Cling to the main vine, not the loose one.

Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua

Thoughts on Teaching and Learning of Mathematics

Lesson #2 •This has become a well read page.Revised 5/1/2020

What is Your Main Vine?

- to be clear about the purpose of learning mathematics

- 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 asan 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 decidedthis whakataukiwas 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 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 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 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 beyond secondary.

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, Cheers.

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 "Engagement".

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 to read.

Some readings

1. Andy Begg at NZAMT 2015 WK 3.2

2. Andy Begg at NZAMT 2015 WK 7.3

3. Know the Learner Questions

4. Interviewing Students - Sample form

Teacher TASK• Your Main Vine.

Write about and Discuss. Draw!

• 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 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 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 isfun, 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 almostalwayson time to classes modelling another key competency.

JH

Now write yours!