Earlier in the year I wrote a post titled “Maths Extension/Enrichment with Edmodo“, outlining my plans for an enrichment/extension program for high achievers in Maths at school. It took longer than anticipated to get started but from the start of Term 3 (July), I met with 5 Grade 6 students, 8 Grade 5 students and a couple of very bright Grade 4 boys on a weekly basis for an hour. ( Another teacher does the same with Grade 3 and 4 students ).While we can argue that research suggests mixed ability groupings are more beneficial ( for the rest of the week, these children work in that environment), I am in no doubt that the program has been a resounding success and a great sense of engagement and enjoyment has been felt by all involved, including the Maths teacher!
Whether it is enrichment, extension or a mix of both, which was a point of contention with some readers back in the original post, I am not sure. Regardless, some great mathematical thinking is taking place every week between an enthusiastic, engaged group of students.
The weekly lesson itself takes no time to plan. I simply upload a problem to the MEP (Math Extension Program) Edmodo group at the start of the week so the students can check in for some preparation time before we meet. Don’t get me wrong, I know exactly what I want out of the lesson when I select the problem and I send a post lesson report to the classroom teachers outlining what we did. The beauty of what we do, though, is that we don’t know what will result from the lesson until it is over. There is no chalk and talk, no pre-task explanation of what to do, no expectations that we have to solve it at the end of the hour. What you will see is a group of mathematicians sitting around together, sharing strategies, discoveries, questions verbally, through demonstrations on the whiteboard or via iPads or by posting on Edmodo.
What has improved throughout the term has been their problem solving skills, collaborative discussions, use of technology aids to organise and simplify the process ( Numbers on the iPad has been a real winner, using formulas to test and monitor conjectures, as has Explain Everything to record ideas and share via the whiteboard) and most importantly, their ability to articulate their thinking and learning, both their successes and failures ( something they haven’t experienced much beforehand).
A great example of the whole process is our last learning experience, which lasted over two weeks. Most of our problems have come from the well established Maths Enrichment website, nrich. ( another worthwhile site is New Zealand Maths ). The beauty of nrich is the incentive to have your solutions published on their website, giving bragging rights to those who succeed, either partially or fully ( more on that later) Our last problem before the holiday was Summing Consecutive Numbers. The problem is presented via an introductory video that explained the nature of the task. Each student had their own iPad ( its only a small group – we could have used the laptops) so watched it independently. After a two minute debrief to make sure everyone understood the task, we went straight into solving the problem. Beforehand, though, we made a pact that we would publish our solution on nrich, which always had to be posted by the 21st of each month, which just happened to be the last day of Term 3 ( we had previously missed deadlines or solved old problems, so this was our first chance.)
What was great about this particular problem was that the task itself was simple to start with – just adding numbers – but discovering and proving patterns and formulas was a real challenge that need real arguing and collaboration. During the first hour, the students were so focused on discovering patterns. Every idea they had, no matter how small, was posted on Edmodo. This proved to be an important step as the following week we were able to refer back to all of our discoveries. LEt me interject here and state that I was an active part of this as well. Before the lesson started, I was none the wiser about the solutions so I became an authentic learner with my group, making conjectures and testing theories side by side with them. (I talked about the importance of being a learning role model in a previous post). Some children used Numbers spreadsheets to arrrange the numbers into common sets as we investigated, others jsut used pen and paper while others used Explain Everything to brainstorm every idea they had. At the end of the sessions, we had over 60 posts on Edmodo and had made some amazing progress and they continued on over the weekend and into the following week determined to meet our deadline.
The following week, we met with all of our discoveries articulated on Edmodo and we were ready to write our Proof of the Summing of Consecutive Numbers. The final result was exceptional and is published below for your viewing pleasure.
Consecutive Numbers Proof
I showed their classroom teachers and my fellow MEP teacher and they were blown away by the depth of articulation and understanding in the submission. I merely guided them through the process of writing the proof but it is all their work (some sentence structures needed some modelling). To a person, they all requested a copy to put in their blogs and digital portfolios and now wait excitedly for the news it is posted on nrich’s website next month. Regardless, I am going to showcase their effort at the School Assembly, much to their satisfaction of being recognised for being mathematicians.
Being such a successful and rewarding experience, I then started thinking – should this just be the domain of the MEP group? Why can’t the other students in their grade follow the same process? It’s not as if they don’t do problem solving based tasks. This task in particular could have been entered into by ALL the students at different levels and the MEP students could have worked with the others to extend their thinking. The more I work with my group, the more I realise this model of collaborative problem solving should be done more at school. Sure, some of the less able students would not have arrived at the sophistication of thinking these high achievers attained but they could have contriubted to the adding and would have discovered some of the lower level patterns.
I think we have to stop thinking that not all students can enter into these tasks. Nrich is full of problems for all ability levels. Its my new goal to attack at school. I still think these MEP students deserve their time together to work with like minds. But I also think everyone deserves the experience they are getting. It’s what a differentiated curriculum is all about.