Before beginning Term Three, Pete and myself sat down and worked out how we could approach the term working with the P/1/2 unit. We asked to feedback from the teachers who we had already worked with and they mentioned that they would like to see us demonstrate the lesson structure more before they attempt it with their students. From our analysis, we also felt that five weeks didn’t give us enough time to work with teachers and make long-lasting change in their practice. After developing a structure that we felt would better support teachers, we worked with our Principal to adjust the timetable so we were better utilising our release time.

We created a term overview where we broke the term into three distinct stages Term 3 PMS Overview P.1.2

Stage One: Watch us – model teaching approach

Stage Two: Watch you – shifting planning towards teams with our support

Stage Three: Delve deeper – how can we turn good lessons into great ones?

We shared our plans with the P/1/2 unit who were excited to get started.

From there, we looked at their term planner to see what they were aiming to teach at the beginning of the term. With their focus to be Place Value, we took inspiration from Ann Downton’s presentation in relation to how to use the Mathematics Online Interview (MOI) data and the growth points to guide our lesson design. One of the lessons she provided at the PMS Learning Block 2 was titled Prove Me Wrong which was published in Prime Number: Volume 30, Number 4. 2015.

We decided to do our lesson study using this lesson. The structure of how we are working with the unit allowed us multiple opportunities to observe each other teach and hold debrief with each other but also other colleagues.

The challenges that we think may arise are:

• How do we assess student understanding in a manageable way?

We decided begin the lesson with a visualising numbers acitivity. This demonstrated to students that we see numbers in different ways. We felt that this was important as it linked well to the lesson ‘you can solve this problem in lots of ways too’. It also allowed us to spend some time practising subitising which Di Siemon mentioned in her presentation is a critical part of Early Years Maths learning.

Introducing the problem with a challenge and a misconception was a highly effective way of engaging the students. Pete used me as the stimulus – Sam thinks that 19 is bigger than 31. He said it has to be because the 9 in 19 is bigger than the 1 in 31. Prove him wrong. I had students running up to me in the yard for the next two days telling me that I was wrong… and silly… and how could I not know about the tens! The TENS Sam!

Notes:

Visualising Warm Up

“I see 4. That’s all I see”, “I’m thinking”, “I saw the body of a dinosaur. I saw it’s mouth, an upside down smiley-face and an eye.”, “I saw a 4 on a dice and a one and another one. I’m not sure about the bottom thing.”, “I saw three here, three here and three here.”, “Still thinking…”

We reflected on our first lesson and both noted that we didn’t have many students thinking in tens. After a discussion of how to do this and looking through the evidence we had captured in our lesson, we decided to use a picture of a students work to provoke their thinking in the next lesson. A prep student had solved the problem, counting out frogs one-by-one into two piles. One pile had 19 and the other 31. She was very clear in her understanding that 31 was bigger 19 because the pile with 31 was ‘waaayyyyy’ bigger. It was hard to disagree with her thinking but it did give us the perfect image to move ahead with the next lesson.

Tweaks from first lesson:

• Changing teacher thinking: don’t expect mastery in the first lesson. A relentless consistency with small adaptations each lesson will allow students to gain a deep understanding over time.

• Managed the lesson and delivery of instruction: what do we want students to do once they have solved the problem in one way.

• Enablers and extenders: prepared but didn’t use. This would be easier for a classroom teacher to do as they know their students well.

• Visual numbers warm up: varying success between different classes.

Visualising Number Warm Up Version 2

Prove Me Wrong 2

Pete again said that “Sam thinks 26 is bigger than 42…” this got a few eye rolls from some Prep/One students who couldn’t believe I was so silly! Then we introduced the photo from the last lesson.

Pete asked the students, “It’s pretty hard to tell that there is 31 in that pile… How can we make it a easier to count the numbers?” We changed the materials that were available to make it more obvious what we were wanting the students to do. We included pop-sticks, frogs on logs, abaci, unifix blocks along with counters etc.

Students:

“I’m trying to make the top number by outing all the pop-sticks in one pile.”, “I’m trying to make them end-to-end so it’s easier to count.”

T: “Why are you using the logs?”

S: “I know that the logs have 10 bumps.”

T: “How do you know?”

S: “I counted them. Then I counted them on another log and it was the same. I’ve got 30 and I’m making 42.”

Student was given enabler – 8 and 17

“I actually have acorns! I’m going to use them to hold the logs together!”

Counted one-by-one, had 20, took five off. Counted again and then added two more to make 17.

We both felt that there was a clear growth in student understanding from the first lesson to the second. A lot more students were able to say that 42 is bigger than 26 because it has 4 tens and 26 has 2 tens. We used the growth points as a guide for our assessment and if they were able to demonstrate how they came to this conclusion we marked them accordingly.

Using the students as teachers is a powerful tool and teachers need to be skilled questioners to direct student learning. Having regular opportunities to stop, look at a student’s approach and discuss it as a class seemed to be a great way to engage students and expose them to varied approaches.

Second lesson – focus on thinking in tens, greater or less than

Insights:

• Challenging students with a picture from the last lesson of a successful yet tedious strategy. This allowed us to guide students thinking towards using tens to count collections with greater ease.

• Becoming more familiar with the students and the lesson as we had already taught it.

• Seeing what other classes at later stages are doing, gives a great insight to where my class could head and what direction I will lead them in/strategies I will expose them to.

• Using the students as teachers can be really powerful.

• The use of language as a tool for motivation “Sorry to interrupt your work but we’ve got a problem. Can you please come over to this table and see if you can help us?”

• Exploring the problem with the students. At no time we’re we the experts and we became more comfortable with teaching through well-chosen and timely questions.

• Young kids can show incredible persistence whether it be tying a rubber band, taking the time to think about what they’re going to say or working on challenging extenders… We need to encourage and acknowledge these amazing skills in not only Maths lessons, but all subject areas.