E209 Week 9 - Shape & Measurement (reader ch 23 (difference between …
E209 Week 9 - Shape & Measurement
In Week 7, you read about maths described as ‘a connected network of multifaceted ideas’ (Askew et al., 1997, p. 353).
Measurement, and space and shape are closely linked to each other but so, for example, are measurement, number and place value, as the audit questions on converting between units of measurement exemplify.
Jones (2003) problem solving hard to teach -does time allow various approaches? can staff follow the child's thinking. Will child get to a satisfactory answer??
resisting audit -
bad example of oblong and how solve number square !!
capacity = litre (l) . Volume = cubic metre (M3)
found out more by googling !!
reader ch 23
area & perimeter - fields & fencing p.346
moving perimeter changes area which many people find odd p.349
1m3 = 1,000,000 cm3- a million cubic centimetres
solid volume measured in M3
LiQUID volumr- ml or litres (but this is not specified SI unit (p338) just internationally recognised for liquid vol & cap
the space taken up
only containers have capacity!?
reader sounds like only liquids
The maximum amount that it could hold !!!
1ml = 1 cm3
is the correct term
but you can't feel the mass
everyday language but incorrect p.328-9
you feel the weight (the mass impacted by gravity)
continually comparing in maths (which longer? Which bigger? which heavier? p.333
a is related to b. B is related to c so can we assume A and c are related? Sometimes depends on the context (eg -not if mirror image)p.333. eg (p234) if A>B & B>C the A>C and vie versa.
same as moving counters about still got same amount
lumps of dough if change shape still same mass
liquid can be confusing as if taller container kids think more p.334
CUBIT = length of your forearm !!?
approximation & estimation
all measurements can only be this depending on accuracy of measuring device
use language 'to the nearest'
means something if temp 0 degrees. or start time in an 'interval' recorded as 0hours.
proof by Exhaustion p.43
self evidently true eg
deductive reasoning p43
counter -examples& special cases p41
not necessarily the arts more 'thinking outside the box'
Craft, A. (2010) ‘Teaching for possibility thinking: what is it and how do we do it?’, Learning Matters, vol. 15, no. 1, pp. 19–23.
Anna Craft agrees
Teaching for creativity, then, involves teachers ‘standing back’ to allow students to ‘step forward’: it is their creativity which is centre-stage.
Teaching for Possibility Thinking
everything in life involves being creative & thinking 'what if' - from mud &grass 'soup' to taking a short cut in traffic
GCSE students mistakenly thought non 'arty' subjects were not creative. Then they realised their error
some structure is essential to guide /support
Sir Ken Robinson 1999 report into creativity in education, All our Futures (NACCCE, 1999).
AV- optional study
anaethatising our children ! should awaken them
schools are factory !!
do not all work the same based on manufacture date !!
collaboration is best but at school 'don't copy, it's cheating'
shouldn't be isolating people
LOVE DRAWINGS !!!!
Schroeder and Lester (1989) distinguished between teaching for problem-solving, teaching about problem-solving and teaching via problem-solving.
Brown and Walter (2005) referred to problem-posing as forming part of problem-solving, where children not only ask ‘what if?’ but also ‘what if not?’
Jim Clack (2011) used the term ‘shiny maths’ to refer to shallow or even irrelevant representations of data, where the aesthetic attractiveness of a coloured-in pie chart or tessellation becomes more important than the underlying mathematical learning
School who created an amphitheatre
Is making a net the teacher gave you template for creative??- v prescriptive!
GREAT QUOTE FROM OLLERTON (2010) Life is full of problems and puzzles to solve. Maths created so we could count & measure to solve such problems
Askew and Wiliam (1995). identified 4 types of problems
19 Handshakes- Triangular numbers
Problem solving great for differentiation - common start. have extensions ready
(Askew, 2016, p. 51)-
changing the way a question is asked (to Black and Wiliam’s (1998) research (Inside the Black Box), the Qualifications and Curriculum Authority (QCA)
(Adapted from Jeffcoat et al., 2004, pp. 10, 34)
different categories of questions
good for TMA!!!
all probing questions is exhausting! balance is good & include humour (adult act dumb) study guide S7.3