Wednesday, May 26, 2010

How I learned to master math after deserving to flunk

From Practically Flunking 9th grade algebra to learning how to make straight “A”s in Math, this post is dedicated to Zach. I wish you the best of skill buddy. You can do it, and if you can do math you can do anything!

I made it through 9th grade algebra with a “D”. I think I really deserved an “F”, but the rest of my grades were good and I don’t think my algebra teacher wanted to be the one that caused me to be held back a grade. So, she passed me with a “D”.

In my first semester of college which finally came 12 years later, I learned the secret to making all “A”s in math without cheating. I would continue to successfully use this secret to make all "A"s all the way through Calculus III the highest math I needed for my computer science degree.

My problem in the 9th grade...

All the way through high school I only did what was necessary to get by academically. Usually that amounted to an easy “B”, an occasional “A”, and sometimes a “C”. I wish I knew way back then that I had the potential to do well in math and would eventually even like it. After my near flunking out experience in 9th grade algebra I steered clear of difficult maths except for one geometry class where the teacher was exceptional and I did well.

In 9th grade algebra I found most of the teacher’s lectures always went over my head. The mathmatical gears in my head never meshed, they always missed. I solved simple equations through trial and error substitution. Anyone who understands algebra knows how stupid that is and how unnecessary. Equations balance! The equal sign acts as a fulcrum. What you do to one side of the equation, you also do to the other side and it remains balanced. It's all pretty simple to me now, but for some reason I didn't get it in the 9th grade.

My 9th Grade method of solving an equation:

Equation: a - 3 = 5
1st attempt: Try 10 for a; 10 - 3 = 7 oops, too large.
2nd attempt: Try 7; 7 - 3 = 4 oops, too small, pretty close though and the number is one below so a must be 8! Bingo! made it through that one.

What I should have known to do and oh so easy...

Equation: a - 3 = 5
step 1: Isolate the "a" on the left by adding a 3 to both sides: a - 3 + 3 = 5 + 3
Note: I added a 3 to the left side and to the right side so everything still balances across the equal sign. It’s like balancing a board on a fulcrum. If you add 3 pounds to only one side it will tilt out of balance, but if you add three pounds to both sides it will still be in balance.

step 2: adding 3 to the left side causes the 3 to disappear leaving only the a. Adding the 3 to the right side that has a 5 involves simple addition: 5 + 3 which is 8.

Pretty simple stuff if you understand it.

So, what was my problem? There is more to algebra than simply solving equations. There are rules such as knowing the order of operations, how the use of parentheses affect the order of operations etc. Algebra is foundational. It does take a little effort to assemble the building blocks. If any are weak or missing, everything you build above may eventually come crashing down. You also have to practice your art to keep it strong. Use it or lose it. My foundation was weak. Most of the stuff the teacher lectured on went over my head because I didn’t have the proper foundational blocks in place. She always asked if there were any questions. I didn’t know where to begin to ask, so I always kept my mouth shut and counted on my stupid trial and error method to get me by with a “D” I didn’t deserve. Ouch!

I covered why I didn’t go to college after high school in my post the road to Army Flight School. I finally did get around to my 1st college semester in the spring of 1982 after working a season in Alaska and having money in the bank with nothing to do, so I thought I’d try college.

Since I had not been in school in a long while I only took two classes; an english composition class, and an algebra class. My algebra class was for either intermediate or beginning algebra a little below college algebra, which was good because algebra is foundational and my foundation was weak so I needed to start low if I was going to have any chance at success.

Finding my Silver Bullet... It almost seemed like cheating, but it wasn’t.

Since I only took two classes I had some extra time on my hands. One day prior to algebra class I had some extra time and was bored trying to decide how to spend it. I decided to look over the section the algebra teacher was going to lecture on that day before going to class. I had to be bored to attempt to wade through that on my own. WOW! What a difference it made though.

It seems that it is not easy wading through algebra content on our own trying to make heads or tales out of it by yourself. Key issue: I wasn’t attempting full mastery, I was only attempting to get an initial introduction to the new terms and concepts covered in the section. I also looked over the example problems and toyed with working them. Doing this lined my mathematical gears up and got them ready to mesh! It would prove to be a secret weapon to mathematical success for me.

The teachers lecture that day was like having the icing put on a cake. I followed her completely. I was able to ask intelligent questions when necessary. My gears meshed and smoothly turned like a well oiled mechanism. My understanding and grasp of the subject matter increased significantly. It felt like cheating, but anyone could do it and I even found it as a recommended technique in a chemistry textbook. I fortunately just stumbled on it. The feeling in class was so awesome that I made it a habit to take a peek ahead before any math lectures for all my classes all the way through Calculus III and I managed to make easy “A”s all the way through with the exception of one teacher I just didn't click with whose class I dropped and took again with a different teacher with no difficulty.

This new found secret weapon totally revolutionized my attitude toward math, and my new found ease of success even made it fun.

A little extra...

Taking a peek ahead was my silver bullet and my main key to success with math. There are a couple of other key points to be aware of too.

1). As mentioned previously math is foundational, so don’t feel bad about starting at a lower level if it is necessary. Getting in at the right level will increase your chances of success and increase your enjoyment at tackling the math giant.

2). You also have to work plenty of problems. Math is a huge jungle with numerous interconnecting trails. The more problems you work the easier the trails will be to identify and travel. It is very similar to following trails through the woods. Well traveled trails are easy to follow and stay on. Rarely traveled trails can be difficult to pick out and follow. Your teacher is like a guide showing the way. It seems so easy with the guide present and showing you, but if you fail to wear the trails down the weeds and jungle will grow up and make the trails difficult to find and travel, so get in the habit of doing your homework and working lots of problems.

3). It is a balancing act to stay on top of the algebra ball. As long as you are on top it is doable. If you allow yourself to fall off the ball, it can be very difficult to climb back up. It takes a commitment and an effort to stay on top: a) Take that peek ahead, b) always work your homework problems, c) work extra problems if you have the time and inclination, d) and get extra tutorial help if you need it. By doing these things, even you can easily become king of the algebra jungle!

Unless you like wasting money or someone else’s time, don’t get a tutor until you have given a) take that peek ahead, and b) always do your homework; a chance. If you have done both “a” & “b” and still find you need extra help, go for the tutor assistance too when necessary. I've never used a tutor, but my math agility helped me to successfully tutor others.

Teachers can sometimes make a difference too. If you find you're not clicking with a particular teacher after trying all of the above, watch your drop date and try a different one. I did drop Calc III and took it again during a summer semester. Summer semesters go by fast and furious. I told myself I wouldn't attempt a difficult course like Calc III in the summer, but it turned out well with the right teacher when I had to because of time constraints. Also if you find yourself placed in a higher level class than you are ready for and things just aren't clicking like they should, don't feel bad about moving to a lower level class to get your foundation built up to where it needs to be. I did this once too after a long separation between college semesters when I needed a little extra help knocking the rust off.

Now for a little story...

I had been making all “A”s after implementing “a” & “b” mentioned above. This college professor was a beautiful woman and also did a good job covering the subject matter. Some guys liked taking her class just because she was so sweet and beautiful besides competent. It was test day. I was confident with my secret weapon of peeking ahead in place and working plenty of problems that I would do well and the test would be a cinch. All my algebraic trails were well worn and easy to follow. It was also fun. I felt like king of the algebraic jungle and expected a good outcome.

Wow! I even got through this particular test in record time! That seemed a little strange because working problems does take a bit of time even when you are good. I accepted my record time and turned my test in knowing I nailed every problem I worked perfectly.

When the teacher passed out our graded tests, I had a big fat “C” plastered across the front. I looked a little shocked and then turned the page over. There was a whole page of unworked problems on the back. No wonder the test went so fast. I still managed a “C” even though I skipped a whole boat load (page) of problems. A male student next to me saw what I had done and looked at the teacher and said with concern, “You are going to give him a chance to make that up?”

The teacher flashed a pretty little smile with a wink at me and said, “He doesn’t need it.”

And I didn’t... I had sure come a long way from where I had practically flunked 9th grade algebra. And, it sure felt good!


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