Exploring Insights and Addressing Misconceptions

Hello, my name is Susie James and I teach a year 4/5 split class at Glen Huon Primary School in Eaton, Western Australia. I was a late bloomer to teaching and have only been teaching for five years. I absolutely love all of it apart from maths!! As a child I consistently struggled with maths, and had to work very hard to pass my maths exams to go to university. I am the result of absolute rote learning and sometimes feel I have no idea why I do things. Since I began teaching I have had to completely re-learn how to do maths, and then how to teach it. When the opportunity of taking part in the Champions of Maths Program was raised I jumped at the chance.  I desperately wanted to be able to explain and verbalise maths to my students in the best way possible, and also to gain more of an understanding of math concepts. I am passionate about teaching and really don’t want my students to suffer because I am unable to convey and explain maths concepts. I want my students to enjoy maths and not have the same fear of it I have had for thirty years!!

The first time all of the Maths Champions met was very interesting, and Shyam initiated a very useful discussion about our goals and how the journey was going to progress. It seemed quite unstructured from a teacher point of view, however as the weeks progressed I recognised the reasoning behind this and Shyam has tailored a program of guidance and teaching to suit all our needs.

I’ll skip straight to my second lesson, as the first lesson was really an opportunity for Shyam to see me in action and to provide some feedback. Very daunting to have a maths guru come and watch me in action, and I was just about shaking in my boots!

For our second lesson we were given more direction and had to produce a Problem Solving lesson with the following criteria:

– Students work in small groups

– After the activity encourage discussion among the class

– Incorporate random visible grouping (RVG)

– Use vertical non-permanent surfaces (VNPS)

My Problem Solving lesson incorporated the symbols used in a deck of cards and involved formulating, modelling recording authentic situations involving operations and comparing large numbers with each other.

In my class I have 29 students with a huge variation in abilities, including two high-functioning autistic children, one who suffers from severe anxiety. So not only was I concerned about the content, I knew tears would be shed when I randomly grouped the children and that one of them would really struggle with new people in the room, a change in routine and a change in how I was teaching. So it was a true moment of delight seeing this particular child so engaged and taking the task to the next level, albeit on his own. Once the other students had moved on emotionally from being randomly grouped, they too were all very engaged and really enjoyed the task and seemed to want more!!!

The beauty of this program is the great constructive feedback from Shyam and fellow colleagues. The debrief session afterwards is supportive and helps to direct where to go from each lesson and how to improve. It was clear that the discussion part of my deck of cards lesson was too brief and the introduction a little too scaffolded. But on the whole, I came away from this lesson feeling elated that I had managed to pull it off but not sure where I was going with it. Thankfully the next Champions workshop provided me with more understanding and direction.

We focused on how to use the five practises for orchestrating productive classroom discussion which engages and encourages deeper learning. The ethos behind this is how to get students to think more, think better and think about the right things. The five practices of Anticipating, Monitoring, Selecting, Sequencing and Connecting are all practices that teachers do, but not necessarily with consistency and fidelity and to the extent that is required to maximise understanding. Learning these strategies and putting them into practice has made what is implicit in teaching more explicit.

The goal for the fourth lesson was to focus on pre-empting and addressing misconceptions, and guiding the children through reasoning and thoughtful discussions. This lesson was on decimals and ordering and comparing numbers with decimal parts. Two misconceptions I knew my students would struggle with were the longer the number the larger the number, and confusion over the zero holding a place value. In all honesty, I felt very out of my comfort zone as decimals for me was a concept that I seemed to have conveniently not grasped as a child. The night before this lesson was an all-night, stay awake vigil, going over the concept and how the lesson was going to go. I met with Shyam before my lesson and voiced my concerns about being unable to convey what I wanted to say in the best language and confuse the children further.  I asked Shyam if he could step in to rescue me if needed.

In groups of four, with four different coloured pencils, each child would take turns to choose a number and mark it on a spiral between 0 and 1.

Students kept taking turns until one of them had marked three numbers next to each other. I had enabling (to assist those who were struggling) and extending strategies (responses to extend children and get them to reason more deeply). All was going terrifically well, the children were engaged, the timing was good and the discussion was so fruitful. However, unexpectedly the students demonstrated misconceptions that I had not addressed and was not ready for. Super maths guru Shyam stepped in and eloquently addressed the misconceptions. This not only gave me great modelling of language to use to help explain misconceptions, but the students really appreciated how he reasoned with them and I felt totally supported, even though inside flailing wildly.

I have since constructed a huge number line going around my room and the children and I are on a voyage of discovery into decimals, fractions and percentages!

So where to from here…… I am now scheduling a regular weekly problem solving lesson in order to practice my new skills. My maths partner Rachel and I will be presenting and sharing these new lesson plans and strategies with the Glen Huon cohort and even spreading the word to the community via parents.  What is bizarre and equally worrying is that I am choosing to read and gain more knowledge about maths, which is leading me to believe that I may almost like maths! (perhaps a misconception of my own that I need to address!!)

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