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E209 - BLOCK 2 MATHS week 7 - number & place value (COUNTING (https…
E209 - BLOCK 2 MATHS week 7 - number & place value
place value- hundreds, tens, ones,...move the digits along do not just add zero!!
helpful glossary of terms at the end of each chapter in Haylock and Manning (2014).
in 1999 suddenly NUMERACY was adopted instead of maths Haylock and Manning, 2014, p. 21)- numeracy hour etc.
‘Numeracy and mathematics’ (Education Scotland, 2016)
Numeracy is the ability to process, communicate, and interpret numerical information in a variety of contexts.
(Askew et al., 1997, p. 336)
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=3.1
oh shut up- all BS. just rebranding !!
writers definitions of maths and numeracy all differ ! s3.1
SKEMP (1989)
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=3.2
2 types of maths understanding
instrumental
implementing the fundamental skills necessary for a task
relational
understanding how links across the subject
this Skemp said was the key to being good a good mathematician !! absolutely
two basic types of cognitive style:
grasshopper
inchworm
(Compton et al., 2007, p. 4)
listed the characteristics of each
(Poustie, 2000, p. 9) appreciates everyone is a combination of both
1025- 998
S3.2 reckons putting this vertically will make people work it out written using a set process.If put horizontally gives people more scope. I didn't I just rounded up and did it in my head- wow I am a grasshopper.
Skemp’s work was built on by a number of researchers, including Chinn and Ashcroft (1998) and Poustie (2000)
Askew and his colleagues in 1997
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=3.3
grasping maths as a whole is more important than subject knowledge
children must learn maths crosses over into other areas
Oh Askew are you trying to make everyone a grasshopper? not everyone is !!
1.connectionist orientation
teaches associated concepts concurrently (fractions, percentages, decimals) if one approach doe not gel, teacher finds another, example displayed children explaining how they solved problems and assisting one another
more frequent assessment and testing and more elaborate systems of recording and profiles.
quote!!
https://www-tandfonline-com.libezproxy.open.ac.uk/doi/abs/10.1080/13664539700200030
p341-6
Transmission orientation
clearly laid out- don't get it you're thick- teacher explains same process again (the teacher is an inchworm!!)
Discovery orientation
multiple methods. even if superfluous. practice.
teachers not favouring one style were in all categories of effectiveness.
Connectionist- all in top gain category. trans &discovery lowest (moderate) catagory
interestingly those studying Maths A level & Degrees were worse maths teachers not better- struggled explaining basics (in discussion of Askew paper) - I get this !! So far ahead of the kids cannot relate. also are maths specialists natural teachers??? Also this is primary level-it's easy. secondary; expert level needed!!
(Askew, 2016, p. 50) likens connectives teachers to improvising performers on stage - well yeah !!!! hence y the maths graduates struggled - not performers !!
‘collectively creating
COUNTING
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=4.1
stable order principle
one to one correspondence
Cardinal principle
abstraction principle
order-irrelevenace principle
Compton et al.
AV: old video !!! great ref
4.2 NUMBER LINES
Paola Iannone
empty number lines great for larger numbers (mm)
https://www.atm.org.uk/write/MediaUploads/Journals/MT197/Non-Member/ATM-MT197-09-12.pdf
most yr 1 use number tracks which are good for counting and carinal numbers but no use for fractions
As I expected Iannone's argument is why introduce something that will become obsolete and alternative must be introduced later. Just start with number line and it's done !!
2006 or 2007????
number washing line AV cute
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=4.2
diff from number tracks (numbers in the gaps not on the lines)
in every classroom under the board
with Dr A Cockburn at the University of East Anglia and funded by the Economic and Social Research Council (RES-000-22-0851)
4.3 DECIMALS
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=4.3
NUMDRUM
invented by John Harrison,-
supposedly good for dyslexia
http://eds.a.ebscohost.com.libezproxy.open.ac.uk/eds/detail/detail?vid=0&sid=e583e7b7-2571-42fc-9b4e-e3d4dbb80250%40sessionmgr4006&bdata=JnNpdGU9ZWRzLWxpdmUmc2NvcGU9c2l0ZQ%3d%3d
aka decimal helical number line
an alternate to number square is the vertical 'Kingston Square' but is known as the 'upside down number square'!
5.1 NUMBER OR NUMERALS
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=5.1
what we say is different
5.2 NUMBER WORDS & SYMBOLS
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1444839§ion=5.2
11-19 difficult as wrong way around. Plus twenty, thirty not clearly 2 10s, 3 10s. Plus 40 can sound like 14
Welsh really well laid out.
French even more confusing than English
Reader CHAPTER 6
https://study.sagepub.com/haylock6e/student-resources/problem-solved-videos/chapter-6-numbers-and-place-value
online video - place value cards great!!!!