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.