Hi it’s Jodie Walton again and welcome back to our Alcoa Champion of Maths blog. What a busy time we have had with this wonderful mentoring program. My first blog entry covered ‘Discussion is Critical to Understanding’. This time around I would like to talk about getting students to participate verbally, without the fear of getting the answer wrong. Throughout the program, one of the main emphases has been on discussions. Discussion between the students as well as discussion with the students to try and increase mathematical understandings.
This year I have a class where many of the students are very reluctant to voice any opinion on mathematical matters. Have you ever had one of those classes that are chatty all the time until you ask them a mathematical question? Then there is stunned, terrified silence, except for those 3 souls who always have an answer. Well, that is the class I have this year. During the year I have managed to get more students to give answers and participate in discussions, but frankly, many days feel like I have been at a dentist surgery trying to pull out all those teeth. I have used all those great strategies like pulling names out of a hat, ‘Popcorn’ sharing and my favourite ‘Think Pair Share’ to try and get students to participate in the discussion only to call out a name and have total silence, the class sitting and waiting patiently or sometimes not so patiently.
While doing the reasoning element of our program, Shyam put up some problems that promoted discussion within our group. Not only were they interesting problems, but the great thing about them was that there were no wrong answers. After much investigation, I have found many more such problems and many of them are available free on the internet.
So in this blog, I am going to share a few which I have found work very well in my class and how I have put them in place to promote mathematical discussion, increase confidence, and enhance vocabulary. You may be able to tell that I am thrilled with the way these problems have worked.
Because there were so many different types of problems I decided to create a PowerPoint presentation for the week. I needed to enhance my PowerPoint skills and thought this would kill 2 birds with one stone (or keyboard). Each day I would present a different type of problem as my warm-up activity. The week started with Estimation Monday, 2 Truths 1 Lie Tuesday, Which One Doesn’t belong Wednesday, Think, Notice, Wonder Thursday and finishes the week with Cube Conversation Friday. There were many others I could have used as well, but I decided to stick to these 5 to start with.
I got these problems from Steve Wyborney’s website (https://stevewyborney.com/). He has a blog that he writes regularly and has many great things that you can download. The estimation problems I used were from his “20 Days of Number Sense & Rich Math Talk” blog. I decided to start simple, remembering my main focus was for non-threatening discussion and participation. The estimation task involves the students having to guess how many ornaments are in the vase. After sharing with each other, followed by class discussion, the answer is revealed. A new picture is then shown with a different amount of ornaments and further discussion (wow, lots of discussions) and the answer is revealed again. This process is repeated until the fourth picture. During the discussions I encouraged the students to tell me how and why they came totheir estimation. By the last picture their estimations were fairly close to the actual amount of ornaments.
2 Truths and 1 Lie Tuesday
The problems I used for this activity were from Mashup Math (https://mashupmath.com/freemathpuzzles). Again you can get many of these activities for free. You can even sign up and receive weekly activities. For this activity I got the students to work in pairs with a whiteboard and marker. Their task was to work through the problems and try and find which problem is the lie. Again there were loads of discussions as the students tried to explain to each other and then, in their enthusiasm, to other pairs why one statement is true and another isn’t. Pairs were then encouraged to get up and explain how they proved if a statement was a truth or lie. The rest of the class was keen to follow up on whether they agreed or not.
Which One Doesn’t Belong Wednesday
This is my favourite discussion activity. The answers are so varied that I can get all my students – a class of 23 – to give a different answer. Even the reluctant ones will share their ideas. There are many varied images that you can use from agoogle search and many different themes and topics that you can use, which can lead to the main topic for your lesson. This was the first one I put up and I was amazed by some of the answers that were given. From simple answers like ‘the 5 is a wiggly line’ to more complicated responses like ‘the 1 doesn’t belong because it isn’t a prime number’ (yes they do remember somethings from last term).
Think, Notice, Wonder Thursday
The students really liked this activity and it certainly promotes discussion. In fact all of my students wanted to have a turn to share their ideas with the class. I have found that so far the discussion isn’t strictly mathematically orientated, but with guidance and modelling I am hoping to lead the students in this direction. A photo is displayed on the board and the students are encouraged to come up with a think, notice or wonder comment. The first few times of doing this activity I encouraged the students to complete this activity verbally. I then decided to get the student to record 2 statements for each, a total of 6 statements. I gave them 5 minutes and many students were able to come up with multiple statements. The image I used for this week’s activity was from Mashup Math (https://mashupmath.com/) I got the image from a book that I purchased so won’t be able to show it on this blog (you know all that legal stuff), but I will describe the picture to you. It was a colourful picture of large tubs of lollies (candies). Each tub was a different colour and there were different types of lollies in each tub. The image gave the impression that the tubs were deep and that there were many more extending from the picture frame. Below are some of the statements that students gave me in regards to this image.
‘I noticed that some of the tubs are different sizes.’
‘I think it looks like a health risk.’ Who says that we can’t combine other subjects with maths?!
‘I wonder how far it spreads out because the outer crates are cut off so maybe there’s lots more beyond the picture?’
‘I wonder how deep the containers are?’ (this is from my most reluctant mathematical participant).
Cube Conversation Friday
Finally we come to Cube Conversation Friday. These activities were from Steve Wyborney’s “20 Days of Number Sense & Rich Math Talk” blog (https://stevewyborney.com/).
After going through a couple of examples of how this activity worked the students were very keen to discuss their ideas with each other. These photos aren’t showing students putting up their hands to answer questions, but of them discussing with each other how they saw the cube pattern.
This final photo shows a student explaining how he saw the different configurations of cubes and how they helped him determine many cubes there were in total.
In conclusion I hope that I have been able to encourage you to give these wonderful activities a chance. My aim was to promote mathematical discussions in a safe, non-threatening environment and to increase reasoning, justification and vocabulary skills within my class. These warm-ups are certainly helping me achieve this goal.