Blog Post #525 Critical Thinking – an “old/new” approach

Critical Thinking – an old/new approach!!

Critical thinking and problem-solving are crucial attributes for living.  We have to think every day. (My brother-in-law used to kid and say he was a government employee, he didn’t have to think!!)

Maybe you are driving in a new location and are lost – how can you solve your dilemma.  You have to be two places at the same time, how do you decide which one has a priority?

I named today’s blog “an old/new approach”.

I have been doing tutoring this fall in algebra.  I have two regular high school juniors that I spend time with – that are fighting their way through intermediate algebra.  

Now, think back to your days in algebra – and your life today.  Do you ever get a question as you are in line at the grocery store to solve X2 + X – 12 =0? No!!  Do you ever get asked if it takes a kayaker two hours to go upstream, but only half-an-hour to go downstream and the rate of the stream is six miles per hour.  How fast does the kayaker go in still water? NO – you one is going to ask you that. (I’ll answer that one later)

Nobody is going to ask you algebraic equations in real life – so why do you need to spend a couple of years on such problems in high school?  My answer is that algebra teaches you critical thinking and problem-solving in a very unique way.

By doing algebra problems back in the day (normally 9th grade and 11th grade) you trained your mind to figure out what was going on; you analyzed the situation; you may have drawn a model or a chart – and you learned to solve such problems.  

I taught computer programming many times in my teaching career – and again knowing how to think critically was essential.  The logic to solve algebra, the logic to program computers, the logic to get through life comes from training your brain to sort out the important aspects, understand the problem and being able to sit down and work your way through the problems.

I have enjoyed (yes – ENJOYED) doing this algebra tutoring (and it has come back very quickly).  

One of the important aspects of warding off Alzheimer’s is using your brain – do puzzles, do activities, THINK – and solve problems.  

For me (a former high school math teacher and college professor), I am finding that doing the algebra does work my brain.

So, an ‘old/new’ approach.  Stop by your public library and check out an algebra book – and work through some problems (and definitely try working those dreaded story problems too).  It just might be an activity to stimulate your brain and rekindle those critical thinking and problem-solving skills.

What do you think?


Problem answers:  1) X2 + X -12 =0  can be factored (wow – do you remember that?) into (X + 4) and (X – 3); set each to zero and you get solutions of X = -4 and X = 3

2) for the kayak problem, the distance the kayaker rows upstream and the distance he/she rows downstream is the same.

Let’s make X equal to the kayaker’s speed in still water.  So if the stream flows at 6 miles per hour, you get 2(X – 6)  (the speed going up the river is the kayaker’s speed in still water minus the flow of the river – so X-6) and the time is two hours – that is Rate * Time = Distance

Going downstream it takes a ½ hour – so ½(X + 6) is that distance.

Putting them together you get this equation:

2(X – 6)   = ½(X + 6)

And as you work it out, you get X = 10 – or the kayaker goes 10 miles per hour in still water – so upstream he is going 4 miles an hour against the flow – so in two hours he/she goes 8 miles; and downstream he/she is going 16 miles an hour – so in ½ hour, he/she would go 8 miles.

(By-the-way, if a kayaker can row at 10 miles an hour he or she is very fit and strong!!!)

And … last comment – for Minnesota and northern friends – there is a town on the banks of the St. Croix River called Stillwater (as well as a Stillwater in Oklahoma).  Sometimes my brain says so, that person goes so fast in Stillwater, how fast might they be in Minneapolis!!!



Posted by Bruce White

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