TEACHING MATHEMATICS FROM A CHRISTIAN PERSPECTIVE - Enabling students to connect, succeed and thrive

TEACHING MATHEMATICS FROM A
     CHRISTIAN PERSPECTIVE
          Enabling students to connect,
              succeed and thrive

Peter Muddle, Deputy Principal Teaching and Learning,
        St Philip’s Christian College Gosford

QUESTIONS TO ADDRESS
• In a distinctly Christian educative environment, can the teaching of
  Mathematics be harnessed to strengthen a school approach to a
  student’s cognitive, physical, social, emotional and spiritual
  wellbeing?
• Is Mathematics a vehicle to provide opportunity for students to
  actively practise and live out the values being fostered by a school?
• Can it be a place where values education and character formation
  are cultivated while students are given opportunity to develop
  competence and autonomy?
• Is it possible to foster positive relationships and connectedness
  through engagement with learning and educational endeavour in the
  Mathematics classroom?

TONIGHT
•My story
•Why is it important?
•How can you do it? Some examples and
 advice
•How can you not do it? Will you leave
 feeling more uncomfortable about the way
 you have been teaching mathematics?

MY STORY

3 TYPES OF CURRICULUM

•Explicit Curriculum
•Implicit Curriculum
•Null Curriculum

EXPLICIT CURRICULUM
“Explicit curriculum refers to the plan for learning set by a
teacher or school board. A class's explicit curriculum is
what that class is designed to teach. This includes the
topics covered by the class and any documents included
in the lesson plan, such as textbooks, films and web
sources. Explicit curriculum also refers to a teacher's
plan for her class, regardless of whether this plan is seen
by her students.”
(J Zamboni - https://www.theclassroom.com/5-types-curricula-classroom-8013624.html)

The content of our classroom lessons.

IMPLICIT CURRICULUM
“Implicit, or hidden, curriculum refers to lessons that students take
from teachers' attitudes and the school environment. This learning can
be either conscious or unconscious. For instance, the location of a
teacher's desk at the front of a classroom underscores his authority
and positions him as the center of the class's attention. A school's
rigid class schedule may make students perceive learning as an
inflexible and authoritative process. Implicit curriculum can also refer
to how educational institutions reflect larger social norms. A teacher
who models a society's dismissive attitude toward a subject, for
example, will communicate that attitude to his students.”
(J Zamboni - https://www.theclassroom.com/5-types-curricula-classroom-8013624.html)

The environment of our classrooms that tell a story.

NULL CURRICULUM
“Null curriculum is closely related to explicit and implicit
curricula. It refers specifically to any subjects that are not
covered within the context of a class. This may refer to subjects
that are passed over due to a teacher's bias or larger social
prejudices. It may also refer to subjects that are discouraged or
explicitly banned from being taught by school authorities. A
teacher should consider her null curriculum carefully. By not
teaching a subject area, she communicates its irrelevance.”
(J Zamboni - https://www.theclassroom.com/5-types-curricula-classroom-8013624.html)

The things you just can’t not teach!

WHY IS IT IMPORTANT
•What does your faith in God impact upon?
•As Maths teachers are lovers of numbers,
 what % of your life do you think God is
 interested in?
•How different is your teaching in a school with
 freedom to explore these ideas, than if you
 were teaching in the local state school system
 (i.e. where these freedoms are denied)?

COLOSSIANS 1
15 The Son is the image of the invisible God, the firstborn over all
creation. 16 For in him all things were created: things in heaven and
on earth, visible and invisible, whether thrones or powers or rulers
or authorities; all things have been created through him and for
him. 17 He is before all things, and in him all things hold
together. 18 And he is the head of the body, the church; he is the
beginning and the firstborn from among the dead, so that in
everything he might have the supremacy. 19 For God was
pleased to have all his fullness dwell in him, 20 and through him to
reconcile to himself all things, whether things on earth or things in
heaven, by making peace through his blood, shed on the cross.

COLOSSIANS 1
15 The Son is the image of the invisible God, the firstborn over all
creation. 16 For in him all things were created: things in heaven
and on earth, visible and invisible, whether thrones or powers or
rulers or authorities; all things have been created through him
and for him. 17 He is before all things, and in him all things hold
together. 18 And he is the head of the body, the church; he is the
beginning and the firstborn from among the dead, so that in
everything he might have the supremacy. 19 For God was
pleased to have all his fullness dwell in him, 20 and through him to
reconcile to himself all things, whether things on earth or things in
heaven, by making peace through his blood, shed on the cross.

ABRAHAM KUYPER (1837–1920)
     •“In the total expanse of human
      life there is not a single square
      inch of which the Christ, who
      alone is sovereign, does not
      declare, 'That is mine!'”
     •What then are the implications
      for us?

IMPLICATIONS
For the things that we teach? For the way that we teach?
choosing examples, choosing activities, dealing with
difficult students
The time we give to our students … The questions we
ask them
The way we point them to Jesus

So why then, is it so difficult to plan for?

DIFFICULTIES AND BARRIERS – A FEW SUGGESTIONS

• Maths is so skills-based so it is too hard to think about …
• Textbooks are so prescriptive and easy to use …
• Maths teachers are not very creative …
Or is it:
• “We are so busy” – no time to plan.
• “The curriculum is so full” – no time to implement.
• “I wouldn’t know where to start”–need some help to get
  going.

A FEW GOOD BOOKS
•Teaching Redemptively
 – Donovan Graham
•TR in 10 seconds:
•Christian Teaching is:
 - What we teach
 - How we teach/treat
 our students

KATHERINE A. LOOP – BEYOND NUMBERS:
 A PRACTICAL GUIDE TO TEACHING MATH BIBLICALLY

As Christians we are in continual warfare. We
constantly have to fight our tendency to live
and think independently from God. The Bible
never excludes math from this combat zone.
In math, as in everything else, we need to
guard against independent thinking – any sort
of thinking that encourages us to trust
ourselves, operate independently from God,
or view something with our own human
reason (p21)

KATHERINE A. LOOP – BEYOND NUMBERS:
A PRACTICAL GUIDE TO TEACHING MATH BIBLICALLY

Reflecting back on her time as a student, Loop
recalls:
“While in other subjects I questioned my textbooks
and checked out their teaching against Scripture, I
simply accepted everything my math book said as
infallible”
Perhaps not only infallible, but also neutral,
directionless

ON NEUTRALITY
 War was the central theme in math books too. School boys
—because the Taliban printed books solely for boys—did not
calculate in apples and cakes, but in bullets and
Kalashnikovs, something like this: “little Omar has a
Kalashnikov with three magazines. There are twenty bullets
in each magazine. He uses two-thirds of the bullets and kills
sixty infidels. How many infidels does he kill with each bullet?

Seierstad, A. (2002). The bookseller of Kabul. New York: Back Bay Books.

WHY IS THIS SO SHOCKING TO US?

KATHERINE A. LOOP – BEYOND NUMBERS:
  A PRACTICAL GUIDE TO TEACHING MATH BIBLICALLY

This books contains great advice around planning lessons:
“In short, whenever you teach math, strive to:
      - Show the student how the concept reveals God’s character/design
      - Teach them to really know how each rule or technique describes
      a real-life principle God created and sustains, and
      - Equip them to use the concept practically.
To help convey these ideas, you will frequently want to incorporate:
      - The history of math, and
      - The practicality of math” (pp 50-51)

KATHERINE A. LOOP – BEYOND NUMBERS:
   A PRACTICAL GUIDE TO TEACHING MATH BIBLICALLY

What this book is:
• Practical, relevant, well-considered
• A book focused on assisting Christian teachers to encourage
  them to ensure that God is at the centre of everything that
  happens in their classrooms
What this book is not:
• A book on teaching Mathematics Christianly that is more a
  philosophical document without a practical edge that will show
  teachers how they can do it!
• Heavy to read.

JIM NICKEL

•Mathematics –
 Is God silent?

JAMES BRADLEY AND RUSSELL HOWELL

 •Mathematics
  through the eyes
  of faith

BETH GREEN – CARDUS INSTITUTE
                   DAY TO DAY EDUCATION THE CONNECTION
                         BETWEEN FAITH & LEARNING

• School effect – attending a Christian school affects the way the
  next generation will talk about religion and practice their faith.
• That the Christian understanding of life should make a
  difference in classrooms. To change the way that students
  think. To develop distinctively Christian teaching and learning
  objectives and processes for their classrooms.
• See anew – to look again at the opportunities within the
  curriculum.
• Choose engagement – strategies that will specifically engage
  the students.
• Reshape practice – attention on the routines and habits of the
  classroom.

HOW CAN YOU DO IT? EXAMPLES AND ADVICE

 •NO!

KEY AREAS – HISTORY OF MATHEMATICS

APPLICATIONS OF MATHEMATICS

LIMITATIONS OF MATHEMATICS

MATHEMATICS IN NATURE

CHALLENGE YOUR STUDENTS TO RESPOND

Van Brummelen (1990): “If our goal
for a Christian approach to education
can be summed up in one phrase, it is
that we must guide students to be and
to become response-able disciples of
Jesus Christ.”

3 STORIES OF MY STAGE 4 CLASSROOM

•Year 7 Mathematics – Open Doors Project
•Year 8 Mathematics – Can a bottle help
 those in our community?
•Year 8 Mathematics – Can we save our
 school oval?

BUT FIRST - TBD
•A helpful tool for planning
 for effective implementation
•Biblical Rationale
•Threads
•Essential Questions
•Enduring Understandings

THREADS

YEAR 7 OPEN DOORS PROJECT
• Problem presented
• Space to discuss
• Let go of control
• Maths in action
  • Surveying
  • Estimation
  • Rates and ratios
  • Financial Mathematics and Algebraic Modelling
  • Graphs

YEAR 8 COAST SHELTER PROJECT

ITEMS NEEDED
Priority #1                  Priority #2
•Tins and packets of soup!   • Sugar
•Long Life Milk – 1L         • Small containers of
 containers                     coffee
                             • Packets of pasta
•2-minute noodles            • Pasta sauce (like
•Cereal                         Raguletto/Dolmio etc)
•Small tins of tuna.

STAFF V STUDENTS

SO HOW DID WE DO?
It’s not really that important …

IT’S MORE ABOUT
•Student awareness
•An understanding of how
 Christians might think in this
 space – even for those who
 don’t know Jesus – yet!
 WWCD
•Thinking of others before
 themselves

BUT FOR THE RECORD
$630 worth of goods for Coast Shelter.

PRAISE GOD FOR THE OPPORTUNITY TO PROMOTE OUR
          CORE VALUES IN OUR CLASSROOMS

• Christ First - we want to honour Christ in all things.
• Serve One Another - we want to appreciate the unique God-
  given potential of each person.
• Strive for Excellence - we want to aim to do our very best all
  the time.
• Do What is Right - we want to always behave in a Christian
  manner.
• Build Community - we want everyone to feel they belong.

YEAR 8 MEASUREMENT ACTIVITY – SAVING THE SCHOOL OVAL

THE CHALLENGE
•While building the new Senior School building,
 can we maintain enough parking spaces (we
 need about 95 of them), but keep a full-size
 school football (soccer) pitch.

•So what are the questions? Think about that
 for a minute … What questions come to mind?

SOME QUESTIONS
• What are the dimensions of a full-size football (soccer) field?
• How big does a parking space need to be?
• How wide does a road need to be in between 2 lines of parking spaces?
• What are some advantages and disadvantages of having a football field
  taking up oval space?
• How can the football field be used to make links to the local community?
• And – how can this activity explore a practical use for the learning
  undertaken in the classroom, develop resilience in our students, make
  them feel as though they are making a contribution to the life of the
  college?

OTHER EXAMPLES – IN 2 MINUTES
Living below the Line – Can you live on $2 per day? – Year 10 Maths
The TIME assignment – Year 7/8 Maths
Planning a budget – Year 9/10 Maths
Fibonacci Numbers and the Golden Ratio – Year 7 Maths
Mathematics by Micah Challenge – Preparing a fundraising event – Year 9 Maths
Go Get Cars – Year 7 Maths
The Christian School Casino – Year 7 Maths.
Deal or No Deal – Year 8 Maths
10-frame maths and blessing dollars – Kindergarten Maths
Sequences and Series – Is it better for Christians to Rent or Buy? – Year 12 Maths
Advanced
Olympics Vs Paralympics – Year 7-10 Maths
Christmas presents and department store catalogues – Year 2 Maths

A FEW MORE EXAMPLES
V8 Supercars Excursion – Year 10 Maths
Urban Challenge – Year 10 Maths
People working to make a better life for others through architecture, engineering,
accountancy etc – Year 11 Maths
Barbie, similar figures and body image – Year 7/8 Maths
Football World Cup – Years 7-10 Maths
Planning a holiday – Year 11 Maths Standard.
Introductory Calculus – maxima and minima problems – Year 12 Maths Advanced
Mathematical Induction – the limits of proof – Year 11/12 Maths Extension 1
The perfect team – Year 4 Maths
Rates and Ratios – Year 8 Maths

A FEW MORE THOUGHTS
• Reflection questions are a must – make the effort to connect the dots.
• Involve their parents – set discussion homework (it might be the only homework the parents
  can do with their year 9 child!)
• Allow the students to ‘tell you what they really think.’
• Don’t assume that the students are Christians but ask them to answer questions that allow
  them to demonstrate / articulate a Christian response to the needs of the world around them.
• Think about the end of the topic from the beginning. What are you trying to achieve? Pray
  about it.
• Discuss ideas, thoughts and opportunities in the unit with your colleagues. Collaborative
  learning is a brilliant thing. Some of the best PD money has been spent on coffee, not
  courses!
• Ask meaningful questions where necessary, join the dots – it’s often necessary.
• If it’s not there, don’t force it.

PREPARING TO TEACH A NEW UNIT
•Week 1. Write rationale
•Week 2. Rewrite rationale
•Week 3. Choose a unit and brainstorm Christian
 perspectives with colleagues
•Week 4. Write a whizzbang wonderful out-of-box
 launch lesson
•Week 5. Explore and program a series of echoes
 back to the launch in the rest of the unit

WHAT DOES GOOD LOOK LIKE?

Good
Good quality teaching is;
    professional,
        contextual,
              differentiated,
                   relational and
successful in equipping the students with skills and
knowledge.

WHAT DOES BETTER LOOK LIKE?
Better
Better quality teaching is;
     professional,
          contextual,
                differentiated,
                     relational and
successful in equipping the students with skills and knowledge
….has links to things biblical at times where it seems
appropriate

WHAT IS BETTER THAN BETTER?
Best
Best quality teaching is;
     professional,
            contextual,
                 differentiated,
                       relational and
successful in equipping the students with skills and knowledge.
… has the content of the teaching flowing out of a gospel-centred
perspective / biblical worldview.

HOW CAN YOU NOT DO IT?
• Over to you – will you be happy to continue teaching
  your class by textbook, or will you try something
  different?
• Romans 12:1-2 NIV - Therefore, I urge you, brothers
  and sisters, in view of God’s mercy, to offer your bodies
  as a living sacrifice, holy and pleasing to God—this is
  your true and proper worship. 2 Do not conform to the
  pattern of this world, but be transformed by the renewing
  of your mind. Then you will be able to test and approve
  what God’s will is—his good, pleasing and perfect will.

HOW CAN YOU NOT DO IT?
Romans 12:1-2 The Message Version
So here’s what I want you to do, God helping you: Take your
everyday, ordinary life—your sleeping, eating, going-to-work, and
walking-around life—and place it before God as an offering.
Embracing what God does for you is the best thing you can do for
him. Don’t become so well-adjusted to your culture that you fit into
it without even thinking. Instead, fix your attention on God. You’ll
be changed from the inside out. Readily recognize what he wants
from you, and quickly respond to it. Unlike the culture around you,
always dragging you down to its level of immaturity, God brings
the best out of you, develops well-formed maturity in you.

CONCLUDING REMARKS
“… mathematics is not the means of denying the idea of
God’s pre-established world in order to play god and create
our own cosmos, but rather is a means whereby we can
think God’s thoughts after Him. It is a means towards
furthering our knowledge of God’s creation and towards
establishing our dominion over it under God”
Rushdoony, R.J.(2001). The Philosophy of the Christian Curriculum. Ross House Books, Vallecito, California.

John Van Dyk once said that “Teaching Christianly might just
be the hardest job in the world.” No truer is it than right now.

THOSE QUESTIONS AGAIN
• In a distinctly Christian educative environment, can the teaching of
  Mathematics be harnessed to strengthen a school approach to a
  student’s cognitive, physical, social, emotional and spiritual wellbeing?
• Is Mathematics a vehicle to provide opportunity for students to actively
  practise and live out the values being fostered by a school?
• Can it be a place where values education and character formation are
  cultivated while students are given opportunity to develop competence
  and autonomy?
• Is it possible to foster positive relationships and connectedness
  through engagement with learning and educational endeavour in the
  Mathematics classroom?

QUESTION AND ANSWER TIME

•An opportunity to share your thoughts,
 ideas and questions from this session.
•Do you have any feedback on what
 you have heard tonight?

CONTACT AND ANOTHER RESOURCE

•Peter Muddle – Deputy Principal Teaching
 and Learning, St Philip’s Christian College
 Gosford – peter.muddle@spcc.nsw.edu.au

•Connect - https://www.connect.cen.edu.au/