Sunday, 17 December 2017

Wet Weather Recess Symmetry

Wet weather recess times can be a great opportunity for children to play and explore mathematical concepts. 

One of the options children have been choosing to do is to create half or a quarter of a symmetrical shape / pattern. Then, they give it to a classmate to see if they can continue making the shape symmetrically.

Here is a design a student created and gave to a classmate:


Identifying the two lines of symmetry, the classmate was then able to complete the shape:


Another example:

.....and what their classmate created:

Those choosing to do this during their wet weather indoor recess times have really been enjoying trying to create challenging shapes:

Saturday, 16 December 2017

Student Agency Classroom Strategy

Student agency is being given more thought and focus in the new PYP changes. Student agency refers to giving children a level of control, choice, autonomy and power of their learning.

We all know that when children are given choice in what and how they learn, the learning engagement rises significantly.

This was our last week before the Christmas holidays and I wanted to experiment with a different way of offering stronger student agency for maths.

The children were given the table (below) of learning experiences on a Google doc.

The learning experiences were divided into three columns. The first column were to be carried out individually (to ensure each child had some personal thinking time), the middle column needed to be done with a partner (to ensure different strategies were being explored through sharing) and the third column they could choose to do alone, with a partner or as a trio. 

To help broaden who they were learning with, they could only do a learning experience with a certain classmate once. I had been noticing lately that some children were consistently choosing the same partners to learn with so I wanted to help them see the benefits of broadening their learning partner choices.

The top three learning experiences were mandatory and they knew those three needed to be completed by the end of the week. These were chosen as informal formative assessments where I was able to observe who might need additional help in our future ratios and probability units and what sort of help would be needed.

Provided those three were completed by the end of the week, the children were able to choose any of the other learning experiences. There was no expectation to complete any others. This allowed them to put as much or as little time needed. 

Christmas Maths

With a Partner
(Choose a different partner for each activity)
Choice: Individually or with a partner
(Choose a different partner for each activity)

Materials Needed:

° Doc (link above)  

Materials Needed:

° Doc (link above)
° whiteboard for creating strategies

Materials Needed:

° Doc (link above)
° whiteboard for creating strategies

Materials Needed:

° Doc (link above)
° Map
° ruler

Materials Needed:

° Doc (link above)
° square centimetre paper

Materials Needed:

° Doc (link above)
° boxes
° ruler

Materials Needed:

° Doc (link above)
° Whiteboard
Design a Christmas tree ornament out of triangles and rectangles.

Eg angels, stars, etc

Then create a strategy to measure its surface area
What is the surface area of the Christmas star?

Materials Needed:

° Christmas star
Estimate the number of Christmas baubles in the box on the laptop trolley.

Rules: You cannot pick up the box.
Write your estimation on a sticky note and place it with your name in front of the box.

Materials Needed:

° Doc (link above)

Google Doc Link to the Table (above)

Estimating: How many Christmas baubles link

N.B Doing this again, I will offer two or three levels of word problems to help cater to different learning needs like normally is offered in our class. (I was pretty rushed Sunday night creating all this, so I really need to put some more time into creating different levelled options for the mandatory learning experiences)

The week of learning was incredibly successful. There was always high levels of engagement and there was genuine excitement when they knew maths was the next learning we would be doing. Children were opting to do these learning experiences when they extra time to choose what learning they did. Some children were spending an impressive amount of time trying to create strategies and they were developing their own hyptheseses to prove or disprove. (The probability elves combination saw some students displaying strong perseverance and amazing mathematical trail and error skills to try and create a strategy)

There were some conceptual understandings or skills that some children might need to learn to do some of their learning experiences, so I suggested that we have 10-15 mini-inquiries that the children could sign up for each day over the week. There was a request to learn how to measure the area of a triangle in an easier way, so that was offered on the board and some children chose to sign up for that mini-inquiry with me on one of the days during the week. Not all children ended up signing up for it and that was alright. Those mini-inquiries were a great way to create and test hypotheses they formed. Some samples from that mini-inquiry small group:

Wonderfully, a student offered to run their own mini-inquiry. They had become really curious about the most effective strategy to solve the '12 Days of Christmas' problem. Four children signed up and they independently ran their own mini-inquiry where they shared the strategies they had used and then they tried to determine which were the most effective strategies. The group didn't need me to ran this and observing, it was fabulous to hear of some of the connections and patterns they had discovered whilst trying to solve it. Some samples:

By creating this tallying strategy, this learner was able to see a pattern that the day determined how many more gifts were given. They continued to test their hypothesis and proved it was true.

Another small group had been completely engaged and curious to find an effective strategy or pattern with the probability combinations elves' uniforms problem. They had spent over an hour creating multiply hypotheses and testing them out. They offered a mini-inquiry which a few classmates also signed up for where they shared discoveries and wonderings they still had:

I was curious to find out why there was such a positive buzz towards their learning and so in class and group discussions, I heard the following reflective feedback:

° They loved having choices- both what to do and who to do it with

° They liked how there was a range of active learning experiences and others that required sitting down. One student shared how they felt they could learn according to their mood- if they were in a high energy mood they could do the more active activities.

° They liked the sense of accomplishment and responsibility in having the three mandatory activities to complete (Some shared a sense of pride when they had completed those three)

° They liked how there was a mixture of different mathematical thinking- measuring area, ratios, fractions etc

° They liked the flexibility of learning where they wanted to and with whom.

° Some shared how they liked being 'forced' to learn with a different classmate each time as they thought it helped everyone to feel more included (interesting!)

° They also liked how they felt like communityof mathematicians by sharing strategies they had created / used when others might be stuck with ideas.

° They loved the theme of Christmas. There were suggestions that we should try to always do a week like this when other holidays arise such as Valentine's, Easter, student birthdays etc.

Thinking about their reflective feedback, I plan to set up learning experiences more often like this for the rest of the year. There is a lot of research for the benefits of student agency and I think when we can create and experiment with different approaches to honouring this in our classrooms, we can help raise the engagement of curiosity in our learners.

I loved their idea of creating their own mini-inquiries for classmates to sign up to participate in and definitely want to explore that strategy a lot more after the holidays.

Wednesday, 13 December 2017

Estimating How Many Christmas Baubles?

There are lots of benefits for giving children opportunities to estimate.

Estimating is an important mathematical tool that helps children make sense of numbers and helps them to test the reasonableness of answers they create amonsgt other things. Estimating, I think, can also help children feel more confortable and relaxed with numbers.

As Christmas is approaching, we created strategies to try to esimate the number of baubles in the box:

I deliberately put in some large and small baubles to extend the thinking needed:

We have been recording the strategies we used to estimate. Lots of interesting strategies have been emerging and the children have been applying some of these to change their estimates before we reveal the exact amount.

Here are some sample strategies:

The children have been discussing each the different strategies amongst themselves as the week has progressed and without prompting from me, they have been evaluating the effectiveness or ineffectiveness of strategies being tested.

When we can give children opportunities to naturally be engaged and to discuss mathematical strategies, we know we are on to something good.....

Sunday, 10 December 2017

Peer Teaching: Multiplying Decimals

The Power of Peer-Teaching

We have been inquiring into multiplication strategies and analysing which are more effective than others.

We are now at a point where we continue to add wonderings to our wonder wall about how we could apply those strategies to decimal numbers.

So, today we combined our wonderings of multiplying decimals with visualising what we are doing when we multiply them.

We had groups of 4 and we began using the 'chalk talk' visible thinking routine. In this routine, a large paper is placed in the centre of the group. Each member writes their ideas, wonderings and understandings on the paper at the same time. It is a silent discussion. The members are encouraged to read what others have written and respond by helping them understand, ask a question for clarification or to add on their idea etc.  It is a powerful strategy that ensures each child has an equal amount of 'talk time'; it also allows each child to have an opportunity to collect their thoughts and think how to best communicate their understandings.

To tune into our learning today, we did a 'chalk talk' about decimals. Sample below: 

After our chalk talk, as a class we shared some ideas that emerged. We could only share what someone in our group had shared. We use that strategy a lot especially with 'talk and turn'. I like to think that if the children are encouraged to only share the ideas of others, then they start to listen more intently to their partners. Some very interesting discussions about decimals emerged and we added some more wonderings to our wonder wall to investigate later.

I then posed the question:

How is visualising numbers helpful?

Turn and talk.

The children shared some of their understandings with their partner and then we discussed as a whole class some things our partners told us that we thought were interesting.

From these routines, we had already tuned into what our learning will involve today:

1. Decimal numbers

2. Why we should value visualising numbers.

We often peer teach in our class and we constantly reflect on our peer teaching so we are now at a point collectively where we understand how peer teaching is helpful to our own learning and we are using much more effective and creative strategies when we do it. 

I explained how we are going to inquire into different ways we can visualise multiplying decimals. 

Each group member was to watch a YouTube that explains a different strategy for multiplying decimals.  It was their responsibility to understand the strategy well because their group members will be depending upon them. This sense of responsibility to others instantly engages the children. 

I showed the steps on the data screen that we would follow:

Inquiring Into How To Multiply Decimals

Step 1: Watch and learn

Step 2: Prepare: How will you teach the strategy?
What could you do to engage your group?
Be creative in your approach.

Step 3: Practise teaching the strategy by yourself.
Reflect on what you could do to improve.

Step 4: Teach your group the strategy

Step 5: Ask for feedback from each group member on how well you taught
the strategy.
Each group member will use the '2 and 1' feedback routine:

           ° Two things you did well
           ° One thing you should focus more upon next time you peer
              peer teach

Partner A
Partner B
Partner C
Partner D

Base 10 materials

Hundred grids

Hundred grids

Only whiteboard

From the beginning and throughout, every child was completely engaged in their learning. Lots of creative ideas emerged and lots of reflecting happened as they thought about effective ways to teach their group members.

Samples of what the peer teaching looked like:

Listening to the '2 and 1' feedback the children were providing to each other about their effectiveness in teaching was formative to me, but more importantly informative to the children who will be able to expand upon that in future peer-teaching activities.

We grouped together at the end for an oral reflection.

I asked:   What do we think or feel about our learning today?

All the children felt proud in what they had achieved. A lot commented on how they deepened their understandings of what decimals are or what happens to decimal numbers when we multiply them. Others remarked on how they could evaluate the effectiveness of some of the strategies compared to others. Everyone agreed that visualising was very helpful to understand what we are doing when we multiply decimals. A few commented on how they learnt more creative ways to peer teach.

Finally, all the children agreed that they really enjoyed the learning and that is always key to effective learning and mores to help children develop their passion for mathematical thinking.

Monday, 13 November 2017

Lead In to Multiplication Inquiry

To begin our new unit inquiring into multiplication, I wanted to find a way where I could gain an informal glimpse of where each child was already at with their conceptual understanding and at the same time give them an opportunity to rethink what they already know. 

So, I posed this question:

The children wrote their ideas on a shared paper (so that they could be perhaps be inspired by other ideas being generated in their group). 

To help encourage some diverse thinking, we were reminded how visualising in maths is a key element, so how could we visually show what multiplication looks like.

This served as a very useful pre-assessment to help gain an insight of where each child was at with their conceptual understanding of multiplication.

After some time, we then chose two ideas we had and shared those with our group. This generated some interesting discussions and helped with some misconceptions a few of us were harbouring.

We then swapped our paper to the next group. They read through the ideas and then drew a smiley face beside one of the ideas they found interesting.

The children found it interesting to see what their classmate had found interesting about their understandings and found out orally why they thought so.

Our collective understandings:

We then discussed as a class what the 'big ideas' were that we understood about multiplication.  We had a good understanding that multiplication is repeated addition and some shared the connection with division.  When one student theorised that multiplication sums are the same, giving the example of 3 x 7 = 7 x 3, another student questioned that. 

To help with this wondering, I drew the following on the board:

Which does this represent?   3 x 7    or   7 x 3?

Most of us thought it represented 3 x 7 and a few of us thought   7  x 3

Some children were asked to share their reasoning and eventually, as a class we concluded it must represent   7 x 3 because 'the times symbol represents groups of'.  With this situation we are looking at 7 groups of 3, so it must represent 7 x 3. 

We then sketched what  3 x 7 would look like on our paper to help us solidify this understanding.

As a provocation to help raise curiosity and spark wonderings to explore in our unit, the following was posed: 

We used the 'think-pair-share' routine.  We spent about 10 minutes thinking of different possible strategies and were encouraged to try to also create our own. The strategies didn't need to be effective, we were more importantly trying to find as many different strategies as we could. 

We then shared and discussed these with our group. Lots of great discussions took place especially with the more creative strategies they made. 

Our groups then decided which of these strategies worked and if so, they published them and added them to their group poster.

When we completed our posters, we passed them around to see other strategies others in our class came up with and we discussed a few of these together as a whole class.  

For our reflection, we had some time reflecting our learning in our maths diaries.( Link to Maths Reflection Diaries )  

Using our reflection thoughts, we shared these with our group and then as a whole class we came up with the following big ideas:

This has also sparked some interesting wonderings which we will use in the unit to find out about:

Creating provocations to being number units can be a bit challenging to design. It needs to be able to cater to a broad range of different understandings and to also spark lots of wonderings which will form the inquiries.  Looking at our initial wonderings, I think this provocation was quite successful. The children were really engaged and enjoyed the creativity aspect of creating their own strategies. 

Once we have begun exploring different strategies for multiplication and begun evaluating them, I'm sure they will enjoy this creative challenge I did last year with my class: