26 June 2019
My name is Rachel Spalding and I teach Year 2/3 at Glen Huon Primary School in Eaton, Western Australia. I also co-lead the Maths Committee at our school. I am currently participating in the Alcoa Maths Enrichment Program: Champions of Maths (ACoM).
Growing up, I loved Maths. I still love Maths. I tutor four Maths students outside of school hours from Years 5, 7, 9 and 10. If I could deal with the behaviour management of high-school students, I reckon I’d be a Mathematics specialist teacher. I love crunching numbers and finding answers – however, I can now see that it’s the fluency aspect that I enjoy the most. I’ve never really been a “problem-solver”, as I’m more about collecting and analysing data. I wasn’t aware of this, until now.
I am about to take you on my journey through my first six months of the ACoM program, detailing what I’ve experienced so far, what aspects of my teaching have changed and what I hope to experience in the second-half of the program.
Now, I’m a bit nerdy at times. Get through the next few paragraphs where I satisfy my ‘nerdiness’ but bore you to tears, and I promise I will then get into the good stuff.
Our first workshop with Shyam Drury was mainly about discussing an article: Effective Teachers of Numeracy by Mike Askew. Shyam talks more about this in the first blog entry here. The exploration of three very different teaching approaches (the orientations) featured in this article really interested me – I had never heard of any of these terms before, let alone understand which one I was. I was very excited to complete a self-assessment survey to find out which orientation I was most like.
Here comes the nerdiness…
According to this survey, I am a mix of all three: connectionist, transmission and discovery. This frightened me! What kind of teacher am I? Do I even know what I’m doing? If I’m not following a consistent approach, how are my kids going to consistently learn? So, I not only read on, but decided to research other papers in which these three roles were explained.
- - In the discovery approach, learning is the priority over teaching and the speed of learning is determined by the students. Students use their own strategies to work things out themselves.
- - In the transmission approach, the teaching becomes the priority and consists of repeated information and working out using standard, taught routines.
- - In the connectionist approach, there is a much greater relationship of teaching and learning between the teacher and the students. Various methods of calculation are taught in this approach, and students choose and use those which are efficient and effective.
In other words, “the discovery and transmission approaches can be considered as opposite ends of a teacher scale of guidance, with the connectionists somewhere in the middle.” You can read more here.
I was greatly reassured by Mike Askew that a teacher could practice connectionist principles and transmission principles when he said “no one teacher did, or is every likely to, fit exactly within the framework of beliefs of any one of the three orientations; many teachers combined several characteristics of two or more orientations.”
BINGO! I’m all good. How about you? As promised, here comes the juicy stuff!
I was really nervous about my first lesson in front of Shyam and Susie (my Glen Huon colleague). Actually, I was really nervous before every lesson in front of Shyam and Susie. It’s daunting knowing that there will be two adults in the room watching your every move! We were instructed to teach a 30-40 minute maths lesson that would be part of our normal routine – nothing special required.
Nothing special required? Be careful what you wish for!
My lesson was definitely nothing special. It involved very little participation from me at all! My students were asked to survey the class with the question “What faction are you in?” and construct a tally chart and bar graph with their collected data,. And off they went! Hopefully the past week’s introductory lessons on Statistics & Data had had some effect on the kids. I spent a lot of time on the setup and modelling part of the lesson, as I always do, and this enabled the students to get started straight away with little assistance.
The amount of positive and constructive written and verbal feedback I received from Shyam regarding my lesson was exciting – there were things I’d done well and things I could work on. This also helped to remind me that this is a coaching program, rather than an assessment of my competency as a teacher. The three of us participated in a discussion about our lesson’s on the same day, which was very valuable while the content was still fresh in our minds.
My next focus, derived from Shyam’s feedback, was to connect the task with a reason, as according to Shyam, you should always have a question the students are trying to answer, or something meaningful they want to find out. For example, in today’s lesson, I could have set up the story with something like:
“We have a new student coming into our class and we need to determine which faction to put them in. I wanted to have the factions pretty balanced, so let’s find out how many people there are in each faction and then figure out which one would be best to put her in.”
So, I took this literally. Like, really literally… I discovered an activity on the nrich.maths.org website where students were required to solve the following:
And I linked it to the way a grocer might order his capsicums at the supermarket!! Really Rachel???
“Alright kids, I want you to have a look at this image. Think about this poor fruit & vegetable worker at Woolworths who has been asked to change the order of his capsicums to something different every day. How many possible solutions are there?”
I must admit – the picture did spark some interest!! The kids were excited to get cracking, so off they went.
And so many started drawing real capsicums!! All these young Picasso’s and Van Gogh’s of the world focusing on the shape of their capsicums rather than the main idea of the activity… systematic patterning!
It sure gave the three of us a giggle after hearing Shyam say “When I said link your task with a reason… I didn’t mean quite that specific.”
Needless to say, the students really enjoyed the lesson and not one group was able to solve the task in the lesson. That afternoon, the kids said “Miss Spalding, can we solve that capsicum problem now?”
The following day, I gave them time to have another go, after explaining how to systematically approach the problem to efficiently work out the answer and make sure they can find all outcomes. This involved explaining to the students they should start with one colour on top and only switch the bottom two colours, then start with a new colour on top and so on. Here are some examples of the students beginning to grasp how to use a systematic approach with this particular problem (except these photos are after we added a fourth colour – blue). I promise the kids are grinning!
My next focus, derived from Shyam’s feedback, was to reduce the amount of instruction time at the start of my lesson to give the students more time to play and try, fail, discover. He also mentioned that the purpose of a task does not have to be real world – there just needs to be a clearly understood goal the students are working towards – in this case, working out all of the solutions was enough of a goal as the kids were engaged through the challenge. In other words, no more capsicums.
My third formal coaching lesson was a great success, although I still spent too much time on the introduction of the lesson.
Some children built a sandpit in a square shape. They used ten vertical posts on each side of the sandpit to mark the boundaries. How many posts did they use altogether?
From this lesson, I wanted my students to work towards three goals:
- Understand the problem – and arrive at the answer of 36 posts (40 is incorrect as this shows the students are counting the corner posts twice)
- Draw a diagram to show problem-solving
- Plan and communicate in random groups.
Although the kids worked well together, this problem was really tricky for them, and they had difficulty with many elements that I had not thought about prior to the lesson. The largest obstacle was the idea of drawing the diagram in bird’s eye view – “Bird’s eye what, Miss Spalding?!”
But the positive? Here is a common misconception across the whole class – a concept I can explicitly teach them in the next few lessons!
Another one of the major obstacles that came up in the original task was trying to draw a square with ten posts on a side - free hand. They weren’t able to line up the sides, so couldn’t be sure about how many posts were needed altogether. So Shyam suggested I use a smaller number and start with tiles around a garden next time, as they are flat and easy to draw. This should allow them to focus on the main ideas, like not counting the corner post twice. After spending FIVE lessons on bringing these elements and strategies together, we worked out the answer to the original problem, and my goodness – the kids were so chuffed. Not only had they found the answer, but they had persevered and remained engaged over five problem-solving lessons all derived from one small problem. So many misconceptions were able to be discovered and addressed after one question. Amazing!
Definitely my favourite and most successful lesson so far. This was literally how it went:
“How many fingers are in the room? GO!”
Very little instruction, one question, one task. Their faces were priceless after I gave them this task – there was definitely a loud “OoooooOOoh!”
And off they went! Of course, four of my top kids were randomly grouped together, and wrote ’25 x 10 = 250’
Group 1: “MISS SPALDING WE’RE DONE!!!”
Blimey! How in the world…?
Me: “Sorry boys… I forgot to tell you… you can’t count the thumbs…”
There was my extending activity. That should keep them going…
B from Group 1: “Well, everyone has two thumbs right?”
D from Group 1: “Yep.”
B from Group 1: “So, we just do 2 x 25, which is 50. There are 50 thumbs in the room.”
D from Group 1: “OH! And that off 250 is 200! MISS SPALDING WE”RE DONE!”
The thinking power and ability to communicate in this group astounded me. They had completely blown me away – and one of them was only Year 2! What these boys had done in their group gave me so much content to run with in the post-activity group discussion. They explained to the rest of the class how they had come up with their number sentence and how they worked together and listened to each other’s ideas. We talked about where the numbers in the number sentence came from and what they represented.
Since this lesson, we have completed this activity again, this time adding in toes. Every group was able to arrive at a successful solution and represent their solution in a number sentence.
Bingo! So very awesome.
So there you have it. Six months of fun. There has been so much more going on behind the scenes – many more problem solving activities taking place than just these four, but I’ll save the rest for the next blog.
Bring on Round Two.