I’ve recently returned from the BASTOW Leading Mathematics Elective: Measurement and Geometry ran by Larissa Raymond and Tony Flack. During the two day workshop I was presented with the ‘Three Phases of Teaching MEASUREMENT’. After listening, discussing and participating in the activities, it led me to ponder how much time in my lessons do I prioritise to the exploring phase? By exploring, I mean touching, making, experiencing, measuring, estimating, comparing and playing with materials. I know reflecting on my own learning style, touching, drawing and visually seeing something is crucial for my own engagement and retention of information. Even at the measurement and geometry day, as an adult, I was the student who needed to move around, talk, draw, touch and have multiple exposures in order to make a meaningful connection.
Investigating this question has led me to reflect on my recent lessons with the intention of critically thinking about the value of giving students explore time. To my surprise, often the most interesting aspects of the lesson have come from listening to what the students have said and orchestrating a discussion or experience rather than what I had planned in my documents.
Find below some of my experiences and reflections from my 5/6 class.
6K walk – click here to see a full overview of the lesson
6 km was such an abstract term for some students. They knew that 6 km was a fair distance for water and that it was of significance, but understanding how much time and effort it would take to get that water became more profound as the explore phase went on. The elements of the explore phase added value to their understanding of the big ideas of estimation, measuring and understanding length within a context.
Observation through exploration
Shown by
6km is hard for students to estimate
‘What if we just walked to our drink taps and back, would that be 6km?
‘What if we walked around the school?’
Having students discuss and debate how far they thought 1 km was in relation to the school and their town proved useful as it showed the need for exploration.
The students found it hard to link distance with time
‘We have 10 minutes left, can we do another 6km walk to map our journey?’
Converting between cm and m needs to be put into context.
Students debating if it is 100 cm in a metre or 1000.
The students were making links to when you would use cm and when you would use km.
Students needed to personalise the concept in order to make an understanding. Eg. I ran the cross country and it was hard. You’re telling me it’s two cross countries!
Our school cross country was a 3 km run, which meant three laps of the outside of our school and one lap internally. So we would double it!
Our students were exhausted after the run, or it took them a very long time because they walked.
‘I wouldn’t like to do cross country every time I wanted a drink!’
The value of exploring outside
Students were engaged in the task and making connections with things around the school. Eg. Distance to the chook shed, laps around the garden, distance between the footy goal posts. Being outside sparked curiosity and they were excited to share their findings.
Don’t assume students know how to use measuring equipment such as tape measures and trundle wheels.
The conversations created by students trying to use a trundle wheel that didn’t click. ‘When does it tell you how far we’ve gone?’ ‘One turn of the wheel can’t be the same as a metre!’
Choice is valuable when exploring.
Choosing where to go and the method to use proved to be valuable. Students were trialling equipment, trialling methods and discussing as they went. The ability to choose a way of exploring provided students with a context to see what was efficient and what was not.
How many of my jumps would it take to beat Mike Powell? – click to see overview of lesson
Observation through exploration
Shown by
Visualising a distance is difficult
Students using their prior knowledge to estimate 8.95m. Trialling and comparing their guesses with each other was the most valuable learning. The guess and check element created robust discussions and curiosity.
The students loved talking about their own jump and themselves
Students were engaged and actively talking about length. ‘My jump was 2.32m, what was yours? Oh that’s bigger than mine’
The most powerful link they made was comparing their jump to the world record and their peers. I jumped 2.32 and you jumped 2.42, you only just beat me!
Understanding length in the context of an event (world record jump)
How did he jump that far?
It wasn’t until the students attempted the jump that they truly were impressed with the record. Sometimes it felt like the students expected to be ‘pretty close’ to the 8.95 m bench mark and were shocked when they compared.
Measuring for a purpose
Watching the YouTube world record video, then estimating and then measuring with a tape ensured that students were curious and really wanted to find out the actual length. Each jump provided a purpose for measuring – they wanted to measure their jump.
Students could see the role of the decimal
When discussing, students were converting between cm and m. This led to the discussion of the purpose of the decimal in this situation. This then led to ordering, renaming, adding and subtraction of our long jump data.
Beads
After some inspiration, I thought I would try bringing in a bag of beads and seeing where the lesson went. Currently we had been working on division, fractions, decimals and percentages and had the idea of linking these but was open.
After my story shell of how I came to be in possession of such a usual bag of caterpillar like beads, I asked them what they wanted to know. ‘How many?’ ‘How many of each colour?’ ‘What sized necklace could we make?’. With those prompts I emptied the bag and watched them explore.
