Transcript Numeracy across the curriculum

Starter
Try this………
101 - 102 = 1
Make one move to create a true statement.
101 =102 - 1
101- 10²= 1
Numeracy across the curriculum
Problem Solving and the approach to calculations
Objectives
• To consider current images of mathematics and
mathematicians;
• To explore numeracy V’s Maths;
• To introduce activities to develop numerical literacy / oral
communication skills;
• To improve interpretation and presentation of graphs, charts
and diagrams;
• To improve reasoning and problem solving;
• To explore possible areas for inter-departmental cooperation in
this type of activity (consistency).
Why do we need to raise standards in numeracy?
8% of the
children are
below L3
KS2 SAT MATHS
Current Year 7
2
15
3A
3B
42
3C
32% are
below a level
3 or below
4A
4B
74% below
a level 4a
or below
76
4C
5A
5B
40
5C
N
Grand Total
7
180
L4+  64%
L5  22%
Is numeracy a problem?
Views of mathematics
Mathematics is …
• an important subject
• nothing to do with real life
• a boys’ subject
• something you can either do or you can’t
• about learning rules
• about right and wrong answers
I'm sorry to say that
the subject I most
disliked was
mathematics. I have
thought about it. I
think the reason was
that mathematics
leaves no room for
argument. If you
made a mistake, that
was all there was to
it.
Malcom X
A good calculator does not need artificial aids.
Lao Tze (604-531 B.C.) Tao Te Ching
I remember once going to see him when he was
lying ill at Putney. I had ridden in taxi cab number
1729 and remarked that the number seemed to me
rather a dull one, and that I hoped it was not an
unfavourable omen. "No," he replied, "it is a very
interesting number; it is the smallest number
expressible as the sum of two cubes in two
different ways.“
Hardy, Godfrey H. (1877-1947) Ramanujan,
London: Cambridge University Press, 1940.
I am ill at these numbers.
William Shakespeare, (1564-1616) Hamlet.
I can’t do maths!!!!!!!!
"It is difficult to understand why so many people must struggle with
concepts that are actually simpler than most of the ideas they deal with
every day. It is far easier to calculate a percentage than it is to drive a car."
(Dewdney 1993, p. 1)
To many people, the words "math" and "simple" do not belong in the
same sentence. Math has such an aura of difficulty around it that even
people who are quite competent in other areas of life are not ashamed to
admit they can't "do" math. Innumeracy is more socially acceptable and
tolerated than illiteracy
(Dewdney 1993; Withnall 1995).
Influencing Attitudes
• Poor learning experiences and fear of getting the ‘wrong’ answer
contribute to the negative impression many adults have of
mathematics. Problems can be created if these views are passed
on to pupils by staff or parents.
• Some teachers may put pupils under pressure in their lessons to
perform mathematical routines that are insufficiently developed or
are unfamiliar, this can reinforce negative feelings which pupils
may already have.
• Some teachers may avoid the mathematical elements of their
subject, thereby losing opportunities to demonstrate the necessity
of mathematics.
Maths V’s Numeracy –
What is numeracy?
“…an ‘at-homeness’ with numbers and an ability to cope with the mathematical
demands of everyday life… An ability to have some appreciation and understanding of
information which is presented in mathematical terms, for instance, graphs, charts or
tables or by reference to percentage increase or decrease.”
(Cockcroft Report, 1982)
“Numeracy is a proficiency which involves confidence and competence with numbers
and measures. It requires an understanding of the number system, a repertoire of
computational skills and an inclination and ability to solve number problems in a variety
of contexts. Numeracy also demands practical understanding of the ways in which
information is gathered by counting and measuring, and is presented in graphs,
diagrams, charts and tables”
(National Framework for teaching Mathematics, 1999)
Task 1 - Which of these are maths tasks and which are numeracy activities?
•
•
•
•
Reading graphs
Planning a journey
Calculating area of pond liner required
Working out the length of a diagonal line using
Pythagoras
• Drawing a pie chart
• Converting metres to centimetres.
• Mixing paint
Numeracy is a fundamental life skill.
Being numerate involves developing a confidence and competence in using
number that allows individuals to solve problems, interpret and analyse
information, make informed decisions, function responsibly in everyday life and
contribute effectively to society. It gives increased opportunities within the world
of work and sets down foundations which can be built upon through life-long
learning.
Whilst numeracy is a subset of mathematics, it is also a core skill which
permeates all areas of learning, allowing pupils the opportunity to access the
wider curriculum.
It is therefore important that all teachers look for opportunities to develop and
reinforce numeracy skills within their own teaching activities and through interdisciplinary projects and studies.
Numeracy – Mathematical literacy
NUMERACY IS NOT JUST ABOUT NUMBERS. Numeracy is a socially
based activity that requires the ability to integrate math and
communication skills (Withnall 1995).
It is intricately linked to language: words are the tools for
translating numerical code and giving it meaning. Words can have
everyday meanings as well as math meanings: for example, "and"
is a conjunction, but in math it can also mean "plus."
Some words are math specific: numerator, multiplicand, divisor.
Interpretation of these words can cause confusion for people with
low literacy levels.
Why is maths talk so important?
In studying mathematics students are expected
to:
• discuss
• explain
• describe
• argue a particular point of view (for
example, justifying a strategy for solving a
problem).
Why do it?
Maths is about problem solving
Problem solving requires thinking skills
Thinking skills require academic language
The iceberg model
• Basic interpersonal
communicative skills
• Cognitive and academic
language
1.
Look at these
pairs of words.
How do you
recognise if
these words are
being used
mathematically?
Task 2 – Mathematical literacy
1.
Add four more pairs of words with dual meanings.
2.
Are there any words that have three or more meanings – mathematical or
other (for example, “square” as in number, in shape or as units of area)?
3.
Put three of these pairs in a context – a sentence or question to show usage.
4.
How can you make the meanings more explicit?
Mathematical V’s every day
How many words
can you think of?
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•
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•
•
•
•
•
•
Sign
Even
Area
Odd
Average
Volume
Digit
Order
Roughly
•
•
•
•
•
•
•
•
•
Mean
Table
Net
Face
Times
Count
Difference
Operation
Take away
How can you help?
• Use concrete reference in your room
• Use Numeracy / literacy mats
• Encourage discussion
Model the language - What am i?
•A hexagonal prism which is about 15 cm long and
½ cm wide. It usually has a cone at the end.
•A ring drawn in the air about 15cm diameter, now
cut away a quarter of it. Attached to the ends of
the remaining part of the ring are 2 cylinders
about 1cm deep with a diameter of 5cm.
Numeracy in Ofsted inspections
What are they looking for?
• whether there is clear understanding and consistent practice among staff in the
development of pupils’ mental skills, written methods of calculation and use of
calculators;
• if pupils can identify and use an efficient strategy for the calculations they need
to do;
• if pupils cope well with the mathematical demands made in different subjects, or
are held back through lack of mathematical knowledge or poor basic skills in
numeracy;
• how well numeracy and, where appropriate, other mathematical skills are
taught, developed or practised in other subjects
Activity – Mental and oral work
Reading scales
• Everyone reads scales in everyday life –
thermometers, tape measures or speedometers
for example.
• Yet this is an area of mathematics which pupils
often find difficult to transfer to other subjects.
Scales
0
10
3
© Crown copyright 2001
Scales
0
20
6
© Crown copyright 2001
Scales
2
3.5
© Crown cop yright 2001
7
Which numbers are you happy
with? (Work these out!)
147 + 149
= 296
224 ÷ 4
= 56
79 + 52
= 131
162 – 28
= 134
87  6
= 522
Calculating
Mental methods
Mental + thinking tools + jottings
Written methods
Calculators
Strategies
Number Facts:
Doubles and Halves
Number Bonds
Times tables facts
Number Techniques:
Decomposition
Multiply and divide
by 10, 100, 1000 etc.
Change the order
Equivalences
Nearest 10 and
adjust
Calculate the answers in your heads.
Then think about
the methods you used.
42 + 35
45 + 46
6 + 78
37 + 199
And subtraction…..?
67 – 32
54 – 28
60 – 19
2005 – 1996
Demonstration 1032 – 786 using an
empty number line, for example:
So 1032 – 786 = 14 + 200 + 32 = 246. This method
is very flexible –different pupils might choose
different sized ‘steps’ to suit their thinking – but
widely applicable.
Partitioning
56
50
6
56=50+6
46
Decomposition of 58 - 32
50 – 30 = 20
8–2=6
20 + 6 =26
58 - 32
50 + 8
- 30 + 2
20 + 6 = 26
Starting with what child can do mentally
Thistens
stage introduces:
Start by dealing with the
Expanded layout based on
Child can use known subtraction
facts
partitioning
1)Lining up vertically
2) Specific position of
operation symbol
3)Lines to delineate answer
152 - 41
100 + 50 + 2
- 40 + 1
100 + 10 + 1 = 111
How are children expected to
multiply and divide now?
Bar Chart to show representation of
non-numerical data
Graphs
8
7
6
5
4
3
"Bar Chart" to show representation of continuous
data
2
1
0
walk
train
car
bus
other
Mode of Transport
Frequency
Number of pupils
10
9
9
8
7
6
5
4
3
2
1
0
0
Height (cm)
Why is it incorrect?
Number of pupils
Incorrect Use of Line Graph
10
9
8
7
6
5
4
3
2
1
0
walk
train
car
Mode of Transport
bus
other
Axis
eg
0
10
20
30
40
50
60

NOT
0
1
2
3
4
5
x
Washing Up
Real-Life Graphs
Give a plausible explanation for the shape of this graph.
© Cr own copyright 2001
Common difficulties in
Handling Data
• Graphs and charts are incorrectly drawn or labelled
For example, the bars in a bar chart representing the
votes cast for candidates in a school election are
joined together or are of different widths
• Graphs and charts are read incorrectly or interpreted
inappropriately
For example, the vertical scale marked in thousands
on a population graph is misread: 350 000 is read as
350
Common difficulties in
Handling Data
• Mean, median and mode are confused or used
inappropriately
For example, the mean is used when referring to the
average monthly rainfall in India
• Data are represented by inappropriate graphs or
charts
For example, a pie chart is used to represent the
distances of the different planets from the Sun
Common difficulties in
Handling Data
• Activities are aimless or contexts inappropriate
For example, vast quantities of data are collected without any
consideration of the purpose of the enquiry
• Undue time is spent on mechanical skills and there is
insufficient emphasis on interpreting data and making
inferences
For example, pupils are taught to draw pie charts or calculate
a mean without understanding of when it is appropriate to
use these or how to interpret them
The numeracy outcomes are organised
around the following themes.
• Estimation and rounding
• Number and number processes
• Fractions, decimal fractions and percentages
• Money
• Time
• Measurement
• Information handling
All teachers should integrate outcomes from these different
themes, enabling pupils to make connections in their learning
through taking part in meaningful experiences within relevant
contexts.
Links to other subjects:
History and Geography
Collect data
Display of data
Interpretation of data
Line of best fit
Rates (Per hundred, thousand)
Scale
Grid references
Area/distance
Application of the 4 operations
Technology
Length, Area, Volume
Mass/weight
Collect, display and interpret data
%, decimals and fractions
Costings
Application of the operations
Ratio and proportion
Science
%, decimals, fractions
Mass/weight
Handling Data
Manipulate formulae
Speed/distance/time
Standard form, large and small
numbers
Measures, Area, volume
Application of the 4 operations
Square and square roots
Proportion and Ratio
Line of best fit
IT/Business Studies
Use of spreadsheets
Formulae
Use of money
Profit and loss, break even
%, decimals and fractions
Data collection sheets /
questionnaires
Display and interpretation of data
Application of the 4 operations
Modern foreign languages and
technologies (home economics):
Planning and making a French meal –
quantities of ingredients,
measurement, using scales.
Numeracy outcome: I can use my
knowledge of the sizes of familiar
objects or places to assist me when
making an estimate of measure.
RE: Presentation of data relating to
ethical issues.
Numeracy outcome: Having discussed, .
can interpret and draw conclusions
from the information displayed,
recognising that the presentation may
be misleading.
Numeracy outcome: I can work
collaboratively, making appropriate
use of technology to source
information presented in a range of
ways, interpret what it conveys and
discuss whether I believe the
information to be robust, vague or
misleading.
PSE: Population statistics,
casualties in battles and
wars
Numeracy draft outcome:
I can solve problems by
carrying out calculations
with a wide range of
fractions, decimal fractions
and percentages, using my
answers to make
comparisons and inform
choices for real life
situations.
Enterprise courses:
Numeracy draft outcome:
I can budget effectively,
making use of technology
and other methods, to
manage money and plan
for future expenses.
What you can do?
‘All teachers have responsibility for promoting
the development of numeracy. With an
increased emphasis upon numeracy for all
young people, teachers will need to plan to
revisit and consolidate numeracy skills
throughout schooling.’
- Building the Curriculum 1
Task
• Create a learning mat for your subject area.
1. Look through the numeracy policy and make
yourself aware of the various numeracy strategies
available for you to use in the classroom.
2. Ensure that you use the correct terminology in your
class room.
3. Display the various different types of graphs and use
the numeracy mats to help your students in lessons.
4. Encourage your form to become actively involved in
the puzzle for the day competition, perhaps enter as
a class.
Conclusion
• Oral and mental mathematics includes much more
than rapid recall of number facts and mental tests
• There is a clear progression in calculation skills from
mental skills through jottings to written methods and
the use of calculators.
• Pupils should be encouraged to approach a
calculation by first asking themselves what is the
most appropriate method: mental, written or using a
calculator.
STEM
• Are you making the pupils aware of stem
careers linked to your subject area?
• STEM is a big area of focus in the UK currently –
what do you do to promote STEM? What does
the school do?
• What skills are required for STEM?