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

Individually	With a Partner (Choose a different partner for each activity)	Choice: Individually or with a partner (Choose a different partner for each activity)
Baking Christmas Biscuits Materials Needed: ° Doc (link above)	Elves' Uniforms - Possible Combinations Materials Needed: ° Doc (link above) ° whiteboard for creating strategies	Christmas Word Problems   Materials Needed: ° Doc (link above) ° whiteboard for creating strategies
Santa’s Workshop Map Materials Needed: ° Doc (link above) ° Map ° ruler	Christmas Trees- fractions / decimals Materials Needed: ° Doc (link above) ° square centimetre paper	Wrapping Christmas Presents Materials Needed: ° Doc (link above) ° boxes ° ruler
12 Days of Christmas 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.		Four Christmas Maths- Challenging 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.

Maths Reflection Diaries

Maths Reflection Diaries

I have been uber excited about this idea I thought I'd trial with my class this year.  I wanted to find a way that would honour the learner's need to reflect and process their thinking in a free way that works best for them and at the same time could become a useful assessment tool for me to gain a glimpse of what is going on in their mathematical minds so I can better help them in their journeys.

As we all know, as teachers, we take risks all the time in trying new ideas- lots of flops and sometimes amongst them some great successes.  At the moment, I am feeling this 'maths reflection diary' is going to be a wonderful success.

The idea is pretty simple, I cut in half some exercise books ( I figure if the space the children reflect in is small, then it is less intimidating- there is that sense of satisfaction when we feel we use up a whole space) and on the front taped some thinking symbols we could trial:

We have discussed the John Dewey quote, but as reflecting in maths is new to these learners, we didn't go into so much depth about the meaning behind the quote, but in a month or so after they have gathered more diary entries, we will revisit the quote and see how our thinking about it has changed.

After a maths learning experience a few times a week, we spend 5 minutes reflecting about the learning and thinking we have done.

We choose symbols from the table to help visualise the reflecting we are doing. We are encouraged each time to remember that visualising and creativity in maths are key and some children are picking up on that are drawing their thinking, but most at this stage are still more comfortable in writing sentences with the symbol beside each.  That is where they are at and that is perfectly fine.

From this simple routine, I am gaining so much insight into each child's mind. I am able to see where they feel they are being successful and where they may be struggling.  But more importantly, this routine gives each child the valuable time to actually reflect on their learning and it also gives the a voice that they might not otherwise have in the classroom if we are doing whole class discussions. Those of us who may be less courageous or even introverted have a platform to also share what is going on in their mathematical mind. additionally, it gives them a valuable opportunity to think about who they are as a learner and to process the concepts being explored.

Furthermore, it allows me as the teacher to create a dialogue with each child.

We have only started or diary reflections this week and yet there is so much rich thinking and future potential they could take them.

NB: The fold their paper in half so each time they reflect in their diary is half a page.

This student's creativity and need to visualise in mathematical thinking shines in his entries:

Sometimes it can really valuable to see misconceptions some might be nurturing:

I feel I am building a stronger relationship with each child by giving them the daily written feedback and I can tell that because they know I will respond to their diary entry on the same day, they are progressively putting in more thought and some who are reluctant and taking risks to experiment with visually representing their thinking. 

In  a few weeks, we will discuss ways we could improve our reflection diary- perhaps we could add or improve on the symbols or any other ideas they feel might help deepen their learning through reflection. I'm sure they will come up with even better ways than I have.

Reading and responding has instantly become one of my favourite parts of the day. :)

Here is the link to the cover page if you'd like to have and print:

Cover Page Link

Valuing Creative Thinking in Maths

What message do we want to impress upon children of what maths is about?

When our children leave our year level, what would we like them to feel mathematical thinking is about?  How would we like their perspectives on maths to have grown, deepened and changed by the time they move up a year level at the end of the academic year?

This year, one of my goals is to help the children in my class to appreciate the wonders of number relationships and connections. That our number system isn't something to fear, but to play and make discoveries about. I also hope to impress the idea that mathematical thinking isn't about getting an answer. An answer is merely a byproduct of the rich process we can take our minds when creating and evaluating strategies. 

To help deepen our understanding that maths is about creative thinking, today we looked at the following context problem:

Stuffed with Pizza

Andrés and Margarita are stuffed with pizza!

Andrés ate one-quarter of a cheese pizza. He then ate three-eighths of a pepperoni pizza  and finally ate one-half of a mushroom pizza.

Margarita ate five-eighths of a cheese pizza followed by another half of the mushroom pizza.

All the pizzas were the same size. Andrés says he ate more pizza than Margarita because Margarita did not

eat any pepperoni pizza. Margarita says they each ate the same amount of pizza.

Who is correct?   /    How many different strategies can you create to solve it?

The key to opening up an investigation like this, I think, is changing the last part to state 'how many different strategies.........'

If we present children with closed problems where the answer is deemed what we are valuing, then we can only expect children to think the correct answer is what is important.

When presented with this problem, I asked my class, "What do we think we are valuing in this investigation?"

As we have been doing learning experiences like this a lot of the year, happily, we were able to identify that we are valuing creative thinking. Others thought we are valuing how there are many different ways to solve a problem and that they are all good. Another shared how in maths we should try to evaluate different strategies to see which are more effective and why that is so.

When I hear the children sharing these understandings, I feel like the big messages of the year are settling in their minds and this is also observable by their much more positive perspectives on maths.

If we as teachers, feed children the perpetual message that maths is about answering closed questions, then it is no wonder why so many children develop negative attitudes towards it. If we help children see how maths is about being creative, they more freely take risks with their thinking and begin enjoying where their minds take them.

Children buddied up with their table partner to create different strategies to solve the problem. Loads of rich and deep discussions took place. Loads of trial and error and lots of peer teaching of some misconceptions being harboured also took place. Listening in to the diverse discussions, it made me realise how all this amazingthinking and learning could never be taking place with a traditional chalk-n-talk maths lesson. Real mathematical thinking was taking place and children were feeling passionate about their creativity.

After some time, partners then published some of their strategies on paper and these were then shared around the room. As others read their strategies, they used post it notes to give constructive feedback. This strategy further helped us to see even more possible ways we can visualise and problem solve in maths.

Some of our ideas:

After sharing our strategies, we then used Padlet to write a short reflection about this learning experience. Here are some responses:

When we read reflections like this, we have to know we are doing something right in our classrooms......

Maths is Creative Thinking: Measuring Time

Maths involves creative thinking.

When kids are given opportunities to discover this and why creative thinking is important to mathematical thinking, even those who might harbour negative feelings, become much more open-minded towards maths. They start to rethink and understand that maths is not about getting an answer.  It helps them to understand that mathematical thinking is about coming up with your own ways to try to solve problems. It is about creating your own strategies and then reflecting on their effectiveness. It involves analysing strategies to find their pros and cons. 

Often, in traditional maths learning classrooms, children are spoon-fed strategies to replicate and then repeat. That robs them of rich opportunities to create their own strategies and to really delve into the concepts being explored. When we give children opportunities to creatively come up with their own strategies (and allow those strategies to be mad or ineffective) we help tear down those misconceptions that there is only one way to solve problems. We also help tear down feelings of apprehension some children harbour fearing they are not doing the 'right' thing. 

When we ask children to be creative in maths, we are giving them the much needed freedom and opportunity to explore the way their mind works. 

That's important.

We all think differently and we should be encouraging children to develop their own thinking processes, not programming their brains to think a certain way.


To begin our investigation into ways we can measure elapsed time, we used a Padlet and shared our initial understandings by answering the question: 

How and why is creative thinking important in maths?



Padlet is a wonderful way to give a voice to everyone in the class, not just those courageous enough to share their thinking.

After ideas were shared, we were asked to find someone else's thought that made is think about it differently then we had. 

I like this strategy for a few reasons:

1. It encourages children to actually read and think about others' thinking.
2. It helps validate the thinking of class members and helps them feel their thinking is appreciated.
3. It helps generate deeper levels of discussion. When a student shares another students' idea, we all become more involved in analysing it.
4. It is a more active way of sharing thinking. When we discuss orally, some children miss out of the initial and then struggle to catch up with what is being discussed. Using the Padlet, they can read and see what thought is being discussed and this helps them to think about it more.


We then used another Padlet to share and discuss our understandings of:

How does visualising help us with mathematical thinking?



These thinking and discussions helped 'set the scene' for the sort of thinking and investigation were about to do.


We then looked at the following problem:





Using the phrase 'How many different strategies.........' instantly makes the enquiry open-ended. There are now many possibilities and that is what we are valuing.

To help us understand what we are valuing, I explained how the strategies we create do not have to be the most effective. In fact, we should try to challenge our thinking by also creating mad, ineffective strategies because they will help us with our thinking. We can create strategies that will take a long time to help save. That's alright.  Let's just explore different possibilities.

We used the think-pair-share routine.

Children had 10 minutes creating different strategies on the paper.

After 10 minutes, we discussed what we thought about creative thinking.

Some very in depth and interesting reflections emerged such as:

° Before I thought creative thinking was just about doing something in a fun way. Now I understand that you actually need to think really hard and deeply about something. 

Everyone agreed that creative thinking does require 'hard' and deep thinking.

° I think it's interesting that creative thinking is a balance between hard thinking and fun thinking. 

° I get different answers with the different strategies I created and I'm trying to find out why.

This last comment is exactly where we want children to be: without being prompted, find reasons why a strategy is working or not. We all agreed this was a great thing she was doing.




I then explained we were going to do a 'silent gallery walk' to see what others were experimenting with and exploring as possible strategies.

Why do we think we are going to do this?

- So we can see how creative we can be?

- We could be inspired by other people's ideas and use them?

That's interesting.  Do we think it is alright to use other people's ideas?

- Yes, because we might see an idea and be able to change it to make it even better.

- I don't think we should just copy someone else's idea though. It's the same as stealing their thoughts and pretending its yours.

- But we can be inspired by someone else's idea and see if we can be even more creative with it.

-Its similar to what we did last week with creating logos. We learnt that designers often collaborate and share all their ideas to make a great idea together. If we see someone's strategy we like, we aren't speaking it. I think we are becoming a team with that person. Even if they don't know they are part of the team.


With those ideas we agreed that the purpose is to be inspired. If we find an idea interesting, we should try to experiment and play with it.

Some of our creative strategies:

So many unique and interesting thoughts can emerge when we give children the freedom......

We then silently walked around examine the strategies being created. When children found something inspiring, the returned to their seat and continued creating different strategies to solve the problem.  

After another 10 minutes had passed, table partners then shared their strategies with each other. Some rich discussions took place as they analysed the strategies and the reasoning behind them. The children naturally evaluated the effectiveness and visual creativity without being encouraged to.


To expand our creative thinking further, we then looked at our next task:



The new strategy created needed to have an element from each person. Some initially felt this was too tricky, but after time we all found possible solutions to do this. 


We then shared our new strategies on the data screen.  We explained each person's strategy and then how they were combined.  Their classmates were encouraged to ask them questions about the thinking process rather than the product and that generated some interesting perceptions on what creative thinking entails.




Partner Sample:

Partner A's:

Partner B's:

                         

New Combined Strategy:

Another Pair showing each's strategy and then combining it: 

We then wrote a quick reflection using the following prompt:


Here are some excerpts from our reflections:

° I feel like this is the first time I've ever really understood what creative thinking is REALLY about. I used to think it was just fun thinking, but I know now that it involves hard and complex thinking too. 

° ...we can even take the easiest word problem and make it super complex when finding ways to solve it. 

°......visualising helps me make sense of what I am trying to work out in my mind.

° This helped me discover that I can create many different ideas and I feel more successful as a mathematician. 

°......helps me make more sense of what I'm doing.

° .....When I kept hitting road blocks with the strategies I was trying to make, it made me think of ways I could solve them. Actually, so much thinking went on in my mind doing this. I was amazed that my mind could handle them all so well. 

°I like how there isn't any pressure when we are creating different strategies. Its fun and challenging at the same time.