Making Learning and Thinking Visible




Bo Perkins, Woodland Heights Public School, Thames Valley District School Board.



“How do I get a Level 4?” “I got a Level 3+, why didn’t I get a Level 4?” This is a common question from students and parents, especially around report time. My answer, besides the standard “Go above and beyond” is usually “You need to communicate your thinking. You need to show what you know and make it clear” Being able to see what students are thinking and being able to see what their thought process allows teachers to get inside their head and we can even see where mistakes happen. When thinking is visible, we are truly able to see a student's understanding and learning.



 Old School vs. New School 



Growing up I hated Math. It wasnt that I was bad at it, I received 70’s and 80’s growing in Elementary school. I knew the procedure I was taught but I didn’t understand why I was carrying a 1. My generation and the ones before me were told, “This is the way and that's how it is done.”  The formula for a triangle is ½ b x h, don't question it. It wasn't until I started teaching and attended a Math PD when I was shown why this is and it made perfect sense! It is the same as a rectangle just cut in half!  Was I learning back then?  Was I genuinely applying knowledge or was I simply regurgitating a formula and placing numbers in? Now, I teach to understand. I teach the way I would wanted to learn. This is what they have now labeled “ New Math”.






 Multiple Strategies 



People for other generations, struggle to understand this “New Math” and almost immediately discredit it or say “ the old way is better”. However, what works for one person doesn't always work for another. This is true not just in math but in everything.  People use a range of strategies to accomplish what they are trying to do. The way myself, and many others are teaching math now is just this.  We provide students with multiple ways of solving questions.  When we Multiply 3 digit by 2 digit questions, we teach our students that they can do a range of things to make it easier for themselves so that not only do they get the answer they understand it.  We show that you can Decompose a number and break it down, we teach to use Open arrays, we use number lines to show the jumps you take, and yes we do teach the algorithm, but we teach it as the final understanding. 






 Wipebook Workbooks



Every morning, my students enter the class to a number talk. Our current focus is Multiplication as this is an area of need. Students come in and take out their own Wipebook Workbooks and dry erase markers and work independently to show as many ways as they can to solve the question. The Workbooks are amazing for this because it has 4 writing surfaces. Students are able to show at least 4 different ways and not have it all jammed on one board. And allow me to see and check in with what strategies they are using and which ones still give them some issues. It's a quick and easy way to assess the needs of my class. 






They also work great with our 3 part math lessons. My class right now is working with multiples and factors.  They are able to practice multiple ways of finding both multiples and factors at the same time and it allows them to check their own work as well as prove it to me in various ways.



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