Working Mathematically (Aust Curriculum Proficiencies) The New
NSW K-10 Mathematics Syllabus incorporating the Australian
Curriculum Communicating Understanding Problem Solving Reasoning
Fluency
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Working Mathematically
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Technical Language Words that mean the same in ordinary
language eg. equal Words that are only used in mathematics eg.
parallelogram Words that have totally different meanings in
mathematical context. eg. volume Literacy in the Numeracy
Classroom
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Slippery Words Literacy in the Numeracy Classroom
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... and quite often multiple meanings SCALE
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Language considerations Prepositions: by, in, to, on, for We
came by car. Multiply 3 by 2 Prepositions can change meaning
Increase by 7 Increase from 7 Increase to 7 Literacy in the
Numeracy Classroom
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How do you verbalise 7 - 5? 7 minus 5 7 take away 5 take 5 from
7 from 7 take 5 subtract 5 from 7 Literacy in the Numeracy
Classroom
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How do you verbalise 7 - 5? The difference between 7 and 5 How
about... The difference between 5 and 7 Literacy in the Numeracy
Classroom
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Concrete Pictorial Abstract Essential process Some children
will skip through the pictorial stage very quickly BUT Very
important that we explicitly teach children how to operate in the
pictorial stage. Abstract includes being able to operate with
numbers without needing to assign them to objects. This is often a
difficult concept for children to grasp. Literacy in the Numeracy
Classroom
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Pictor ial Concr ete Abstr act
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Mathematicians are like Frenchmen: whatever you say to them
they translate into their own language and forthwith it is
something entirely different. Johann Wolfgang von Goethe (Maxims
and Reflexions, 1829) Les mathmaticiens sont comme les Franais :
quoi que vous leur dites ils traduisent dans leur propre langue et
sur-le- champ c'est quelque chose entirement diffrent. Johann
Wolfgang von Goethe (Maxims and Reflexions, 1829) Literacy in the
Numeracy Classroom
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Mathematics Vs Numeracy Literacy in the Numeracy Classroom
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Numeracy Vs Mathematics Whats the difference?
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Numeracy Vs Mathematics What might the difference look
like?
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We know a student can do 2 + 3 = 5 Where to next? We want to
assess his ability to use that knowledge in real life. What do we
do? Numeracy Vs Mathematics Whats the difference?
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We present the maths within a word problem which is (hopefully)
designed to reflect a real-world situation. When we do this we can
(an do) leave some students behind. Some of those students who are
left behind are quite capable of doing the maths but... Numeracy Vs
Mathematics Whats the difference?
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Is the problem Reading or Maths?
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Anne Newman Languages Educator 1977 An analysis of sixth-grade
pupils errors on written mathematical tasks. (Victorian Institute
of Educational Research) 1983 Strategies for Diagnosis and
remediation (Sydney) Newmans Error Analysis Literacy in the
Numeracy Classroom
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Reading Reading the actual words within the problem
Comprehending Understanding what has been read Transformation
Process skills Encoding Carrying out a transformation from the
words of the problem to the selection of an appropriate
mathematical strategy Applying the process skills demanded by the
selected strategy Encoding the answer in an appropriate written
form Literacy in the Numeracy Classroom
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Reading Comprehending Transformation Process skills Encoding
Literacy in the Numeracy Classroom
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Reading Comprehending Transformation Process skills Encoding
Poorly worded Question Carelessness on the part of the learner Lack
of motivation on the part of the learner Literacy in the Numeracy
Classroom
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Reading Comprehending Transforming Processing Encoding Literacy
in the Numeracy Classroom
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Reading Skills Technical Language Names Physical Factors
Reading Vocabulary Limitations Literacy in the Numeracy
Classroom
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Assist with reading where appropriate Reading Literacy in the
Numeracy Classroom
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Naplan Test Administration Handbook 2012 Year 3 and Year 5
During the Numeracy Test only, you can assist a student by: Reading
the questions, but you must not read the numbers or symbols within
the questions (p6) During the Numeracy Test, you MUST NOT: Read the
numbers or symbols Explain the meaning of any symbols, numbers or
mathematical terms Interpret any graphs or diagrams (p6) Literacy
in the Numeracy Classroom
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Assist with reading where appropriate Reading Provide a context
Insert own name Literacy in the Numeracy Classroom
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Brett Literacy in the Numeracy Classroom
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Assist with reading where appropriate Reading Provide a context
Insert own name Dyslexia & other physical factors Literacy in
the Numeracy Classroom
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Comprehension Skills Technical Language Names Physical Factors
Comprehension Vocabulary Limitations Information Overload Literacy
vs Numeracy Comprehension STLA, Reading Recovery etc.
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Super 6 Strategies Making Connections Predicting Visualising
Summarising Monitoring Questioning Literacy in the Numeracy
Classroom
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? Comprehension Literacy in the Numeracy Classroom
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Visualising Predicting
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How many sausages can each person have? How many sausages does
dad need to buy altogether? How many sausages will be left over?
How many sausages still remain? How many more sausages does dad
need to buy? How many people can dad feed? Literacy in the Numeracy
Classroom
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Comprehension Skills Technical Language Physical Factors
Transformation Vocabulary Limitations Information Overload Literacy
vs Numeracy Comprehension Scattergun approach Multiple choice Key
terms Literacy in the Numeracy Classroom
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Scattergun Approach/Multiple Choice A barbecue was held for 36
people and there were 3 sausages for each person. How many sausages
were there altogether ? A.39 B.12 C.108 D.98 Added the only numbers
in the question Divided the only numbers in the question Multiplied
but did not know how to carry the one or made a careless error.
Correctly solved the problem OR was aware of the internationally
known rule If in doubt answer C. Literacy in the Numeracy
Classroom
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Make an Estimation Literacy in the Numeracy Classroom
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Process Skills + - X = 0.5 Kg mm ml Literacy in the Numeracy
Classroom
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Equals (=) does not mean this is where the answer goes. Please
try not to say put your answer after the equals sign. Literacy in
the Numeracy Classroom
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Please write 5 number sentences starting with 5 + 5 = How many
correct number sentences are there? Open Ended Question Higher
Order Thinking Literacy in the Numeracy Classroom
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Encoding Appropriate form Ignoring Estimation Not following
instructions Literacy in the Numeracy Classroom
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Lots of practice at the various types of question. Teaching to
the test Teaching about the test Quality Teaching Questions What do
you want me to learn? Why is this important? What do you want me to
do? How well do you want me to do it? Literacy in the Numeracy
Classroom
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Teach the process to the children Think out loud Entrench the
process into Classroom & Whole School practice Teach numeracy
comprehension strategies Perhaps use maths questions in reading
groups they are another text type. Show the students the tricks
Ensure they are familiar with the different types of questions.
Lots of practice Literacy in the Numeracy Classroom
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Have High Expectations Expect the children to know where they
are stuck Explain metacognition (Thinking about your own thinking)
Expect the children to do some metacognition Expect the children to
try the strategies before they get your help. Reward effort
Literacy in the Numeracy Classroom
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Newmans Prompts Literacy in the Numeracy Classroom
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Is the problem Reading or Maths? Maybe he was just
insufficiently motivated to read the sign!
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The formulation of a problem is often more essential than its
solution. Obtaining the correct answer may be merely a matter of
mathematical or experimental skill. Albert Einstein Literacy in the
Numeracy Classroom
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Let the maths serve the conversation rather than having the
conversation serve the maths Literacy in the Numeracy
Classroom
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The most important tool for this shift is in our pocket. Using
the students immediate environment will almost certainly increase
engagement. The initial conversation will usually be about where
the photo was taken encourage this as bait for the hook.
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Literacy in the Numeracy Classroom Ask the shortest possible
question! Withhold as much information as you can and encourage the
students decide what is needed and what is important. Steer the
conversation in the direction you want it to go but Be less
helpful
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Literacy in the Numeracy Classroom What might the question be?
What information will you need to include for the students to be
able to work out the answer? How can you use the picture to
support/create multi-step questions?
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Literacy in the Numeracy Classroom
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There are 12 people at a barbecue and there are 36 sausages.
How may sausages can each person have? Literacy in the Numeracy
Classroom
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The Language of Narrative Dad is having a barbecue and he has
asked the neighbours to come along. There will be 12 people at the
barbecue and dad has bought 36 sausages from the butcher. My mate
from next door says he is going to have 7 sausages but I said that
is unfair. How many sausages can each person have if they all have
the same number of sausages and there are none left over? Literacy
in the Numeracy Classroom
Slide 74
In 2011 Naplan Yr 5 Numeracy 29/40 questions followed this
format Yr 7 Numeracy Non-Calculator 25/32 questions followed this
format Yr 7 Calculator 27/32 questions followed this format
