the main vine, not the loose one.
Kei hopu tōu ringa kei te aka tāepa, engari
kia mau te aka matua
Thoughts on Teaching and Learning of Mathematics
What is Your Main Vine?
- to be clear about the purpose of learning
- to be aware that what is taught is not necessarily
what is learned.
"What have you(I) noticed?"
This is a beautiful question. One of the best.
Next to "How do I know?" [or "How do you know?] " this question
stands out loud and clear as an indicator of mindfulness,
being engaged, aware, alive!
My Understanding of the Main Vine from the NZC Whakatauki
(inside last cover page).
Kei hopu tōu ringa kei te
aka tāepa, engari kia mau te aka matua
A whakatauki is a metaphor. Meaning is made by each person
who reads it. When the NZC was crafted someone or group decided
this whakatauki was most appropriate to mathematics. Choosing the
main vine when climbing a tree is quite important for longevity.
Likewise in mathematics understanding the main threads or vines is
important to longevity. Without a wide "big picture" view of
mathematics a teacher is left "in a small boat in a large sea".
See - https://en.wikipedia.org/wiki/Mathematical_anxiety
I notice in many schools mathematics teachers have no obvious
"main vine". When queried they demonstrate they have no main vine.
Often the teachers have studied mathematics so perhaps their
teachers had no main vine either. My job is to help teachers
discover their main vine or help them create one.
I have been pondering the whakatauki (saying) at the head of the
Mathematics and Statistics page since 2007 when the current New
Zealand Curriculum was first published. The NZC has a "front end"
and a "back end" and talks about vision, principles, values and
key competencies in the front and has a structured guide for the
eight learning areas in the back. Most mathematics teachers are
concerned only with content and the "back end". This is an
arrogant and short sighted stance and must change to be more
inclusive. Mathematics is important but not that important. It is
through mathematics we help make great citizens.
"Cling to the main vine,
not the loose one". NZC. Kei hopu tōu ringa kei te aka
tāepa, engari kia mau te aka matua.
I have pondered this again and again. What does it mean? I
wondered why such an obscure saying would head the Mathematics and
In 2016, Dec I finally made meaning of it for myself. This
happened, curiously enough, driving to the very last meeting with
my colleagues in the contract I was working during 2012 to
2016. I had noticed that many teachers trying to teach
mathematics have a "cherry picked degree" and many maths
departments have a "cherry picked course selection" and many
students in schools have a collection of "cherry picked credits"
and this leads to a "cherry picked career" in this world we all
wake to every morning.
The term "cherry picking" refers to the way one will pick the
easiest and closest fruit. Not necessarily the sweetest, or the
best, or largest, or hardest. In a similar way I notice schools,
departments, teachers, students, teaching and learning informed by
"cherry picking". Nearest (easiest) is not always the best option.
The main vine is not present for many. There may be vines but
there is no main vine. The result is confusion. Students become
disinterested in mathematics and just see it as an untidy,
uncontrollable, impossible to remember, mess of ideas and methods.
Teachers do not have a "big picture" understanding of concepts and
connections. Schools just want credits and ignore the quality of
qualification. Teachers move away from the firm direction
students often need and the time and hard work needed to learn new
ideas. Departments just do their own thing without connecting to
other learning areas. The world becomes a cherry tree and no one
sees the orchard. No one notices another farm next door or city
down the road.
I constructed my degree with a main vine called applied
mathematics. It was not the easiest pathway and I had to work at
it. Applied mathematics includes statistics, physics and pure
mathematics, computer and electronics ideas and skills,
engineering basics and technology skills. I was intrigued by fluid
dynamics and still explore that complex world every so often. I
distinctly remember as a 15 year old (1966) when choosing the
maths, applied maths and physics senior course that it was going
to be a hard slog but the journey would be worthy.
I have a strong work ethic and aim to complete jobs. I experiment
to prove things and take "applied" to the limit by insisting on
doing a lot of building, maintenance, and problem solving
myself. I am quite a creative thinker, an inventor and enjoy
solving problems. My Mother saw this trait as improvising. I have
to know stuff and seldom believe anything I hear unless it fits my
perceptions. There is a lot of garbage, nonsense and absolute poo
out there and it is only getting more common. Hence C = critical
reflection is vital.
I once thought the Age of Aquarius would be an enlightened world
and looked forward to a future of science, technology, space
exploration, peace and one world. Now I often say that "The world
gets stupider every day!" From Wikipedia - "Traditionally,
Aquarius is associated with electricity, computers, flight,
democracy, freedom, humanitarianism, idealism, modernization,
astrology, nervous disorders, rebellion, nonconformity,
philanthropy, veracity, perseverance, humanity, and
Unpacking "The Main Vine"
A "Main Vine" means having an agreed common purpose about what is
needed and how to get there. It means the easiest path may not be
the one we choose. It means having a "main vine" and creating
"main vines". It means keeping your head when all about you are
loosing theirs. Desiderata
come to mind. It means having a clear idea of "Graduation Profile"
and what a student will be when they move to the next stage.
Learning is about key competencies such as participating,
collaborating, contributing, communicating, thinking and managing
self (NZC). CCCC
is a similar concept. Creativity, Collaboration, Critical Thinking
and Communication. There are other "C's" that could be added such
as Connectivity, Curiosity, Cultural Awareness, Citizenship all in
no particular order. There are many C's...Coffee, Christmas,
Mathematics is broadly about relationships and connections. The
NZC describes Number and Algebra, Geometry and Measurement,
Probability and Statistics all wrapped around Problem Solving and
Applications. The way number connects to measurement and geometry,
algebra describes patterns and generalizations in all strands, and
probability explores randomness and chance for making sense of
data and fuzzy problems.
Having a "Main Vine" as a teacher is about deep knowledge of
Learning and Mathematics. You know your main vine is flimsy
when you can not describe what you are teaching or apply it to new
situations. You know your main vine is a dodgy when students are
not engaged or over time become disinterested in your classes.
Having a main vine means consistent messages, expectations,
understandings and a respected knowledge of the subject. It also
means you ask and find out new things as an Inquirier.
When this base is established students have a chance of developing
a main vine as well. Often, in talking to students and adults they
will relate how they had one good teacher! How many good teachers
do you need? All teachers are probably good in some aspects so in
my view the rather haphazard way our schools are organised is
quite useful for most students to get a range of views and
experiences. Some teachers do stand out and it is worth pondering
why this is so.
Usually when a student is playing hooky or being difficult there
is a competency that is in need. This poor behaviour is a plea for
help. It is the brain being a magician again and constructing
knowledge and truth where there is none. Behaviour should be
viewed as a positive data not negative. Each student has a story.
So now some critical reflection .
Hence Lesson #2
• Having a comprehensive knowledge of mathematics and statistics
is vital for a mathematics teacher. Be a problem solver and an
ask-er of questions.
• Knowing how mathematics connects and being prepared to learn
when new connections are needed. Investigating!
• Knowing what students need to learn in terms of competencies
is vital. Behaviour tells all.
Begg at NZAMT 2015 WK 3.2
Begg at NZAMT 2015 WK 7.3
the Learner Questions
Students - Sample form
Write about and Discuss. Draw!
• Your Main Vine.
• Your understanding of key competencies? How do you develop these
for each and all?
• The common messages across your lessons? Your expectations!
Just for Comparison, My Main Vine
In mathematics I tried to build an increasingly complex world of
number and algebra, geometry and measurement, probability and
statistics and develop perseverance in problem solving and a
curiosity about everything. In physics I tried to build a world
where reason and experience met and agreed, where theory and
experiment confirmed each other, where mathematics become sensible
and applied. My grand plan for each student was to have them
become a curious learner and problem solver, a seeker of truth and
upholder of good humour and have fun. Always it was about
developing an increasingly complex thinker.
We never know what students are really learning. I like to think
they are learning mathematics but they may well be learning how to
persevere, or question, or be collaborative, or how not to teach!
The CCCC's are very very important. I think there are 9C's. It is
the way students talk to each other and myself, the way they
organise themselves, the responsibility they develop and so on and
on that is the real learning. A student who is very
uncommunicative is one who needs to be nurtured into talking.
Students, usually boys, need to write and we need to normalise
writing for these lads. I expect complete written sentences that
explain and reason. Keep the bar high.
A thread of the main vine for me is fun, enjoyment and
colour. My classrooms always had wall displays in continual
change. Student work of all styles, A3 summary caterpillar trails
of daily lessons. I needed a 30 sided room. My door was always
open. I was almost always on time to classes modelling another key
This is to help look around
my pages. I have tried to make it consistent in all
chapters. The Planned chapters are only ideas at the