both a science and maths teacher. The day finished, my team of supporters from Petrosains helped pack up, and headed to the mandatory 4th breakfast for the day in the room adjoining the workshop hall. I was still working out if the overly sweet cordial, or the syrupy Tai Terek was the less likely to induce an immediate diabetic coma, when the teacher returned with her son, Ryan, aged 7.

She wanted to say thanks for the day, but also wanted Ryan to meet me ( clearly a slow news day in KK). I got talking to Ryan and his mum, about his school day ( while Ryan helped clean up the fried noodles). Ryan was going to a Chinese school in KK, one that was dominated by traditional instruction, and Ryan - while clearly very bright - was often in trouble - he asks questions a lot.. like his mum.... "I get bored".. I told him I understood, "I got bored at school too, got into trouble".

I had packed up all the materials, so didn't have much I could engage him with, but I did have a set of my cards I use to help people learn and experience binary, and logic, and powers of  2, and a cluster of related activities. I have introduced teachers to this, and even the most maths phobic can normally end up comfortably interpreting a binary number within 5 or so minutes. But I hadn't tried this on anyone quiet as young as Ryan.. and i was only expecting to have him explore some counting activities using the cards.

I asked him how he liked maths, and counting - he said liked maths - and counted up to 20 for me.
He was still using his fingers for some of his basic counting, and while he got there in the end - he was still at that stage of being a little hesitant in his counting. I asked if he did additions.. and yes he did those too.. and we did some simple examples. He was still at the stage of adding by sequential counting up from one of the numbers, and used his fingers to help.

I asked if he'd like to see a different way of counting -- "yeah sure".. So i arranged the dot cards I have made, from 1,2,4,to 8. and asked if he could count the numbers of dots on each card.  He did, but he still counted the dots up on his fingers, didn't seem to be subitising at all..  i was surprised ( but what would I know). By showing combinations of cards, and a little practice ( yes even I accept some drilling is necessary ), Ryan was soon fluent in flipping the cards, and had found the sequence needed to count from 0 to 15. I then introduced the 0/1 cards under the dot cards, and we repeated the task flipping both sets in tandem. A few minutes later we were just using the 0/1 cards, and Ryan had got it. He could count up, or interpret any random combination. His Mum took a few minutes longer, and was a little ..dazed.. at seeing what her son was doing.. dazed and proud.

He wont encounter this in his schooling until he is 14 or older, and perhaps only if he does a computer course. But by then he might be way ahead of the teachers. Certainly the use of such binary numbers itself is not a core skill. yet the mix of symbolic  reasoning, pattern, sequencing, combinations, place value and logic, embedded in the activity - NOT TO MENTION his curiosity and self worth are critical skills that he will deploy each and every day.

I said he could keep the cards..Sometimes igniting curiosity and a passion to learn is as easy as 1,2,4,8.