A Detracked Math Approach to Promote Respect, Responsibility and High Achievement
Collaborative Planning as a Process
Counteracting the Language of Math Ability
Selecting and Sequencing Complex Tasks
Why Isn't Miguel Learning Math?
Introducing the Big Ideas
Links for readings for PD 6:
Selecting and Creating Mathematical Tasks
Classroom Interactions Around Problem Contexts and Task Authenticity
Teachers Promoting Student Mathematical Reasoning
(...oops, I now realise that all links simply take me back to gmail 😕
But... this link to Kelly's Slideshow should work!
Ref to reading breakdown of tasks into low and high level cognitive demands.
Ref to reading breakdown of tasks into low and high level cognitive demands.
A high level of cognitive demand involves the requirement to make connections: require ch'n to dig deeper and connect to the big ideas/conceptual ideas.
This all comes down to teacher practice and teacher actions.
Mathematical practices: reasoning, justifying, generalising and making a claim which can be backed up with proof, representation. This is why the connect and generalising part of the session is so important.
Teacher actions: Why do you think that? (plus 2 more questions - add later)
SO important for the teacher to stand back and notice and listen. Sometimes the teacher does need to step in and reposition a group (status issues, etc.).
Asking the children to solve a problem in a particular way is reducing the level of cognitive demand. It is OK 'pause' the whole group and get one group to explain how they started the solving.
And it's OK to sometimes have less of an emphasis on context.
Remember: 15 minutes small group inquiry time. 15 - 20 minutes share and connect. Too much time and behaviour or other problems might set in.
It's very easy to turn a low level cognitive demand problem into a high level one by adding a simple sentence, e.g., "Show your thinking in 2 different ways", or "Justify and prove".
It's good to add the "Show using cubes" requirement in, once a week or so.
Lesson openers that force children to look for similarities and differences 'beef' up the cognitive level.
Website: which one does not belong (and why)
As a lesson opener: ___ is double ___.
Children can have a minute or two on their own with a piece of paper/pencil before turning and talking.
Remember: "Do we agree? Disagree? Turn and talk. Why?"
Another good warm up: Two fractions are super easy to compare. What might they be?
In warm ups make sure there's lots of turn and talk time, justification time and 'how do you know that' time.
Closed question examples:
- 3+ 7 = ?
- 13 + 17 = ?
How can you make these open questions?
- Turn the questions around
- Ask for similarities or differences
- Replace a number with a blank
- Ask for a number story
- Change the question.
3 + 7 =
- write a word problem for this equation
- think of another way to represent or write this equation
- write another equation that has the same answer
- draw this problem using pictures or show using materials to justify your thinking.
Area and perimeter: start these problems in Year 2.
Some problems can extend over several days; however, your connects will be different each day.
Visual Patterns: link
Represent your thinking in a table. You can use this statement during the generalisation, e.g., Here's a table which one group has used. How could you put your information into a table. Turn and talk.
See LTP.
Assessment purpose:
Discussion re purpose, current practices and how the information is used.
A new way... link?
The NAGs are very broad. We need a range of evidence and we need to triangulate.
Administration so assessment tasks:
Teacher uses assessment task as the problem with half the class, with children completing the task individually, and teacher scribing if necessary.
See Fraction example at Level 1. It includes a 'push' to see whether children might be heading into Level 2, knowing more about fractions than required at L 1.
At L 2:
- Do you agree or disagree?
- Can you explain why?
- Can you write some fractions that are =?
- Can you prove that they are = in different ways?
This avoids Maths anxiety. Children are just proving what they know. It's not a test. It's a snapshot of a point in time.
These snapshots can be kept in a clearfile. Every student will have their own clearfile which is kept throughout their schooling to show progress across their schooling.
Tasks can be relatively open tasks which can show their level of thinking regardless of the task itself.
Schools can email Bobbi who will share assessment tasks in particular strands at any level. Many tasks cross levels - the students' responses will indicate the level they're operating at through their response.
See the Algebra task. Nice and open-ended!
Students should always be consolidating what they are doing in their group anyway, so there should always be that 'on your own' Must Do/Can Do section during the time when their half of the class isn't involved in problem-solving with the teacher. This avoids that anxiety, resulting from 'this is a test situation'.
Moderation:
Very similar to the way that we've moderated writing for ages now. Have the Elaborations out so that we know exactly what we're expecting at each of the levels.
Reflection after the moderating is the most important part. Reflection about the teaching:
- Student strengths
- Areas for improvement and misconceptions (important)
- Possible tasks going forward
More links:
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