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
Jim Hogan 2017 • Teacher
Introduction and Lesson #1 • RELATIONSHIPS - KNOWING the student
and discovering THEIR NEEDS.
Introduction and Why...
I have been wanting to write a book about the teaching and
learning of mathematics for some time now. How do I start? How
will it be organised? What do I say? What do I know that others do
not? How can I share what I know? Will anyone take any notice?
There are plenty of books about mathematics, about number and
geometry and so on. I learned using Durell Algebra and still have
a copy, PSSC physics, and likewise, still have a copy. As a
teacher I used Andy Begg's "Moving with Math" Series, Bill
Elwood's "It a Maths World" series and more recently the David
Barton Series "Alpha, Beta, Gamma". They are all great references
and give deep insights into mathematics through explanation,
diagram and graded exercises. The more recent series all had
problems that offered challenge to some students as extra
learning. Used appropriately a text book like a work sheet has its
I met Andy, Bill and David. Great people, deep thinkers and my
heartfelt gratitude for all their hard work, perseverance and
study that went into crafting the mathematics books that have
helped thousands of students. For me Andy is remembered by the
word "relationships". Bill by "Fibbonacci". David by "detail".
I do not need to repeat these masterpieces. I am more interested
in the interface between the teacher and the learner. I will use
those masterpieces and others but it is the tenuous human
interaction called relationships that allows learning to blossom.
Ako; the bi-relationship of respect and knowledge. This interface
needs to be nurtured.
In the following chapters I try and unpack aspects that I see as
important conduits and builders to help young people become
persevering, collaborating, critical, communicative, creative,
curious, respectful and appreciative using the Learning Area we
call Mathematics and Statistics.
Another interest is explaining why so many people say "I was never
any good at maths". Hence... "Mum says she was never any good at
Maths so I am not either!" Everyone can learn mathematics and
actually have fun and enjoy the experience. I want students to say
"Oh Cool! Maths again! I like maths" and after the lesson "Thank's
Sir! That was fun!"
I think Math-phobia is a mental disease of the modern world and
one, as math teachers, we must know more about to help prevent
infestation. It is a disease embedded in society, upheld by
teachers and mathematicians, scientists and politicians, parents
and students. I think it it is so severe it can manifest itself as
discalulia, another of these modern syndromes invented to help
explain lack of achievement in mathematics. The brain is a very
capable magician. How, from the thousands of variables involved in
learning mathematics, is it that a person is so sure that the one
variable called "being good at maths" was the exact factor that
caused the lack of achievement? It is the magician, the brain, at
I start by beginning. Now. Here.
I organise it on a computer in .html so it can be accessed
willy-nilly, forward and backward as need arises. This is how
learning happens so I write in the same way. I write so I can edit
and amend as I re-read and proof what I mean to say. I add and and
change things. I respond to comment. I persevere.
I hope these pages inspire you to explore or revisit an aspect of
teaching and learning in your own practice and that you become a
better practitioner as a result. I honour all the teachers who
gave me their patience and all my colleagues who inspired me learn
more and answered all my questions. I honour all my students who
taught me so much and now stop me in the street with "Hi Sir!" or
"Hogy!" and tell me about their journey. Thank you.
Lesson #1 • RELATIONSHIPS - KNOWING the student and
discovering THEIR NEEDS.
- to increase your understanding of the need
to establish a robust learning relationship with every
student in your care.
I have spent the last 16 years as an advisor of mathematics
and statistics visiting many schools, meeting hundreds of
educators, running many workshops, answering and sending thousands
of emails, driving more than 500,000km, organising conferences,
creating many new resources and discovering many others, enjoying
many hundreds of hours in the peaceful solitude of my own mind
finding truth in mathematics, proving things I needed to prove and
reading books I needed to read. It has been a very rewarding time,
very satisfying and I can only recommend the pathway. Ask any
search engine "Jim Hogan NZ" and you will find my history and
story as it happened.
- to interview two students to build
student-teacher relationship to inform student learning
Who am I?
I grew up on a farm in the Manawatu near a little place called
Maewa on the main trunk line. Our family donated 9 acres of native
bush now called Maewa Bush to the QE2 National Trust. Maewa means
"a quiet walk" and the bush is that. I learned many things on the
farm about life, surviving and food. I became resourceful,
curious, creative, critical and communicative. I learned to
collaborate and worked with diverse groups mixing with old,
wealthy, poor and young.
I enjoyed school at Lytton Street (1956-1964) and Feilding
Agriculural High School (FAHS) as it was known then (1965 - 1969),
gained one prize in Applied Maths and Chemistry in Sixth Form
(Y12) and was a Prefect in my final year. I had a many magnificent
teachers and paid for most of my studies at university and many
beers by becoming a #1 Chain Slaughterman at Borthwicks Freezing
Works and working there for about 8 seasons in the 1970's.
I grew up in the Cold War, Sputnik and Man on the Moon times.
Computers were becoming smaller and more available. Physics
teacher Jock Tennant, ex Sapper in RA, built a computer that could
add a couple of binary numbers and explained how it did so in one
physics lesson. Who could not become interested in mathematics at
that time! I later became a Ham Radio operator now ZL1AJQ and
built many gadgets, clocks, radios and power supplies. I once
invented a cloud counter!
I worked as a meteorologist for a few years after gaining a double
major in applied mathematics and physics and then spent 30 years
in a classroom teaching maths, science, physics and computing
(when computing was interesting). Like most teachers I had many
jobs to play out as a teacher including being a Dean, HOD, House
Leader and ran clubs for Tramping, Ham Radio, Fishing and
Pythagorus (mathematics). I learned to teach when I become a
teacher! I think I learned mathematics and physics then too. I
certainly was learning a great deal more than any of my students!
We learned together.
I now live in Taupo beside our Great Lake Taupo. It is a large
puddle with 62 cubic kilometers of water. This is enough for
every person on Earth to have a crystal clear glass of potable
water. I have traveled to Italy a few times, France, UK, USA,
Australia and several Pacific Islands. I am glad I traveled the
world when I did. New Zealand is a very nice place to be and I
enjoy every day right here.
I now have a small vineyard and winery tempting fate and
challenging nature to produce a fine Pinot Noir in Taupo on the
cool Central Plateau at 345m above sea level. There are today 1200
bottles of a very drinkable Burgundy style Pinot Noir in my
cellar, all quite dark and full of berry flavours. My
favorite tools include a fishing rod, a chainsaw, a hammer, a
spade, a computer, a radio and a vehicle. I play golf, walk the
dog and shoot possums that stray near the fruit trees. I learned
how to do cryptic crosswords in the NZ Herald over the last few
years and usually get them out within and hour or so. I love
learning new things. I dreamed of the WWW internet when I was a
kid. I loved Thunderbirds!
Ce moi! I learn by doing. I learn in many ways. I strive to be a
Hence Lesson #1 and a Task.
The first thing a teacher must do is to create a relationship with
every student by sharing themselves as a person. So must each
student for each other and for each teacher. As I have done above
so would a teacher intent on building a learning environment do so
for each class situation. People like to be connected and when
this happens the platform for sharing and learning takes place.
The Māori word for this is ako, a mutual understanding of respect
• How do you build relationships in the classroom with your
• What deliberate actions or activities do you engage in to
promote robust learning relationships?
• How do you have students share who they are?
and an Action...
• Interview two students and collect all the knowledge you have
about them. The wheel in the picture gives a few sample questions.
There are some forms and examples around but start with school
records, genealogical data, previous math tests, ans ask them
about sports, family, ambitions, reading, learning, friends and
let them talk. This is not prying, it is getting to know them.
• A SELF CHECK - List all the students in one class and write ten
things about each one... all from memory.
• The Benefits of Knowing Students as Learners
Developing an in-depth understanding of each learner enables
1. Create a psychologically safe environment for
2. Determine each student's readiness for
3. Identify multiple access points to the
curriculum to increase engagement and success.
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 moment.
SO YOU CAN READ IT!
All pictures on this site can be copied and enlarged.