The Role of Mathematics in the PYP - Day 3

Our first activity on day three was to order these into which you do from most to least: Written computations, mental computations, estimation or calculators?

After this we had two readings: Nine Ways to Catch Kids Up by Marilyn Burns and 10 Big Math Ideas by Marilyn Burns. We read them in pairs and then had to use post-its to write a Word-Phrase-Sentence. You do not then need to read all of the two articles to get the gist. You can differentiate the articles by reading ability.

Word-Phrase-Sentence

Ma & Pa Kettle math videos on Youtube were suggested as a good resource. A good idea was to use strips of paper to display the length of students limbs. Another strip was used to measure the circumference of the head. These were then attached to the wall. 

Use all three forms of assessment: assessment for learning, assessment of learning and assessment as learning. Summative assessment tasks should be UbD. Everything is done in UbD. MTPYPH should be brought to all planning meetings. Simple oral check, can I say my big numbers on a sheet. Students could do this in pairs.

Tania Mansfield Sharing

An example of a summative assessment task would be to plan a field trip. They would work out transport, accommodation, research hotels, food and pay for activities. When reporting use the Math scope and sequence to highlight where every child is. Do it at each reporting period in different colors. Summative assessments do not have to be grand projects they may be simple and are to assess the central idea. Cooking something would also be a great example of an assessment task.

Planning

If it does not fit, do not try to make it! Do not be scared to change your yearly plan! If in doubt, leave it out!

Transdisciplinary Planning

Tania gave us a table with the six units across the top and the five math strands across the side. We then looked at a summarized scope and sequence document and just ticked what would fit naturally. We then went on to look at a year long overview, which are also broken up into six week plans. Everything that does not fit in is then done on stand alone planners. The same central idea might be used throughout the whole school.

It was a fabulous three days of learning and as Tania said from the start, they way she taught was explicitly inquiry. I learned a lot!

The Role of Mathematics in the PYP - Day 2

When we came in for day two our work was up on the walls. There was a photo slide show on the whiteboard of our work yesterday. It was obvious that our work was being celebrated. We then began with a Math song. It was a funny one in karaoke style.

Student work on display

We read MTPYPH p.82 Constructing meaning about mathematics, Transferring meaning into symbols and Applying with understanding. We also read the introduction sections to the mathematics scope and sequence. Tania mentioned INCA assessment similar to MAP.

When we went on to applying with understanding market days were mentioned when the students have to use money in real life situations. Tania suggested 60% of the time on constructing meaning, 10-15% on transferring meaning and 25-30% of the time on applying with understanding. Plan a field trip would be another example of a summative assessment.

We then did a "Loopee" - I have 49 who has 5x5, I have 25 who has 3x4. This needs to be in a safe environment where mistakes are not frowned upon.

First, second, third, kids on little bikes

Kids have to share half during their snack.

Look at the 5 strands, use a picture of a bicycle.

We did the same activity with a map. There are multiple ways to learn the strands of number and shape & space by looking at the streets, parks, shapes on the map. We decided to use string to measure the distances of the ring road. At the end we had a gallery walk where we walk around and look at each other's work.

Sorting shapes

We were sorting shapes. There were no right or no wrong answers.

After lunch we played Making 10s. For this game five cards are put down. The idea of the game is to get the most cards. To do this you have to make 10. You may do this in anyway, but a picture card is 10. 

Concept map is a good assessment.

Concept Map

TED Talk from Dan Mayer was a very good video. 

We should have Math journals. Students need to reflect on their Math learning. This is another way to get the conversation going. Dialogue journals build up a great relationship with you and your students. 

The Role of Mathematics in the PYP - Day 1

In November I had the pleasure of learning from Tania Mansfield on the Role of Mathematics in the PYP.

She told us from the very start that, explicitly the things we do in the workshop are things you can use in your classroom.  The live binder for example is where Tania shared all of the workshop documents. This seems to be similar to Edmodo but I prefer the Edmodo interface. One of the first strategies we were taught was to show fingers if we needed more time. She also reminded us to tell her if she is speaking too fast.

We introduced ourselves using Maths. Tania pointed out how the who we are unit, is at the start of the year. We introduced ourselves using mathematics: favorite number, height & birthday. Other ideas were: I have 3000 ruppeses in my wallet, impotent dates to me or I have flown xxx miles.

The Blob Tree below was used determine prior knowledge and how we were feeling.

Blob Tree

Session two began with Tony Ryan’s Thinker Keys. The Reverse Key - Think of something in life that is not a Math problem? Everything is related to Math. How we organize ourselves is a transdisciplinary theme that lends itself to Math. 

Wonder wall – What are we wondering? It is for the children to question and ask. Make sure you use it…

Wonder Wall

Lines of inquiry and summatice assessment criteria given at the start. We wrote our essential agreements through the PYP attitudes. EAs should be few in number, refer to things done, be positive, observable & agreed by everyone. We did a Think-Pair-Share 

Next we did Living Graphs to represent: the level you teach, years teaching the pyp, stand nearest to the strand you prefer, when you were in school how you felt at Math (3D). We also looked at Mathematical Glyphs - students make their faces using shapes. Biography Glyphs - Parents have to guess if no names are on there.

Living Graph

Next we did a C.O.R.I. - Collect Organise Represent Interpret. This activity had all five of the strands in it. We all had a sticker on our book. This determined who we would work with. It was another strategy for mixing up the class. There were always lots of resources on hand and we had to do a two minute presentation at the end. Everything was stuck up on the walls after the presentation. We learned from each others work and saw that our work was celebrated. A CORI could be used for creating a rubric. Visual dictionaries, could be used to support EAL students. We need to be sure whether we are checking for math understanding or language understanding. We played another  game with two coins called heads up. We had our hands on our heads or bottom while Tanya tossed a coin.

For our final session we were asked to come up with a definition of a Math learner. We played a game called place value bingo and then did some reading. We did the 3 Rs - Review, Remind, Reflect before going on to an activity where we were asked to estimate a length of string. People used a number of different strategies to guess the length of string. The point was that we all come into the activity with prior knowledge. 

Reading RRR - Review, Remind, Reflect

The day wrapped up with rocket writing - we had to reflect by writing for 3 mins. What a day!

Writing Central Ideas

When people first begin writing enduring, essential understandings, they are often very general and obtuse. The overuse of the verbs impact, affect, influence as well as the verbs is, are and have is a major reason for these weak statements. Learning how to scaffold your thinking using questions is a powerful tool for tightening, clarifying, and developing generalisations to deeper levels of sophistication. To scaffold a generalisation from a weaker Level 1, use and answer the questions "How?" "Why?" and "So what?" Read through the following example of a scaffolded generalisation from the bottom up (Level 1 to Level 3).

Level 3: Severe disruption of a community's social and economic infrastructure leads to feelings of loss, anxiety, confusion, and anger. Or, severe disruption of a community's social and economic infrastructure requires strong leadership with the ability to problem solve, communicate effectively and collaborate to get things done.

So what-is the significance, or effect, if the social and economic, infrastructure is disrupted?

Level 2: Natural disasters can disrupt the social and economic infrastructure of a community.

How do natural disasters impact a community?

Level 1: Natural disasters impact a community.

Note that we want to drop the weaker Level 1 generalisations in our units and teach to Level 2. Teaching to this level will raise academic standards because we are teaching deeper, conceptual specificity. Level 3 can be used to differentiate and challenge advanced learners, or you may wish to take all the students through to Level 3.

Here are some additional scaffolding samples from a ninth grade physics unit on constant acceleration developed by Matt Watson and Cathy Harne, Twin Valley School District, Elverson, Pennsylvania:

Level 3: The velocity of an object can be determined from an x-t graph even if the x-t graph is curved.

So what is the significance?

Level 2: By drawing secant chords and solving for the slope of the chord, one can determine the instantaneous velocity of the object at an intermediate clock reading.

How does the slope determine the velocity?

Level 1: The slope of an x-t graph can determine the velocity of an object.

Erikson H. L., 2007, Concept-Based Curriculum and Instruction for the Thinking Classroom, Corwin, CA.

Creating a Concept Based Inquiry Lesson - Part 2

The following lesson has been taken once again from the work of Lynn Erickson. Her work has perhaps been the biggest help to me as I prepared for my new role as PYP coordinator.

Marianne Kroll, a master teacher featured in the ASCD video Designing Integrated Units: A Concept-Based Approach, shares a lesson she used for helping third grade students see how facts provide a "pattern of evidence". This evidence can be used to develop timeless, transferrable big ideas (generalisations). Marianne explains, "The teacher keeps the generalization in mind as the lesson is planned, and constructs a chart using the concepts from the generalization as column headings" (See Figure 1).

 Grade 3: Lesson on Natural Disasters

Enduring understanding: "Natural disasters affect daily lives and the economy of a community."

Guiding Question:

• "What is a natural disaster?"

Teacher Note: After discussing the idea of a natural disaster and having students name some different kinds of natural disasters, provide them with internet or other appropriate reading material on Hurricane Kartina. Ask them to use sticky notes as they read, to mark places that tell about the impact of the hurricane on the daily lives or economy. Then use the following questions and fill out the Hurricane Katrina example on the chart with student responses. Leave the "Big Idea" column until each row has been filled in.

Figure 1               Natural Disaster Graphic Organiser

Natural Disaster	Impacts: Daily Living	Impacts: Economy	Big Idea
Hurricane Katrina (2005 southern U.S.)
The tsunami in Southeast Asia (2004)
Forest Fires that threaten a community

Source: Marianne Kroll, Curriculum Consultant, Eleva, Wisconsin

• How did Hurricane Katrina change the daily lives of people in communities like New Orleans?
• How did Hurricane Katrina affect the business and economy in New Orleans and other involved communities?

After taking students through the Hurricane Katrina example, provide them with resources to compete the same process (in cooperative groups) of filling out the chart  related to the 2005 tsunami and forest fires. You could either specify a particular geographic location where forest fires threaten communities, such as southern California, or you could have them generalize how forest fires would threaten the daily lives and economy of a community based on their work with the disaster just studied. It is important for the teacher to keep the relationship between the concepts in mind when constructing the chart.

Reference

Erikson H. L., 2007, Concept-Based Curriculum and Instruction for the Thinking Classroom, Corwin, CA., p. 103-104.

Creating a Concept Based Inquiry Lesson - Part 1

What is inquiry and what is an inquiry lesson? I hope to begin to address these questions in this blog post.  The following paragraph has been taken from Page 29 of Making the PYP Happen and is the definition of inquiry that I have heard used on the different IB courses I have taken. It is a good start at defining inquiry, now lets figure out how to make the PYP happen!

Inquiry, interpreted in the broadest sense, is the process initiated by the students or the teacher that moves the students from their current level of understanding to a new and deeper level of understanding. This can mean: exploring, wondering and questioning, experimenting and playing with possibilities, making connections between previous learning and current learning, making predictions and acting purposefully to see what happens, collecting data and reporting findings, clarifying existing ideas and reappraising perceptions of events, deepening understanding through the application of a concept, making and testing theories, researching and seeking information, taking and defending a position, solving problems in a variety of ways.

The work of Lynn Erickson helped me further understand how to plan quality lessons and deepen my understanding of the inquiry way of teaching. In her book Concept Based Curriculum  and Instruction for the Thinking Classroom she does a great job of unpacking what a concept based education should look like. The following is taken from Chapter 4 of her book, the chapter is on lesson planning. 

Quality lesson plans meet certain criteria. They are:

• coherent - There is a clear link between what students must know (factually), understand (conceptually), and be able to do (skillfully).
• interesting - The lesson is motivating to students. They want to participate. 
• time-worthy - The lesson is worth time spent.
• standards aligned - The lesson supports the deeper intent of academic standards (the often-implied conceptual intent) as well as the factual and skill-based expectations. 
• differentiated - The lesson meets the learning needs of different kinds of learners to maximise successful learning. 

On the final point of differentation the work of Tomlinson and Edison (2003b, p.3) is quoted. I will again use it here as a reminder to myself and others of the classroom elements that can be differentiated or modified.

• Content - The subject matter and skills
• Process - How students create a personal connection to what they must know, understand, and be able to do
• Products - The evidence for what students know, understand, and are able to do
• Affect - The synergy between thought and emotions
• Learning environment - The classroom "climate" and operating procedures

I hope this helps you as much as it has helped me understanding how to develop an inquiry lesson. If you would like to have a closer look at the PYP curriculum documents they can be easily found by doing a Google search. I found them here.

References

Erikson H. L., 2007, Concept-Based Curriculum and Instruction for the Thinking Classroom, Corwin, CA.

International Baccalaureate Organisation, (2009), Making the PYP happen:  A curriculum framework for international primary education, (2009) International Baccalaureate, Cardiff, Wales.

Tomlinson, C.A., & Eidson, C. A. (2003b). Differentation in practice: A resource guide for differentiating curriculum, grades 5-9. Alexandria, VA: Association for Supervision and Curriculum Development.

The Structure of Knowledge

Have you ever wondered why the PYP is structured the way it is?  What is concept-based learning? I did! While constructivism, understanding by design, a transdisciplinary program and inquiry are probably the main components of the PYP, concept-based instruction is what is is all about. During the summer, I read a book called, "Concept-Based Curriculum and Instruction for the Thinking Classroom", by Lynn Erickson. It has given me a much deeper understanding of how the PYP is set up and what it is trying to do.  

Perhaps the most valuable chapter of the book for me was Chapter 2, The Structure of Knowledge. I am going to summarise it here for my own reference and for anybody who would like to understand how the PYP works in a little more depth. This was not covered in Making the PYP Happen, when I took it online in 2015.

Lynn Erikson (2007)

Theories are defined as explanations of the nature or behaviour of a specified set of phenomena based on the best evidence available (assumptions, accepted principles, procedures). Theories are supported by best evidence rather than absolute facts. Some examples are: The land ridge theory of early human migration, the VESPR theory in chemistry, or the big bang theory of the universe origin.

Principles or Generalisations are also known as enduring understandings, central ideas or essential understandings.  A Generalisation is two or more concepts stated in a relationship that meet these criteria: generally universal application, generally timeless, abstract (to different degrees), supported by different examples (situation). Generalisations must be tested against, and supported by the facts. They may need quantifiers (often, can, may) in the sentence if they are not always true. Some examples are: Organisms adapt to changing environments in order to survive, Individuals or events can create key turning points in history, Numbers can be added together in different ways to reach a common sum,  or The combined use of subtle and bold colors in a rendering can suggest complexity of emotion.

A Principle is also two or more concepts stated in a relationship, but they are considered the foundation "truths" of a discipline. Principles do not use quantifiers (often, may, can) in the sentence. Critical understandings in a discipline (e.g., the axioms of mathematics, or the laws of science). Like the universal generalisations, principles are referred to as "enduring or essential understandings" or as "big ideas" in educational circles. Some examples are: The supply and demand of goods and services affect cost, In the absence of forces, an object at rest will stay at rest, and an object moving at a constant velocity in a straight line will continue doing so indefinitely, Any straight line can be extended indefinitely in a straight line, and All right angles are congruent.

PYP Key Concepts - Lenses (whatedsaid.wordpress.com)

Concepts are often referred to as lenses, used to look through. The factual/conceptual integration of thinking should be a conscious design goal for curriculum and instruction. Concepts are mental constructs that "umbrella" different topical examples and meet these criteria: timeless, universal, abstract (to different degrees), different examples that share common attributes. Concepts do transfer. A higher level of abstraction than topics because of their generalisability. Concepts come at different levels of generality, abstractness and complexity. Examples are: System, Order, Habitat, Value or Linear function.

Topics organise a set of facts related to specific people, places, situations or things. Topics do not transfer. They are related to specific examples. Examples are: Ecosystems in the Amazon rain forest, The war in Iraq, The Pythagorean theorem or Picasso's paintings.

Facts are specific examples of people, places, situations or things. Facts do not transfer. They are locked in time, place or situation. Examples include: The tropical nature of the Amazon rain forest creating a dense rain forest or 2 + 2 = 4, 3 + 1 = 4.

I hope this helps you get your head around the PYP. The vast majority of the above information was gleaned from the source below.

Erikson H. L., 2007, Concept-Based Curriculum and Instruction for the Thinking Classroom, Corwin, CA.

Student-led Conferences

Communicating with parents has always been one of the most important aspects of my teaching. I wrote a post about it some time back. This year was my first time to facilitate student-led conferences and, boy, were they an incredible learning experience. 

A student-led conference is basically the student inviting their parents to the class to share in the learning journey. As it was my first time to hold student-led conferences, I contacted my old mentor from my first year of teaching, Helen Teese. She explained the process to me and also how she has been organising the PYP Exhibition with her class for the past six years. 

I took what I learned from Helen and brought it to my class and then asked them how they would like the conferences to go. My students are particularly sharp and immediately decided what they wanted their parents to see. After a short lesson on social skills, the students decided they would meet their parents at the door and bring them through four stations. We decided we could schedule four groups at the same time.

1. The first station was student portfolios. These portfolios contain samples of student work throughout the year. Some of the pieces are selected by students and some by teachers. We decided that we would show our parents some of our recent Mathematics understanding in our portfolios at this station.

2. After this, parents were escorted to two chairs facing the Smartboard and our current inquiry cycle. In the PYP, there are six units of inquiry and we teach using different versions of the inquiry cycle. The students actually walked through the different parts of the inquiry cycle, explaining the research process to their parents. 

Student Explaining the Inquiry Cycle

After this, the student immediately went over to the Smartboard, opened their most recent UOI summative assessment and went through it. For this particular unit, we decided upon a form or presentation. Students were given a choice of a poster, PowerPoint, Scratch animation or anything else that covered the criteria.

Action - Teaching Others what we Learned

3. The next station was the Literacy station. In our class, we like to write books collaboratively and then either print them or make them into digital stories to share online. Have a look at one book we made here. This is an excellent way to teach both the reading and writing components of the Literacy scope and sequence as well as the transdisciplinary skills. I had planned to have a laptop set up so the students would just show the video but, due to technical difficulties, we had to change plans and read the stories. The students also highlighted the scope and sequence outcomes we had been working on while creating the books.

Reading and Displaying Literacy Skills

4. The final station was a reflection station for the parents. They were asked what they liked best about their child's work. Some of the students were over the moon with the positive responses from their parents. Parents were also asked how we could improve the conferences for next year. This feedback was then analysed by the class. The teacher then emailed or had the office staff call the parents to address their ideas. One parent said he would like to come into the class ore often. He was called by the office and welcomed to make an appointment to come in anytime he would like. It is very important to follow up with parent requests if you want to really develop the culture of your school!

Finally, clearly labeled displays like the one below were on the walls for parents to see what the students were learning. 

Previous UOI Display in Waiting Area

This is probably one of the best ways of reporting that I have ever learned!

My First Year Teaching the PYP

In the world of international education it seems the International Baccalaureate has risen to the top in terms of reputation. Getting into the "top schools" can be a nightmare if you do not have experience in one of the IBs three programs. I am writing this more for myself to look back upon and as a reflection (of my first year teaching in the IB) than for the public, but somebody wanting to break into the system may find it useful. I have key words in italics, which could be dropped in at an interview!

First of all, the more well established IB schools that I applied for were not even considering applicants unless they had PYP experience. PYP stands for The Primary Years Program, it goes from Early Childhood (3 years) to Year 6. For a school to be authorised by the IB to deliver the PYP, all teachers who teach the program must have Category 1 training in a course called, "Making the PYP Happen in the Classroom". If you have done this training and know some of the IB lingo, you will be at an advantage in an interview. The course costs about 760 Singapore dollars and may be found here.

IB PYP Wheel from www.ibo.org

I have to say, the PYP is incredible. They have taken the best bits of education and packaged it in a really good bundle to sell to schools. Constructivism, Understanding by Design, Concept based Education and Inquiry are some of the basic building blocks of the program. You teach six transdisciplinary themes a year. This is very different from traditional systems where the subjects are separate. In the PYP, the specialist teachers plan their lessons with the homeroom teachers so the students experience continuity throughout the program. Most of the Mathematics and Literacy is taught in a unit and all of the Social Studies and Science is in there. The rest of the Math and Literacy is taught as stand-alone.

There are five main parts to the PYP: knowledge, concepts, skills, attitudes and action.

Knowledge - This is the six transdisciplinary themes and the subjects that are taught. Examples of the themes are, "Who we are", which has a Social Studies focus, or "How we express ourselves", which has an Arts focus. PE is called PSPE (Personal, Social and Physical Education) and could be transdisciplinary, planned and taught with the homeroom teacher, or stand-alone where the PE teacher would create a unit alone.

Concepts - The concepts are often referred to as lenses in the IB programs. We look at the inquiry or lessons through them. Some of them include: change, perspective or reflection. This aspect of the program is epic! I am still a bit confused between these concepts and the concepts in the central ideas. After reading the work of Lynn Erikson, I learned that a central idea or enduring understanding is made up of two concepts in a relationship. It may be a generalisation or a principle. I will not go into this yet, until I fully understand it myself.

Skills - There are five transdisciplinary skills which I believe are going to be called approaches to learning (ATLs) in the upcoming PYP update. They are: social skills, research skills, self-management skills, thinking skills and communication skills. These are then broken down further and should be carefully planned into the curriculum. You may find all of this information in the book, Making the PYP Happen. Just Google it and you will find it easily.

A version of the Inquiry Cycle from my classroom floor

Attitudes - There are 12 attitudes such as empathy, independence and creativity that we try to develop in the students. Another related and hugely important part of all the IB programs is international mindedness. This is summed up in the IB mission statement and in the ten learner profile attributes. Some of these are: caring, thinker and risk-taker.

Action - Finally, what is by far the best part of the program in my opinion, students are expected to take action after they have learned. This can be anything from turning off lights to campaigning for students to stop wasting food. Some awesome examples may be found on a blog called, "Sharing the PYP".

Employee of the Year - Primary School

So to sum up my first year, I believe I have just scratched the surface of the possibilities with the PYP. My background in UbD and inquiry from teaching the Queensland curriculum has really stood to me, but I have a lot to learn. If you want to learn more about the PYP quickly, follow @kjinquiry, @whatedsaid and join in on #pypchat on Twitter.  This has been an incredible year of learning for me!