Teaching as Inquiry 2019 - 2nd Reflection - First Steps

Maths has always been one of my favourite subjects to plan for and teach. As a result of the professional development sessions we have had with Dinah Harvey and the readings and videos I have watched, I am MORE passionate, MORE enthusiastic and MORE excited to plan for and teach maths than ever before. I put this renewed enthusiasm down to the fact that I wholeheartedly believe that that principles that my approach is based on is the best way to help students not only develop their capabilities as mathematicians, but for them to grow in confidence to actually see themselves as mathematicians.

We are now half way through Term 2 and it is time to reflect on what changes I have made to my programme, and what effect these changes have had on students' number sense and confidence as mathematicians.

The initial areas that I have been focusing on are:

- Using Images and visual representations
- Planning activities that have multiple entry points and have a low floor and high ceiling.
- Using deliberate acts of teaching i.e. questioning to prompt them to think about their answers and explain their thinking.

Using Images

Here are some examples of the rich tasks that we have completed recently that deliberately include visual elements.

One of the first things that has been obvious is the increased level of engagement that students have shown completing these tasks. Students are quick to begin the tasks and are often still deeply engrossed in their work when the call is made to pack up.

The increased visual focus of these lessons has helped students to connect learning and see patterns and relationships in numbers. One example is the way students have been able to link timestables with arrays and then transfer this knowledge onto calculating area. The Venn diagram activity and the Multiplication Stars helped students to identify patterns and see commonalities between the different timestables.

 It has also been fantastic to hear the conversations between students discussing their thinking and challenging each other on their solutions. One example was a discussion I heard between two boys when attempting to re-design the school using the scale 1cm square = 1m square. They were trying to work out what size to make the hall on their map and got into an intense debate about how big it needed to be and what dimensions it should have. Having a 1m square drawn on the ground helped the students to visualise how big a 1m square actually is. This would have been difficult to visualise without them being about to see what 1m squared looks like.

Multiple Entry Points and Low Floor/High Ceiling

I have a big range of abilities in my class (Stage 4 - 7). Therefore, when planning my rich tasks I have made a conscious effort to ensure that the learning is accessible to all students, but also challenges students to extend their thinking and stretch their abilities. One way I have done this is by setting activities that have multiple solutions or approaches. One such activity was the Garden Tiles task:



This task could be completed in a number of different ways and the minimum required knowledge to achieve success was for students to know the properties of a square i.e all sides are equal. It also offered the opportunity for more able students to learn about square number and apply their multiplication knowledge to make calculations around how many and what sized tiles that they could use.

Deliberate Acts of Teaching - Questioning.

This is actually been harder than I first imagined. When discussing a students work with them there have been times when I have had to restrain myself from leading students to an answer or taking the opportunity away from them to think by giving them too much information.

Some of the questions I have regularly been asking students are - Explain to me what you have done so far? Why did you decide to do it that way? And, what are you going to do next? These questions force students to think about what they have done, and more importantly justify why they have done it the way that they have.

There have often been significant pauses after these questions or limited responses. At this point I have to remember to resist the urge to 'save' students by feeding them the answer.