"Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualisation, and flexibility, the mathematics comes alive." - Jo Boaler
During 2015/2016 our staff did a lot of finding out about maths, we had not engaged in maths PLD for a while and it certainly was an eye opener for us. I am lucky I work with a reflective, innovative and open staff, as many of the ideas really challenged what we were doing at the time.
Visual maths wasn't an area I had ever given much particular thought to, but the value of it quickly slotted into place in my thinking. Obviously as junior teachers we use a lot of materials and encourage visual strategies. However I was surprised to hear our maths facilitator talk about the imaging stage, and how some children would never get there, and that was ok, just to move them on. As a learner myself I know that I never really imaged...in fact my fingers are my friends. I am not sure who else remembers hiding fingers under the table or behind their back to work out problems....because we were never allowed to use them. I remember looking at those 100's 10's and 1's blocks we were given to help us work on place value and not having a clue what they meant. I don't remember drawing pictures and I don't remember using any other materials. In fact I don't really have any memory of directing any of my learning, or creating anything unique that wasn't teacher prescribed.
"When we don’t ask students to think visually, we miss an incredible opportunity to increase students’ understanding and to enable important brain crossing." - Jo Boaler
Could this be why I never made solid connections in maths until I allowed myself to again use visual strategies that worked for me as an adult?
Obviously Number Agents is based around materials and encouraging the active use of these, along with drawing or patterning to problem solve. It is always awesome to hear that this is now something as a school we can and should continue encouraging.
Children must be given time to experiment with materials, to see the beautiful nature of maths in the world around them, to interact with it, to generate their own thinking, to make their own connections in this way. This allows them to make solid connections.
"Visual mathematics is an important part of mathematics for its own sake and new brain research tells us that visual mathematics even helps students learn numerical mathematics." Jo Boaler
"In a ground breaking new study Joonkoo Park & Elizabeth Brannon (2013), found that the most powerful learning occurs when we use different areas of the brain. When students work with symbols, such as numbers, they are using a different area of the brain than when they work with visual and spatial information, such as an array of dots. The researchers found that mathematics learning and performance was optimized when the two areas of the brain were communicating (Park & Brannon, 2013). "
"Visual mathematics also facilitates higher-level thinking, enables communication and helps people see the creativity in mathematics."
Extracts have been taken from Jo Boaler's work on mathematical mindsets. Full article can be found here.
"We owe it to our children to be innovative in our approaches to mathematics, to ensure they see what a beautiful area of learning mathematics is. Because mathematics is so much more than remembered facts." - Agent 81
Further reading here.