Data Handling Maths Planner

Creating a PYP Maths Planner:

Experimenting with different ways to create and implement PYP maths planners over the years, I've found the following the key elements in helping a maths unit become enquiry-based, student-owned, flexible for differentiating student needs and to allow each child to feel successful as a mathematician:

° The central idea is pivotal. The language needs to be simple enough for each child to understand it and it should allow for a wide range of student-generated questions that they or we as a whole class could enquire into. The central idea should be useable for students to record the reflections on what they have learnt during the unit. 

° Beginning in the first few sessions by introducing the central idea and asking students to generate questions we should find out about to become experts on the meaning of the central idea arouses student curiosity and instantly lankes the unit student-owned as they decide what they need/want to learn.

° Lines of inquiry must link up with a PYP key concept to guide and deepen the conceptual understandings. Using the key concepts instantly makes the maths unit enquiry-based rather than a traditional skills-oriented unit of learning.

° Give the central idea on a large A3 paper as a summative assessment. During the unit, students are given 5 to 10 minutes every few sessions to record what they have discovered. This reflection time allows the students to deepen their understanding of the central idea which is the essence and whole purpose of the unit.    

Example Summative for Place Value /Number Systems Unit

Example Summative Using Central Idea for Measuring Time Unit








PYP Planner for Data Handling Unit 
(Google Doc link below):


Transdisciplinary Theme:  

How we organise ourselves



Central Idea: 

We can investigate data more easily with suitable graphs.

Student-generated questions when unpacking our central idea:

Unit of Inquiry Link (Migration: Where we are in place & time):

°  Function:  analysing data to determine migration patterns

Lines of Inquiry:

° FUNCTION: Ways we can analyse data

• Create memory hooks to help remember what the mode, median, mean and range are. Display memory hooks on wall for reference.
• Students grouped into 5. Time how fast they can sprint across football pitch forwards and backwards.  Gather data and analyse- mean, mode, mean, median
• Bowling scores - mean Students imagine they have been bowling with 5 different scores. Then use these to calculate their average score.( what is an average?  How do we know if we have calculated the average correctly?) Next, calculate the average scores of group partners and then the entire group's average. Bowling Scores Mean Home learning (Based on student-generated scores in class for next week)
• Reading graphs (pie graphs, line graphs) google docs
• Students toss pillows and record distances. Then decide ways the collected data can be analysed and suitable graphs.
• Students collect own data from class and then select ways to analyse the data and select suitable graphs to convey it. Eg, languages spoken, number of countries travelled to, number of places migrated to (UOI link) etc

° FUNCTION: How to create line and pie graphs

• Pie graphs: students given circles to determine simple amounts of pie graph % (peer teaching)
• Pie graphs: number of languages we speak, number of countries we have travelled to etc.  Collect data languages migration countries etc Students determine which graph most suitable to convey data and explain why
• Line graphs: choose type of temperature / precipitation graph of Lausanne to create Creating line graphs: differentiated between 3 types
• Students select a city in:  the Northern Hemisphere and the Southern Hemisphere and record daily max and min temperatures as a line graph on back wall for a fortnight. Calculate daily range in temperatures.At end of fortnight, calculate different ways to analyse the data: mode, median, mean, general statements etc.  Discuss reasons for difference in temperatures between the two hemispheres.
• Interpreting pie graphs home learning

° REFLECTION: How to determine suitable graphs to convey data

• activity google doc: which graph is suitable and unsuitable. Think-pair-share
• Student time sprinting and student created data collecting activities: determine a suitable graph and explain why you felt it was the best choice

° CONNECTION: How we use graphs in our daily lives

• Use graphs for migration group enquiries requirement; analyse the data in the graphs
• Students find graphs in local newspapers etc during the unit to discuss in groups of why they were used

°  FUNCTION (Migration Unit Link) analysing data to determine migration patterns  

• Use graphs for migration group enquiries requirement; analyse the data in the graphs and present analyse in peer groups

What opportunities will occur for transdisciplinary skills development and for the development of the attributes of the learner profile?

Thinker: determining suitability of graphs for different data

Thinking Skills: Analysing data in different ways

Communication Skills: Presenting data in various graph forms

PYP Planner Google Doc: Data Handling Maths PYP Planner

Applying Types of Inquiry in Maths Learning

What type of maths inquiry do we employ the most and the least in our classrooms?

	Demonstrated Inquiry	Structured Inquiry	Guided Inquiry	Open Inquiry
Posing the question	Teacher	Teacher	Teacher	Student
Planning the procedure	Teacher	Teacher	Student	Student
Drawing conclusions	Teacher	Student	Student	Student

How can we veer away from the dominating structured inquiry approach in maths?



Looking at our first maths unit this year (below), I wonder what types of inquiry should be employed and when?

_____________________________________________________________

Maths Unit

Central Idea:

Our base 10 number system evolved for a variety of reasons and led to place values that extend infinitely in both directions.


Lines of Inquiry:

° FUNCTION: How our Hindu-Arabic number system place values extend infinitely in both directions

° FUNCTION: How our base 10 number system works

° CAUSATION: Reasons we can multiply / divide whole and decimal numbers easily by 10, 100, 1 000 etc

° CONNECTION: Differences & similarities between our Hindu-Arabic and 
other ancient number systems Eg, Roman, Egyptian, 
Babylonian etc

° CAUSATION: Reasons the Hindu-Arabic number system was formed

° FORM: What the location of negative numbers in relation to zero is like

°CONNECTION: How we use negative numbers in our real lives

______________________________________________________________

Lead In:

As a lead in for the unit, we will discuss whether or not numbers really do exist or not. If all the people in the world suddenly vanished, would numbers still exist? I've done this in the past and its fascinating what children think about this and how they support their reasons. The discussion also leads to many questions they generate and quite a few obvious 'light bulb' moments as children realise maths is a concept, its not a concrete entity in their lives.

Then we will share theories we might have of why our number system is based upon 10. (A common and interesting theory is that it is because we have 10 fingers. Later in the unit, we will revisit this idea and the children will create their own number systems based on 3 or 7 etc imagining that is the number of fingers people had)

Presenting the Central Idea to small groups to generate questions they would need to know the answers to to have a deep understanding of the central idea will also allow an inquiry-based learning feel and student ownership to begin to form in their minds. These questions will be displayed beside the central idea and will be addressed as the unit unfolds.

Looking at the planner, perhaps I could allocate a different type of inquiry structure to each line of inquiry.....

Lines of Inquiry:

° FUNCTION:  How our Hindu-Arabic number system place values

  extends infinitely in both directions

( Open Inquiry: Give students the beginnings of a number place value line with positive and negative place values. Individuals or small groups generate questions and devise ways to find out how place value works in both directions. Able to use laptops, manipulatives etc to explore. Share what we did and what we discovered)

° FUNCTION: How our base 10 number system works

(Guided Inquiry: Identify elements of our number system by analysing number grids etc. Discuss theory behind having a base 10 number system: 10 fingers. Provocation- What is people had 3 fingers or 7 fingers? Individually or in small groups, create a base 3 or a base 7 number system. How would it work? How is it similar or different to our base 10 number system? Share with class)

° CAUSATION: Reasons we can multiply/divide whole and decimal

numbers easily by 10, 100, 1 000 etc

(Guided Inquiry: Invite some students to show how we can multiply and divide numbers by 10 and 100. Students then enquire into the patterns and changing of place values when we multiply and divide by 1 000, 10 000 etc. Extend this enquiry further with finding out how this works with decimal numbers - money - and negative numbers)

° CONNECTION: Differences & similarities between our Hindu-Arabic &
other ancient number systems Eg, Roman, Egyptian, 
Babylonian etc
(Open Inquiry: Provoke student questions by showing parts of ancient number systems. Groups generate questions they want to discover about a particular number system, explore and share enquiries)

° FORM: What the location of negative numbers in relation to zero is like

(Structured Inquiry: Look at temperature readings around the world where there is a negative temperature and explain its meaning using number lines)

° CONNECTION: How we use negative numbers in our real lives

(Structured Inquiry: Brainstorm and ask parents at home to collate ideas together for discussion)

Looking at this, I feel it is fairly student-centred as they will have quite a lot of opportunities to take ownership of their learning and it will hopefully set the tone successfully of the expectations in how their maths learning will be for the year......

Reflecting for Improving......

School starts back next week and so I'm starting to get my head back on in how to inspire my students to appreciate, and dare I say, enjoy maths.

At the end of last year, I asked my students to complete a short survey on our maths programme so I could find out how I could improve it further this coming year. I've just finished rereading their feedback and found some interesting results.

For context, it's important to understand my students have come from years of the Everyday Math textbook 'programme' which thankfully has just been ditched in favour of creating PYP Maths Planners this year. 

One of the questions I had surveyed my students:

One of my big goals this year was to help each of you to enjoy and find maths more interesting than you did before. How successful has our maths learning been with this?

I find maths a lot more enjoyable and interesting.	13
I find maths more interesting, but not really that much more enjoyable.	2
I find maths learning more enjoyable, but not that much more interesting.	0
I find maths about the same as when I entered Year 6	1
My appreciation for maths learning has decreased a bit this year.	0

I find maths a lot more enjoyable and interesting.	13	81.3%
I find maths more interesting, but not really that much more enjoyable.	2	12.5%
I find maths learning more enjoyable, but not that much more interesting.	0	0%
I find maths about the same as when I entered Year 6	1	6.3%
My appreciation for maths learning has decreased a bit this year.	0	0%

That's pretty good feedback I think, though as mentioned, when you inherit kids who have come from the Everyday Math textbook, it's not that big of a challenge to help inspire them into mathematical thinking when you use an inquiry-based learning approach.  I had kept tally marks over the year of the number of activity sheets I had given my students in maths during class time and had reached 24 and each of them I had made so they were inquiry-based. Not bad I think, though I'm making it a personal challenge to decrease that this coming year.

When asking how they felt about our maths learning this year, almost every student responded in a similar way: the Everyday Math textbook they had used in previous years was boring, they didn't use to like maths, they never felt maths was interesting or enjoyable.

Some sample responses which sums up the general feeling of my students:

° "I have found it a lot more interesting and fun than my previous maths classes because instead of doing boring stuff from textbooks, we do hands on activities and we do activities that will be useful later in life."

° " I thought I learnt a lot more because with everyday math it was so boring and it was always the same. Now we can investigate what interests us and make our own questions to enquire into."

° "I've never been allowed to enquire into things I want to learn about in maths. I didn't really want to learn much in maths but this year I want to learn so much more. This year is the first time I have wanted to learn about maths."

° " I was so bored of everyday maths but now I know maths is like a puzzle and a mystery that I like to discover."

° "My attitude has changed a lot because I used to hate maths and I always struggled. I now want to try harder in maths because I know that it isn't that hard as it used to be in previous years."

Reading through these, it's not that surprising to me that they have enjoyed maths a lot more without textbooks, a really awful textbook at that. I had heard this sort of feedback throughout the year and students who used to believe they were 'not good' at maths were often remarking how easy they were finding maths this year.  

That, I feel is one of the big benefits of using PYP planners for maths and treating maths in a similar way we treat our Units of Inquiry: we tune into the topic, generate questions to explore, find out what we personally want to learn and share our findings.  Those who have been led to believe they are 'bad' at maths when given opportunities to enquire themselves quickly discover they can and are successful mathematicians.  

Textbooks don't allow those children to feel like that.  Textbooks are geared towards the middle bar and if you haven't developed those key mathematical concepts or skills pegged at that middle bar, you will always be made to feel you struggle even if your teacher is differentiating for you with different activities. Kids clearly know if the rest of the class is doing page 126 and the teacher has given you some handout, that it means you aren't 'clever' or 'good' at maths. 

Equally, when we treat maths the same way we treat our Units of Inquiry, those with more advanced mathematical understandings are given opportunities to really take their learning much further than I could hope to help them achieve. This is mostly because they know what they want to learn. They know where their understanding is at and with just some slight guidance in the tuning in stage of the maths unit, I can help them with suggestions of what they may want to explore in relation to that maths topic. 

All done without a textbook or worksheets.....

____________________________________________________________

When asked how I could help improve the maths programme next year, there weren't too many suggestions, but quite a few mentioned wanting to be given the opportunity to do even more personal enquiries into maths topics:

° "Doing even more personal maths enquiries because I like to learn new things about parts of the topic that I am more interested in."

° "I think we learn more when we can choose what to enquire about so you should let next year's kids do even more personal enquiries. I have never done that before and I really liked it a lot. I felt like I was a real mathematician."

° "Apart from the interactive activities we did, the best part of maths for me was when we investigated our own questions so you should definitely do that more."

This I found really interesting. I knew they enjoyed that part of our maths learning cycle and could see their pride in what they were discovering. I certainly saw every student becoming increasingly more successful at enquiring into their own interests with deeper questions. As the year progressed, they became stronger at thinking of aspects of a maths topic in focus that they could explore with less and less guidance from me. I need to think how I can incorporate this even more next year!!

What was holding me back last year not to allow personal enquiries even more so than we were doing? 

How can I free myself even further from not needing to be concerned with standardised testing results?

I think I should really ensure that every maths topic this year must include a few days where the children are given ample opportunities to develop and explore their personal enquiries in maths. Those personal enquiries in themselves did serve as really useful assessment tools where I could easily identify their strengths and weaknesses as mathematicians and as inquirers. 

Remember to do this Graeme!

When I look at their feedback (below) of maths topics they felt they improved their understanding the most, I can clearly see that the topics selected were those they were given the most time for their personal enquiries. They were the topics I stood back the most in the unit and just guided when needed for suggestions of what they might want to discover next.  

A maths topic I feel I greatly improved in understanding this year was:

Question	Count
Number systems	1
Mental strategies	7
Angles	4
Probability	10
Measuring time	6
Measuring volume & capacity	5
Measuring area & perimeter	3
Reading graphs	2
Fractions / decimals / %	12
Ratios	11
Measuring length	4
Measuring mass	4

Number systems	1	6.3%
Mental strategies	7	43.8%
Angles	4	25%
Probability	10	62.5%
Measuring time	6	37.5%
Measuring volume & capacity	5	31.3%
Measuring area & perimeter	3	18.8%
Reading graphs	2	12.5%
Fractions / decimals / %	12	75%
Ratios	11	68.8%
Measuring length	4	25%
Measuring mass	4	25%

I think this is really telling of what makes maths learning the most effective. The topics ranked the least were the topics that were more teacher-directed with me giving them activities and not giving them enough time to create and explore their own enquiries. 

The more I stand back and give students the time to explore their personal maths enquiries, the more memorable and effective the learning is. When children are given opportunities to take ownership of their own learning, even in maths, the learning is far more successful.

Remember this Graeme!!!!

Creating a PYP Maths Planner

Why?

Prior to becoming a PYP teacher, when I reflect upon my teaching I think I was a so-so maths primary teacher.  I understood the skills and concepts children in my class should be learning and tried to make maths learning fun mixed with the all-important skill rote learning routines I had also grown up with whilst in school which still seemed to be the expectations of the day.

Joining my first PYP school 7 years ago, I started experimenting with how we could use the PYP framework with maths learning.  


I began playing around with central ideas for my students to explore and lines of inquiry that matched PYP key concepts. That became a big game changer for me in how I'd help guide my students towards their maths learning and importantly, allow them to take ownership of their learning.

When we create a successful maths planner using a strong central idea married with supporting lines of inquiry (matched with key concepts) some of the benefits are:

° students have a clear understanding of what the unit is about 

° it gives them freedom to explore areas of maths thinking that interests them

° it transforms the learning to become inquiry-based learning in a natural way

° it creates a shift from skills-oriented to more meaningful concept-oriented learning

° it provides them with opportunities to take ownership of their learning

° by generating their own questions to explore they are doing what real mathematicians do and their engagement increases

° they gain a sense of pride in what they have decided to enquire into




How?

Central Idea:

The tricky part, which I still stumble over occasionally, is getting that great central idea.  It takes time and a lot of thought to create a central idea that allows children to:

° foster a curiosity towards the concepts

° instill a need to explore skills & strategies

° to be broad enough to allow students to take ownership and inquire into avenues that they find interesting in that particular maths strand. 

° should be able to cater to all the different inquiries when they reflect during their summative (see below)



Looking at the PYP Maths Scope & Sequence, the conceptual understandings can be a good place to start creating a central idea. Tweaking them to add some grit for students to inquire into rather than just being told the fact needs to happen. 

(I wish the IB would create some 'think tanks' and share possible central ideas with possible lines of inquiry out to PYP schools as a starting block for teachers.)



Present or Don't Present a Central Idea?

There are two camps it seems amongst PYP teachers: those that present a central idea towards the beginning of a unit and have it displayed for constant reference and discussion and those that don't reveal the central idea till the end of a unit or have children determine what the central idea could be as a summative.

Personally, I'm in the former camp and so I feel it is important to discuss a maths central idea early on in a unit.  By presenting the maths central idea, kids are encouraged to generate their own questions in small groups of things they feel they need to know and what they need to do to gain a deep understanding of it.  This provokes curiosity towards the maths topic and also allows them to take ownership of their learning because they will be given opportunities to explore their own questions during the unit. 

Quite often we are in the midst of a maths unit and when I see all the different avenues the children are taking their learning, I can find faults in the central idea we are discussing.  The central idea can sometimes feel limiting to where they have actually gone with it so at the end of the unit, we discuss how the central idea could be improved.  This serves as a in interesting reflection activity for the children and it helps me create better central ideas for next year. My students enjoy when I share with them: "This was a central idea students last year created. Let's explore it and see what changes we think we should make to it over the next few weeks." They appreciate the idea that there new central idea they create will then be used in the following year for the next students to explore and possibly debate over its effectiveness.


Lines of Inquiry

Using the PYP key concepts to form lines of inquiry, I feel, is an easier process. You can look at the maths concepts and skills you want the children in the unit to explore and so use this to create the lines of inquiry.



An example maths unit:

Central Idea: When angles co-exist, connections and relationships form.

° FORM: What different types of angles, triangles and quadrilaterals are like

° FUNCTION: How we can estimate and measure the size of angles

° CONNECTION: Patterns and relationships that exist between angles

° CONNECTION: How we use angles in our daily lives


Because the maths unit becomes student-led due to them generating their own questions to explore from the central idea, sometimes areas outside the planned lines of inquiry are examined.  I think this is great.  

The children needn't be constrained within the lines of inquiry I had planned for the unit. Usually I don't share the lines of inquiry with the children anyway. I use them as a personal skeleton guide of where I feel the learning should go based on the scope & sequence. If particular students or the class as a whole,aren't taking their learning to broad enough avenues, then I can refer to these to help guide the class.  

Everytime I create a maths unit, I always create a line of inquiry using 'connection'.  

Eg,  CONNECTION: How we use angles in our daily lives

       CONNECTION: How we use mental maths strategies in our daily lives

       CONNECTION: How we use 3D shapes in our daily lives


This serves as a reminder to me that I need to guide the children to understanding why we are learning about this maths topic.  Children need to know the relevance of what they are learning and by finding a connection that what they are learning does or will relate to their own life experiences, they will become far more engaged.  An easy, but powerful way for the children to inquire into this is they will often ask their parents how they use this particular maths in their lives.  We collate all the parents answers and discuss together. 


Since the unit becomes student-led, the summative assessment needs to accommodate all the diverse learning that took place. It would be ridiculous and grossly unfair to have my class all inquire into different avenues of a maths concept only to then hit them with a traditional maths test which wouldn't serve any real purpose.  So, what I have found to be a powerful assessment (and reflection) tool is to simply give the children the central idea and they write /draw what they understand about it.

Here are some blogspots explaining how the summative assessment works and the advantages I have found in using them:

°   No more maths tests!!!

°   Measuring Time Summative Assessment

°   Probability Summative Assessment





Blogpost with some example central ideas & lines of inquiry I've experimented with:

Example Central Ideas & LInes of Inquiry