the main vine, not the loose one.
hopu tōu ringa ki te aka tāepa, engari kia mau ki te
Thoughts on Teaching and Learning of Mathematics
Lesson #2 • Revised
This has become a well
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 you know?" [or "How do I 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 ki te
aka tāepa, engari kia mau ki te aka matua
A whakatauki is a metaphor. The meaning of a metaphor is
different for each person. This is one reason I have trouble with
such things, and books and movies. I have been trained in
mathematics where we try very hard to convey exact meaning and
understanding so when I say "Think of a point A" every one knows
exactly what I am thinking. The Māori language is a metaphor.
When the NZC was crafted someone or some-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
by being quite mystified about the question. My job includes
helping teachers discover their main vine.
I have been pondering this whakatauki for 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".
The"front end" talks about vision, principles, values and key
competencies and has a structured guide for the eight learning
areas in the "back end". I notice most mathematics teachers are
concerned only with content and the "back end". This is an
arrogant and short sighted stance and must change. Mathematics is
important but not that important. It is through mathematics we
help make great citizens. It is the front end of the curriculum
that is actually most important and as Math teachers we develop
all this in the context of mathematics and statistics.
"Cling to the main vine,
not the loose one". NZC. "Kei hopu tōu ringa ki te aka
tāepa, engari kia mau ki te aka matua".
I have pondered this again and again. What does it mean? I
wondered why such a seemingly obscure saying would lead or
represent the Mathematics and Statistics pages.
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 mathematics
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". We must be brave and
not necessarily choose the easiest path. We need a main vine.
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.
Struggle and challenge is good for you.
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, disconnected, 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 the 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
mathematics, applied mathematics and physics senior pathway that
it was not the easiest and was going to be a hard slog but the
journey would be worth it.
I have a strong work ethic and aim to complete jobs. Everyday I
set myself a task that must happen. 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 improvisation. 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
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 irresolution."
Unpacking "The Main Vine"
A "Main Vine" means having a clear 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
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 beyond
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 about relationships and their 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 a bit dodgy
when students are not engaged and over time become disinterested
in your classes and in mathematics. 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 Inquirer.
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? (ANS = At least one!") All teachers are probably good
in some aspects at least so in my view the rather haphazard way
our schools are organised is quite useful for students to
get a range of views and experiences. Some teachers do stand out
however and it is worth observing and 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. I talk more about this in a later chapter called
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. Be a struggler!.
• Knowing how mathematics connects and being prepared to learn
when new connections are needed. Investigating and inquiring!
• Knowing what students need to learn in terms of competencies
is vital. Behaviour tells all. It is an open book to learn how
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 with my students 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. I welcome all questions.
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
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 at least
9C's. It is the way students talk to each other and you, 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. Have high expectations.
Anyone can learn anything!
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 with 30 connected rooms. My door
was always open. I was almost always on time to classes
modelling another key competency.
Now write yours!