Maths Extension – engagement with nrich and Edmodo

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.

Maths Extension/Enrichment and Edmodo

Addressing the needs of all students in your Maths Classroom can be a real challenge. Do we stream based on ability? Do we use collaborative mixed ability groups? What’s the role of rich,open ended questions and differentiated curriculum? How do we pitch to the middle 50% but still cater for the upper AND lower 25%? It’s a challenge I’ve been grappling with for 25 years. Recently, I’ve been considering the use of Edmodo to provide access to extension and enrichment Mathematics opportunities for the more able students in the classroom. ( For those unfamiliar with Edmodo, click here for a description) This is my plan. I would be interested in feedback on its potential effectiveness before going further with it.

Identifying the target group
This is not a simple task. The standard method these days seems to be the standardized test. In Australia, we have NAPLAN, the yearly national assessment task targeting Years 3,5,7 and 9. Debating its merits here is not my intention today. I see its usefulness in quick identification of the higher achievers in a current group of students. I would then administer the next level test to these able students to gauge how far their abilities extend beyond the current class level. For example, after selecting a group in Grade 6 based on Grade 5 results from the previous year, I would give them the Year 7 test. Using data analysis, I’d identify their strengths and learning needs for future programming and targeted areas for extension and enrichment.

This would only be a starting point. Standardized tests are a narrow form of assessment that don’t necessarily identify fully the student’s need for extension in Mathematics. I’d continue to evaluate the children within and outside the extension group. I’m sure during the year I would identify children who could join the group for extension in specific areas they excel in. The beauty of using an open, collaborative, independent learning platform like Edmodo is that students can opt in and out of specific tasks or units of work.

The Edmodo Extension Maths Program
This is how I envisage setting up and running an Extension Program in Mathematics within the standard classroom environment.

First I would set up a Maths group for every student in the class. I wouldn’t want the Extension group to stand out from the crowd by having sole access to Edmodo for Maths. I would use this area to post problem solving tasks that the whole class could engage with, links to quality Maths sites that students could use to consolidate understanding in current units and revise past lessons as well. I would provide opportunities for discussion of strategies used, allow children to share their understanding, ask questions that both teachers and students could answer and share with the class. I’d allow for the possibility of using iPad apps like ShowMe or Explain Everything to post audiovisual explanations or lessons created by teachers or lessons. I would also post resources children could access to support them while working independently. The extension group could have a lead part in sharing their expertise with other classmates in this main Edmodo group. they could even create their own mini “Khan Academy”.

I would then create a subgroup within the main Edmodo group for my Extension/Enrichment group. I envisage this group being formed from able students across all classes in a particular grade level, possibly across several if there are able students in lower Grade levels who could qualify. I would plan for this group to access materials and concepts beyond what is available to the main group but accessible through the same platform as everyone else.

Obviously there would need to be some significant planning and negotiation with all class teachers to ensure this worked within their programs. consideration would have to be made about how these students would participate in both the extension sessions and regular class lessons. I see this happening in a number of ways.

Option 1. The students begin the lesson with the rest of the class. When they have received enough instruction on what is expected of them, they move on to completing required work for their class teacher independently, leaving their teacher to work with those who need support. When they complete the set task, they submit it on Edmodo through the assignment section and then enter their Edmodo Extension Sub group to collaborate on the higher level tasks assigned by me. They communicate with each other either personally if in the same grade or via posting their strategies, solutions, suggestions, questions, comments on Edmodo for the rest of the Extension group to respond to. Their work will be completed digitally and submitted through the Assignments section of Edmodo so that I can feedback and collaborate with them on the tasks.

Option 2. Alternatively, for one session a week, the group would meet with me and work on high level problem solving tasks and extension work related to the unit of work their class in currently involved in. Using online enrichment programs like the website nrich, the group would be collaborating on problems, sharing their possible solutions and strategies not only with each other but by submitting group or individual solutions on the nrich site for other like minded students to collaborate on through global forums. I envisage opportunities for the students to use technology such as screen casting computer programs or iPad apps I previously mentioned like ShowMe to record their solutions and strategies audio visually. Using a site like nrich, which would allow them to self select problems to solve would give them the freedom to challenge themselves both individually and in teams. It would also give them the option to opt in and out to return back to their class if they choose to.

Option 3. A third model could be a choice of making daily decisions to complete regular class work as homework and deciding to work in their extension groups or individually on Edmodo on a daily basis. As their test results would have already indicated in being selected for the program, they have most likely mastered the skills being taught in the regular class program and a simple completion of the tasks for homework would satisfy their class teacher’s need for evidence they have understood that area so they can report on it later in the year. This option fits a Personalized Learning model commonly encouraged in today’s schools and would allow the student to remain engaged in Maths at or beyond their level rather than going through the motions of completing simple tasks.

How Edmodo would help me implement this program

  • All links to nrich and teacher/student created work would be posted on Edmodo, with individual entries tagged or saved in libraries so that students could always have easy access to the tasks.
  • The collaborative nature of leaving instant comments and feedback allows the group to stay in contact with each other outside of school to continue their problem solving together. This could become engaging homework, with the teacher able to remain in contact and feedback on the work they post on Edmodo.
  • Each member of the group can work on their own problem solving and submit it to me or their teacher independently of the group for personal feedback before sharing with group if they choose to.
  • The function of the Assignment process in Edmodo allows for children to receive private feedback and allow the teachers to collect, collate and mark each submission, enabling effective assessment to occur at all points in the program. Teachers can submit rubrics and criteria for marking the work on Edmodo so the students know what is expected of them. I have had success with such use last year working with a Literature Circle group.
  • The fact that all students from the classes are also using Edmodo for their Math work as well means that all students can easily be given the opportunity to opt in to or out of the Extension group at any time without any extra planning or organisation by the teachers. I think this would be an important option as it would encourage other students to take on the challenge of extension tasks if they choose to.
  • Other teachers can be given co teacher status and become involved in the program, either as observers or contributors. This would allow for professional feedback on the suitability and effectiveness of the program.

These are my initial thoughts and obviously this kind of radical change to the status quo of primary schools as I have experienced them would involve leadership, class teacher, parent and student discussion. I need to think through this more and would appreciate feedback from others on how they have managed the needs of the more able students in their classrooms. I would really appreciate readers leaving a comment and contributing to the conversation of extending and enriching the learning of the able mathematician.