As an observer, I was focussed on the types of questions Lucie asked and the use of materials for scaffolding. The former focus, being something that I am trying to develop across all curriculum areas myself. The latter, being a goal of the MDTA teacher I mentor. I wanted to see best practice so that I would know how to support him in the use of materials and scaffolding strategies in his instructional group lessons.
I tried my best to write down all of the questions Lucie asked to see if I could identify any patterns. What I did notice, was that there were many closed questions in the beginning to middle part of the lesson. Upon reflection, I think this is was for many justified reasons:
- This was the first time working with these students and so she needed to gauge their levels and level of number knowledge.
- She had to repeat key information and so by asking questions over and over again, she was able to consolidate key knowledge.
- Due to the urgent need to accelerate the learning of these students, Lucie had to prioritise how much time to spend on each area of learning. So she may have made the decision to get 'surface knowledge' 'out of the way' so that she could get to the strategy learning and the deeper questions faster.
- Lucie mentioned "Being a good mathematician means you’ve got to be right and you’ve got to be quick." This means that we need to have quick number knowledge. This may have been the reason behind such 'quizzing questions.'
Towards the mid-end part of the lesson, the questions became a bit more open ended. Questions like: Why do you think that? Can you tell me why? What if...? Where did you get that answer from? I think this may have been because...
- They were at a stage now, where they had the knowledge, and were now being extended to transfer that knowledge into problem solving and strategy learning.
- Lucie was trying to encourage students to make the connection between what they already know and what was being learnt.
This affirmed my practice, because I too, aim to prioritise learning time in such a way, that do not spend more than the necessary time on what students should already know. Rather, I like to spend time on the extending of ideas and I try to aim for accelerated learning. Meaning that students are making bigger leaps within a lesson, rather than lots of little steps over a series of lessons.
Questioning and cognitive engagement are a big focus for me, as part of Manaiakalani. Through this observation, I was able to see how I might structure my lesson and the types of questions I might ask. I saw how I might prioritise learning and my attention in order to achieve accelerated outcomes.
Scaffolding - Materials
I observed fantastic use of materials to help the students to visualise and to support their thinking. Lucie used:
- Pre-prepared circles cut out for the students to divide into fractions and to shade.
- Pom-poms (or "lollies")
- Lolly vending machines outlines for students to 'fill'
- Post-it notes for writing of the abstract fraction symbols
- Fraction 'flip cards' that displayed a range of fractions that were easy to flick through, rather than to draw them, or create them using the foam fraction pieces. They were great for a quick fraction knowledge check!
Through the use of such materials, students were able to make connections between the continuous (shape or region) to the discrete (set or number) and the abstract symbol (e.g. 1/4).
From this discussion, I am motivated to head to the $2.00 store to get some more creative materials that will help to engage the learners in my class!
Scaffolding - Folding Back
There were two instances, where Lucie folded back. In this case, one step back, two steps forward is a good thing. The first instance was when students were no longer thinking about their responses - but calling them out - or, guessing. Lucie stopped the lesson and encouraged students to think before they responded. This helped the lesson to slow back down to a steady workable pace that all students could participate in. By recapping what had been learnt so far, students returned to thinking through the process, rather than calling out random numbers.
The second instance, was when there was a noticeable difference in the two halves of the groups. One half was calling out and contributing ideas at a rapid pace, the other half were mute. To ensure that it was because of shy-ness, rather than lack of knowledge, Lucie folded back to work with halves. Something that all group members were confident with. She went on to say "You know halves, that's too easy, so now we are working on quarters." We concluded from this that these students were able to use this strategy, they were just very shy to contribute ideas and because of that, were not able to process the new learning.
In our professional follow up discussion, we talked about the possible use of speaking frames to help structure speech. I have these somewhere in my teacher cupboard/files and will get these back out! The second strategy was to have a tangible ‘speaking tool’ to hold such as a koosh-ball or plastic microphone.
Light Bulb Moments
I had three lightbulb moments during this observation:
- ‘Creates’ in maths don’t need to be fancy. The simpler the creates the more depth you can add into the description and discussion.
- As we continue to 'figure out' what Learn, Create, Share looks like in Maths, I am realising more and more, that it is perhaps the most simple creates that are better. In maths, it is the thinking, articulating of that thinking and reasoning behind decisions that are the most important. In the observation, Lucie instructed: "Here is your cake - you are going to show me three quarters on there (circle card cut outs) -you might need to fold, shade in…" Students were 'creating' their own versions of what three quarters looked like to them. They were also negotiating, decision making, thinking and problem solving. Taking a photo of this with a written description along with it, is a much more valuable 'create' for students who are in need of accelerated learning, rather than spending a week creating a poster with a similar message.
- OTJs = do they apply the knowledge to problem solve and strategies - need explicit teaching on this.
- One thing that Lucie mentioned in our follow up discussion was the fact that OTJs should not be based on number knowledge alone. They need to be based on how well students transfer this learning to problem solving tasks and to new strategies. This means we need to allow for more opportunities for students to show that they can. This leads me to the third light bulb moment.
- Accelerated learning means that we need to provide rich tasks that integrate all strands together.
- Because we are aiming for accelerated learning, can we really justify spending two weeks or more on one strategy or even strand? I believe that it is through rich tasks that help to integrate all number knowledge, strategies and strands, that students are given opportunity to transfer their number knowledge to real life problems, and give teachers opportunities or 'teachable moments' to extend thinking and introduce new concepts. E.g. Miss Kyla wants to buy a bag. It is $20 but there is a 30% off sale. How much will Miss Kyla have to pay? Through this task, students are required to do the following:
- Find a tenth of 20 = $2 (division, decimal, fraction knowledge)
- Multiply 2 by 3 to find 30% = $6 (mult/div knowledge)
- Take away 6 from 20 = $14 (add/sub - could use tidy numbers, number line etc).
- This has inspired me to think about how I might structure my maths lessons in the future.
- This also highlights the need for teachers to understand, with depth, the strand expectations, knowledge expectations and strategy expectation so that they can conduct formative assessment through these tasks for individual students.
It was such a great lesson overall. As I missed a bit of PLD from Lucie last year due to Maternity Leave, I found this lesson motivating and affirming. I am excited to deepen my knowledge about Maths as I have always felt that this was my personal area for development out of Reading, Writing and Maths. Thank you Lucie Cheeseman for presenting a great lesson!