A Little Geometry, Triangles, and counting to 180.

Some simple concepts regarding triangles and 180...This student up until quite recently found triangles to be confusing and stupid.  But with a little directed discovery and explanation things very rapidly started making sense.  Geometry is often easy for visual learners because they can see it...this is not a primarily a visual learner,  this is a kinesthetic learner. He is good at sports and the reason he showed up in the first place was because if he got an F they wouldn't let him play.

"If you can count to nine tell me if something is same or different or not and identify a rectangle I can teach you math if you want to learn it...and you need to be able to speak a language preferably English." Is basically how our lessons started and at first he was incredulous. After an hour triangles were EASY. Now we just have to work on the negative associations he has built up over the last two years...he got a D in algebra and hated it. I showed him problem solving and factoring and he was hooked.

Next we will mix in a little algebra...this vid also brings home the fact that knowing your addends by heart makes a BIG difference. Concepts build on concepts and skill sets build on skill sets...soon instead of "2" they will put something like 4x - 20 there. And the student will have to figure out that 4x - 20 = 80.   Which is a snap if they understand problem solving concepts but just adds to the confusion if they just got a "D" in algebra and hate it and none of makes sense. Hero Zero and No Fun Get Back To One to the rescue.

In this video a student I am tutoring discovers that the stuff he thought was hard might not be so hard as long as he can count to 180. The angles of triangles always add up to 180 and using a little logic and reasoning we see why the exterior angle and the two non-supplementary angles add up to 180 degrees. I did a lesson already using directed discovery so that he was able to pretty much figure that out for himself he just couldn't elucidate it well so I showed him using some symbols and it really started making sense. (See also vid below.)

You can't see the x but it is the other angle in the triangle.

This student is a little camera shy and as with all students, tends to behave a little bit differently when the camera is on which adds a little pressure. This is another student that was in danger of not being able to play sports because of his math grade and apparently he's pretty good at baseball...and does "ok" in his other classes except, of course, math.

From what I can see he is indeed a kinesthetic learner and once he gets his hands on the blocks a lot of math problems fade away. (Do you see what I did there? I crack myself up.)

Now we are ready for a "complicated" problem like this on to the left. Looks like it might be tricky but again if you can count to 180 it's not very hard. Turns out it's just two problems stuck together.  Suddenly it's pretty easy except for the part that he sees a problem like this and automatically runs a program in his head that this is hard...but then it turns out to be easy and the program is modified. Soon he will be able to understand even poor explanations because he will be running a program called "this is easy I can do this."

The geometry wasn't making any sense to him nor were the explanations he was getting from his teacher, so he quit paying attention and this turns into a loop that ends with an "F." BTW he tells me probably 90% of his peers are bombing tests and getting poor grades. I'm pretty sure the teacher is just as frustrated if not more than the students.

Anyhow, once he starts understanding basics concepts and the generic ideas all they can do is switch the numbers...and test scores go up dramatically....and people think Crewton Ramone is magic. But it's not magic it's just math....and knowing when to start counting to 180....



Oh and BTW Happy New Year.

"Perpendicular To"

Short explanation of a symbol in geometry, with a very lame explanation of how to use a negative inverse to make a perpendicular line.... After further review we did a much more thorough lesson on how to make perpendicular lines with slope intercept form. Anyhow math really is no fun if you don't know what the symbols mean.

Crewton Ramone Two Shorts on Geometry

Remembering  complimentary angles and supplementary angles can be tricky. It also causes some people to think all math is, is memorization.

I always hear questions like, "can this do algebra, can this do geometry, can this do calculus?"...with "this" meaning Mortensen Math and the blocks. How do you apply manipulatives to Geometry or Trig? The basic concepts remain the same throughout the mathematics.

In cases like this all we are doing is learning vocabulary:



So there is a fast way to remember vocabulary. The problem is when you confuse vocabulary with understanding concepts or where you confuse memorization with conceptualization and problem solving. Some seem to think there is no difference between memorizing vocabulary words and memorizing formulae or addends or multiplication tables. Nothing could be further from the truth. We can "figure out" or use an algorithm that requires some thinking and doing to derive the quadratic, or even πr² or something simple like how to remember 9's times tables rather than just commit a bunch of facts to memory but with definitions there is no "figuring out" per se you either know it or you don't.

Although with reasoning and logic you may use induction or deduction to figure out a word's meaning it's not quite the same as knowing enough algebra to solve for x when given a second degree polynomial in standard form set equal to zero.

ax² + bx + c = 0 and coming up with the quadratic formula...and just memorizing the quadratic formula. With complimentary angles and supplementary angles it is very difficult to deduce which one means two angles which when added add up to 90 degrees and which one means two angles which when added add up to 180 degrees, unless you know quite a bit more English than the average highschooler has at their command...you either know what "table" means or you don't. Same with complimentary angles and supplementary angles. Don't confuse memorizing definitions of words or terms with wrote memorization of formula.

Now once we have the definitions down we can start to do some simple problem solving.



Turns out this stuff was super easy after all. We also covered distance formula which as just slightly advanced Pythagorean Theorem and a few or math terms and definitions that come with geometry like parallel and perpendicular, and then the names of angles, and poof, a few problems and the hour was over.