Going deeper with DMIC

We have now been doing DMIC (Developing mathematical inquiring communities) and it is time to look back and step up our game and move forward. 

We talked about embracing new ideas and how the hardest part of this is letting go of the old, things that are not working so well or need to be let go to get more.
One of these things is the numeracy project it was discontinued in 2009 as it does not address the needs of all learners we as a country have done something no other have in slitting strategies and knowledge. We shouldn't however throw out the key ideas of the numeracy project it is about changing the delivery of the learning.

Reflecting back:
We have all learnt so much and this means that things are moving faster. We now have more confidence and this has had a huge impact on the way we teach. We also still have challenges but these are more around going deeper and exploring more the balance of child and teacher talk and norms and mathematical discussion.

Arguing Mathematically:
We want kids to challenge each others. It is easy to get kids to agree it is harder to disagree and provide a reason when you ask "why".  Kids need to be challenged when they are right as well as when their answer is wrong. Pushing for hands down allows kids have more opportunity and pushes them to try.
It pays to use a bit of wait time when using agree and disagree as this provides time to form opinions and they will have more to share. We want kids to be able to justify why and how they did things so that the process of the mathematical thinking is the focus of the learning not just the answer.
We must require that there is an individual and collective responsibility for learning and sharing.
We are teachers and we must still model what we expect them to say.
We need to be specific with our praise, we often say that was great but need to state what was great and why so children really understand.

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DMIC 2019

The focus of our Discussion around DMiC today is looking at how we plan maths. We are using the Curriculum Elaborations and as a team create learning outcomes from theses larger ideas. Today we focused on statistics with the aim of creating pathway of learning outcomes coming from each team in the school. 

We focused on statistical investigation and worked to create learning outcomes that are measurable and doable. We need to be able to see these learning outcomes in what the students do, not what they are thinking. 

Level 2

Statistical investigation

S2-1: Conduct investigations using the statistical enquiry cycle:

posing and answering questions

gathering, sorting, and displaying category and whole-number data

communicating findings based on the data.

We want to have a continuum of types of graph. For example at level 1 pictographs, level 2 building of pictographs with picture represents multiple objects, add bars graphs. By building up the knowledge of different graphs so that when the reach level 4 and even level 5 they have meaning knowledge of all graphs so they able to conduct robust statistical investigations.

Why? and So what?

By having this understanding of where kids start and where we need them to get to we can make sure each year builds on what they have already done so what each year is a stepping stone to new learning and they have all the knowledge they need by year 8 and we can send them off to high school with a sound knowledge that will set them up for life. 

DMiC Developing assessment exemplars

We have had a lot of questions about how assessment works within the DMiC pedagogy.

What we discussed today is why are are assessing?
We assess for our teaching to know what we need to do. To identify gaps and see student needs. We also must consider what we are collecting with each assessment and how that will be used in our teaching.

When we assess we find gaps in what we have taught and what has been learnt and this allows us to adapt our teaching a find next steps for ourselves and our learners. We also need to be aware of how these assessment impacts on our awareness of students ability, needs and helps us to report to parents.

What does assessment involve?
We are using evidence to make decision for many different reasons. We also have to communicate the evidence that we find from assessment for parents, boards, government and of course our learners. This communication is for different purposes both summative and formative for kids that is setting goals for themselves a long side their teacher.

Aim:
Our aim for assessment is to create some exemplar that allow use to moderate the understanding across the school. We need to have exemplars that work for us and our school. We want to know the learning trajectory for our kids.

In order to create these exemplars we needed to first have unit plans, learning outcomes based on curriculum elaborations, a learning trajectory and assessing the learning.

Students can set goals for themselves for the unit and they can self assess these goals. This could be based on the use of a few problems in the area and creating a list of goals which students could select from. The amount of goals and how this works would depend the students, their needs and how the teacher scaffolds the goal setting.

The aim is the push the individual accountability.

The exemplar tasks could include open questions that ask for all of students knowledge of a question.
Write and draw everything that you know about one half and one quarter?
Heather says she can prove 3/5 is the same as 6/10
Can you show some different ways she might do this?
What other fractions are the same? Can you prove they are the same in at least three different ways?
Can you put the fractions in order from smallest to biggest:
2/3 3/4 5/10 3/9
Show how you know.

The aim of a DMiC lesson is to touch on many levels so that students can show what they know and see the possibility of them extending beyond their year level or below their year level.

We are creating a trajectory and learning outcomes for patterns and relationships:

Inquiry update Term 4

This year I have learnt a lot so far but also seen some gaps in my teaching and my implementation. Recently I tested my inquiry group on the gloss test again and conducted the vocabulary survey again.

My findings were interesting.

Gloss

What I noticed was that three of the six in my target group have made progress in some areas of maths. I found the shift in fractions interesting was this area is high in topic specific vocabulary that students did not know earlier in the year. This links to the data form the vocabulary survey in which I found students understanding of mathematical language tested earlier in the year had improved greatly.

Vocabulary Survey 

I am wondering if Students A and B's lack of shift has to do with the way in which they engage with others in mathematics as these students skill struggle to talk positively to others and share their ideas in DMiC.

DMiC Professional learning

Social and Academic Status

Updated 12 April 2019

How does status change in our classroom. When do children hold academic status. Children who have a range of language stills seem to have more status to the other kids. Status is given for many reasons and this can impact the way that children interact. Can we plan our lessons to change the status for kids? How can we talk as teacher to evaluate or change the status? 

How does this affect behaviour? 

-Children will often raise to the belief of others. If one thinks I can do it then why should I. 

-If children believe that someone else holds all the power they may choose not to share. 

What we believe about our academic abilities and those of others is often form my our perceptions rather than reality. 

What we value and push for in mathematics will be reflected in the way the children engage in maths.

What do I think the kids think being smart in maths look like:

-Sharing their ideas

-Explaining their thinking

I want to support students to think about:

-Never giving up

-Challenging each others thinking

We read an article by Jo Boaler. This article talked about the different elements of maths. 

Multidimensional Classrooms

This talked about elements of a multidimensional class. It talked about adapting the problems so they are group worthy. Every child has something to add. We can get students to share a small part and this can add status and support the whole groups thinking.
In the classroom this looks like an expectation that everyone can participate. The problem is open to multiple strategies and potentially answers. Children learn that there is no correct way of doing it, they can all achieve. 

Assigning Competence

This is when the teacher actively raises the status of the students by praise the Mathematical thinking and sharing. This can be done to provoke the class to think about an idea but also build students confidence, status and increases the visibility of the students ideas which could be missed if the teacher did not actively engage and support that student by raising the status of their idea. As a teacher it is important to be specific about what you are praising as this make sure that students know it is not empty praise.
It is about how we know our children and what praise works best for them to assign competence. It is all about relationships. It requires the ability to step back and open your ears to the groups that are working to pick up what working. It is about setting the expectation that they share that great idea that you heard. 

Student responsibility 

Getting students to take responsibility for the groups thinking. Removing the individual responsibility and put it on the group to make sure everyone understand and can justify. This can be done by the teacher coming in with a question for one student and then if the student doesn't  know moving away and giving the responsibility back to the group to support the development of this thinking. This can be feed in through the group norm discussion and the praise you provide. We talked about how this links to the vocabulary because students need to explain their ideas. Even if a group really struggles there is so much you can praise and affirm because mathematicians do not always get to a fully formed answer.
This needs to be a part of our groups norms, we should expect that everyone understands and enough students to say "I don't understand" and get them to ask questions. The more to praise the student responsibility and when they take these responsibilities for their own learning so students know that this is what we do it maths. Reasoning and providing evidence is a key skill our kids need to succeed in education and life.  

Don shared an example in which and group did nothing they could not start. During the sharing back the teacher said "You are the most important group, you struggled today and so it is everyones responsibility to make sure you understanding and it is your responsibility to ask questions."

High expectations 

Students appreciate challenge, having difficult problems and making sure you push students forward with critical questions and getting them to use these with each other. Again it comes down to how it it set up in your class and what you expect.
If you have a question ask each other not the teacher. It is all about putting the responsibility back on the learners. What do you think? It is also about encouraging them to consider more than one way of solving a problem. This can be effective for higher level learners, sometimes drawing out the problem is extremely challenging with complex problems.

Effort over ability

Praising what students have done and reminding them they can keep stepping up and doing more. Praise those who lesson and try their very best. Make sure no matter what the ability of the students they are pushed and challenged so they put in all the effort they can. This builds students who keep going and trying even when faced with huge challenges.
You gotta get up and try, try, try -Pink It is about being motivational in the way you encourage learners to try. Celebrate the little things praising the little moments. By choosing a group that didn't get it right you are able to praise effort over ability. 

Learning Practices

This is about stopping at any point and revisiting the learning practices. What are we doing to learn? This can link back to the class norms. Teacher need to know what practices you are looking for and value will help you to notice and praise and teach to this practices. 

DMIC Professional learning

The Journey

As we begin to feel more comfortable it is time to let go of some of the things we have picked up. It is time to think more about what every child brings to the mathematics learning. 

When we think about our social group it is not as much about how 'good' they are at working with numbers but about all they bring. Do they talk a lot and are good at sharing? Are they all very quiet and need a chance to speak? 

It's time to:

-Think about how they work together

-Do the Boys and girls work well together

-Keep quiet and give the kids time to talk and 'wait time'

-Give opportunities to talk with turn and talk etc. 

-Try to keep your language inclusive, 'we' your groups learning. 

Justifying and Arguing Mathematically

This is about extending students thinking and pushing kids to reason and explain. It is time know to choose justification norms which we can now add to our mathematical discussions. I believe it is time to build on our group norms and add to the norms. This may be We provide reason for our mathematical problem solving, or We agree or disagree with mathematical thinking and explain why. 

As a school and a team we could build up and back of questions and prompts that will require students to justify and argue. 

Require that students prepare wats to re-explain in a different way an explanation to justify it. 

We talked about how we as teachers can make justifying happen. I have been using these reasoning prompts: 

Generalising: 
This comes towards the end and often the kids are struggling to focus. You may want to jump straight in a leave the warm up until the end. What questions with extend the generalisation.
-Does it always work?
-Can you see any patterns? What are the patterns?
-How is this the same or different from...?
-Would it work with all numbers?
-Look at multiple examples is the rule the same?
-Could you do this with.....?
-Does it still work...?