OUCOE N2 Focussing on the Future – Learning from the Past 2007 University of Otago Principals’...
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Transcript of OUCOE N2 Focussing on the Future – Learning from the Past 2007 University of Otago Principals’...
OUCOE N2 Focussing on the Future – Learning from the Past 2007
University of Otago Principals’ and Numeracy Lead Teacher’s N2
Seminar
“Focussing on the Future- Learning from the Past”
12 -13 July 2007
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Today’s discussion A brief look back 2002-2006 The importance of mathematics
knowledge – basic facts, place value, fractions and decimals
The importance of teaching the language of mathematics
Recognising that number knowledge and strategies underpin all areas of mathematics teaching – algebra, geometry, measurement and statistics
True/False Number Conjectures A useful Teaching Tool
Accessing Funding Support for Qualifications
OUCOE N2 Focussing on the Future – Learning from the Past 2007
0%
10%
20%
30%
40%
50%
60%
70%
80%
2002 2003 2004 2005 2006
Year
Per
cen
tag
e o
f st
ud
ents
Additive
Multiplicative
Proportional
Percentage of year 6 longitudinal students rated as at least advanced additive on the strategy domains
Do they continue to improve? Tracking the progress of a cohort of longitudinal students - Andrew Tagg and Gill Thomas
Looking Back
OUCOE N2 Focussing on the Future – Learning from the Past 2007
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
2002 2003 2004 2005 2006
Year
Per
cen
tag
e o
f st
ud
ents
Additive
Multiplicative
Proportional
Percentage of year 6 longitudinal students rated below early additive on the strategy domains
Do they continue to improve? Tracking the progress of a cohort of longitudinal students - Andrew Tagg and Gill Thomas
Looking Back
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Knowledge: Basic FactsAddition & Subtraction Addition – - “adding on” “plussing” “joining sets together”- “adding tens both on and off the decade”
- forwards number word sequence, place value- facts to ten, facts to twenty, zero, facts to 100, 1000
Subtraction –- “taking away”, “minussing” “splitting numbers
into sets” “subtracting tens both on and off the decade” Backwards number word sequence, place value,Facts to ten, facts to twenty, zero, facts to 100, 1000
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Knowledge: Basic Facts
Multiplication and Division joining and separating groups (of the same
size), factors and factorising, primes Times Tables twos, fives, and tens, zero, fours, threes and nines sixes, eights, hundreds, sevens
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures(after Megan Franke UCLA)
Conjecture One4 + 2 x 9 = 9 + 2 x 2
true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures
Conjecture Two81 - 27 = 9 – 3 x 9 true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
How far have we come? Basic Facts
“In our time there has been a decided reaction against excessive memorization and against drill methods of teaching, but there is a danger that such a reaction might carry us too far. The tables in arithmetic must in the last resort be memorized; the mistake made in the past was in making memorization the first step”Syllabus of Instruction for Public Schools Education Department of New Zealand (1928)
OUCOE N2 Focussing on the Future – Learning from the Past 2007
How far have we come? Facility with Numbers
“If facility is to be obtained … it is not enough merely to repeat tables in unison every day, or to do repeated tests, or to answer quick fire questions. Used exclusively such methods are wasteful because they do not result in efficient learning. …Alone they are now quite indefensible because they give too little practice to the children who need it most, and too much practice to items that are already well known.
. They do not individualize the learning sufficiently…”
Suggestions for the Teaching of Arithmetic in the Junior School Department of Education (1958)
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Knowledge and StrategyGeneral Pattern for Teaching“If there is any general rule for teaching arithmetic …it is that understanding and memorization depend on each other and go on together; that in the early stages of learning most weight should be given to understanding, and when understanding is well developed more attention should be given to making the learning secure – memorizing so effectively that children are able to uses facts and processes with reasonable facility… and in new situations.
” Suggestions for the Teaching of Arithmetic in the Junior School, Department of Education (1958)
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Basic Facts
“It is flexible thinking that is reflected in derived facts that should be the goal of mathematics teaching rather than simple recall of facts without meaning.”
Jenny Young Loveridge (2007)Patterns of performance and progress on the
Numeracy Development Project (Numeracy 2006 compendium – in press)
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures(after Jenny Young Loveridge (2007) in press)
Conjecture Three3/4 + 7/8 = 10/12 true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Conjecture Four
Abbot and Costello7 x 13 = 28 True/False ?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Language of Mathematics “Many failures in arithmetic are due to an
inability to read directions. ….Teachers should look ahead for new words children will need and teach those words. …”“For example if subtraction is best understood as ‘take away” in the initial stages of learning, then ‘take away’ should be the first words that a child associates with the process”
Suggestions for the Teaching of Arithmetic in the Junior and Middle School. Department of Education (1958)
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Language of Mathematics Language must be explicitly taught Number Word Sequence: – “ty” words
and “teen” words Place Value: 67 – six tens and seven ones Fractions: ¼ - one quarter, 2/5 – two fifths Decimal Fractions:
23.58 – two tens, three ones, five tenths, eight one hundredths
Word stems – cent- (100) , tri- (three) kilo (1000) etc …
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Number Knowledge and Strategies
Underpin all mathematics teaching and learning
Numeracy Book Nine – have you opened it yet?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Number Knowledge and Strategies
Geometry eg: Addition facts to 9 (90), 18 (180)
27(270) 36 (360) Measurement
eg: Calculating Perimeters and Areas Multiplication tables
Statistics eg: Numeral ID especially larger
numbers for data sets
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures
Conjecture Five2 x 180 = 0 true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures
Conjecture Sixn2 = n4 divided by n2 true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Homework Make up your own true/false
conjectures and share them at your next syndicate or staff meeting.
Use them with your students during your next mathematics unit for independent activities or as an excellent formative assessment tool.
How about your next Board meeting?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Homework Question – does your mathematics
content knowledge need improving? Question – does your mathematics
pedagogical content knowledge need enhancing?
Ministry provides 50% fees subsidy for graduate and post graduate study
So…think about enrolling for 2008 as your personal professional development.
OUCOE N2 Focussing on the Future – Learning from the Past 2007
In summary A brief look back 2002-2006 The importance of mathematics
knowledge – basic facts, place value, fractions and decimals
The importance of teaching the language of mathematics
Recognising that number knowledge and strategies underpin all areas of mathematics teaching – algebra, geometry, measurement and statistics
True/False Number Conjectures A useful Teaching Tool
Accessing Funding Support for Qualifications