Bobbi Hunter, Massey University
Presentation
Background
* NZ has alarmingly high levels of Māori and Pāsifika (and other) students not achieving curriculum standards at Year 8.
* Teachers can fall into deficit thinking about certain groups (Nieto 2002): "These children come to school knowing nothing." Shift it to....what can we show this children, how far can we extend them?
* Show the purpose of maths....why do you need this, in your every day life ? e.g. manage finance etc
* Values to think about bringing in to the class/learning:
The Best Evidence Synthesis of Maths, outlines the effective features of maths in primary school are:
* Students working as a community (cohesive, functional and equal group). Students grouped for abilities tended to have fixed ideas of their capability in maths, so mixed level groups are preferable
* Language for key maths ideas is provided/modelled and scaffolded ad students use this to explain and justify their thinking/approach to a problem
* Maths problems that use students' own worlds as a context (related to their age, cultures, likes etc) and are genuine, real-world challenges
Developing Mathematical Inquiry Communites
* Big ideas: rich, challenging mathematical thinking & reasoning through inquiry
* Students work in groups (social, not ability based)
* High expectations for all
* Inclusion and elevation of culture
* Teachers learn and work alongside students
* Being stuck or finding maths hard is something that happens to everyone in maths at times
Mathematical Practices
These are the things that successful mathematics learners do...i.e. reading a problem and knowing what to do. Includes: questioning; generalising; developing a mathematical explanation; justifying; representing using pictures, materials, numbers etc; constructing arguments; using mathematical language; using the associative, commutative properties (e.g. knowing 9x2 is the same as 2x9). How can teachers do this? Set up a situation/problem, then explicitly discuss/highlight to the class/student when someone shows a practice.
The Approach
Prior: role play active listening & non active listening (e.g. ask 3 questions to find out more about what another said; rephrase what someone said), and sense making (e.g. provide a stimulus and ask 2-3 children to share what it meant to them). Monitor teacher language - 'show us' not 'show me'. Design 'complex tasks' or complex problems. Complex tasks engage students more deeply in mathematical processes and ideas (Jackson et al 2012).
Key features are:
* Complex tasks allow for multiple solutions and methods
* Context based: discuss the context with the students and make it relevant - it must be real world
* Involve key mathematical ideas: teachers and students discuss these after reading the question (i.e. where students say it in their own words, rephrase, add to another's interpretation etc)
* Use a common language: highlight explicitly when students use appropriate maths ideas and language. Provide the correct mathematical term if a student describes an idea (scaffold language)
* Maintain cognitive demand: do this by not suggesting or hinting at a particular solution/method. Avoid providing aids / tools e.g. a table. Have children explore and create their own representations, then build on this by linking them/showing others' ideas/representations.
Management:
Split class in half, and see each on alternate days. Others are given a teacher or self-directed task/options. Students work in 2-3 (juniors) or 4 (seniors). Give them one challenging problem and encourage students to record multiple representations. Consider effective social grouping so that all will get involved and not defer to others.
Structure for Juniors:
10mins: Warm up (whole class)
5-10mins: group norms outlined (active listening, pen sharing etc) & problem
5 mins: think time & pair discussion. Encourage the children to use materials, pen/paper and note what strategies/processes they are using so you can tell
5 mins: large group discussion
Then, give a similar problem with different numbers.
5 mins: think/draw time
5 mins: pair discussion
10 mins: large group discussion time (and connect to the big idea at hand)
The Launch:
First focus is on the context. Ask all children to read the problem for themselves, and then ask different students to share what is happening in this story. Ask others to revoice, add on to, or say the problem in their own words, until they all understand what is being asked. Then ask, what is it asking us to do? (this will generally involve a big idea). Use the Talk Moves.
Then:
NB: some children may want some think time on their own first. Allow groups to work on the problem; thinking, sharing, discussing and notating their work (one pen, one piece of paper). Roam and observe, but avoid coaching ...just notice and reflect, "I heard you say something interesting," and let children lead and discuss their thinking - facilitate the group with their problem solving. Ask a group to explain their solution to the class, step by step, and taking turns. Encourage others to ask questions. Communications & Participation Framework: Teacher actions to engage students in maths. Use reflective questioning to prompt further thinking. After that, provide a second, similar problem using different numbers, and follow the process above.
Reflect:
On your teaching using the Communications & Participation Framework (link above).
Independent Task Examples (for the non-teacher time)
* Open ended problems e.g. there were 24 legs in the farmyard. What animals were there? How many legs did each group have?
* Sorting/categorising: e.g. give children a range of materials and ask them to group anyway they can
* Ask: how many things in the room have something to do with 4?
* Have children write their own problems for peers (i.e. during the independent time), and make the problem about their culture or family
Wonderings & Tips:
* Value of service: can we bring this into learning with cross groupings/tuakana-teina?
* Show children how to call for a pause within the session (this requires monitoring their own understanding of what is going on)
* Basic facts: weave into open ended problems e.g. combinations to ten
* ALLOW children to use the strategy that they prefer....as long as they can justify it, and generalise it for other problems. Avoid inferring/saying that one strategy is better than another (e.g. avoid - "I'll show you a faster way to do this,"). Children need to feel confident about the maths they know and use...and all students will get exposure to different strategies and practises from others in the group.
* Map the problems you set across the Progression Framework
* Stop using 'hands up'...develop a environment where anyone can be called on at any time, and risk taking & mistakes are prized. Try, 'Can you say what it means to you?' or '...in your own words...'.
* What about emergent children who are still developing recognition of 1-10 or 1-20; and one to one counting....when others are working with 3 digit numbers?
14.2.18 Taking this approach into my Teaching
I have used this approach in my contact class this week.
What worked?
* Having children in teacher-chosen partners (mixed ability). Some re-pairing was done while other pairs were coached on working together (LR & LM)
* Doing some simple games/warm ups in partners to begin with.
* Open ended problems engage and challenge the students, and have allowed for different solution making.
* Sharing a pencil and paper helped both children take ownership (except two pairs who were more engaged when they each had a pencil. These children were easily distracted without a pencil, but did talk and create a shared maths drawing when each given a pencil - E&D; B&A&H)
My next steps
* Some pairs (e.g. E & P) are not working together....one leads and the other nods, but cannot explain the work or picture. In response, I am going to explore what active group work looks like tomorrow. I will use a simple video link of children working and talking together; and give the children a simple problem to practise working together.
* I need to explicitly teach and discuss collaborative skills: questioning, revoicing, saying I don't understand, disagreeing, facing each other, all using materials at some stage (tomorrow's plan).
* I need to build a much deeper understanding of the curriculum at this level, and big maths ideas.
* I am looking forward to collaboratively planning and possibly teaching from next week.
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