Friday 11 August 2017
8:30
Beginning dialogue around 3 areas;
- Effective Teaching (more effective)
- Content- add/sub - mult/div
- Observations (mild stress)
- Assessment (evolving, more effective but less work)
Anticipation or Participation (Martin Simon, Ron Tzur)
- Teacher is working with children and children are participating, seems as though they are capable. Later, the children do not use the skills. The children were participating but did not get to the point of being able to anticipate when the skill is needed without the teacher.
- We want independent anticipation; when the child can retrieve the skill when needed. We want them to function without us.
- “If we do this (to the equipment) what's going to happen next?” (without using the equipment). “If this happens, then what?”
Hands
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fingers
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Build up the table.
Change context (to $5burgers).
Again, again.
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5
6
7
8
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25
30
35
40
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- As a school we must own the learning of the child.
- Counting is not addition
Models (Bruce’s Slide)
- Physical, pictorial, analogies, known facts or processes, algebraic.
Models should help students engage with the mathematics and not simply solve the problem in front of them.
- Transparency Does the model act like glass in a window (you see through it), or a curtain (draws your attention to it)
Concrete*Literal*Abstract
- Symbols LAST, often irrelevant, not necessary to operate on numbers
- “Let’s pretending” children need be past being completely literal before being able to ‘do’ maths
Transparency (Bruce’s slide)
What maths are we modelling? Eg learning to add 10s
Consider these two scenarios
- There are 23 students in the class. You have an extra 10 children joining the class today.
- You have $23 in your purse. You get given an extra $10
Do different images of the 10 come to mind? Ten individuals or one ten?
Counting model or addition model?
Beware of clutter. $347+$299 Only $1 is important. Place value houses.
Question: Where do you come up with all the stories?!?!
Response: There is no book of available stories. What is the framework I am using? Think about what is more likely to work.
Principle: what is the maths you are teaching? What will help children to see it and use it (participation and anticipation)? What works well, why does it work, do more of it. And share it
Place Value. 42. Forty two. Forty is four tens. Forty two is four tens and two ones.
Vary equipment and models.
Vary equipment and models.
Break 10:15-10:45
Which model is better to use?
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$60 was ⅔ of the prize. How much was the prize?
Draw a model (it propels them to the answer)
$30
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$30
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$30
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⅗ of children came to school in a car today. That was 45 children. How many children
15
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15
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15
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15
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15
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“X By numerator, divide by denominator” or “divide by numerator, x by denominator” but we never know which model to use. The model is correct but does not children do not connect to it.
Counting
“Counting is the enemy of mathematics”
Mathematics is: Manipulation interpretation and communication of quantity
The = sign allows us to simplify (the goal of mathematics)
Some disagreement about 25+43
Zoe does NOT think we should ‘pretend’ 20 is 2 and 40 is 4. The maths is 20 and 40 is 60, not 2+4 is 6.
Counting (on and back) is not necessary if basic facts to 10 are known.
Counting and skip counting are meant to be quick transitory phases.
Gelman and Galistel’s (1978) five Counting Principles are often referred to in the literature as being necessary skills for children to obtain when learning to count (Marmasse, N., Beletsas, A., & Marti, S., 2017; Young-Loveridge, 1999) These are:
· Stable order where the correct number words are consistently said in the correct order
· One-one where the counter says only one number word for each item counted and counts each item only once
· Cardinality where the counter knows that the last number word used on the last item counted is the amount in the set
· Abstraction where it is understood that the items in a set need not be identical to each other
· Order irrelevance where the counter knows that the amount in the set will be the same irrelevant to what order the items are counted
Each of these skills are acquired over time, and often quite slowly.
(zoe’s assignment)
Counting across the gap. (animals in the sea context - blocks on blue lid)
Bruce suggests teaching bonds instead of family of facts. Zoe believes the children need to see relations between quantities and facts. Actually, Zoe sees it as the same thing. ‘Family of facts is just recording the bond in a conventionally accepted method’
Bruce says repetition is different to rote learning. Basically, rote learning made ‘fun’.
Semantics
Lunch 12:15-1:00
Beads on a string. - measurement, percentages
Card games (claim)
Objective = fluency
Number strings
8+7=15
28+7=35
58+7=65
What will happen?
38+7=
Observations
The most important thing that happens in your classroom is not the teacher, it is the learning. The purpose of observation is to look at the learning.
-what is the learning? “What learning did you see today?”
-what is the process?
Not attacking the teacher. We just want to get to the purpose of the lesson.
“The students are here, we want them to be here, so I’m doing this













