Literacy in the Numeracy Classroom

transcript

WelcomeBrett Meek

Hunter Central CoastPSP Consultant

brett.meek@det.nsw.edu.au 4972 3010

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

Slippery Words

Odd evensum

squareface

sideedge

weight

... and quite often multiple meanings

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

How do you verbalise 7 - 5?

7 minus 5 7 take away 5 take 5 from 7from 7 take 5

subtract 5 from 7

How do you verbalise 7 - 5?

The difference between 7 and 5

How about ...

The difference between 5 and 7

6 – 2 = What is the difference

between 2 and 6?

0 5 6 7 8 9 101 2 3 4

Concrete

Visual/Pictorial

6 – 2 = 4Abstract

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.

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)

Mathematics Vs

Numeracy

Numeracy Vs MathematicsWhat’s the difference?

MATHEMATICS

NUMERACY

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

What do we do?

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 ...

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

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

Reading

Comprehending

Transformation

Process skills

Encoding

3 + 2 = 3 + 2 = 3 + 2 = 3 + 2 = 3 + 2 =

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

Reading

Comprehending

Transforming

Processing

Encoding

Reading Skills

Technical Language

Physical Factors

Reading

Vocabulary Limitations

Assist with reading where appropriate

Reading

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)

Reading

Provide a contextInsert own name

Reading

Provide a contextInsert own name

Dyslexia & other physical factors

Comprehension Skills

Technical Language

Physical Factors

Comprehension

Information Overload

Literacy vs Numeracy

Comprehension

STLA, Reading Recovery etc.

Super 6 StrategiesMaking ConnectionsPredictingVisualisingSummarisingMonitoringQuestioning

?Comprehension

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?

QuestionInformation

Comprehension Skills

Technical Language

Physical Factors

Transformation

Information Overload

Literacy vs Numeracy Comprehension

Scattergun approach

Multiple choice

Key terms

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’.

AB C DLiteracy in the Numeracy Classroom

Make an Estimation

Process Skills

÷ = ½0.5

Kg mm ml

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

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

Encoding

Appropriate form

Ignoring Estimation

Not following instructions

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?

• 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

• 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

Newman’s Prompts

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

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

www.youtube.com/watch?v=g5IKIrIQ1kc

Let the maths serve the

conversation rather than having the

conversation serve the maths

1592 24

11 6 784 44

• 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.

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”

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

1211 10

What will the question be?

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

1 3 2 3

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?

Resolution: The Answer

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

Thank youBrett Meek

Hunter Central CoastPSP Consultant

brett.meek@det.nsw.edu.au 4972 3010

Please travel safely

Literacy in the Numeracy Classroom

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