The Wilkie Way
Newsletter March 2017
Professional Learning Opportunities
Collecting and Using Data for Teaching & Learning Mathematics
Date
Location
Venue
9 March
Christchurch
Aranui Wainoni Community Centre
14 March
Invercargill
Ascott Park Hotel
15 March
Dunedin
Pacific Park Motel
REGISTER IMMEDIATELY FOR THESE SOUTH ISLAND
WORKSHOPS - A FEW SPACES STILL AVAILABLE
29 May
Levin
TBA
30 May
Porirua
31 May
Paraparaumu
Kapiti Coast Community Centre
1 June
Wellington
TBA
12 June
Palmerston North TBA
13 June
Whanganui
151 on London
14 June
Hawera
TBA
15 June
New Plymouth
TBA
This workshop will look at a range of data collected using commonly used assessment
tools as well as rich learning tasks, assessment screens, pre & post tests.
The workshop will also present an evidence collection sheet to be used for collecting
assessment evidence over time to give a picture of a students learning for an OTJ.
The workshop will also make use of Wilkie Way teaching progressions and the Wilkie
Way interpretation of the learning progressions that sit behind PaCT
Register online at www.thewilkieway.co.nz Learning Workshops
I am currently working with two schools using centrally funded professional learning
and we are ironing out the teething problems and beginning to understand how we
can make the development plan works for the benefit of the school (not just MOE).
If you are planning centrally funded professional learning and require a facilitator
who specialises in the teaching and learning of primary mathematics, including
assessment and moderation, building teaching content and pedagogical knowledge
please contact [email protected] to enquire of availability.
MOE put in an extra step in that facilitators require permission to work out of area - this is a
way of them keeping tabs on the central travel budget so get in quick!
1 ©Copyright N C Wilkinsons Ltd 2017. All rights reserved.
How do you (and your students) think about mathematics?
Mathematics an abstract construct of the human mind and mathematical objects have no
relation to reality.
Mathematical objects are real and necessary for our daily experiences.
Dehaene (1997) a cognitive neuroscience researcher listed three identified perspectives:
Platonist: These individuals think of mathematics as existing in an abstract place but the
mathemtics they study is real. Mathematics exists outside the human mind and the function
of mathematics is to discover or observe mathematical objects.
Formalist: For these individuals mathematics is a game in which one manipulates symbols
in accordance with precise rules. Mathematical objects such as numbers have no relation to
reality. They are defined solely as a set of symbols that satisfy certain theorems.
Intuitionist: These individuals believe that mathematical objects are merely constructions
of the human mind. Mathematics does not exist in the real world but only in the brain of the
mathematician who invented it. Neither arithmetic, geometry or logic existed before humans
appeared on earth.
Where do you classify yourself?
Your perspective on the subject will affect your approach to designing and presenting lessons
in mathematics.
In considering how the brain works for learning mathematics it would seem that the
intuitionist perspective provides the best account of the relationship between arithmetic and
the human brain:
• Humans are born with the innate mechanisms separating objects and for determining the
numerosity of small sets of objects. (Subitizing)
• Number sense is present in animals as well, and thus is independent of language and has
a long history in the development of our species.
• In children, the capability to do numerical estimation, comparison, finger counting, simple
addition and subtraction arises spontaneousy without much direct instruction.
• Mental manipulation of numerical quantities is carried out by neural networks located in
the parietal areas of both brain hemispheres.
Intuition about numbers is deeply rooted in our brain. It is one of the ways in which we
search for structure in our environment.
Just as specialised brain circuits allow us to locate objects in space, so do circuits in our
parietal lobes allow us to effortlessly determine numerical quantities. (For more information
see David A. Sousa How the Brain Learns Mathematics Hawker Brownlow 9781741704570)
However the number system for recording numbers is man - made. During the history
of people on earth many recorded number systems have been invented and many
more forgotton as a newer more sophisticated system has been invented as the use of
mathematics develops.
Until the invention of zero as a number - zero as nothing of something the modern number
systems could not exist.
The most commonly used number system used for whole number arithmetic is about 2000
years old and is a multiplicative system based on groups of ten. The digits used are 0, 1,
2 ©Copyright N C Wilkinsons Ltd 2017.. All rights reserved.
2, 3, 4, 5, 6, 7, 8, 9. About 500 years ago the system was extended to include decimal
fractions.
In the world of computers the most commonly used number system is a multiplicative
system based on groups of 2. (Binary) The digits used are 0 and 1
Computer science uses a multiplicative system based on groups of 16. The digits used are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f.
A multiplicative number system can be based on any
size group but the group of ten is directly related to the
way we read and write numerals in every day life. It is
therefore essential students understand the base 10
number system.
The Wilkie Way Teacher Handbook will provide you will all
you need to know about our number system and more.
It includes some historical facts which will fascinate the
students. The importance of language to calculating.
Teacher content knowledge, classroom activities and a
CD of student follow up work and other resources.
Available from the online store
www.thewilkieway.co.nz
$75.00 (10% discount for subscribing schools)
The Wilkie Way Teacher Challenge
Write the numbers 1,2,3,4,5,6,7 - one in each hexagon so that all three
lines across the middle of the hexagon add up to a total of 12.
3 ©Copyright N C Wilkinsons Ltd 2017.. All rights reserved.
New material on the Wilkie Way Members Content Pages
Problems:
Graduated problems: Homonyms & Homophones
Problems for developing conceptual understanding:
Curriculum Level
Title
Level 1
Eating Biscuits
Level 1 - 2
Dragons
Level 2
Wally the Worm
Level 2 - 3
Bead Strings
Level 3
Tom goes Fishing
Level 3 - 4
Sauasages at Camp
Level 4
Marathon Runner
Concept
Exploring place value
part/part/whole addition
Working with time
Proportional reasoning
Multiplicative relationships
Percentages
Rates
This now makes 17 problems in each of the level bands
Planning & Assessment
Wilkie
Wilkie
Wilkie
Wilkie
Way
Way
Way
Way
Addition & Subtraction Progressions
Multiplication & Division Progressions
Fractions Progressions
Measurement Progressions
Practice Workbooks
Numbers to 100 (Place Value)
Follow Wilkie Way on
Facebook to be updated
of new resources as soon
as they are uploaded.
School subscription $275 per annum (from date of subscription) paid via paypal
(GST receipt will be sent) No school credit card? - contact charlotte@ncwilkinsons for
invoice option.
Individual subscription $30 pr annum (from date of subscription) paid via paypal
Subscribe at www.thewilkieway.co.nz - password sent to the email address used on
payment and you have a wide range of numeracy resources at your finger tips with
more being added every month.
4 ©Copyright N C Wilkinsons Ltd 2017. All rights reserved.