First, contemplate this problem and it’s vast entirety. https://www.youcubed.org/tasks/leo-the-rabbit/
These are two great videos delving into the depths of math teaching:
And some additional food for thought is here:
The spiralling Leo the Rabbit problem can be found all over the internet…
What connections can you make between the two resources you accessed?
I noticed that video presenters focused greatly on creativity as a medium for mathematics learning. They both focused on needing to take the time to explore in many different ways in order for the learner to make independent conclusions. They also noted that observations are meant for discussion with peers, and should be received with sincerity.
“Forget about calculating the actual answer – why does this pattern exist? The right answer is the one that satisfies you.” Stuart Jeckel suggests scrambling the numbers using creativity, colour, numbers and pictures.
“When we’re not comfortable with math, we don’t question the authority of numbers.” Dan Finkel – Renee Decartes “I think, therefore I am.” A person confirms and denies, wills and refusals and that imagines and perceives – the kind of thinking involved in every math class every day.
1) Start with a question – so there is room for thinking
2) Time to struggle – persevere when struggling with a genuine question
3) You are not the answer key – ‘I don’t know, let’s find out.’ You create space for the kind of thinking required for deep learning.
4) Say ‘yes’ to your students’ ideas – accept it, study it and disprove it or approve it if necessary, instead of being told your wrong by the teacher
5) Play – playing with math is the gift of ownership.
We can’t afford to misuse math. Authentic learning is important.
Paul Lockhart argues that math is as creative as music and painting and the primary reason that students become frustrated with math is that they are not allowed to invent and use original ideas, comparing rote learning to not painting until all colour combinations are learned and paint my numbers are mastered, and only ever doing scales and transposing in music. An interesting perspective, indeed.
What might be the benefits of embracing the ideas?
When mathematics is thought of in a creative way, it brings on many more possibilities of engaging with the problem. I know that from learning about one issue thoroughly we can begin to understand similar ones around. A snail shell exhibiting the Fibonacci sequence is only related to Rabbits jumping up a stair or two if a creative person can make that connection. Students will feel validated when learning is authentic.
What challenges or obstacles do you foresee?
Using lengthy questions in a classroom inducing frustration due to time constraints would be my primary concern in the classroom. There is already a multitude of information that we as elementary teachers need to teach, so how will we ever teach these ideas along with the very important, and basic math that should be learned for any foundation in study? I feel that students would feel both a great sense of pride, and also a deep frustration due to the lack of obtaining a real and true final answer. This method seems a little like we want every student to find the struggle that took place before any mathematical formula was ever invented. I struggled with Leo the Rabbit because I KNEW that there was a formula and I wanted to know it. I’m glad that I struggled first, but it took way longer than I thought. And my creativity was flourishing, but mostly it was just repetitive annoyance. Finding the final answer was the only solace.
What might math teachers do to overcome those obstacles?
Teachers might assign these lengthy questions for family learning as homework… but that is also another debate in and of itself. An alternate would be to integrate math as much as possible into other learning across the curriculum.
This task has made me think of teachers, and re-inventing the wheel. I am constantly thinking that I am in fact re-inventing the wheel because the amount of collaboration that is needed to ‘pull-off’ a cross-curricular, dynamic math lesson every day is astounding. Where are the resources for a Leo the Rabbit lesson every day? I feel that as a teacher I should let the students struggle to find the answer, but I feel in the core of my being that the answer should be shown after sufficient time is given for the struggle to learn it. I feel that the struggle is necessary but if the problem has already been solved, the struggle should end at fully understanding the solution.