Maths S2 Number: Practicing Adding and subtracting using different strategies

A simple lesson on number, following on from a powerpoint on number (several slides, emphasis on different ways to count on):

1. One group doing algorithms from the board. STRATEGY: using written algorithms
2. One group working with the teacher doing base 10 blocks: showing the teacher the answer to sums he gives them eg 213 + 38. STRATEGY: 
3. One group on the computers (2 per computer) playing 

• CMIT games: Darts Game, Addition Wheel http://www.curriculumsupport.education.nsw.gov.au/countmein/children.html
• Ambleside games: Addition machine, Subtraction machine http://www.amblesideprimary.com/ambleweb/mentalmaths/additiontest.html

The most popular board game was CMIT Darts Game. The algorithms on the board needed to be complemented by some harder ones for the early finishers. 

Maths S2: Graphing

Saw an interesting lesson on graphing.
First students completed a game together on the IWB: http://www.bbc.co.uk/bitesize/ks1/maths/organising_data/play/
This was a good introduction to graphs, a subject which the students had not previously encountered.
Then the teacher used the regular whiteboard to conduct a survey of hair colour. (Interesting how many students asserted that the Eurasian kids had brown hair, when several had black hair.) Then they drew this graph in their books. There was a lot for them to learn in this lesson - they picked up on the word 'axis' from their work on the globe, but some had difficulty copying the graph in their books.

Maths S2: Number Patterns

Just saw a maths lesson on number patterns. After using an IWB activity where students made number patterns on a 100 chart, they were split into three prearranged groups.

One group was making patterns with shapes with the teacher,

One group was colouring patterns on a 100 chart,

One group (with whom I was working) was playing a computer game: http://www.bbc.co.uk/schools/ks2bitesize/maths/number/number_patterns/play.shtml
This was by far the most popular rotation. However, it includes negative numbers (which most of the students said they were not familiar with). Also, many students figured out that they could solve both rounds more quickly by trial and error than by working out the correct number pattern.

The older BBC game has naff graphics, but has some advantages over the current game:
It only occasionally uses negative numbers;
it isn't against the clock, so they have more time to figure it out; and
there are more choices which makes trial and error less enticing:
http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/number_patterns.shtml

How Teachers Learn: Helen Timperley

After writing my last post, I remembered something Helen Timperley said earlier this year about the teacher as 'adaptive expert'. Timperley is a lecturer at the University of Auckland, and (among her other distinctions) is a big fish in the relatively small pond of the study of teacher professional learning. She looks at all the different kinds of professional learning that teachers engage in, to figure out the features of professional learning that is successful enough to actually get all the way through to the classroom. Her publication on Teacher Professional Learning and Development is here.

She based her discussion on How People Learn, in her words 'one of the most profound pieces of work in education.' Teachers are people too: so how teachers learn is the same way as how students (and everybody else) learns:

1. Learning must engage the learner's preconceptions
2. It needs to lay a deep foundation of factual knowledge organized in a conceptual framework - again this is the same for students and for teachers, and for people in general.  Learning plans for students need to be developed so that they are linked to a conceptual framework. The key job for school leaders leading professional learning in schools is to help teachers develop conceptual frameworks that are consistent. so students see the coherence
3. It must encourage and presuppose a self regulatory approach – so teachers can take control of their own learning.  The teacher is an adaptive expert, and this way of working is critical in the age we live in now. Teachers don’t do ‘this’ or ‘that’: they have to be adaptive. Teachers need to be able to identify when routines work and stick with them, and when they need to be changed and change them. 

The difference between teacher learning and learning at large is that teacher learning needs a specific feedback loop within the classroom, as teacher learning needs to be put into practice, and the success of this is measured by the success of student learning. As adaptive experts, teachers need to respond to feedback from students on how their learning is going, and adapt the teaching accordingly. Taking this responsibility, to identify what they need to learn, learn it, apply it in the classroom, monitor the effectiveness according to student outcomes, and then

Revolution in the Classroom: What's not to love?

Four Corners ran a fascinating documentary this week, Revolution in the Classroom. It followed a state government pilot to give 47 schools more autonomy over staffing and budget. The schools spent their money on strategies to provide teachers with guidance and feedback on their work in the classroom. Toronto High, for example, funded a Teacher Development position, to work with teachers in the classroom and focus on their teaching. The schools’ HSC and NAPLAN results spoke for themselves. It seemed to be a perfect ratification of the importance of improving teacher quality by giving feedback.

The central point that I will be taking away from Revolution in the Classroom, though, is the confirmation that feedback is key: both to teachers to tell them how they are going, and back to students to let them know how their learning is going. That doesn’t necessarily mean relying on another teacher in the room, or even on student focus groups about how they think their learning is going, though these are hugely valuable wherever they are possible. The feedback that is continuously available to teachers is the student’s learning, and it is crucial to make this learning as visible as possible as it happens.

As John Hattie says,

“The critical element is the way in which teachers use assessment to find out how they’re having an impact and with whom. The critical element is teachers getting feedback from the kids about whether those kids are making growth, where they’re making a difference. The critical element is schools that work with teachers to know that kind of difference. (10 mins)

I couldn’t help wondering why the Teachers’ Federation would be opposed to something that seemed so successful (11.55). Having dug into it a little, I understand a bit more. The Boston Review makes clear that the State Government sees devolution of power as a cost-cutting possibility: quite simply, principals do the work that would previously have been done at head office. Extra funding provided for the pilot scheme would not be budgeted for a wider rollout.

The answer seems quite clear to me… The State Government knows that to improve student outcomes it needs to improve teacher quality. Even if it didn’t know that from the pilot, there is plenty of research pointing that way. Having seen the strategies that work in the pilot, why can’t it provide schools with the resources to implement similar schemes? If having a Teacher Development officer works to provide teachers with feedback on their lessons, why not give schools at least the choice of having one – not by rearranging their own budgets to take resources away from somewhere else where they are necessary.  Maybe it’s expensive – but it seems a small price to pay.