Transcript OU Lead Teachers and Principals seminar

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
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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
Looking Back
Percentage of students
80%
Percentage of year 6 longitudinal students rated as at least
advanced additive on the strategy domains
70%
60%
50%
Additiv e
40%
Multiplicativ e
30%
Proportional
20%
10%
0%
2002
2003
2004
2005
2006
Year
Do they continue to improve? Tracking the progress of a cohort of longitudinal students
- Andrew Tagg and Gill Thomas
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Looking Back
Percentage of year 6 longitudinal students rated below
early additive on the strategy domains
45%
Percentage of students
40%
35%
30%
Additiv e
25%
Multiplicat iv e
20%
Proportional
15%
10%
5%
0%
2002
2003
2004
2005
2006
Year
Do they continue to improve? Tracking the progress of a cohort of longitudinal students
- Andrew Tagg and Gill Thomas
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Knowledge: Basic Facts
Addition & Subtraction
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Addition –
“adding on” “plussing” “joining sets together”
“adding tens both on and off the decade”
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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 One
4+2x9=9+2x2
true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures
Conjecture Two
81 - 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 Strategy
General 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 Three
3/4 + 7/8 = 10/12
true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Conjecture Four
Abbot and Costello
7 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
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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
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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
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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 Five
2 x 180 = 0
true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
True/False Conjectures
Conjecture Six
2
4
2
n = n divided by n
true/false?
OUCOE N2 Focussing on the Future – Learning from the Past 2007
Homework
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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
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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
OUCOE N2 Focussing on the Future – Learning from the Past 2007