A solid maths central idea can generate powerful, student-driven enquiries.

To introduce our new unit exploring volume and capacity, each child was given a copy of the central idea.

Occasionally I ask what is the purpose of a central idea to help solidify our understandings. Today some students shared that they saw the purpose is:

- So we know what we are about to enquire into.

- So we can decide what we want to find out.

- It gives us the freedom to investigate what we want to find out, but with a direction.

- They help us to understand what the big concepts are that we will explore

- To give us clues about what we will discover.

- To give us a big picture idea of the maths we will be thinking about.

That's pretty stellar understanding I think. And this from a class that at the beginning of our year only perceived a central idea to be a topic to learn.

To unpack it, we determined which were the key words in it:

We then thought about what we knew for UNITS. Students recorded on their copy any units they knew for measuring volume / capacity.

We then looked at VOLUME and recorded our understandings- what is volume? How and why do we measure it in real life situations?

We repeated for CAPACITY and then for OBJECTS we recorded things people in real life might want to measure the volume/capacity of and why.

Finally, we then looked at STRATEGIES. What strategies do we know? Eg, Perhaps we know a strategy for measuring the volume of a cube etc.

In between some of these, we were reminded that this is a PRE-assessment simply to find out what we already know. Some of us might have a lot of experience with volume / capacity in previous years and some not. It's great if you know a lot and its great with you don't know a lot.

After this, we then looked at those key words and recorded wonderings we have.

- What do we want to find out?

- What are we curious about?

- To become an expert on our central idea, what things might we need to find out?

A students began recording their wonderings, some began sharing.

This created some really interesting discussions.

One student wondered whether air has volume.

This got us all thinking. Does it?

- We can't see air so it can't have volume. I think an object can only have volume if you can see and touch it.

- When we turn a fan on, we can feel air push against our face. So, because we can feel it, maybe it does have volume but I'm still not sure.

- I heard that when astronauts return to earth their muscles are weak because there is no air in space. My theory is that air must have volume because it pushes on our muscles on Earth, but not in space.

- Since volume is the amount of space an object takes up, I can't hold air in my hand and measure its mass. I think an object must have mass to have volume.

We coincidentally had a blown balloon in our classroom from a group enquiring into science.

I held it up.

What does this make us think about whether air has volume or not?

- It doesn't show that air has volume. It shows the capacity of the balloon.

- But then the air must be a unit of measurement. If you wanted to blow the balloon up more just before it bursts you would know its capacity. That must mean air has volume.

- Could you measure the air in the balloon? If we could find a way to measure if it has mass, it would tell us if it has volume.

- Why does volume have to have mass? I don't think it does.

- In space there is black matter everywhere between all the objects. I think black matter is like air on Earth. I think you could measure how much black matter there is so that must mean we can measure the volume of air in our classroom.

More amazing ideas and justifications of theories being formulated were discussed. We decided to put this on our our wonder wall to come back to and hopefully find a way to get an answer.

Another interesting wondering was whether we can measure the volume of an object without knowing the capacity and vice versa. The student said she felt their might be a connection like there is between area and perimeter. As she explained, we can't find area without knowing the perimeter, but we can measure the perimeter without knowing the area. She wondered if there was a similar connection between volume and capacity.

We liked that wondering a lot and also put it on our wonder wall to investigate later.

Walking around during their wondering recordings, I noticed how defining capacity was a bit shaky for quite a few students. I hoped this wondering would up in sharing and it did. The kids in my class aren't afraid to ask big or little questions- not that 'what is capacity' is a little question, but because we always value any wonderings that are shared the students do feel all their questions are valued. This is really a key component of creating an enquiry-based classroom culture. If students are intimidated to ask questions, a lot of valuable learning potential is lost.

When a student shared how they wondered what capacity really meant, I asked for a show of hands who else felt that way. Quite a few raised their hand.

It's not often that I can feel like a magician pulling out a rabbit at a perfect moment, but this is was one of them. I had a slideshow activity to help determine the difference between volume and capacity I had used created and used last year. I had kept it opened in a tab for when the right moment in our unit it should be used. This was the moment.

Slideshow:

Is it volume or capacity?

(feel free to copy and use :) )

We discussed the first few slides and to make it more active, when we came to the images and had to determine whether it was volume or capacity the children raised their hand in a letter V for volume or C for capacity.

It was apparent (and expected) that volume and capacity is tricky to understand. The liquid scenarios were the trickiest.

Towards the end and by discussing each, everyone was able to determine a V or C more confidently.

Pre-Assessment samples:

Looking through the pre-assessments gives me a pretty good clear picture of where each student is at and perhaps where some misconceptions lie. Identifying those gives me a good idea of types of learning experiences I need to create and include to address so those students come to their own understandings rather than being told.

When it comes time for ability grouping for certain learning experiences I will have a better idea of how to group (Though for this unit the majority of learning experiences will be mixed ability groupings)

The other benefit to this type of pre-assessment is that it also functions as the students creating their own maths planner in a sense. They are now curious and invested in our unit because they know they will be given opportunities to explore their own wonderings and share their discoveries.

This makes it enquiry-based learning- students having a voice and their wonderings being valued and explored.

Some students might finish this unit finding out strategies to measure the volume of a hexagonal prism and others why using cubic centimetres as formal measurement is useful.

I don't think every student needs to leave this unit all with the same understandings and that's why I don't give them stupid maths tests as a summative (see link ideas below)

They have entered the unit with diverse levels and should leave as such. What each student should leave the unit with, however, is a strengthened understanding that they are successful mathematicians and with stronger problem solving and enquiry tools.

For this particular unit, the formative and summative is open-ended (like always). The central idea has been printed on the reverse side of the pre-assessment. As we progress through the unit, they will reflect on what they have learnt and record by unpacking the central idea further and also adding new wonderings to explore. Instead of a stupid test, that will be their formative and summative assessment task for our maths unit. They will chose two PYP attitudes they feel they developed and reflect how. My feedback will be a rubric assessing what they showed themselves to be as communicators and inquirers from the Learner Profile.

If we don't pre-assess, we don't know the learning direction and needs. If students aren't given an opportunity like this to draw upon prior knowledge, they stumble unnecessarily in the beginning of a unit. We should value this reflecting time that children need to give them the confidence and the tools to wonder and explore.

As we left for lunch, I overheard a few students coming up with ideas of how they might be able to measure the mass of air in the balloon. You know you are doing the right thing when your students are still talking about a discussion when the football pitch is calling their names.

Some related links:

No More Stupid Maths Tests!!!

Positive Maths Assessments

Strategies to Make an Enquiry-Based Maths Classroom

Power of Student Questions for an Enquiry-Based Maths Classroom

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