Teaching a Christian Worldview in the Math Class
Date: February 11, 2010
Presenter: Brett Edwards
Contact: bedwards@accak12.org
“The chief aim of all investigations of the external world should be to discover the rational order
and harmony which has been imposed on it by God and which He revealed to us in the language
of mathematics.” – Johannes Kepler
In my 9 years of teaching mathematics, the most difficult thing for me has been how to communicate to
my students a distinctly Christian worldview of mathematics.
This is not to say I haven’t struggled with how to teach a particular concept or idea or how to
control a wild class, etc.
By far the thing I have spent the most time blankly staring at a blank lesson plan is how to help students
see how what we do in the math class relates to their lives as Christians.
Q.
Why is it so difficult for the Christian math teacher (or at least myself) to know how to inculcate
a Christian worldview of mathematics?
1. We were not taught to think this way ourselves when we were students.
o I am a product of a public school system that taught me God had nothing to
do with academics and especially not mathematics
2. We have a misconception about what teaching a Christian worldview constitutes.
o Teaching a student in Bible class who the author of Romans is is not
inculcating a Christian worldview
o Chapel once a week does very little if the child is not immersed in the gospel
the rest of the week
o A daily Bible verse or prayer before math class is NOT inculcating a Christian
worldview
o Teaching the students to think of the cross every time they see an addition
sign is NOT teaching Biblical worldview
o There are many Bible teachers that are communicating a lot of Biblical
information to there students but they are not giving their students an
ability to analyze the world through a Christ centered perspective
o The point is that Christian worldview is difficult in EVERY class because most
of us are children of Caesar trying to teach in a way that we were NOT
taught ourselves
3. Our students have not been prepared by their own parents, their own churches and
even their authorities within the school to think of mathematics as an area where
God applies
o I was told by a teaching friend of mine who is a Bible teacher and also
teaches at a Christian school. He said that once when having a conversation
with this principal, the principal told him how sorry he felt for the science
and math teachers at the school. My friend asked why and the principal of
a conservative Christian school said that math and science teachers don’t
get to teach about the “important” matters of life. It’s the Bible teachers
that get to teach the important things while math teachers teach the
subjects unrelated to spiritual things!
o This is not helped when week after week, chapel messages emphasize that
“while math, science and history are important… the most important thing
they can do is give their life to Jesus” please don’t hear what I am not
saying
 Sure if I had a choice, I would rather my students understand the
gospel than the Pythagorean theorem but I don’t think it’s
appropriate to phrase it this way
 It’s like saying “while being nice to your neighbor, loving the orphan,
and respecting your elders are important things… the most
important thing you can do is give your life to Jesus”
4. We want to believe there is a magic formula, a 3 step process to teaching Christian
worldview in mathematics
o I naively thought that I just needed to get my hands on the right book,
employ a few nifty techniques and within 6 weeks my students would be
seeing Jesus in every equation the worked out
o We have to retrain our minds and see how we can find the Lord in the math
class room
So, here we are, we have established that it is a difficult task. I now embark on a the daunting task of
trying my best to tell you what I have learned in my short 9 years of teaching mathematics how we can
communicate a Christian worldview of mathematics.
How do we communicate a Christian worldview in mathematics? Is God silent? as James Nickel asks in
his book.
I. Emphasize the presuppositional aspect of math.
II. Explore and emphasize the mysteries of mathematics.
III. Teach students to see math as a quest to find the order and harmony of God in nature.
IV. Instill a passion for truth and beauty in our students.
V. Last resort, math class is a very valuable training ground for the mind.
I.
Emphasize the presuppositional aspect of math
a. Students must understand that not everything is proven in mathematics
o It is critical for them to understand this because the world tells them from day one
that math and science does not accept anything on faith which couldn’t be farther
from the truth
o All math and science performed is based on presuppositions, things assumed to be
true
b. Let’s see an example relating mathematical proof and how our student’s might use this style
of reasoning to give support for their faith in the Christian God
o Euclid’s Elements offer us a great example of how even the mathematician must
grant some things as true without proof.
 The foundational textbook for Western mathematics is Euclid’s Elements,
436 propositions proven with a rigorous logic still respected by all
mathematicians and scientists today
 However, to even start the textbook, Euclid grants that he is unable to
prove anything unless he assumes some things to be true
 The things Euclid assumes to be true are 5 postulates and 5 common
notions… he was unable to prove them but he would not be able to make
mathematical sense of the world if he didn’t first assume them to be true.
 This is where student’s must see the connection to their faith in the
Christian God. Even the Geometer must have “faith” in these 5 postulates if
he wants to make sense of the physical world.
 Christians must admit their inability to prove mathematically or scientifically
the existence of God
 But if our students can see that only when they accept God as true, the
same way Euclid accepted his 5 postulates as true, can they then make
sense of the world… they will then be armed with the reasoning skills to
attack an unbelieving world
 Looking at our world with an atheistic worldview does not give the
foundation to understand good and evil, what is beautiful, what is true, etc.
o Greek Geometry was focused on a logical process of If… then… statements to give
support for a particular proposition. For example, let’s see how this reasoning
works with proposition 1 from Euclid’s Elements.

o
o
o
o
After constructing the above with compass and straight edge, Euclid reasons
like so…
 If AB and AC are both radii of circle A, then they are equal.
 If AB and BC are both radii of circle B, then they are equal.
 If AC is equal to AB and BC is equal to AB then AC is equal to BC.
 If all the sides of triangle ABC are equal, then ABC is an equilateral triangle.
In the same manner, we as Christians give justification for our faith.
 If the Christian God is true, then the Bible is true.
 If the Bible is true, then man is made in the image of God.
 If man is made in the image of God, then it is a sin to kill man.
I am not arguing for a robotic like defense of the faith. In conversation, the
Christian student would not want to rattle off a bunch of “If… then…” statements
thinking the goal is to logically corner their unbelieving friend.
 However, the reasoning that it takes to understand mathematical proofs is
the type of reasoning that Jesus, Paul and others use to defend the Christian
faith
 Obviously there are many “if… then…” type statements in the Bible but let’s
look at two Biblical examples of such reasoning skills
 “For those whom He foreknew, He also predestined to become conformed
to the image of His Son, so that He would be the firstborn among many
brethren; and these whom He predestined, He also called; and these whom
He called, He also justified; and these whom He justified, He also glorified.”
 If a, then b. If b, then c. If c, then d. Thus if a, then d.
 Our students must be able to communicate this type of thinking and the
math class is a great place to cultivate such skills.
Let’s now look at a related aspect of mathematical reasoning we get from Greek
mathematics.
Euclid’s Elements also introduces an ingenious method to proving propositions
called a reduction ad absurdum which is a proof by contradiction

Proposition 6 of the first book of the Elements is Euclid’s first use of the
reduction ad absurdum

If we know that angles ABC and ACB are equal, we want to prove that AB
will be equal to AC
In order to do this, Euclid assumes that AB and AC are NOT equal
He assumes the opposite of what he is trying to prove knowing that this will
create a contradiction thus proving the contrary
If AB is not equal to AC, then one must be greater, we will pick AB to be
greater.
If AB is greater, then there is a point on AB which will make DB equal to AC.





When looking at triangle ABC and triangle DBC , we can see that AC is equal
to DB and BC is common to both triangles and angle DBC is equal to angle
ACD, we can then conclude that triangle ABC (blue) is equal to triangle DBC
(red) because of proposition 4 (SAS)

What’s the problem? This is absurd! This can’t be true and we then retrack
each step finding that the only fault in our reasoning can be our first step.
o How does a reduction ad absurdum relate to our Christian faith? It has a very
importation relationship.
 In the same way that we reason above, we can follow the line of reasoning
that results from unbelief
 If we assume the opposite of what we believe to be true, mainly that there
is no God and the atheistic evolutionary worldview is true, what does this
assumption require.
 If there is no God, then the Bible is not true.
 If the Bible is not true we are not made in the image of God.
 If we are not made in the image of God, then man is an animal.
 If man is an animal, then moral absolutes make as much sense as they do in
the animal kingdom.
 If moral absolutes are meaningless, then there is no good and evil or right
and wrong.
o Few unbelievers would be willing to accept such a conclusion but where is the logic
wrong?
c. Even mathematicians are forced to except certain things on faith
“To Descartes this result, God’s existence, was more important for science than for
theology, for it afforded the possibility of solving the central problem of the existence of
an objective world.” - Math Historian Morris Kline (Mathematics and the Search for
Knowledge)
d. Faith is required to play both the game of mathematics and the game of a meaningful life
i. What the moral atheist and the unbelieving mathematician have in
common
o They are both inconsistent with their presuppositions
o
The moral atheist claims we there is no God, we come are descendants of
primordial goo and we are simply another mammal.
o After accepting these presuppositions, they then inconsistently adopt an absolutist
moral world where there is good and evil, right and wrong.
o Descartes rightly understood that the existence of an objective world could only be
true if God were true.
e. Conclusion - Our students need to learn in the higher levels of mathematics that all
understanding (even in the sciences) is presuppositional, based on things assumed to be
true with no ability to prove them. Yet, it is only when these things, Euclid’s postulates or
the existence of God, when accepted as true that we can then make sense of the world
around us.
II. Explore and emphasize the mysteries of mathematics
a. Connect this lack of understanding with the only solution an infinite God
“Oh, the depth of the riches both of the wisdom and knowledge of God! How
unsearchable are His judgments and unfathomable His ways!” – Romans 11:33
b. The more we learn in the arena of mathematics, the more we find out how much there is
we truly don’t know.
c. Goldbach’s conjecture states that Every even integer greater than 2 is a Goldbach number, a
number than can be expressed as the sum of two primes.
o 4 = 2 + 2 (both 2 and 2 are primes)
o 6 = 3 + 3 (both 3 and 3 are primes)
o 8=3+5
o 60 = 17 + 43
o Goldbach’s conjecture has been proven true by computer for all even numbers up
to 1018 or 1,000,000,000,000,000,000.
o But this still does not constitute mathematical proof. It is still a mystery.
d. Another goal for number theorists has been to find a formula that will generate only prime
numbers.
o One of the great number theorists of all time, Leonhard Euler attempted to solve
this problem with the formula n2 + n + 41
 Starting with n=0, it worked all the way for n=0, n=1, n=2… n=39
 It was when n=40 that the formula finally failed (41 * 41 = 1681)
n2 +
n+
41
n
Outcome
n
…
Outcome
n
…
Outcome
n
…
Outcome
n
…
Outcome
0
41
Prime
1
43
Prime
21
503
Prime
41
1763
Composite
61
3823
Prime
81
6683
Composite
2
47
Prime
22
547
Prime
42
1847
Prime
62
3947
Prime
82
6847
Composite
3
53
Prime
23
593
Prime
43
1933
Prime
63
4073
Prime
83
7013
Prime
4
61
Prime
24
641
Prime
44
2021
Composite
64
4201
Prime
84
7181
Composite
5
71
Prime
25
691
Prime
45
2111
Prime
65
4331
Composite
85
7351
Prime
6
83
Prime
26
743
Prime
46
2203
Prime
66
4463
Prime
86
7523
Prime
7
97
Prime
27
797
Prime
47
2297
Prime
67
4597
Prime
87
7697
Composite
8
113
Prime
28
853
Prime
48
2393
Prime
68
4733
Prime
88
7873
Prime
9
131
Prime
29
911
Prime
49
2491
Composite
69
4871
Prime
89
8051
Composite
10
151
Prime
30
971
Prime
50
2591
Prime
70
5011
Prime
90
8231
Prime
11
173
Prime
31
1033
Prime
51
2693
Prime
71
5153
Prime
91
8413
Composite
12
197
Prime
32
1097
Prime
52
2797
Prime
72
5297
Prime
92
8597
Prime
13
223
Prime
33
1163
Prime
53
2903
Prime
73
5443
Prime
93
8783
Prime
14
251
Prime
34
1231
Prime
54
3011
Prime
74
5591
Prime
94
8971
Prime
15
281
Prime
35
1301
Prime
55
3121
Prime
75
5741
Prime
95
9161
Prime
16
313
Prime
36
1373
Prime
56
3233
Composite
76
5893
Composite
96
9353
Composite
17
347
Prime
37
1447
Prime
57
3347
Prime
77
6047
Prime
97
9547
Prime
18
383
Prime
38
1523
Prime
58
3463
Prime
78
6203
Prime
98
9743
Prime
19
421
Prime
39
1601
Prime
59
3581
Prime
79
6361
Prime
99
9941
Prime
20
461
Prime
40
1681
Composite
60
3701
Prime
80
6521
Prime
100
10141
Prime

Euler’s formula was later found by a computer to generate prime numbers
47.5% of the time which is surprisingly good
“It will be another million years, at least, before we understand the primes.” – Hungarian
number theorist Paul Erdös
e. The mystery of Pi
o Someone could easily do an entire lecture or even series on the mystery of Pi.
o Pi is this remarkable number, with no pattern that makes sense of the natural world.
o No mathematician in the world can make sense of why this crazy number seems to
pop up so much.
o One remarkable instance of Pi in nature is a study conducted by Hans-Henrik
Stolum, an earth scientist at Cambridge.
 He has found that the ratio of between the actual length of rivers from
source to mouth and their direct length as the crow flies comes out to an
average value slightly greater than 3.
 In fact, this ratio is approximately 3.14
 Why is this?
 God has hidden His signature all over the world for our pleasure.
f. The mathematician Kurt Gödel proved that a complete and consistent mathematical system
was an impossible task. He proved it was impossible with two theorems…
o First theorem of undecidability - If axiomatic set theory is consistent, there exists
theorems that can neither be proved or disproved.
o Second theorem of undecidability - There is no constructive procedure that will
prove axiomatic theory to be consistent.
o
To sum this up, Gödel is making that statement that no matter what set of axioms
are being used, there would be questions that mathematics can not answer,
completeness can not ever be achieved by means of mathematics.
o Gödel’s theorems along with much of the mathematics of the last 200 years have
been a tough pill to swallow for many mathematicians
o Many mathematicians and scientists, the champions of human reason, had believed
that reason and logic would soon be able to solve all the mysteries and riddles of
the world.
o They envisioned a time when reason would unveil all secrets but Gödel’s theorems
argued that even human reason was unable to unlock all the mysteries of the world.
o Is this a problem for the Christian?
 Of course not! “…How unfathomable are His ways!” – Romans 11:33
 We confess the inability of human reason to understand the depths of God
 We still ought to do our best to understand what we can all the while
confessing that the finite man can never fully understand an infinite God.
III. Teach students to see math as a quest to find the order and harmony of God in nature.
“For since the creation of the world His invisible attributes, His eternal power and divine
nature, have been clearly seen, being understood through what has been made, so that they
are without excuse.” – Romans 1:20
a. The explorations in math give us a greater understanding of the nature of God
b. I want to look at two illustrations where we see a discovery of the order and harmony of
God in nature.
c. The first was by Pythagoras, an unbeliever, who still believed the world to have been
created in an orderly fashion with mathematics at its foundation.
o Legend has it that one day on his way to work, Pythagoras was passing a blacksmith
when he heard beautiful and harmonious sounds coming from the anvils being used
by the blacksmith.
o He was convinced that there was a scientific law creating such harmonious sounds.
o He investigated the anvils and found out that harmonious sounds were created by
hammers that were simple ratios or fractions of each other.
o Thus, the hammer that was ½ another or 2/3 would create a harmonious sound
while a hammer that was not a simple ratio of the other would create disharmony.
o This idea was then expanded to apply to stringed instruments as well.
d. In the second illustration we see how a scientist explored the laws of nature in an effort to
learn more about the Creator is in the man Johannes Kepler.
e. Kepler, lived from (1571-1630), and is best known for his work as an astronomer .
f. Kepler believed the world was designed by God in accordance with a mathematical plan. He
said;
“Thus God himself was too kind to remain idle, and began to play the game of
signatures, signifying his likeness into the world; therefore I chance to think that all
nature and the graceful sky are symbolized in the art of geometry.” - Kepler
g. It was the relentless goal of Kepler to find these signatures. One of these signatures he
postulated was that the orbits of the six known planets of the time had a relationship to the
5 Platonic solids (the cube, tetrahedron, etc.)
o After great efforts to make this connection, Kepler abandoned the effort seeing that
the data did not match his hypotheses
h. However, Kepler continued in his quest to discover God’s handwriting on the universe and
did so in his most famous contribution to astronomy with his three laws of planetary
motion.
1. The first law was revolutionary. It confirmed the Copernican idea that the Earth
revolved around the sun but departed from Copernicus and rightly stated that the
Earth does not rotate in a circle but in an ellipse.
 Both Ptolemy and Copernicus resorted to what are called epicycles to
explain a certain “unexplainable” phenomena that was seen
 Kepler, convinced their was a more beautiful answer to the question,
abandoned the idea of epicycles and this directed him to the idea of ellipses
which was true
 He also noted in the first law that the Sun was at one “focus” of the elliptical
paths and the other point is merely a mathematical point with nothing there
2. His second law also departed from a long held belief in constant velocities of the
planets when Kepler stated that Earth revolved on an ellipse but at varying
velocities.
 Faster when nearer to the sun and slower as the Earth went away from the
Sun.
 Included in his second law is the understanding that the area of sectors
covered by the Earth were equal for equal time periods. See illustration.
 This finding overjoyed Kepler and reaffirmed his belief that God had used
mathematical principles to design the universe.
3. Kepler’s third law states that T2 = kD3, where T is the period of revolution of any
planet and D is its mean distance from the sun and k is a constant which is the same
for all planets.
 After stating this Third Law in his book The Harmony of the World, Kepler
broke forth in praise of God saying;
“Sun, moon, and planets glorify Him in your ineffable language! Celestial
harmonies, all ye who comprehend His marvelous works, praise Him.
And thou, my soul, praise thy Creator! It is Him and in Him that all exists.
That which we know best is comprised in Him, as well as in our vain
science.” – Kepler
i.
I want to encourage little Kepler’s in the classroom seeking truth and beauty knowing that
harmony exists in the Universe because they know God has created it according to His
nature. His nature being that of truth, beauty, harmony and order.
IV. Instill a passion for truth and beauty in our students
a. Students need to see the value in finding truth in every discipline
o The great Greek mathematician Euclid, when asked by a student the purpose for
what he was learning looked at his slave and said
“Give the boy a penny since he desires to profit from all that he learns.”
o Euclid is saying, truth is worth learning regardless of what it profits you.
o We should not tolerate or accept such an attitude in the math class.
b. Our students should desire to seek out and find that which is beautiful and the natural world
provides all kinds of beautiful secrets of they will seek them out.
c. One of the many places in the natural world where we see this harmony and order of the
natural world is in one of the most notable number sequences in math; the Fibonacci
sequence
o Leonardo of Pisa (1170-1250) referred to himself as “son of Bonacci” or “Fibonacci”
which is what he is known as today
o It was in his text Liber Abaci that Fibonacci introduced Arabic numerals
o In his book Liber Abaci, he wrote what may be the most famous sequence of
numbers, named after him
 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89….
 Each of the numbers is the sum of the two previous numbers
o One of the phenomenal things about the Fibonacci sequence is its appearance in the
natural world
 If one were to count the two different sets of spirals on a pineapple, they
would find the two values to be two consecutive Fibonacci numbers
 The same is true for the spirals on a sunflower head and pinecones
d. To help nurture a child’s struggle in a certain discipline we tell them they must be gifted in
other areas and not mathematics. This logically creates a student averse to whatever
discipline in which they struggle. “Mr. Edwards, I’m just not a math person.” You’ve made a
choice to not be a math person. This choice has likely been encouraged by parents,
teachers, etc.
e. The idea of a Renaissance man or woman has vanished from the way we teach.
o The world tells us we need to begin specialization in our children as early as
possible.
o If the student is not gifted at math and will not get a job in that discipline, the world
argues that there is little value in them investing so much time and effort.
o We must resist this thinking and tell our students that the thinking required for
upper level mathematics is valuable for all students.
V. Last resort, math class is a very valuable training ground for the mind
a.
b.
c.
d.
e.
f.
g.
h.
i.
“And do not be conformed to this world, but be transformed by the renewing of your
mind, so that you may prove what the will of God is, that which is good an acceptable
and perfect.” – Romans 12:2
I have had many a student argue to the nth degree why math is worthless yet I still have yet
to hear a student argue that thinking is a worthless endeavor
Not a single student of mine has ever expressed a sincere desire for ignorance
Mathematics is mental weight lifting preparing them mentally for every area of life
We are teaching them to be Christian problem solvers in the math class
Do not allow your students to think the problem solving in the math class does not apply to
any other area of life
The student that creatively finds solutions in the math class will be the same creative
problem solver in family disputes, the same person that finds a solution to a business
dilemma, that finds a creative method to finding justice in the court room, that brings peace
to a church in turmoil… The determination, the will to find a solution that a teacher can
cultivate in a classroom can not help but over flow into other areas of the student’s life
I still have a hard time understanding how a student can fail at understanding how to
develop a proof in the geometry class yet develop a strong logical argument in an English
paper.
Even Lincoln understood the value benefits of mathematical reasoning skills when he said in
an autobiographical sketch the following;
“I said, “Lincoln, you can never make a lawyer if you do not understand what
demonstrate means”; and I left my situation in Springfield, went home to my father’s
house, and stayed there till I could give any proposition in the six books of Euclid at
sight. I then found out what “demonstrate” means, and went back to my law studies.”
– Abraham Lincoln
- The first six books of the Elements contain 173 propositions, it’s hard to
believe but who would doubt honest Abe
Mastery in the math classroom can only help our students in whatever area they will
venture in the future.
Conclusion
 “Mathematics is the language in which God has written the universe.” - Galileo
 Mathematics is understanding in greater detail the handiwork of God. It is learning how our
Lord has created all things.
 We can give our students a Christian understanding of this world if we can
I. Emphasize the presuppositional aspect of math.
II. Explore and emphasize the mysteries of mathematics.
III. Teach students to see math as a quest to find the order and harmony of God in nature.
IV. Instill a passion for truth and beauty in our students
V. Last resort, math class is a very valuable training ground for the mind