Science and Religion

2

I used to believe there was a dichotomy between science and religion. It seemed in the past, that when science could not explain why something was true, we turned to religion and simply attributed to God. There have also been arguments against the existence of a God,
from The problem of Evil to Michael Martins proof, A Disproof of Gods Existence. Even after growing up in a Catholic home, I believed that one person was either religious or logical and scientific, but not both; a Venn-diagram with no overlap. 8 years ago, this all changed when I started teaching at Notre Dame; a Catholic high school. When I make references to Church and Religion, I will be referring to the Catholic Church.

Once I started working at Notre Dame, I met many Catholic Science teachers and was shown that you can be a Catholic logical thinker. My eyes were opened to the reality that this Venn-Diagram does have an overlap. I believe, like others in the past, I did not understand the implications that Religion has on Science and also how Science impacts Religion. I will show, through my own stories how Science and Religion can, and do, coexist.

When I first started teaching Science, I was worried I would go against the teachings of the Church when I started to address the age of our Planet. Before, I took the literal sense of the Word in the book of Genesis which stated that the Earth was formed in six days, some 6000 years ago. Science has shown that the Universe is around 15 Billion years old. An obvious contradiction! After some research, on how I will address this in my Science Class, I read Frank Sheed (1982) say

"one shouldnt be forced to choose between evolution and creation."

and he continues on to say that
"Creation answers the question why does everything exist, why there isnt nothing? While evolution, is a theory, as to how come the Universe did develop once it existed." (Pg. 58)

As well, when Genesis was written, humanity did not fully understand the workings of the universe and these six days just corresponded with the Babylonian creation myth Enuma Elish, and does not really mean God created the Earth in six day at all. Religion now fully accepts the fact the Earth is not 6000 years old and that uses science to determine when God created the Universe
One discussion which arose in my class was around the idea of evolution for Apes versus the creation of humans by God. Again, before looking deeper I believed these were two contradictory ideas, but instead they are not. The Church has said it is not against the idea of evolution, and in fact evolution exists in our current era (Some people will not grow molars), and that the evolution of the body is an almost certain fact. However, religion teaches us that the soul, in which is inside our body, was not the result of any certain evolution but instead infused by God Himself; again not contradictory, but two theories from the same thread of truth.

Due to the limit of words I will not go further into detail, but science and religion also agree on when life starts, how pre maritial sex will lead to increased divorce rates, and many other theories. Science and religion are both logical, deal with science and fact, and truthfully it is
because of Science that my faith is strong.

Permutations and Combinations Lesson 2

Students will learn how to apply the Fundamental Counting Princple with restrictions and Permutations.

Intro: Show the following video:

Since there is an abundant amount of different ways these books are arranged, simply ask
"How would we determine the total number of ways the book shelf could be arranged?"

Next ask

"What would we need to know?"

After some discussion, show the picture of the top left shelf as seen below:

Then I would ask the following questions:

 

1) How many different ways can these books be arranged, if the spine of the book must be facing out, and:

a)  The shelf will only have 4 books and a pink book must be on each end?

b) The shelf will only have 8 books the pink books must be next to each other?

c) All books are on the shelf with no restrictions?

 

The last question is there to assist with introducing factorial notation.

 

Explain that: "!" is the symbol for factorial notation and can be used on any non-negative integer n.  The formal defintion is:

n!=n(n-1)(n-2)(n-3)...(3)(2)(1)

As well as how to get use it on the calculator.

 

I would then go through operations on factorials showing that (n!)(x!) does not equal (nx)! nor does it hold for any other operation.  As well that 0! = 1

 

Next ask for the previous picture:

2) How many different ways can you arrange the books on the shelf if you only want:

a) 4 books on the shelf?

b) 7 books on the shelf?

c) 13 books on the shelf?

 

Using the process, you can introduce nPr, and how the previous answers can be solved with n!/(n-r)!, with guiding the students towards this answer.

 

The formal definition being:

When permutating n objects picking r at a time we would write nPr = n!/(n-r)!

 

 

Ask the students how many diffeerent ways to arrange the letter FILE, then FILL, then FLLL, then LLLL.

 

Let students work and struggle through, and lead them towards the identity of:

 

Organizing a objects where there are n repetitions of one object, there are a!/n! distinct permutations. 

 

From here I have yet to find real life scenarios and would give various questions and words to rearrange such as MISSISSIPPI. (Would love ideas here if you have any...)

 

 

 

 

Permutations and Combinations Lesson 1

Here is my lesson plan for my first lesson in Math 30-1 on Permutations and Combinations. Which covers the outcome: Apply the fundamental counting principle to solve problems.

(My students sit in groups of 4 and 5)

First show the following funny video,

Next, show this video:

After which, ask the question "How many different possible pin numbers could there be?"

Give the students about 2-3 minutes to discuss and then re-ask the last question
"Is there any more information you need?"

This is where you can go in any direction you please.  In my lesson, the gentleman in the movie has either a 4 or 5 digit PIN number (we don't know).

Now allow students to work for approximately 10 minutes.

After this is done, ask the class:

How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Take this time to discuss that you should multiply the different possibilities of having a 5 digit pin, and the possibilities of having a 4 digit pin, and then you should ADD these answers together.

Next show the students the following picture of a hand knit mitten, and explain the following:

Jennifer makes this mitten out of four different parts, the fabric of the entire mitten, the middle "tree or leaf" part, the bead, and the strings which tie them together, and has multiple different colours for each part.

Then ask: How many different mittens can Jennifer make?

I would let students talk as long as they needed until they realized they are missing a lot of vital information.  Ask for any questions or information they might need (just like the previous question) and provide them with the following: (You can change as you see fit)

5 different colours of yarn for the mitten
3 different tree/leaf colours
2 different beads
5 different colours for the string.

Give time to solve and then ask

How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Next, you can go the link https://order.bostonpizza.com/EN#content=/Menu/ViewMenu/&CategoryItemsContainer=/Menu/CategoryGroup/dfa5509b-935b-4776-b157-bfefef2ab654

Which shows that Boston Pizza currently has 4 different types of wings with 21 different flavours of each type of wing.

The problem:  Red Deer Rebels (or whichever local hockey team you want) is having dinner and orders 8 different double orders of chicken wings, how many different combinations could there be?

Again, using the same process students will need to know if you can have more than 1 flavour, and you can have up to 2 flavours PER double order, or they could be the same flavour as well.

After, ask the three crucial questions again, with some leading if needed.

If you have more time I would ask the following question:

Should Alberta, currently, be concerned with the number of phone numbers in the province and truly needed to add the 3rd area code (587)?

Following the same procedure of asking if they require more information and then the three crucial questions of debrief.

What kind of Learner are you?

Here is a wicked visual about "What type of learner are you" from OnlineCollege.org


Compiled By: OnlineCollege.org

How my Dog taught me about Math

Over the summer, my wife and I adopted a puppy found in a local dumpster.  After reading about 3 or 4 books I decided I was going to teach my dog how to sit, stay, roll over, bark and……mathematics.  

How do you teach a dog math?

Very easy, but first you have to teach your dog how to bark.  Once this is done, I have trained my dog to bark twice every time I say "One plus one".  She barks three times when I say "Two plus one".  Lastly, I have trained her to remain silent when I say "Four times zero".

She understands math correct?

Before an argument is started, I do not believe she truly understand math, but only has memorized mathematical commands.  I wonder how many students go through math class with the knowledge similar to my dog; memorized facts, but has very little understanding.  

Years ago, my class was set up in a way that I was training dogs, not teaching students.  I would give students questions out of context, assign redundant homework, and lastly reward speed and repetition with marks.  My dog has taught me a more valuable lesson than I could ever provide to her; there is a large difference between memorization and knowledge.

Cartesian Co-Ordinate System

When teaching about the Cartesian Co-ordinate system I fear that most teachers focus on the how and not enough on the why. The how is taught, traditionally, by the teacher showing the students two number lines, perpendicular to each other, labeling the intersection of the lines (0,0) and then labeling the positive and negative x and y axes. After, the students are then given many different points to label, of varying difficulty, and then given a word problem. The lesson ends with the students working on page XX and completing either the odds or the evens.

This method, I believe, does not allow the students to understand why the Cartesian Co-ordinate system is extremely valuable. Here is how I introduce this concept:

Breaking the class up into groups of 4, each group then picks a wall in my classroom, or in the hallway. Each group of 4 is then divided up into two pairs of 2, and one pair remains at the wall, while the other pair leaves the wall for 5 minutes. I then walk to each wall and point to a particular section on the wall and leave an erasable mark on it. The following task is then given to the pair of students who are waiting at the wall:

You must create a set of instructions, which you leave at your wall, for the other 2 students to read. These instructions can include whatever you would like but the goal of the instructions is to assist your other group members in finding the point. Once you complete your instructions you are to take a picture of the wall, with the mark showing, and then erase the mark.

I supply my students with flipcams, ipods, and iPads to take the picture.

Once this part is complete, the other 2 students are to return, read the instructions and make a mark of their own. Their mark and the picture is then compared. Afterward we do some debriefing as a class. I ask for groups read their instructions, and share on why their instructions worked or didn't work. Every single time I have done this with my class I always get the same remark:

We need some sort of similar explanation which we all understand before hand

It is only then that I introduce the Cartesian co-oridinate system and tell this story:

Some mathematics historians claim it may be that Descartes's inspiration for the coordinate system was due to his lifelong habit of staying late in bed. According to some accounts, one morning Descartes noticed a fly walking across the ceiling of his bedroom. As he watched the fly, Descartes began to think of how the fly's path could be described without actually tracing its path. His further reflections about describing a path by means of mathematics led to La Géometrie and Descartes's invention of coordinate geometry.

http://www.bookrags.com/research/descartes-and-his-coordinate-system-mmat-02