The Question

I have to admit that I have never been one of the students to ask a teacher ‘Why do we have to learn this?’  Perhaps I already saw the applications of Mathematics at an early age or knew that I would need these concepts to succeed in University Mathematics courses.  More likely, I was good at math and liked doing the ‘drill and kill’ problems.  I didn’t think I had to have a reason for learning it other than there was a ‘right’ answer and I enjoyed finding it.  Most students, however, are not like me at all.  I have been lucky enough, or probably just do not have enough experience yet, never to have had a student ask me The Question (which ‘Why do we have to learn this?’ will be referred to from now on in this post).

Depending on the student and the situation, I think I would have different answers.

For a student that I think would respond to humour, I would direct them to the following article:

http://www.theatlantic.com/business/archive/2012/07/the-11-ways-that-consumers-are-hopeless-at-math/259479/

and make a joke about them not wanting to be an uneducated or uninformed consumer.

For a student that enjoys English, I would direct them to this article and make a joke about how even authors incorporate mathematical concepts in their writing.

http://www.guardian.co.uk/books/booksblog/2012/aug/23/tolstoy-maths-daniel-tammet

If the whole class was having a problem with what we were doing, I would explain that understanding mathematics allows us to:

·         Manage our time and money

·         Understand patterns in the world

·         Solve problems using reasoning skills

·         Use technology

·         Be aware of what makes the objects around us work (search engines, technology, motion, etc.)

If students needed a more concrete answer than the one previously mentioned, I would explain how the following topics that are covered in the Pre-Calculus stream of mathematics in my province are/should be relevant to them.

Pre-Calculus Topics:

Trigonometry (specifically the use of radians) – Who decided there were 360 degrees in a circle? Isn’t this arbitrary? Radians are not an arbitrary measuring unit.  They are based on the intrinsic properties of a circle.  Therefore, many complicated trigonometric expressions can be easily reduced and simplified with the use of radians. 

Function Transformations – Function transformations relate a function to its corresponding graph.  Functions describe many real life phenomena and the graphs of these functions are sometimes more easily interpreted than the function itself.  These graphs show you a picture of what is happening.  With knowledge of function transformations, you can determine how the different parts of a function (coefficients, degrees, positive or negative) affect the graph of a function, and therefore the interpretation of the data a function represents.   

Exponents and Logarithms – The functions have many applications including modelling population growth, exponential growth and decay, logarithmic scales eg. Richter scale, pH scale, and they are even used to model the cooling of a dead body (what student wouldn’t find a crime scene application interesting?).

Radical & Rational & Polynomial Functions – used to model real world phenomena 

Permutations and Combinations – The ordering of groups and the number of different grouping possibilities has many applications, especially those related to probability, e.g. the probability that a certain arrangement of runners will win a race.  Permutations and combinations can also help you discover the number of different locker combinations, the number of different license plate numbers, and the number of different poker hands.

Of course, all of the above information will never answer ‘The Question’ for a student who doesn’t want to see the necessity or use of mathematics around them.  For those students, I have no answer ...

Modeling Data with Radical Functions

In my province we need to teach students how to take the square root of a function when given the actual function or a graph of that function (in Grade 12 Pre-Calculus Mathematics).

Why is this relevant?  When would you ever need to do this in real life?

Modeling skid marks in vehicle accidents!

This is one of the only application problems I found that incorporates taking the square root of a function for a purpose (other than to just perform the procedure or do the math).

In this document, my answers (which are hopefully correct and mathematically accurate!) are included in red/blue.

I created this worksheet/problem for students to work on as an application of radical functions because I don’t like telling students the only reason they are learning a certain topic is that it will be on the test or they will need it in later mathematics courses. Sure, every topic does not have an immediate application, but I like to use them whenever I can to keep students interested and for them to see that mathematicians discovered these concepts for a reason, not just for ‘fun’.

Here it is!  Enjoy!

PDF version

WORD version
 
(Hopefully the links work! If they don't, let me know :) )

Any feedback you have, whether positive or negative is greatly appreciated.  This is the first worksheet I have made about radical functions and their applications so I am not expecting it to be perfect!

What's with all the dinosaurs?

From both my screen name, Ms. Philosoraptor, and my blog name, normalcurvasaurus, you can probably surmise that I love dinosaurs (especially velociraptors), math and philosophy.  That would be a slight understatement.  I wanted my blog name to represent my love of these three things, including my love of teaching.  Ever since I was little, I have wanted to become a teacher.  We used to have a fisher price chalkboard in our basement where I would teach my little brother and sister how to add, subtract, multiply and divide.  I also used to give them homework (which they would never complete!) because I liked to mark each question right or wrong to show them where they went wrong and what the right answer was.  I hope my teaching skills have improved since then and I won’t be giving homework that can be so easily marked as right or wrong.  I want my students to become thinkers, and actually THINK about the mathematics they are doing.  I do not want them to just plug numbers into a formula and come up with some answer (which may or may not be realistic) and have no idea what that answer represents.  This is where the ‘philosophy’ component of my blog comes into play.  I took a few philosophy courses in University, I was even planning on minoring in philosophy until I realized there are very few schools that offer philosophy courses where I live (I think just one) and that would not give me an edge in the extremely competitive job market we have.  However, while taking these courses, I realized how closely philosophy is related to mathematics and logical reasoning.  Philosophy involves reasoning from what is known to deduce other facts or truths.  This is what I want my students to be able to do. 

Why normalcurvasaurus you ask? Well, I don’t really have a good reason for that other than it incorporates mathematics and dinosaurs and that is good enough for me!

I guess now would be the time to explain why I love dinosaurs so much.  My parents bought a set of dinosaur books for us to read when we were little.  Each book described a different dinosaur and that is where it all started.  My brother and sister and I then started watching The Land Before Time series, which involved animated dinosaurs getting into trouble and singing.  Then, the first Jurassic Park movie came out.  I began to get really interested in velociraptors, including their hunting and communication techniques which seemed to be really advanced for a ‘primitive’ animal.  Anyways, long story short, and since this is supposed to be a blog about mathematics and mathematics teaching, I love dinosaurs, especially velociraptors. 

(I may or may not have a light blue t-shirt with the above normalcurvisaurus image on it.)

So there you have it.  That is where my blog name and screen name originate.

Now, why did I decide to blog?

I have been stalking reading mathematics blogs for a while.  I believe it first started with Math Teacher Mambo and grew from there.  I then set up googlereader and now follow and read over 150 mathematics blogs (yes I just went and counted, does googlereader tell you this information somewhere??).  I decided to blog to write about my own experiences with teaching, starting with student teaching this year and hopefully growing to ‘actual’ teaching next year when I get my teaching certificate and hopefully *fingers crossed* get a full time teaching position.  I also wanted to join in all the fun that you guys seem to be having!