Modelling and Language

I was modelling a math lesson the other day and the teacher who was observing took notes of everything I said. She typed it up and sent it back to me. I found it fascinating to see my own words reflected back to me. Great reflection. I highly recommend it.

  • I want you to show me eight circles (also demonstrate self)
  • Vocalised how each person did it… rows, lines, groups
  • If you were going to erase two, which two would you erase? Don't do it yet… just show me which ones you will erase.
  • Ok now Erase.
  • What made you do it that way? What made you choose those circles to erase?
  • Was their an easier way to do that?
  • Can you now draw ‘12’ crosses for me.
  • Mine is organised like… how did you organise yours?
  • Can you organise yours a bit more easily?
  • How can you arrange 12 crosses differently?
  • How many do we have here? 12. I'd like you to write 12 here.
  • All students write the number 12.
  • Then I'm going to write this little sign here -. 12 -.
  • What does this sign mean?
  • Now tell me how you're going to erase 5. Which 5 will you take away? Tell me first.
  • Now do it. Now how many are left?
  • Write on your own board 12-5=7
  • What does this sign mean? “=”
  • Talk and discuss the shape of the crosses that are left… oh, Jesse, I see you have 3 in 2 rows. Haru, you have 2 in 5 rows etc
  • Now we are going to do something a little harder…
  • Please draw 13 triangles. Keep it organised, so it's easy to see the number of triangles.
  • Verbalise. What have you got rosa? 4/4/4/1, Jesse 4/5/4, 6/6/1 etc
  • Let's write the number 13. Notice a child making it back to front, number, erase and say, oh sorry I erased your work, can you do it again? If repeats, use little dots to show shapes.
  • If I ask you to erase 4 of 13, show me which will be the easiest to erase… the easiest way to erase 4.
  • Ok erase them now. How many have you got left?
  • How do we write that? 13-4=9.
  • Before I was asking you to do subtraction on the white board. Now I want you to do that in your head. Can you see 9 circles in your head. Organise them in the easiest way. Can you take away 4 of them? Tell me what you have.
  • Ok, now let's use our fingers. Show me 8. Show me how to take away 2. There are 2 ways to take away two. Show me another way.




The Meta Unit (pt 1)

The Meta Unit (pt 1)

This is part 1 of a series of blog posts tracking a change in practice we are trying this year.
This idea came from our frustration with a very busy schedule where sequential Units of Inquiry left little breathing room on the calendar. In order to give ourselves a bit more room on the schedule, we have decided that each Primary class will designate one of their units of Inquiry as a META unit. 

After our initial planning session, two different types of Meta units emerged:

1) The Long Term Project Based Learning

Grade 5/6 will take a unit and do a year long project. On Friday afternoons every week, as a school we have a period dedicated to Community Time/Passion Projects. This class will take that time and apply it to a UOI once a week. The students will negotiate and decide what that will look like.

2) The Central Core

Grade 1 & 2 and Grade 3/4 are going with a different approach. They choose one unit that will act as a philosophical core for the year. It will be weaved in and out of everything. The unit on NEEDS is all about our basic needs as humans (who we are). This will include our needs as learners and as a member of a community. This will be used as a vehicle for reflection and character development.

The other unit is on EVIDENCE, which is all about defending your claim with some kind of support. The class will use CLAIM--SUPPORT--QUESTION as a central philosophy. They will use the other 5 units to inquire into different types of evidence, and different ways of presenting it and analyzing it. There will also be an ancient civilizations aspect to this, but we are still working out what that looks like.

Of course this is just the initial thoughts! We have no idea where it will go, but that unknown quality is very exciting....




To be continued....

Playing with Models

We have been playing with a couple of models, looking for some feedback.

We are trying to make our planning visible for parents to follow the inquiry. We are using metaphors to help them follow along at home so they get how we plan and how an inquiry unfolds.

Would love some feedback.



Good Questions

(also posted at THE LEAD LEARNER, staff blog of Kyoto International School)

Before making a transition to snack, or outside play, or lunch, we gather the children on the mat. We ask them to ask us GOOD question about 'something' (usually the first thing that pops into our heads, clouds, alligators, mountains, etc). When they ask a GOOD question, they can go.

So, what is a GOOD question? And how does an 5 year old know what a GOOD question is?

To support this, we are using this visual metaphor:

Culture of Thinking
A small fish question is a question that you already know the answer to (or one that doesn't really make sense)

A medium fish question is a question that you can probably figure out if you think about it

A big fish question is a question that you don't know the answer to, but you really want to

We have noticed in the several weeks we have started doing this quick little daily activity:

  • the questions are becoming progressively more BIG FISH oriented
  • the children are proud when they ask a good question, and they notice themselves the difference
  • they occasionally self correct their own questions
  • there is a longer pause from the moment the question is asked, to the hand going up
  • they discuss their questions after (during snack)
  • HOW questions are more accessible (and easier to formulate) than WHY questions
  • using a W5 questioning strategy helps get at deeper questioning skills

Catching the Big Fish

We have been using this simple metaphor with our Early Learning 3 students for the last week or so.

Culture of Thinking

It is a simple visual metaphor meant to encourage students to go a little deeper with their thinking. We used it explicitly while we were making collage all about me.

The little fish were the surface ideas. Simple and to the point. Ideas like, "I put a picture of ice cream, because I like ice cream."

The medium sized fish were adding a little detail on top of the idea, making it represent something more about who we are. "I put a picture of ice cream because ice cream is sweet, and I like sweet things."

The BIG FISH were personal connections, memories that we cherish. They were things that are important to who we are as people. "I put a picture of ice cream because it reminds me of going to the park with my grandparents. We get ice cream and sit in the grass."

What mathematics should we teach?


CLAIM: Until about Primary 5 or 6 (age 10-11), we should teach nothing but Number Sense, Problem Solving, and Patterns. No Measurement, no Shape and Space, no Data Management, nothing. Just conceptual understanding of Number, and skill with composing and de-composing numbers (by number I mean number in all its iterations, fractions, percents, decimals, etc). By the time children get to Primary 5 or 6, they are agile with numbers, breaking them down, using operations, putting them back together, using mental math and written strategies, and solving problems.

SUPPORT: Which type of children excel in mathematics? The children that have number sense. The children who see the patterns. The children who are agile with numbers.

QUESTION: Would students be missing out on anything if we stopped teaching Measurement, Shape and Space, or Data Management? Would a stronger foundation in Number sense actually help support these strands?

(I'm not sure I actually believe any of this, just trying to start a discussion)


Using Thinking Verbs to Reflect on Inquiry

I helped a teacher to reflect on a very rich UOI. The children were inquiring into the concept of EXCHANGE. They created their own businesses, made a business plan, worked out expenses/profit, pitched the idea and applied for a loan, did market research, executed the plan, reflected, tried again, paid back the loan. 

We decided to document this process using thinking verbs and simple pictures that tell a story.






Some takeaways- an integral part of the job of a Pedagogical Leader is assisting in reflection, and an important aspect of that is creating documentation, making the learning visible
- ideally, the students should be involved in the documentation process, but to scaffold this process, it is important for the teacher to do it first, to get a sense for how it works
- story is a powerful way to reflect

Some wonderings- How can we use thinking verbs to structure the inquiry? 
- Would it be beneficial to structure the Inquiry Journey up front with the thinking verbs in our pre-planning?
- Would that limit the Inquiry, or would it allow for space to explore?
- How can we feed this documentation back to the students? How can we encourage further reflection?