This blog is reviewing the many areas of note in the Visible Maths book written by @mrmattock.
There are some key contributors on twitter particularly for Maths and remembered this book being very popular on the months of its launch. I was particularly intrigued as I know that whilst I have dipped my foot into bar modelling over the last few years something has stopped me from moving this into a habit in my classroom. I now realise this was down to a lack of understanding of the principles behind the different manipulatives and I am certain this book has allowed me to bridge those gaps.
This book was my hardest read of the summer, not because it was tough to go through, it’s because I was learning so much! I have ended up creating 20 pages full of notes and putting together the summary page for this blog has been challenging because so many areas underpin each other. The book outlines six different manipulatives and expertly talks through their possible strengths and weaknesses which gives a good foundation to the rest of the book. A part of the book which particularly resonated with me was that most of us as Maths teachers have learned Maths by having a method modelled and then we repeated that steps as the teacher showed. My own maths teachers never used counters, ordered-pair graphs or bars to explain concepts – so why should I as a teacher?
As I worked through the book it became apparent why concrete and visual models can allow us to make greater connections between many different topics areas as some start from similar foundations. Think my two personal favourite manipulatives are the use of counters and bars but also look forward to embedding the other models as my confidence develops. The book is so well written as I repeatedly would see a model and think well for this scenario it would not work, then the next page models it perfectly!
There is an excellent section on integers and the four operations which really hooked me into the book. Conceptually I do not think there is a more complex area to teach than the four operations with integers. The use of zero pairs to consistently solve problems and I particularly liked the use of the ordered pair graph when multiplying and dividing integers.
As the book built through the main models I wondered whether more complex representations were going to be possible, particularly with decimals and fractions. A key to a look of this was to redefine what ‘1’ was worth in the context of use with counters or bars for example. If a counter had been worth 1000 previously what if that was worth 1 then what would the 100 counter be worth … For my own teaching i’m going to have to return to these sections a few times to ensure I start with the correct model but my confidence grew throughout the book to the point where I was covering up the visual steps and attempting to start them myself. The key areas of difficulty initially for me was interpreting the ‘-‘ sign two ways either as take away or the difference between.
This was the section where every bit of prior learning came to life. What visual modelling allows you to do is really unpick the maths or algebra behind the question and see the clear connections to previous topic areas particularly on four operations. I found myself slowly moving through the stages from visual to abstract over the chapters on algebra but understand the connections built mean that students are far less likely to make mistakes on this crucial area of maths. Another particular highlight was the visual explanation of why we ‘complete the square’ and how this associates visually.
This book will have a huge impact on my teaching practice over the coming year(s) and would whole heartedly recommend to any maths teachers from all phases to give it a read.