Mathematics and Statistics

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Oct 30, 2013 (3 years and 10 months ago)

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Mathematics and Statistics

Learning Area

2012



Scheme Y9


13


The following document is in three parts:
-


Philosophy and School

Over arching vision links with school curriculum,
NZC guides

and links, student
cohort, policies, discu
ssions, history and knowledge, M
ath
ematics

Learning Area

vision
, policies

and graduate profile.


Te
aching, Learning
Guide
s

for Years
9,
10, 11, 12
, 13VC

Year guides, NCEA links
, lesson
guide

for Years
9,
10,11, 12


Learning Area

Operations

Resources, structure and responsibilities.

Stock

take

of books, calculators etc.
.


Appendices
, Year 10, Year 11, Year 12
/13, Numeracy Info.



School Mission Statement

‘Success through Innovation, Determination and Courage’



Tongariro School

supports building character through cornerstone values,
principles that are consistent, universal and trans
-
cultural which inform and
direct our behaviour and attitudes.


Corner stone values

build character which in turn produces behaviou
r that
benefits the individual, and those in our community. They are the essence of
healthy relationships and build a sense of community and reproduce themselves
when they are practised.


The eight cornerstone values are:

Honesty & truthfulness,
Kindness
,

Consideration and concern for others
,
Compassion
,
Obedience
,
Responsibility
,
Respect
,
Duty



See School Charter Documentation for more detail
, clarification and
interpretation
. Also
www.tongariro.school.nz

for up to date information.

This
scheme and associated documents are available on this website.


2011
Demographics:

Senior School:
-


85
% Maori students, 106
senior
students, 54 boys, 52 girls.

Year 10 33 students

Year 11 33 students

Year 12 25 students

Y
ear 13 15 students

Math
Learning Area

Interpretation and V
ision








Kei hopu



urin
g
a



kia

mau

kite aka matua
.

“Cl o h m v o h loos o .”


“I m h m cs d s s cs s ud s x lo l o sh s qu s s c
and data and learn to express these relationships in ways that help them to make
s s of h wo ld ou d h m.”
-

NZC


“B
y studying mathematics and statistics, students develop the ability to think
creatively, critically, strategically, and logically. They learn to structure and to
organise, to carry out procedures flexibly and accurately, to process and
communicate informat
o d o joy ll c u l ch ll .”

NZC



The Mathematics Learning Area

considers being a
multiplicative thinker
as the
priority need for students at Tongariro School. Such students will know and use
the multiplication tables to investigate, model
and solve problems. The change in
the proportion of multiplicative students at every Year level will indicate the
success of the mathematics department, especially in Years (7,8,9), 10. The
number of NCEA Achievement with Merit
/E

credits will indicate the
success of
students at Year 11. Every credit at NCEA Level 2 or above will be considered a
success.


Achieving Maori success

in mathematics classrooms has a multipronged
approach. These

approaches

include:
-


Developing trusting, cooperative, respectful and

informing relationships
with every student.

Being open minded
, friendly

and communicative.


Keeping a practical approach to learning new ideas foremost


Maintaining learned

knowledge and skills


Providing a dynamic, stimulating and informing wall display


Displaying student and teacher generated work


Providing access to high expense items such as calculators


Involving ICT to enhance learning situations


Supporting pathways of learning to chosen career choices


For Pas
ifica

students and Maori students a strong relationship is developed with
whanau

to support the learning.



Every student will become multiplicative
, a curious
investigator of mathematical ideas and a willing
problem solver.

Special
-
needs students

are attended by personal assistants and supported
by

other programmes within the school. These students are a
lso welcomed into

“no
rmal” classes and learning adjusted to suit needs wherever possible and
planned. Low ability students have learning adjusted to suit current ability
whilst maintaining a high expectation. High ability students are encouraged to
extend their learning in cla
ss time and out of class in competitions, interest
groups and in discussion.



Numeracy at Tongariro School


The Situation

More data needs to be collected and
inter
r
ogated
. However
one year

of
employment has allowed some insights and deductions to be made. The
numeracy data from previous years, the current data all need to be tabled

for use
across the school
.

[See ERO report 2011]

. Data unavailable at Dec 12 2011.


The
literacy

levels of th
e students are likewise very low compared to national
expectations. A fairer statement might be that the variation within the student
cohort is wide in both numeracy and literacy with a general guide that the
students are about a year or so be
hind expectat
ion. Some are more and

some are
less
,

behind. The reasons for this are many, some known, many unknown.



In the mathematics classroom

therefore:
-

-

the reading of questions out loud is encouraged

-

the drawing of the problem asked is demanded

-

the logical devel
opment of the strategy used talked about

-

the recording of the solution using logical mathematics statements is
expected

-

the writing of the answer to the question asked with full sentence
structure demanded

-

reasons given for all steps in a recorded solution

-

each problem solved is critically reviewed

-

posters of projects are developed and presented

-

career paths are monitored

-

ICT is used where ever appropriate

-


In this way literacy is developed in the context of Mathematics and Statistics.


What is success?

T
his question needs to be answered by the Minister, the
Principal and teachers alike.
The i
nterpretation in m
athematics is measured by
the proportion of multiplicative students at any school level, as mentioned
above. Another measure is the number of CL6 pa
sses (Merit or E at NCEA L1),
and another is the number of NCEA L2 passes
(
which measures CL7
performance
)
. In this school success could be the percentage of students whose
attendance is over 80% for any period of time or the percentage of students who
gai
n NCEA L1. The Minister has suggested that success is gaining NCEA L2
.

O
nly
20% of any cohort get to study successfully at CL7 (Y12) [See historical School
Cert, NCEA data on
www.nzqa.govt.nz
].




Level Structure at
Tongariro School

and Other Factors

Tongariro is an Area school. It is not “one” school. It is
currently
three schools
operating on the same campus. The Principal has more of an advisory role and
three DP’s oversee the organization and daily running of the
primary,
intermediate and senior schools.
The intermediate school comprises Year 7, 8
and 9 students
.
Some senior teachers take intermediate classes mainly in
technology. Specialist extension classes are not promoted

yet
.


Further investigation shows a lo
t of copied sheet work with no set text or
programme of work, some note copying from the white board and a class
structure resembling Year 8 homeroom style rather than a more tradition Year 9
class where students move to another class. The current Year 9 s
tudents

do not
get a lot of testing,

extension, or problem solving

and it is likely that as has been
identified by the Ministry
,

most of the Intermediate teachers have little
mathematical knowledge beyond CL3 [See Numeracy Research Reports on
www.nzmaths.co.nz
]


Year 10 is a bridging year

between a class based learning environment of
Middle School Y7 to 9 and the senior school approach of moving students to
specialist classroom teachers. The mathematics programme en
courages all
aspects of the key competencies but stresses mathematical thinking and
communication. From 2012 this year group will be called PNCEA meaning Pre
-
NCEA so that the focus is clearly identified for future success.


During 2011 there were

two teach
ers of mathematics in the Senior school. There
were

three classes in Year 10 2010, usually 2, 2 classes of Year 11, 2 classes of
Year 12 and a couple of Year 13 students using VC but with a tutor for 5 periods
a week.

In 29012 there is a Year 9, 2x Year 10
, 2x Year 11, 3 x Year 12.


The
departme
n
t

is well resourced with texts, calculators, data
-
show and
computers.

In 2011
Year 10 students have 4 timetabled 45 minute math classes
or 3.75hrs if they are on time and on task and stay the whole period. Year 11 a
nd
12 students have 5 timetable 45minute periods.
In Year 2012 current plans are
that Year 9 will have three hours per week, Year 10 three hours per week, Year
11m 12 four hours per week.


The school absenteeism rate is about 20 to 30%

overall with much v
ariation
.
Late to school is a common event and taking days off is common.

In Year 10 the
median is 74% present, half of the students are present between 60% and 81%
of the year, the least is 30% attendance and the most 97%.
This single event
causes learnin
g difficulties that are unsustainable.


Mathematics is learned sequentially and progresses from one lesson to the next
with each building on the
one before. Absence from class
creates a gap in
learning and consequent delay, sluggish performance, frustrati
on, behavior
problems and increase in teacher workload.
A key

priority for this school must
be

to get students to school, on time, ready to learn. [See ERO report 2011].


From classroom observation in 2010

many

students

are

reluctant learners,
undisciplined and not used to
doing homework, study or investigation. A general
description might be they have not yet learned how to learn.


Eve
ry effort
is made to normalize homework and assignment expectations.

It has
been suggeste
d that identified students with learning reluctance or lack of
learning skills be withdrawn for a day or two of intense direction to remedy
these issues and then constantly monitored. Increasing student achievement,
(
and in this school that means Maori suc
cess
)

will then be accelerated to
more
acceptable levels. The community, parents would need to be involved and made
active participants in this process as well.



Implications for Mathematics Programmes Year
9

to 13, 2012.

Statistics requires literacy so

this subject has to be introduced in a practical way
and developed along with the literacy required. The students are quite visual and
kinesthetic learners. Shape and geometry
is

a natural avenue for learning so
these topics form the central theme of year

programmes. Through geometry
number, algebra, measurement and probability and statistics are discovered.
This may well imply that statis
t
ics is not a
core subject for students

until they
have sufficient literacy to support the learning
.


The NCEA L1 awar
d
realistically will

be a two year goal for 50% of the students.


All students will eventually gain numeracy

over 2 years
.


A practical component for mathematics and a context in which mathematics can
be studied will be trialed in 2012. There are some Level NCEA Physics standards
that offer a good reason to know about measurement and measure in a real
context. These papers will

be combined with the mathematics standards selected
to make a course.


There will be two
main
courses at Level 1 with a Work and Study Skills Fallback.


App
Mat 1 wi
ll be a faster pace for the better students, offer 24
cr and will use
a
selection of
achievement standar
ds

including one from Physics. Students in App
Mat 1 will be expected to gain numeracy requirement for NCEAL

1 from
Achievement Standards
.


Mat 2 will be a selection of

the eas
ier standards and offer about 20
cr at a slower
pace.
St
u
d
ent
s failing to show a convincing and sufficient ability that they will
gain numeracy for NCEA through Achievement standards will be guided toward
the Work and Study Skills standards, see below.


There is also a third option for very low achieving students.
Identified students
will be asked to complete the Work and Study Skills unit standards through
which 10 numeracy credits gained will satisfy the NCEA L1 numeracy
requirement.

Course
s

that follow are :
-

Year 9, Year 10, Y11 Work and Study Skil
l
s, Year 11
A
pplied Mat 1, Year 11 Mat 2, Year 12 Mathematics, Year 12 Statistics. The Year
13 cours
es are studied using VC and are not included.






All Course Gui
des • 2012

Overview

All Courses in Mathematics and Statistics for 2012
. This

section

parts are

copied fo
r the
senior
course selection books.


ei hoputo uringa ite a a ta epa engari iamau ite a a matua.


Cling to the main vine, not the loose one.

-
NZC


All
achievement objectives in Year 11 NCEA courses are

at Curriculum Level 5 or
6. All assessment in Year

12 is at Curriculum Level 7 and in Year 13 at
Curriculum Level 8. These are huge jumps in learning progression.
Demonstrating one has the ability to study at a higher level is by
gaining 8 Merit
or Excell
ence credits
. For example, to study at Year 12, 8 Merit credits are
needed from any mathematics standards in Year 11.


The Numeracy Unit Standards are owned by the Work and Study Skills area of
NZQA and are not mathematics standards

for that reason
. These unit standa
rds
are suitable to gain the minimum needed to satisfy the numeracy NCEA Level 1
requirement. They are internally assessed and are set mostly at Curriculum
Level 4.

They are
not a suitable requirement

for progression past CL5.


Most Year 11 students are e
xpected to gain numeracy through the Achievement
Standards over a period of 1 or 2 years depending upon ability. A small group of
students will need to use the Work and Study Skills Numeracy Standards and use
a portfolio of evidence collected from across t
heir subjects to gain the NCEA L1
numeracy requirement. [see
www.nzqa.govt.nz

for all updates].


Problem solving and extension of mathematical thinking are a priority of the
mathematics department. Creating a curiosity in mathematics to explore the
myriad of patterns and mysteries in number is a serious aspect of learning
mathematics. Being able to re
ason, explain and prove why things are, enables an
understanding of the real world that opens doors of opportunity and develops
and enduring and lifelong quest for truth and honesty.


Mathematics is a human endeavor that can develop into careers in techno
logy,
physics, meteorology, geophysics, business, science and engineering.





Yea
rs7, 8 and
9

Mathematics

and
Statistics

The senior school has minimal input into this program
but dialogue with senior
managers of the Middle School involved

connections to e
xpectations. This
department is content with the existing program at Year
7, 8 and 9 which has
number as the key

focus. It is suggested that extension classes for small groups of
between 10 and 15 students of similar ability are involved with investigative

mathematics and problem solving to enhance the existing Year 7,

8,

9 programs
as these
skills

need developing.
The other strands are going to be enhanced
through existing programs in 2012 while maintaining the focus on number to
Level 4 and 5 in NZC. Math
ematics has to be an enjoyable activity for students. A
quiz event and display during mathematics week, or thereabouts is a planned
annual event. Data from Year 9 is shared with this department.


See above for some relevant comments and observati
ons from 2
011

about the
current Year 10 Mathematics instruction.

(Note Year 9 class for 2012).


Focus concepts, knowledge and skills that can be enhanced in Years 7 to 9
include

-

using multiplication to solve problems and using times tables

-

drawing a set of axes to p
lot simple linear graphs

-

elementary algebra of
continuing simple patterns

-

elementary algebra of solving
by guess and check

-

know the names of basic geometrical triangles, quadrilaterials and
symmetrical polygons

-

use isometries and enlrgement

-

Can describe a
pattern in numbers using nth term ideas

-

Knows 8 points of the compass

-

Knows 10 facts of basic geometry of straight lines and triangles.

-

Can use a broken ruler to measure within and without the size

-

Knows units for mass, time, capacity, area.

-

Can use a chan
ce tool such as a die or coin to play a game.

-

Has a working knowledge of the PPDAC investigative cycle

-

Has investigated 3 questions on Census at Schools website

-

Has completed a personal careers pathway investigation (see below)

-

Has completed 3
investigations into a mathematical idea, person or
problem.


This list needs to be reviewed and amended accordingly as identified needs and
issues arise. This could be done along with the formal development of a
mathematics programme for these years.



Ye
ar 9
Mathematics

and Statistics

Overview

and Student Guide

The aim of the mathematics department is to cultivate a
curiosity of
mathematics

in every student and for each to become a problem solver.
Mathematics is not just a set of skills or rules that is t
o be learned; it is a
connected way of thinking.


Mathematical thinking is about being
logical, strategic, creative and critical.

Problem solving and investigation are emphasized and opportunities to take part
in regional and international competitions ar
e offered.

.

There are 6 main strands:



Number



Understanding and using multiplication and proportional
thinking to solve problems



Algebra



Developing skills and algebraic thinking.



Measurement



Practical measuring and estimating to solve problems



Geometry



Exploring and explaining the properties of shapes



Statistics



PPDAC cycle of investigative statistics



Probability



Exploring chance and variation


Assessment

Students will complete an AsTTLe test during the year to measure progress
a
gain
st the NZC Levels 3, 4, 5

in Number Geometry and Algebra. Everyone’s
Numeracy Stage will be monitored.


There will be a presentation of an investigation during the year.


Duration

A full year programme



Course Prerequisite

S
uccessful completion of a
Year 8

Course.


Course Fee

$12

Stationery Required

1 x 1J8 Quad book

CASIO fx82AU (optional)

Pens, pencil, ruler, eraser

Dragon Homework Book ($12)


Future Path

Year 10 Mathematics



Year
9

Unit 9
Guide

• Summary, see Uni
t Guides in File Box for details.


Term 1

Number (3 weeks)

Measurement (3 weeks)

Statistics (3 weeks approx)

CL3/4/5

3 topic tests, multiplication tables
checks as required, EOTerm Com Test.

Number

concerns place value, squares,
square roots, number patterns.

Measurement

is about the SI units,
practical measuring and calculation.

Statistics

is about the PPDAC, doing a
sur
vey, dot plots and box/whisker

Term 2

Trigonometry (3 weeks)

Geometry (3 weeks)

Algebra (3 weeks approx)

CL3/4/5

3 topic tests, multiplication tables
ch
ecks as required, EOTerm Com Test.

Trigonometry

Scale drawing and
enlargement.

Geometry

revises triangles, quad,
constructions, simple proofs.

Algebra

extends the number,
patterning, and simple solving,
substitution, manipulation skills.

Term 3

Percentag
e (3 weeks)

Transformations

(3 weeks)

Probability (3 weeks approx)

CL3/4/5

3 topic tests, multiplication tables
checks as required, EOTerm Com Test.

Percentage

change, increase and
decrease. Level 5 problems.

Transformations

is
about reflections,
rotations

and translations.

Probabilty

in a practical sense,
experimental and simlulation.

Term 1

Algebra (3 weeks)

Revision (3 weeks)

Model Making (2weeks)

CL3/4/5

3 topic tests, multiplication tables
checks as required, EOYear Com Test.

Algebra

manipulation and solving.
More complex and word problems.

Revision

of year for examinations.

Model

making of stellated platonic
solids.


Note, Numeracy is a whole year, every day event and
is used to introduce the day
or lesson. Homework focuses on prev
ious learning and practicing new skills.


Puzzles and problems, Australian Math Comp problems, BOPMA problems and
the li e from “Bro en Calc” Starter of the Day used every day. Problem solving is
pushed as a puzzle skill for enjoyment.


Every student mus
t also produce a project and present this to the class during
the year. This is likely to be a poster, problem solved, model etc.


See Year 9 Guide Mathematics



P
-
NCEA

(Y10)
Mathematics

and
Statistics

Overview

and Student Guide

The aim of the mathematics department is to cultivate a
curiosity of
mathematics

in every student and for each to become a problem solver.
Mathematics is not just a set of skills or rules that is to be learned; it is a
connected way of t
hinking.


Mathematical thinking is about being
logical, strategic, creative and critical.

Problem solvi
ng and investigation are emphasized

and opportunities to take part
in regional and international competitions are offered.

.

There are 6 main strands:



Number



Understanding and using multiplication and proportional
thinking to solve problems



Algebra



Developing algebra skills and algebraic thinking.



Measurement



Practical measuring and estimating to solve problems



Geometry



Exploring and expla
ining the properties of shapes



Statistics



PPDAC cycle of investigative statistics



Probability



Exploring chance and variation


Assessment

Students will complete
an AsTTLe test

during the year to measure progress
against the NZC Levels 3,

4 and 5 in
Number
, Geometry

and Algebra.

Everyone

s
Numeracy Stage will be monitored.


There will be a presentation of an investigation

during the year
.


Duration

A full year programme



Course Prerequisite

Successful completion of

a Year 9 Co
urse.


Course Fee

$12

Stationery Required

1 x 1J8 Quad book

CASIO fx82AU (optional)

Pens, pencil, ruler, eraser

Dragon Homework Book ($12)


Future Path

NCEA L1 Mathematics 1
, either Mat 1 or Mat 2



Year
10
Guide

• Summary, see Unit Guides in File Box for Year 10.


Term 1


Number (3

weeks)

Measurement (3 weeks)

Statistics

(3 weeks

approx
)

CL 4/5

3 topic tests, multiplication tables
checks as required, EOTerm Com Test.

Number

concerns
ratio and
proportion.

Measurement

is about the SI units,
practical measuring and calculation
.

Statistics

is about the PPDAC, doing a
su
rvey, dot plots and box/whisker,
making an informal inference.

Term 2

Trigonometry (3 weeks)

Geometry (3 weeks)

Algebra (3 weeks approx)

CL 4/5

3 topic tests, multiplication tables
checks as required, EOTerm

Com Test.

Trigonometry

introduces sine, cosine
and tangent ratio, Pythagorus.

Geometry

revises triangles, quad,
constructions, simple proofs.

Algebra

extends the number,
patterning, and simple solving,
substitution, manipulation skills.

Term 3

Percentage (3 weeks)

Graphing (3 weeks)

Probability (3 weeks approx)

CL 4/5

3 topic tests, multiplication tables
checks as required, EOTerm Com Test.

Percentage

change, increase and
decrease. Level 5 problems.

Graphing

is of linear relations,
gradient and
intercept, a parabola.

Probabilty

in a practical sense,
experimental and simlulation.

Term 1


Algebra (3 weeks)

Revision

(3 weeks)

Model Making (2weeks)

CL 4/5

3 topic tests, multiplication tables
checks as required, EO
Year

Com Test.

Algebra

manipulation and solving.
More complex and word problems.

Revision

of year for examinations.

Model

making of stellated platonic
solids.


Note, Numeracy is a whole year, every day event and
is used to introduce the day
or lesson. Homework focuses on prev
ious learning and practicing new skills.


Puzzles and problems, Au
stralian Math Comp problems, BOPMA problems and
the li e from “Bro en Calc” Starter of the Day used every day. Problem solving is
pushed as a puzzle skill for enjoyment.


Every student mus
t also produce a project and present this to the class during
the year. This is likely to be a poster, problem solved, model etc.




NCEA L1
Applied Mathematics


A
P

1

Overview

This course is designed for all students who have a continuing interest in
mathematics or plan on a career involving
more advanced
mathematics
and

statistics. Students studying a science, technology or business should also be
studying mathematics.

Students

are expected to complete this course with at
least 16 credits with 8 being Merit so that entry to the Year 12 Mat 1 course is
guaranteed.
The Mat
h

1 is registered with NZQA and students
sufficient

Merit or
above credits can
gain course d
istinction
.
Three

Physics standards are offered
and success could lead to a Physics course at Year 12.


NZQA Registered Mathematics


Applied Mathematics
1

(24cr)

AS91026


Apply number reasoning in solving problems (4cr)

AS91027


Apply algebraic procedures in solving pro
blems (4cr) EXT CAT


AS
92029



Apply linear al
gebra in solving problems
(2cr)

AS91031



Apply
geometric

reasoning in solving problems (4cr)

EXT

AS91032


Apply right
-
angled triangles in solving measurement problems (3cr)

AS91036


Investigate
bivariate num
erical data PPDAC, statistics (3
cr)

AS90935


Carry out a practical physics investigation, linear (4cr)


In addition these achievement standards may be
assessed

if appropriate as
cont
ent from these standards
has

be
en

taught
in previous years and
may be
rev
ised and extended within this course as appropriate.

AS91028


Investigate relationships between tables, eqns

and graphs (4cr EXT
)

AS91030


Apply measurement in solving problems (4cr)

AS91033


Apply knowledge of geo reps in solving problems (3cr)

AS91034



Apply transformational geo in solving problems (2cr)

AS91035


Investigate a g
iven multivariate data PPDAC (4
cr)

(4cr literacy)

AS91037


Demonstrate understanding of chance and data (4cr) EXT

AS 91038


Investigate a situation involving elements of cha
nce (3cr)

(3cr literacy)

AS90940


Demonstrate understanding of aspects of mechanics. (4cr EXT)

AS90938


Demonstrate understanding of aspects of elec and mag (4cr EXT)

AS90936


Demonstrate understanding of the physics of an application (2cr)

(3cr
literacy)


Numeracy is expected to be gained through success in Achievement Standards.


Students are expected to sit
at least one external achievement standard

and the
Common Assessment Task

(CAT)

in Algebra. A selection of internal achievement
standards w
ill also be assessed. To
tal credits offered exceeds 20 and will be
dependent upon student cohort.

See the Course Guide for further details.


Course Completion requires 85% attendance to classes. Official school events
such as Athletics and Swimming Sports

are not absences but any other absence
where normal class
cannot

be suspended is an absence. Absence includ
es
truancy, sickness, tangi
, sporting events for example. 15% absence

from 36x4 is
21
hours of class time. It is the student

s responsibility to cat
ch up with notes
and problems after being absent.


Assessment

Daily and weekly informal assessment drives the lesson progression. Internal
assessments follow learning for that topic. The CAT is expected on 21
st

September. The external examina
tions begin in

early November.


Homework, Workbooks and Exercise books.

Students are expected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book of classroom notes and
exercises, completing a workbook of revisi
on of previous years, establishing a
habit of regular homework
, assign
ments

and becoming a problem solver.


Duration

This is a full yea
r course and is considered to be of 140hrs duration or 180
45minutes periods.


Extension and Challenge Opportunities

A
ustralian Mathematics Competition, National Bank Senior Competition


Course Fee

$20 is expected as payment for the homework write
-
in book.

$20 may be required for a Physics write in book for interested students.


Stationery Required

A mathematics quad boo
k, coloured pencils, pencil, biro, ruler and compass.

CASIO fx82AU
. A physics quad book may be required for interested students.


Future Path

Year 12 Mathematics •
Mat

1 with 8 Merit credits from this course.

Year 12 Physics • Physics 1



NCEA L1 Mathematics
2

Overview

This course is designed for all students who have not found learning
mathematics an easy task but do require mathematics

and statistics

in their
choice of career. The mastering of reasoning with number, measurement and
geomet
ry is emphasized with other strands of algebra, statistics and probability
introduced and developed at an appropriate rate.

Students are expected to gain
numeracy for NCEA Level 1 award and at least 16 credits over a two year period.


NZQA Registered
Mathematics

• Mat 2 (24
cr)

AS92029


Apply linear algebra in solving problems (2cr)

Unit Standard 5223(1cr)

AS91030


Apply me
asurement in solving problems (4
cr)

Unit Standard 26567(2cr)

AS91032


Apply right
-
angled triangles in solving measurement problem
s (3cr)

Unit Standard 5236(1cr)

AS91033


Apply transformation geometry in solving problems (3cr)

AS91034


Apply transformational geometry in solving problems (2cr)

AS91036


Investigate bivariate numerical data using PPDAC (3cr)

(3cr literacy)

AS91038


Investigate a situation involving elements of chance (3cr)

(3cr literacy)


In addition these achievement standards may be assessed if appropriate as
content from these standards has been taught in previous years and may be
revised and extended within this
course as appropriate.

AS91026


Apply number reasoning in solving problems (4cr)

AS91027


Apply algebraic procedures in solving problems (4cr) EXT CAT

AS91031


Apply geometric reasoning in solving problems (4cr) EXT

AS90935


Carry out a practical
physics investigation, linear (4cr)


Numeracy is expected to be gained through success in Achievement Standards
over a two year period
however students not gaining numeracy sufficiency
may

be directed to

focus on gaining the Numeracy Unit Standards

with in
put from
other subject areas.

(10cr).


Assessment

Daily and weekly informal assessment drives the lesson progression.


Course Completion requires 85% attendance to classes. Official school events
such as Athletics and Swimming Sports are not absences but a
ny other absence
where normal class
cannot

be suspended is an absence. Absence includes
truancy, sickness, tangi, MPA, sporting events for example. 15% absence
amounts to a generous 27periods or 21 hours of class time. It is the
student’s

responsibility to

catch up with notes and problems after being absent.


Homework, Workbooks and Exercise books.

Students are expected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book of classroom notes and
exerci
ses, completing a workbook of revision of previous years, establishing a
habit of regular homework and becoming a curious problem solver.


Duration

This is a full year course and is considered to be of 140hrs duration

or 180
45minutes periods. Stud
ents m
ay repeat this course to gain the required credits
in the

follow
ing

year.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASIO fx82AU


Future Path

Year 11 Mathematics •
App
Mat 1 with
any
12

credits from this course.

Year 12 Mathematics •
Mat

1 or 2 with

16 credits
with

8
being
Merit credits from
this course.



NCEA L1 Numeracy
Course

Overview

This course is designed for student
s who
need to gain numeracy and are
identified as having learning difficulties. S
tudents wi
ll have been identified at

CL2 or 3

and other mathematics courses at this level are inappropriate to
undertake. Entry to this course is only with the permission of the HOD

Mathematics.



A variation of

this course is offered in 2012 to support low achieving students
needing
the
numeracy requirement for NCEA L1.


Topics

The following Unit Standards will be available:
-

26623 Use number to solve problems (4cr)

26627 Use measu
rement to solve problems (3cr)

26626 Interpret statistical information for a purpose (3cr)

In addition there
may

be applied mathematics investigations and activities
including

the NZAMT MAP programme.


Assessment

The three unit standards above are internal
ly assessed and have no examination
content.
The Unit Standards 5223(1cr), 5236(1cr) and 26567(2cr)
may be
assessed depending upon need and demand. The MAP programme is internally
assessed

and organized by NZA
MT (www.nzamt.org.nz)
.


Homework, Workbooks and

Exercise books.

Students are expected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book of classroom notes and
exercises, completing a workbook of revision of previous years, establishing a
habit

of regular homework and becoming a curious problem solver.


Duration

This is a one semester course. Failure to complete numeracy allows access to the
second semester to repeat the opportunity.

There is no course completion
requirement relating to absence
.


Course Fee

$10 is expected as payment for the MAP Course and Certificate.

CASIO fx82AU


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

Future Path

Year 11 Mathematics • Course 2 after NCEA numeracy
requirement is gained.
Entry to this course is only with the HODS Mathematics permission.


NCEA L1
Practical Physics

Overview
, not offered 20112.

This course is a one

year

course designed to support students who prefer to
learn mathematics and physical sci
ence through practical study and
experimentation. Expected outcomes for the course include gaining some
physics credits at NCEA Level 1 in experimentation, mechanics and electricity.


Topics

The following Achievement Stands will be available:
-

AS
90935
Car
ry out a practical

physics investigation

(4cr)

INT

AS
90936 Project (2cr) INT

(2cr literacy)

AS
90937 Electricity and magnetism (4cr) EXT

AS
90939 Heat (4cr) EXT

AS91035 Investigate bivariate numeraical data using

PPDAC (3cr)


Numeracy
(10cr

needed
)
can

be gained through success in
the achievement
standards assessed in this course.


Homework, Workbooks and Exercise books.

Students are expected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book o
f classroom notes and
exercises, completing a workbook of revision of previous years, establishing a
habit of regular homework and becoming a curious problem solver.


Duration

This is a full year course and is considered to be of 140hrs duration or 180
45
minutes periods. Students may repeat this course to gain the required credits
in the following year.


Course Completion requires 85% attendance to classes. Official school events
such as Athletics and Swimming Sports are not absences but any other absence

where normal class can not be suspended is an absence. Absence includes
truancy, sickness, tangi, MPA, sporting events for example. 15% absence
amounts to a generous 27periods or 21 hours of class time. It is the students
responsibility to catch up with n
otes and problems after being absent.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASIO fx82AU

Future Path

NCEA L2 Physics


NCEA
L2 Mathematics • Mat

1

Overview

This course is designed for all students who have a career plan that includes
further study at a technical institute or university

to undertake a course in
engineering, science, or technology
. Mathematical thinking becomes q
uite
demanding at this level
, includes intense algebra and calculus development

and
entry is approved only with permission of the HOD Mathematics.

As a guide a
minimum of 8 Merit credits in the Year 11 MP1 course is required for entry.


NZQA Regist
ered L2

Mathematics • Mat 1 (23
cr)

AS
91256



Apply coordinate geometry methods in solving problems
(2
cr)

AS
91257



Apply graphical models in solving problems
(4cr)


AS
91258


Apply sequences and series in solving problems
(2cr)

AS
91259


Apply trigonometric relationships in solving problems
(3
cr)

AS
91261


Apply algebr
aic methods in solving
problems
(5
cr

EXT
)

AS
91262


Apply calculus methods in solving problems
(5cr EXT)

AS
91268


Investigate a situation using a simulation
(2
cr)

(2cr l
it L1.)

Students are expected to sit
both

external achievement standards.


Assessment

Daily and weekly informal assessment drives the lesson progression. Internal
assessments follow learning for that topic. The external examinations begin in
early Novembe
r.
Assignments are a required aspect of course completion.


Duration

This is a full year course and is considered to be of 140hrs duration or 180
45minutes periods. Students may repeat this course to gain the required credits
in the following year.


Course Completion requires 85% attendance to classes. Official school events
such as Athletics and Swimming Sports are not absences but any other absence
where normal class can not be suspended is an absence. Absence includes
truancy, sickness, tangi, MPA,

sporting events for example. 15% absence
amounts to a generous 27periods or 21 hours of class time. It is the students
responsibility to catch up with notes and problems after being absent.


Course Fee

$20 is expected as payment for the homework write
-
in
book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASIO fx82AU

Future Path

Year 13 Mathematics • Calculus with 8 Merit credits from this course.

Year 13 Mathematics • Statistics with 8 Merit credits fr
om this course.

NCEA L2
Statistics • Stat 1

Overview

This course is designed for all students who
intend to undertake study at tertiary
or university level with mathematics as a support subject and statistics as a
requirement for entry.

This course does
not include the formal developm
ent of
algebra or calculus and is
suitable for sc
ience, social science and studen
ts of
mathematics
.

This course

is
about

statistics and probability.


NZQA L2
Statistics • Stat 1

(20
cr)

AS
91260


Use networks in solving problems
(2cr)

AS
91263


Design a questionnaire
(3
cr)

(lit
)

AS
91264


Use statistical methods to make an inference

(4
cr)

(
lit
)

AS
91265


Conduct an experiment to investigate a situation using statistical
methods
(3
cr)
(
lit
)

AS
91
266


Evaluate a statistically based report
(2
cr
)
(

(
lit)

AS
91267


Apply probability methods in solving problems
(4cr EXT
)

(
lit)

AS
91268


Investigate a situation using a simulation
(2cr)

(
lit)


Students are expected to sit
the external achievement
standard
.


Assessment

Daily and weekly informal assessment drives the lesson progression. Internal
assessments follow learning for that topic. The external examinations begin in
early November. Assignments are a required aspect of course completion.


Cour
se Completion requires 80
% attendance to classes. Official school events
such as Athletics and Swimming Sports are not absences but any other absence
where normal class can not be suspended is an absence. Absence includes
truancy, sickness, tangi, MPA, spo
rting events for example. 15% absence
amounts to a generous 27periods or 21 hours of class time.


Duration

This is a full year course and is considered to be of 140hrs duration or 180
45minutes periods. Students may repeat this course to gain the require
d credits
in the following year.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASIO fx82AU

Future Path

Year 13 Mathematics • Statis
tics with permission of HOD.

NCEA L2

Physics

Overview

• not available 2012

This course is a one semester course designed to support students who prefer to
learn mathematics and physical science through practical study and
experimentation. Expected outcome
s for the course include gaining some
physics credit
s at NCEA Level 2

in experimentation, mechanics and
waves
including light
. This course
does not aim to cover all aspects of the physics at this
level but a sufficiency to allow sensible choice at Year 13
for a successful student.


Topics

The following Achievement Stands will be available:
-

AS

2.1

Practical Investigation (4cr) INT

AS2.2

Practical Application (3cr) INT

And c
hoice of either

of the following

(due to time restriction)

AS2.6

Practical
electricity, electronics and magnetism (not assessed)

AS 2.4 Physics of waves (4cr) EXT


Numeracy

contributing to

NCEA

L1

(10cr)can be gained through success in the
achievement standards assessed in this course.


Homework, Workbooks and Exercise books.

St
udents are expected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book of classroom notes and
exercises, completing a workbook of revision of previous years, establishing a
habit of regular homewor
k and becoming a curious problem solver.


Duration

This is a one semester course.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASI
O fx82AU



Future Path

NCEA L2 Physics

(complete course by VC)

NCEA L3 Physics

Engineering, S
cience and Technology, medicine, business.





NCEA L3 Mathematics • Calculus

Overview

• o v l bl 2012

This course is designed for students who enjoy mathematics or plan to pursue an
engineering or related course. Students undertaking this course are expected to
be self
-
motivated and keen to achieve.


Topics

Calculus, trigonometry, complex algebra and adva
nced geometry.


Students are expected to sit all external achievement standards. All internal
achievement standards will also be assessed. Total possible credits 20+.


Assessment

Daily and weekly informal assessment drives the lesson progression. Internal
assessments follow learning for that topic. The external examinations begin in
early November. See Course Guide for further details.


Duration

This is a full year course or two semester course.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.

CASIO 9750G
-
Plus


Future Path

Tertiary institution for engineering, physics, mathematics, business. See careers
websites for specific information.





NCEA L3 Mathematics • Statistics

Overview

• not available 2012

This course is designed for students who enjoy mathematics or plan to pursue a
career in science or social science. Students undertaking this course are expected
to be self
-
motivated and
keen to achieve. Students undertaking the L3 Calculus
course would be likely to take this course as well.


Topics

Statistical methods involved with time series data, bivariate data, modeling,
experimental design, probability distributions and linear system
s.


Students are expected to sit all external achievement standards. All internal
achievement standards will also be assessed. Total possible credits 20+.


Assessment

Daily and weekly informal assessment drives the lesson progression. Internal
assessments

follow learning for that topic. The external examinations begin in
early November. See Course Guide for further details.


Duration

This is a full year course or two semester course.


Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.


Future Path

University for engineering, physics, mathematics, business, science, social
science, statistics. See careers websites for specific information.




NCEA L3

Physics • VC

Overview

• not available 2012

This course is a full year VC course covering and assessing all aspects of physics
at this level. Experimentation and learning support is supplemented within the
school environment.


Topics

The following

Achievement Stands will be available:
-

AS91026


Apply number reasoning in solving problems (4cr)


Numeracy (10cr)can be gained through success in the achievement standards
assessed in this course.


Homework, Workbooks and Exercise books.

Students are ex
pected to develop work habits that will be beneficial in following
years. These include keeping a tidy exercise book of classroom notes and
exercises, completing a workbook of revision of previous years, establishing a
habit of regular homework and becomin
g a curious problem solver.


Duration

This is a one semester course.



Course Fee

$20 is expected as payment for the homework write
-
in book.


Stationery Required

A mathematics quad book, coloured pencils, pencil, biro, ruler and compass.


Future Path

NC
EA L2 Physics



INDIVIDUAL LEARNING PLAN (
ILP
)


All

students in the senior school with co
-
develop an ILP to cater for their own
needs and aspirations. The courses at each level are sufficiently flexible to cater
for most variations.


See ILP resource in M
ath Folder.


The ILP will include:
-

-

career studies

-

pathway planning with Year 10, 11, 12, 13 connections

-

achievement record to date in mathematics and literacy

-

a monitoring reflective journal by the student and the teacher.

-

short

term and longer term goals.



Career
Pathway Investigation
General

This guide is for use by students at Year
7 to
13. It is expected that this unit will
be completed at least three times per year or once per term. The information is
presented once per yea
r to the whole class by each student as part of the
development of public speaking and presentation. These studies are collated in
the ILP folder.


Se Career Unit resource in Math Folder.



Departmental Operations

The
mathematics department consists of
two teachers operating in Room 22 and
21. There is no HOD office as such

and all NCEA student information are stored
in the white cabinet in Room 22.


The resource room contains a wide range of texts, teacher reference and
mathematics equipment. The calcu
lator of choice is the CASIO fx
-
82AU plus at all
levels. Students in Year 12 and 13 may also use the set of Casio 9895 graphics
calculators for more indepth work.
Computers are available with graphing
software and fathom for Statistical work.


Every room
has a data show and these are used to enhance teaching events. Sites
include NZAMT, NZQA, NLVM and Myphysicslab.com.


A more complete list of websites is planned. Likewise a complete stocktake of the
mathematics department as time permits.


Responsibiliti
es

HOD

-

Everything

-

NCEA records

-

Academic Courses.


Ass HOD/DEAN

-

Every thing else

-

Sanity of the HOD

-

MAP courses



Appendix 1 • Year 10 Analysis 2011


Data for the Year 10 students 2010 was provided by the school. This data was
incomplete and not at all
summarised. The data did show that of the Year 10
cohort 2010, a few, 5% were still Counters (CL1), 20% or so were Early Adders
(CL2), the majority 65% Advanced Adders (CL3) and a small 10% Multiplicative
(CL4) or better, Proportional thinkers.



Year 10
Cohort

Nov
-
10

Nov
-
11

Nat Data

Stage 4

5%

0%

2%

Stage 5

20%

2%

12%

Stage 6

65%

52%

25%


Stage 7

10%

26%

40%

Stage 8

0%

21%

21%



The success is the increase in Stage 7/8 or 37%, or 37/10 =370% increase. The
average stage gain was 0.8 (s= 0.6) with some students making zero gain and 3
students making a gain of 2 stages during the year. AssTTLe research states a
0.66 gain is the norm
al for an average student who attends school. [see AssTTLe
research data Fiona Ells]. The cohort made good progress overall but 8 students
made no measureable gain. It must be stated that each numeracy stage is wide
and students can move within a stage, ma
ke progress and not be noticed.


Further analysis comparing stage change with attendance rate shows students
present 80% of the year often gained 2 stages but the correlation showing being
present is better for progress is quite varied and complicated by
other factors.
Those making no gain were also absent over half of the year as might be
expected. (xxxmight be an idea to create this as an appendix and repeat for Year
10,11,12)




0%
10%
20%
30%
40%
50%
60%
70%
Nov-10
Nov-11
Nat Data
Stage 4
Stage 5
Stage 6
Stage 7
Stage 8
The Year 10 cohort

started a about a year behind expectation and about two

years behind national expectation and all but 10% failed to achieve the National
Standard for Year 8 students. [This statement needs to be examined yearly for
each cohort.] In Nov 2011 this cohort had changed and become more
multiplicative and ready for N
CEA L1. The national data also over estimates the
top end performance is now of a similar shape to these students showing that
they have largely caught up. The Stage 6 adders/early multipliers are still over
represented but typical of most secondary cohort
s in other schools.


The
prediction

for 2012 NCEA L1 Mathematics performance is the 20% (8)
Stage 8 students become Merit and Excellence passes and will easily cope with
Year 12 mathematics the following year. The 10 Stage 7 students will gain NCEA
L1 Mat
hematics and then take 2 years to gain the NCEA L2 Mathematics. The 20
Stage 6 students will take 2 years to gain sufficient NCEA L1 mathematics credits
but will gain numeracy through achievement standards. The few Stage 5
students will need to use the Wo
rk and Study Skills Numeracy Unit Standards to
gain the numeracy component of NCEA L1 and will otherwise find mathematics a
very difficult subject in which to gain credits. A special accelerate programme for
these students is advised if success is to be me
asured by NCEA.




App
endix 2

• Year 11 Analysis 2011


The Year 11 cohort was a diverse group of learners. There was a significantly
large group who had low numeracy and were operating at CL 4 or below. The
data shows that while the NCEA numeracy requirem
ent was near 100% the
reliance upon Unit Standards below number 5232 (below CL5 or Group B) was
heavy. This data excludes External results unavailable at the time of writing.


Year 11 Cohort

2011*

2010*

2009*

Total

580

405

386

US

515

389

343

CL5

437

329

316

CL6

78

60

27

AS

65

16

43

ME

19

4

5




There was a significant increase in success using the new Achievement
Standards and a huge improvement (450%) in the awarding of Merit and
Excellence grades. Of the cohort of 39 students 6 gained the pre
-
requisite for
entry to Year 12 mathematics. The exte
rnal results not available at the time of
writing may change this statistic. [The requirement is 8 Merit or better credits,
CL 6 or better or with permission of the HOD].


The problem of what to do with a large group (36) returning Year 11 students
who ne
ed to establish a mathematics platform at Year 11 and the incoming Year
10 students, another 39, implies 3 classes will have to be available for this large
group. The general low achievement caused by lack of readiness for learning and
absence creates this

bottleneck and remains the most significant problem facing
the school. Management are aware of this issue.


One possibility, like Year 12, see below, is to create a Year 11 Statistics focus
course or low algebra option. There are 12 credits and 6 in geome
try that could
form an alternative Year 11 course for returning students. The pathway to Year
12 is then also statistics and that course is available in 2012 as well for returning
Year 12 students, see below.

0
100
200
300
400
500
600
700
Total
US
CL5
CL6
AS
ME
2011*
2010*
2009*
Appendix 3

• Year 12/13 Analysis 2011


The Year

12 students were a very diverse group of learners and included Year 13
students who were unprepared for CL 8 mathematics and statistics standards.
February analysis showed 2 credits at CL 6 and 31 credits at CL 5 for the
complete group indicating a very u
nprepared group and pending difficulties. The
group achieved 65 US Level 1 credits during the year and 19 M/E passes in Level
1 Achievement Standards. The external results were unavailable at the time of
writing and may affect the results. Many of the pass
es were at NCEA L1 however.


One student gained 5 L2 credits and sat the final examinations.


This group will be guided to a low algebra statistics course on return in 2012 if
possible.


The year 13 students were 2 very amazing, self managed students who
excelled
and will easily gain NCEA 3, probably with distinction. Both are intending to
enroll in undergrad degrees at Waikato University in 2012.






Appendix 4 • Numeracy Journe
y


The Numeracy Learning Journey

Refer to
www.nzmaths.co.nz

for all resources, supporting documents, reports
and research papers concerned with the NZ Numeracy Project which was
implemented throughout NZ schools 1998 to 2011. The project created a
language
for mathematics teachers of primary, intermediate and secondary to
communicate effectively about the mathematical thinking being done by
students. The research based project established that students proceed through
a simple 1 to 1 counting, adding, advanc
ed adding, multiplying and to
proportional thinking stages, all of which are heavily reliant on place value
understanding. These ideas are strongly represented in this scheme.


A Brief History of the NZ Numeracy Project

The beginnings stem

from noticing a
steady decline in computational skills in
students and young adults during the 1980’s and 1990’s. The SIMMS study and
later the TIMMS study confirmed the trend and alerted the Ministry of Education
to resource an intervention. The Count Me In Two project
and the UK Numeracy
Project both informed consequent planning in NZ and the NZ Numeracy Project
was created.


Pilot projects

followed in 1999, 2000 and 2001 in primary, intermediate and
secondary schools. The ENP (Early Numeracy Project) was then prioriti
zed, two
years later the ANP (Advanced Numeracy Project) was likewise released to build
on the ENP, then the INP (Intermediate Numeracy Project) was started in 2004
and the SNP (Secondary Numeracy Project) followed in 2006. All of these
projects have since

terminated as most primary and intermediate schools have
undergone the training and the 2011 was the final year for SNP schools. Another
reason for termination was the National Party instigating National Standards in
Numeracy and Literacy as an election p
romise. The funding for numeracy ceased
and the funding for National Standards was created. The same people were
involved in both projects. I was involved as a Mathematics Advisor implementing
INP in 2005 and SNP in subsequent years through out the Waikato
, BOP and
Gisborne regions until 2010. [Update Nov 2011, funding for SSS has now ceased
with contracts going to Cognition Auckland private provider for 2012 and 2013,
afterwhich it will be given to schools. The funding has been reduced from
previous levels

for 2012].


The project created a
huge resource of knowledge

about how people learn
mathematics. We learned that the thinking processes gain complexity and
progress from being unable to count, to counting, to the more efficient adding, to
the very efficie
nt multiplying and thence to complex reasoning of proportional
thinking. Problem solving was stressed at all times, explaining reasoning and
proof likewise.


The
data rich project

established an EXPECTATION (see Appendix) chart based
on data from schools t
hat had undertaken a long
-
term numeracy development.
The expectations are a little high but clearly show the transition of learning to
thin ing mathematically. Around the same time the development of the “new”
NZ Curriculum, implemented in 2010, began, ag
ain, largely by the same group of
people. The net result is that the Mathematics and Statistics Curriculum is
heavily embedded with numeracy principles, philosophy and learning.


The
National Standards

for Year 1 to 8 currently in vogue (see above) reflect

much of the above but also high expectation of mathematics achievement for all
students. Maori Achievement was identified as being slow and all projects
including the Te Kotahitanga Project all aim to improve these levels. [Note the
National Standards are

“aspirational” in that they are quite high. Note also that
dispite what the Year 8 standard says operating on rational numbers remains a
CL5 task, not CL4 (whole numbers) as stated in the standard.]


During my time as advisor I was privileged enough to ex
perience many
conferences, conversations, workshops, presentations, overseas speakers and
conferences and complete my own research to improve my understanding of
learning to think mathematically. I implemented nearly $3M dollars of funding
throughout Waika
to and BOP schools in over 60 schools. I ran countless
workshops and observed hundreds of teachers and students in action in their
classrooms. I had the opportunity to discuss learning at length with many very
clever teachers students of all abilities.


[W
hat remains to be done is a NZ Numeracy Project Report giving regional and
national views and summations of the project impact. This was singularly the
largest investment, over $100M, in mathematics education ever undertaken in
NZ. The questions of “What d
id we learn?” and “Was it worth it?” need to be
considered. Thinking mathematically is important. Perhaps I will write a book.]