High School Math Goals part 2

In part 1, we briefly touched upon how to deter­mine your child’s math jour­ney in high school by exam­in­ing your child’s goals.

In part 2, I will share the goals of the teach­ers in teach­ing high­er lev­el mathematics.

Tru­ly, I use the term, “high­er lev­el” math­e­mat­ics very loose­ly as the high­er lev­el math­e­mat­ics are actu­al­ly in the quadriv­i­um or at the col­lege level. 

High school math cours­es build a bridge between basic math­e­mat­i­cal con­cepts and the high­er lev­el math­e­mat­ics stud­ied in col­lege. Today I will share three main foci of sec­ondary mathematics. 

1. The mas­tery of abstract con­cepts.  As we devel­op, we move from being very con­crete beings to being able to grasp more abstract thoughts.  We see this in all of our chil­dren.  As a tod­dler, “love” meant giv­ing mom a hug, while as a teenag­er “love” means per­se­ver­ance.  In math, addi­tion meant adding apples and bananas in 1^st grade, but sub­trac­tion meant spend­ing mon­ey some­times to the point of the neg­a­tive num­bers.  These neg­a­tive num­bers are an abstract con­cept.  They don’t exist.  You can’t hold a ‑2 in your hand.  You can under­stand what it means to owe some­one $2, but that demotes the num­ber ‑2 to a con­crete exam­ple again.  For that mat­ter, you can’t hold a +2 either.  These num­bers rep­re­sent some­thing that does­n’t exist in the phys­i­cal world.  Young stu­dents don’t under­stand that and many old­er stu­dents strug­gle with it.  High school alge­bra par­tic­u­lar­ly focus­es on help­ing stu­dents take what they thought was con­crete and move it into the abstract realm of thought and the­o­ry.  As adults we con­tin­u­al­ly deal with abstract thought.  Is God spir­it? What does that mean? He is order­ly, even depend­able, but we can’t see Him.  How does our under­stand­ing of a God that we can’t see devel­op? Through the growth that we expe­ri­ence in work­ing through high­er lev­el math­e­mat­ics. Which brings us to focus #2:
2. The com­pre­hen­sion of cre­ation.  Math­e­mat­ics was­n’t cre­at­ed by man. It was dis­cov­ered.  Ancient Greeks, Babylonians,and oth­er civ­i­liza­tions stud­ied the world around them and found order.  They dis­cov­ered that all cir­cles con­tained a hid­den num­ber, that cer­tain plants always had an odd num­ber of petals, that the depend­abil­i­ty of the sun and shapes gave you a way to deter­mine the size of the earth.  By study­ing math­e­mat­ics we are actu­al­ly study­ing the cre­ation of God.  Math­e­mat­ics is the lan­guage of cre­ation. It is the lan­guage that we use to explain some­thing that already exists.  More specif­i­cal­ly, it is the lan­guage that we use to explain sci­ence.   Physics is explained by math.  Astron­o­my is explained by math.  Every top­ic that exam­ines the cre­ation of God can be explained using the lan­guage of math­e­mat­ics. Which brings us to focus #3:
3. The gram­mar of high­er math­e­mat­ics.  Sec­ondary math­e­mat­ics isn’t actu­al­ly high­er lev­el math, but it is a step­ping stone.  Essen­tial­ly, sec­ondary math­e­mat­ics is the gram­mar of high­er lev­el math. It is the foun­da­tion on which all high­er lev­el math­e­mat­ics is based.  If your stu­dent wants to be a physi­cist, then he must under­stand cal­cu­lus.  In order to under­stand cal­cu­lus, then guess what? He needs to know alge­bra.  It is a beau­ti­ful thing when you see the abstract think­ing in alge­bra join with the spa­tial con­cepts in geom­e­try to show the order in the uni­verse in chem­istry.  This is the answer that all high school math teach­ers will give you for study­ing math, but notice that it isn’t the first focus on our list.  Under­stand­ing high­er lev­el math­e­mat­ics is only impor­tant in so much as it brings us clos­er to under­stand­ing God. 

There­fore, study math in high school in order to under­stand abstract con­cepts, but tru­ly study math in order to know God.  That is the main focus.