My name is Arnalise de Robillard and I am a teacher of a Year 4/5 class at Eaton Primary School and a current participant in the Alcoa/Scitech Maths Enrichment Program: Champions of Maths (ACoM).
I am early in my teaching career and one of the benefits to this is that I recall my primary school years and associated average performance in mathematics quite keenly. It was fine in primary school, I performed well on paper and in important tests, but deep down I knew I honestly had no idea. In fact, my aversion to mathematics and general fear of incorrect answers continued through high school until I reached university and discovered that mistakes were something to embrace and undeniably just part of the process of learning. This unsurprisingly conflicted with my well-tuned strategy of “apply the procedure and hope it fits”, and then consequently panic when it doesn’t.
It is important to note that I feel my overall fear of mathematics did not stem from the subject itself but rather my own lack of engagement in mathematical experiences. In reflection, I don’t believe that I ever engaged particularly well in Maths lessons or mathematical discussions. I felt that it was always a struggle to bend my thought process to match any given explanation and so I would take on the essentials to get by and move on, never fully grasping key conceptual understandings. But, I enjoyed learning, I was and am interested to know and understand, and I honestly have always loved the process of discovery. Yet, that did not always coincide with what was happening in the classroom. I don’t think I would be alone in this feeling and I certainly have seen it in my classroom where students can’t seem to find the courage to voice what they are thinking, just in case it is wrong.
I remember being sent (dragged, bribed) to tutoring once a week in early high school to improve my problem-solving skills. Predictably my ‘hope the procedure works’ strategy had begun to have a lower success rate as the problems became more complex. I found that I just did not have that foundation of conceptual understanding to back me up, and so I began to flounder. These tutoring sessions were agonizing at the time (picture badly lit booths with glass partitions separating each student and no airflow). The ‘carrot’ for each session being the chance of playing a Space Invaders multiplication game on the computer. However, after the 50 minutes of intense pressure to give the correct answers, even that gem of motivation lost its shine.
Not only did I find these lessons mind-numbingly boring and unhelpful but more importantly they did nothing to ease my fear of getting the wrong answer. If you have ever stumbled across a Maths problem that you were unable to solve you might agree that it is the mental equivalent of being caught in a tricky yoga position. Your brain just gets stuck. You have a vague inclination of where you want to end up but the way in which you start remains elusive. Not a great time.
So, this for me raises the question of how as an educator I can prevent my students from being metaphorically stuck on their yoga mats, unable to start and incapable of reaching their goal, all the while deathly afraid of falling on their face.
Over these first six months of being in the Champions of Maths program our focus has been to develop our classroom methods and instructional practices and hopefully have a positive impact on the performance of our students. Pedagogically speaking I am passionate about creating a learning environment which removes that fear and allows my students to take risks, think critically and creatively and to develop those deep conceptual understandings that are required to think mathematically and approach unfamiliar problems with confidence. Most importantly I want them to have fun and solve these problems efficiently in a way that makes sense to them.
At the beginning of the program I wanted to address effectively targeting misconceptions for my students because this is something that as a self-confessed overthinker has and continues to boggle my mind. This is still an overarching goal for me, however, over the course of the first classroom visits, I began to notice with the help of some feedback that my students were not working as collaboratively as I would have liked. They were also not participating in discussions productively in order to really engage with the learning goal. Additionally, their engagement in collaborative tasks was inconsistent largely due to the fact that I had not effectively introduced them to visible random grouping. Instead favoring ‘random grouping’ in the sense that the groups changed frequently but were almost always carefully and intentionally planned.
During the second class visit my students had begun to work together in order for a single ‘leader’ to successfully be able to report the thinking that was happening in their group. However, the fear for many was still apparent and I noticed myself continuing to call on the students that I knew could provide an explanation to avoid putting pressure on others. This in turn not only restricted my ability to actively use a variety of talk moves to enhance discussion but also limited the accountability to only select students. At this point I was still very much concerned for the diverse ability levels in my classroom and found it difficult to open up the discussion enough to promote accountability across every group member.
Moving on to the next observed classroom visit with admittedly a fair bit of problem-solving in between! I selected a more closed type of question and my learning intention asked students to apply addition strategies to solve a problem, with a focus on accuracy and efficiency.
George has 97 Pokemon cards, Freddy has 96 and Penny has 123. How many cards do they have in total?
My students applied different calculation strategies and I was able to have more quality conversations with individual students as I walked around to the groups. I was pleased to see that there was more engagement and productive collaboration from my students. Although I found I was getting more from talks with individual students, it was pointed out to me that these quality conversations could be made much more valuable by further increasing the active engagement in the post-activity discussions.
The fourth classroom observation featured a problem with the learning goal of understanding the structure of the numbers in time and the kids really had a lot of fun with this one.
How many times does 5 appear on a digital clock in 24 hours?
The students were engaged in the problem and they were together for the discussion. I was successful in facilitating the discussion around the efficiency of different strategies and participation overall was up remarkably on previous lessons. I decided to continue on with this theme with a follow up lesson featuring another time problem.
As this wasn’t a lesson being observed I spent a bit more time and added a few extra elements, the students accessed the question in their groups via Connect our online portal and I opened up an online discussion thread in addition to our verbal discussions. So much confidence and engagement!
Now to the present and I am really beginning to gain valuable awareness into modifying my classroom methods and instructional strategies to better incorporate the 5 Practices of productive mathematical discussions but also there is a noticeable transformation in my students. Some of my students are beginning to show that they are revising their thinking in response to others during a discussion. Overall, I am seeing a greater inclusion of more of my students across a range of ability levels. I am becoming more skilled in selecting the right students at the right time to speak and above all more students who are often guarded in discussions are volunteering to explain their thinking.
Bring on the next six months!
Find out more about the Alcoa Maths Enrichment Program