OUCOE N2 Focussing on the Future – Learning from the Past 2007 University of Otago Principals’ and Numeracy Lead Teacher’s N 2 Seminar “Focussing on the Future- Learning from the Past” July 2007

OUCOE N2 Focussing on the Future – Learning from the Past 2007 Today’s discussion A brief look back 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 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 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 Facts Addition & 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 One x 9 = x 2 true/false?

OUCOE N2 Focussing on the Future – Learning from the Past 2007 T rue/False Conjectures Conjecture Two = 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 Costelloo 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  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: – 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 Five 2 x 180 = 0 true/false?

OUCOE N2 Focussing on the Future – Learning from the Past 2007 True/False Conjectures Conjecture Six n 2 = n 4 divided by n 2 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 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