We have had a few inputs now on mathematics: and they have all been most useful in helping me to realise that imagination is maths and maths is imagination. Long way to say it; basically think to the limits of space. Endless? Yes. Claire needs to enter the classroom and not just see the earthly game of “ooo, where are the ticks and crosses on my worksheet?” Children need to be exclamation marks and rocket to the next planet of discovery. As Juliet Robertson (2011, 00.33) says: “Maths isn’t about a pencil and paper… it is about using numbers as a tool to understand the world around us.” Our lecturers and Molina (2004) emphasise that children need to realise what the sum is about – and not just recite the steps required to reach the answer (conceptual – former vs. procedural – latter). The depth of understanding must be enough that the child can build their own marshmallow spaghetti tower to hold an egg… and not just to fit the ‘it’s a tower that stands.’ I appreciate that I need to understand how best to deliver subject knowledge in a way that caters for every student too, if my children want to leave as confident individuals. And, doesn’t such success start with consistence in the little habits? Here’s a bad stereotypical student habit: ordering the red and yellow triangles! That’s the pizza habit – that maths can actually solve my guilt with!
There are times to throw a party, celebrate and dive into a box of Dominos. Maybe student life? Perhaps (okay, true). But, a classroom also benefits from having pizza. Children like to socialise and discover things. So… why not ask them to budget for their own party and introduce fractions at the same time? I am back to developing confident, creative and conceptual-focused maths learners: remember the Scottish Government (2019) design principles are for children to have depth, relevance and choice in their learning. By holding a pizza party, a child can be introduced to the fairness of fractions as well as budgeting for their needs. Let me explain (whilst I distract my mind from its desire to seek out the nearest pizza shop). Perhaps I’ll use the technique that we were taught through a sweet story shared in our latest tutorial: count the objects around you! Whilst typing this up, you find myself counting all the flowers in my window view! Sadly, I’ve only found one. Dundee’s library has more leaves (better for symmetry, though!)
Fractions Call for Fairness
Our lecturer was talking about making everything exciting for young children: the same goes for teenagers – which I realised when taking a group of 16-18-year-old Italian teenagers around a fairy trail this Summer! They. Loved it – seriously. Walking can be fun (if you don’t particularly enjoy it) when you have small goals to work towards: so, fractions can work the same way too, I presume! Here it goes (my plan for a pizza party at the end!).
Pre-lesson Activity (Starter):
We introduce what fairness is about – f for fractions and f for fairness. In the end, fair and equal are almost synonyms (kind of!). This could be done using a cake. Oops, food again! Give one student a bigger piece than the other… and watch the chaos unfold or cake end up in your face! Not really.
The students could then explore the meaning of a whole (perhaps look at percentages.) What exactly is the meaning of the denominator compared to the numerator. How do you show how much of something you have using fractions? Visual resources are more important than worksheet questions for a start. Why? Penner-Wilger et al. (2007) found that finger representation whilst counting will increase a child’s ability to estimate well and understand the number-system. The same idea could be applied to fractions: mental representation goes along way. Maybe that’s why it’s the old-story that a face-to-face conversation is better than an email?! Anyway…
Recap fractions and introduce the idea of budgeting: that’s the next stage. Depending on the level of knowledge and depth of understanding of the students, the pupils could explore the cost of pizzas using greater than/less than signs or even percentages! It would be important to also look at some questions on fractions at the end as a formative assessment – okay, well just so you know what to plan next to teach them.
Sequential Lessons and the End Goal
Obviously, you cannot plan weeks and weeks in advance as you are unable to predict the students’ learning progress. UNLESS: a crystal ball has been inserted into your brain. I remember, when on my first-year placement, the teacher saying that they never plan longer than a few weeks because: you must change your plans; AND therefore, your time is most likely into space (and you use up fuel!) However, the end goal should try and remain the same or be appropriately adapted to the pupils. Hello, differentiation!
For instance, some complete the budgeting and other students just focus on fractions. Still, by the end, the class should come together to hold a pizza celebration. That would show that (I think) that we use maths all the time – and that you can have a choice in your learning. And, could a community of enquiry be created all whilst doing this? Maybe!
Now, back to circle time. Well, reflection! Our recent maths lectures have really cemented the idea of discarding textbooks more and more – and trying to make as many things applicable to real-life where necessary. Obviously not everything can be done in that way… but a lot could. Juliet Robertson (2011) discussed having an outdoors master-chef cooking lesson, involving mud and measurement! That does sound like a rocket-fuelled idea – that even astronauts might want to explore. I’m getting excited for teaching maths. Even more exited than I was before. If we make the students realise the everyday value of actually knowing why we carry out a mathematical operation, then our we are on the right route. Ollerton (2004, p.81) does a rather good summary for me: “The ultimate prize is for students to recognise they are learning for their own benefit.” That’s a tad better than pizza, I’d say.
References for this Post:
Molina, C. (2014) ‘Teaching Mathematics Conceptually ‘, SEDL Insights, 1, pp. 1-8. Available at: http://www.sedl.org/insights/1-4/teaching_mathematics_conceptually.pdf (Accessed: 26 September 2019)
Ollerton, M. (2004) Creating Positive Classrooms London: Continuum.
Penner-Wilger, M. et al. (2007). “The foundations of numeracy: subitizing, finger gnosia, and finemotor ability,” in Proceedings of the 29th Annual Cognitive Science Society, pp. 520-525. Available at: https://pdfs.semanticscholar.org/cc16/9648993eccb49088b511d37590f93e3fc1a2.pdf (Accessed: 27 September 2019)
Robertson, J. (2011) Messy Outdoor Maths. 31 March. Available at: https://www.youtube.com/watch?v=Nh_4SEUpSrA (Accessed: 27 September 2019).
Scottish Government (2019) Scotland’s Curriculum: How We Do It. Available at: https://scotlandscurriculum.scot/5/ (Accessed: 27 September 2019).