Literacy in the Numeracy Classroom
WelcomeBrett Meek
Hunter Central CoastPSP Consultant
[email protected] 4972 3010
Literacy in the Numeracy Classroom
New Scheme TeachersThis workshop provides 8 hours of Teacher Identified
Professional Learning for your NSW Institute of Teachers requirements.
It addresses the following standards:1.2.2, 2.2.3, 3.2.4, 6.2.4
NAPLAN
For many people…
Answer
If and then
because
That other syllabus …
Learning to …
Learning about …
Working Mathematically
5 Interrelated Processes
•Questioning•Applying Strategies•Communicating•Reasoning•Reflecting
Working Mathematically(Aust Curriculum – Proficiencies)
The New NSW K-10 Mathematics Syllabus incorporating the
Australian Curriculum
• Communicating• Understanding• Problem Solving• Reasoning• Fluency
Working Mathematically
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
Slippery Words
Odd evensum
squareface
sideedge
weight
third
Literacy in the Numeracy Classroom
... and quite often multiple meanings
SCALE
Literacy in the Numeracy Classroom
Language considerations
Prepositions: by, in, to, on, forWe came by car.Multiply 3 by 2
Prepositions can change meaning Increase by 7Increase from 7Increase to 7
Literacy in the Numeracy Classroom
How do you verbalise 7 - 5?
7 minus 5 7 take away 5 take 5 from 7from 7 take 5
subtract 5 from 7
Literacy in the Numeracy Classroom
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
6 – 2 = What is the difference
between 2 and 6?
0 5 6 7 8 9 101 2 3 4
4
Literacy in the Numeracy Classroom
0 5 6 7 8 9 101 2 3 4
Concrete
Visual/Pictorial
6 – 2 = 4Abstract
Literacy in the Numeracy Classroom
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
Literacy in the Numeracy Classroom
Pictorial
Concrete
Abstract
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 mathématiciens sont comme les
Français : quoi que vous leur dites ils
traduisent dans leur propre langue et sur-le-
champ c'est quelque chose entièrement
différent.
Johann Wolfgang von Goethe (Maxims and Reflexions, 1829)
Literacy in the Numeracy Classroom
Mathematics Vs
Numeracy
Literacy in the Numeracy Classroom
Numeracy Vs MathematicsWhat’s the difference?
MATHEMATICS
NUMERACY
Numeracy Vs MathematicsWhat’s the difference?
MATHEMATICSNUMERACY
Numeracy Vs MathematicsWhat might the difference look like?
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 MathematicsWhat’s the difference?
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 MathematicsWhat’s the difference?
Is the problem Reading or Maths?
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)
Newman’s Error Analysis
Literacy in the Numeracy Classroom
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
>60%
>80%
Literacy in the Numeracy Classroom
Reading
Comprehending
Transformation
Process skills
Encoding
3 + 2 = 3 + 2 = 3 + 2 = 3 + 2 = 3 + 2 =
Literacy in the Numeracy Classroom
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
Reading
Comprehending
Transforming
Processing
Encoding
Literacy in the Numeracy Classroom
Reading Skills
Technical Language
Names
Physical Factors
Reading
Vocabulary Limitations
Literacy in the Numeracy Classroom
Assist with reading where appropriate
Reading
Literacy in the Numeracy Classroom
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
Assist with reading where appropriate
Reading
Provide a contextInsert own name
Literacy in the Numeracy Classroom
Brett
Literacy in the Numeracy Classroom
Assist with reading where appropriate
Reading
Provide a contextInsert own name
Dyslexia & other physical factors
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Comprehension Skills
Technical Language
Names
Physical Factors
Comprehension
Vocabulary Limitations
Information Overload
Literacy vs Numeracy
Comprehension
STLA, Reading Recovery etc.
Super 6 StrategiesMaking ConnectionsPredictingVisualisingSummarisingMonitoringQuestioning
Literacy in the Numeracy Classroom
?Comprehension
Literacy in the Numeracy Classroom
Literacy in the Numeracy ClassroomVisualising
Predicting
• 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
QuestionInformation
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
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
Scattergun Approach/Multiple ChoiceA barbecue was held for 36 people and there were 3 sausages for each person. How many sausages were there altogether?
A. 39B. 12C. 108D. 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
AB C DLiteracy in the Numeracy Classroom
Make an Estimation
Literacy in the Numeracy Classroom
Process Skills
+-
X
÷ = ½0.5
∢
Kg mm ml
Literacy in the Numeracy Classroom
Equals (=) does not mean this is where the answer
goes. Please try not to say put
your answer after the equals sign.=4 + 6 5 + 5
Equals (=) means having the same amount or value
Literacy in the Numeracy Classroom
Please write 5 number sentences starting with
5 + 5 = How many correct number sentences are there?Open Ended QuestionHigher Order Thinking
•Higher order thinking•Deep Understanding
Literacy in the Numeracy Classroom
Encoding
Appropriate form
Ignoring Estimation
Not following instructions
Literacy in the Numeracy Classroom
Lots of practice at the various types of question.
Teaching to the testTeaching about the testQuality 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
• 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
• 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
•Student Self-Regulation•High Expectations
Literacy in the Numeracy Classroom
Newman’s Prompts
Literacy in the Numeracy Classroom
Is the problem Reading or Maths?
Maybe he was just insufficiently motivated to read the sign!
If I’m not back by 5:00 I’m Out to Dinner as
well.
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
Literacy in the Numeracy Classroom
www.youtube.com/watch?v=g5IKIrIQ1kc
Let the maths serve the
conversation rather than having the
conversation serve the maths
Literacy in the Numeracy Classroom
1592 24
11 6 784 44
Literacy in the Numeracy Classroom
• 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.
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”
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?
Construct the Question
A barbecue
12 people
36 sausages
1
1211 10
9
5
8
7
6
3
4
2
1818
What will the question be?
Literacy in the Numeracy Classroom
There are 12 people at a barbecue and there are 36
sausages. How may sausages can each person
have?Answer: 3 or 2 or 1 or 0
Literacy in the Numeracy Classroom
OR 1
2
23
02 2
4
1 3 2 3
Literacy in the Numeracy Classroom
The Language of NarrativeDad 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?
Orie
ntati
onCo
mpl
icati
on
Resolution: The Answer
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
In 2011 Naplan …
Yr 5 Numeracy29/40 questions followed this format
Yr 7 Numeracy Non-Calculator25/32 questions followed this format
Yr 7 Calculator27/32 questions followed this format
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Literacy in the Numeracy Classroom
Thank youBrett Meek
Hunter Central CoastPSP Consultant
[email protected] 4972 3010
Please travel safely