December 14, 2018

Archives for 2013

Apex-Math Videos

I hope to keep my videos:

  1. personal
  2. short
  3. organized
  4. study-ready

Personal:  I want to reach of you as a person, like it is a conversation between just you and me.  I am a veteran teacher and tutor.  I am going to try videos from both angles, on a large white board in front of a class and on a small white board, like we were tutoring one on one.

Short:  Each topic that I want to present, doesn’t need to be long and involved.  I want to get to the point quickly and do many videos.  Each one will allow the topics to be broken down into smaller pieces and some videos will need to be grouped as a cluster to grasp the entire “unit.”  For example, I will teach all the pieces that go along with graphing a quadratic and have one or more videos where I pull all of that together, those videos will assume mastery of the previous videos, but this will allow me to keep each video reasonably short.  No one wants to sit for an hour at a math video!  Let’s learn what to do and move on.

Organized:  Staying organized in mathematics is very important.  I encourage each of you to take notes and stay organized with me!

Study-ready:  Teachers don’t teach students how to study for math tests.  I want to provide individual videos on this topic as it is so important but also provide study notes for the student in each video.  Write down the steps, you will need them.  Very few teachers break down the information, they do an example but all those steps run together, we will always break it down and make notes about what to do.

Topics:  I have so many ideas of topics to do but eventually will start taking requests so that I can help each of you as the school year goes on.  You can always suggest a topic in the comments section of You-tube or emailing directly.  Be sure to like my videos when you leave comments and requests.  There is so much math to get to… Kindergarten through Algebra 2 is my goal but my first videos will start with middle and high school mathematics, especially some of the harder topics that don’t need to be so hard!

 

Changing Math – One Video at a time

Everyone is born with gifts.  Some people are talented at art, some are great “people” people, some are helpers who give to the needy and feed at the soup kitchen.  We all have gifts and we should use our gifts to help make the world a better place.  My gift, from the time I was a little girl, was to teach.  I can teach anything.  I can learn something one minute and teach it the next.  I have the ability to analyze something and break it down into smaller pieces that make it more understandable for people.

I like to learn, I am good at learning, and I know how to take in information, process it, then I can change it to make it easier for other people  to learn.  There are many things in this world that people learn, some are easy and some are more difficult.  One, however, that seems to come naturally for some and not for others is mathematics.  Often those who are born with the ability to understand mathematics are not also born with the ability to understand that it is not as easy for everyone else.  In fact, this very idea creates one of the biggest problems in today’s education.  Just because you understand something, very well and it makes perfect sense to you, doesn’t mean you are also able to explain that information to other people.  It is likely that you can explain the information to like minded people.  Those that grasp math easily, learn math from math teachers who are “okay” at their jobs.  They may even learn math from those that are “terrible” at their job.

However, we have many people in this world who just don’t understand math as easily as others.  It falls on a spectrum, some might be very lost when it comes to grasping math concepts while others can get there if they have strong teachers.  However, all that fall in the category of the “less mathematically minded” struggle without strong math teachers.

So why do we have math teachers that are great and amazing, some that good, some that are okay, others that are not so great, and some that are down right terrible?  Well, all the math teachers are most likely mathematically minded people.  Who would choose to teach math unless it naturally made sense to them?  However, some of those are just people who can do it easily but don’t have the gift of being able to break it down to easy to understand pieces.  Many don’t even understand that some of their student’s brains don’t work like their’s does.  Some are just in a job to get paid because it is easy for them but they have no passion or natural gift for education.  Hence, we get the large variety of math teachers in our schools.  The real problems happen when you get the not so good or worse, the terrible math teacher lined up with the student who really struggles to understand mathematics.  Math builds on itself, one bad step along the way and you can be turned off from math or left in the dust.  And remember, how many different  math teachers does a student get over their lifetime?  For those mathematically minded, what is the probability that a student will get a great/amazing or good teacher each year, year after year?

One misstep, that is all it takes to send a child off the math track.  Does our country do anything once a child shows that first sign of falling behind?  Not really and certainly not to the extent it is needed if we all had the goal to help all students succeed in mathematics.

So, I have been given that gift of being both mathematically minded and having the ability to see things from the perspective of the learning student.  I am also passionate about education, specifically math education.  I spend a lot of time watching how it all falls apart and wondering if one person can somehow scale to reach millions.  I look at what Khan Academy tried to do and it gives me hope but Khan Academy still falls in the “teaching okay,” category and if the world of mathematics education is going to get changed, it must be changed with exceptional explanations, by people who are truly extraordinary in their gift of mathematics education.  This is not to say anyone (myself included) is perfect but part of doing what is right is listening to feedback and making adjustments when your goal is not being achieved.

It is time, therefore, to start one video at a time with content that teaches mathematics in easy to follow steps that a student can not only learn math from but learn how to study math.  In my next post, I will address the goals of my videos and I always welcome comments and suggestions!

Common Core Math 2 – Geometry Unit 1 Vocabulary

As I begin to help students at , a tutoring center in Apex, NC prepare for Common Core Math 2 / Geometry, I have decided to include some of the material online to make it available to all students who are beginning this course. The first thing that a student needs to know about Geometry is that one must learn all of the vocabulary and theorems in order to be successful. There is no other way to be successful in this class. Therefore, I will start with a list of the beginning vocabulary that one should learn and focus on as they begin to study for this course.

Line – Most students know what a line is but it is important to note that a line has arrows in both directions, note it is different from a line segment that terminates with end points.

Line Segment – A part of a line that terminates with a point at either end.

Ray – A mix between a line and a line segment, one end has a point, the other end an arrow.

Plane – Think of a desktop that continues infinitely in all directions.

Co-linear – Points that are co-linear would be points that fall on the same line.

Midpoint – This is the exact middle of a line segment, it divides something into two equal halves. The formula for calculating a midpoint doesn’t need to be memorized if you just remember that it is the average of the x-values and the average of the y-values.

Acute angle – A “cute” small angle that is greater than 0 degrees but less than 90 degrees.

Right angle – An angle that is exactly 90 degrees. We put a box in the corner of the angle to show it is right. In Geometry, we cannot assume an angle is right just by looking at it, if we don’t have proof or see the “box” we cannot assume it is 90 degrees even if it “looks” right.

Obtuse angle – An “obese” angle or fat angle, one that is greater than 90 but less than 180.

Straight angle – A angle that forms a line and measures 180 degrees.

Complementary – Two angles who sum to 90 degrees.

Supplementary – Two angles who sum to 180 degrees.

Adjacent angles – Angles that are next to each other.

Linear Pair – Two adjacent angles that are supplementary.

Bisect – Something that cuts into two equal pieces such as an angle bisector would cut the angle into two equal pieces.

Vertical Angles – Angles opposite each other (often form an X) – vertical angles are complementary.

Perpendicular Bisector – A line that bisects another line by hitting it at a right angle and cutting it into two equal pieces.

Distance between two points – Memorize distance formula or learn how to use the Pythagorean Theorem to find the distance between any two ordered pairs.

Perimeter – Distance around an object.

Circumference – The distance around a circle: C = PI X Diameter.

Area – The space inside a shape.

Radius – The distance from the center of the circle to the one end of the circle. Radius is half the diameter.

Diameter – The distance from one side of a circle to the other going through the center of the circle. Diameter is twice the radius.

Addition Property of Equality: When you add the same number to both sides of an equation, it doesn’t effect the equality of the equation.

Subtraction Property of Equality: When you subtract the same number from both sides of an equation, it doesn’t effect the equality of the equation.

Multiplication Property of Equality: When you multiply the same number to both sides of an equation, it doesn’t effect the equality of the equation.

Division Property of Equality: When you divide the same number to both sides of an equation, it doesn’t effect the equality of the equation.

* The above four properties are what you do when you solve an Algebraic Equation such as: 2x – 5 = 11 (add 5 to both sides: Addition property of Equality, then divide both sides by 2, Division property of equality).

Substitution Property: If two things are equal you may substitute one for the other: measure of angle 1 = measure of angle 2 and measure angle 2 + measure of angle 3 = 180, since measure of angle 1 = measure of angle 2, I can SUBSTITUTE the measure of angle 1 into my other equation making it: measure of angle 1 + measure of angle 3 = 180.

Transitive Property: (Remember as the 3 piece property) If a = b and b = c then a = c. If the measure of angle 1 = measure of angle 2 and the measure of angle 2 = measure of angle 3, then I know that the measure of angle 1 must also equal the measure of angle 1.

Reflexive Property: (Think Reflection): a=a Something always equals itself. It may seem obvious but is needed in proofs.

Angle Addition Postulate: If you have a big angle divided into two pieces the two pieces add together to equal the total angle.

Corresponding Angles: When two parallel lines are cut by a transversal, the angles that correspond with each other are congruent.

Alternate Interior (and Exterior) Angles: When two parallel lines are cut by a transversal, the angles that are on opposite sides of the transversal line but are both inside (or both outside) the parallel lines) are congruent.

Same Side Interior (and Exterior) Angles: When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal line but are both inside (or both outside) the parallel lines are supplementary.

Remembering Congruence of Angles: Vertical Angles, Corresponding Angles, Alternate Interior (Exterior) Angles
Remembering Supplementary Angles: Linear Pairs, Same Side Interior (Exterior) Angles

These are the vocabulary words one should first learn and also be able to apply to concrete problems and proof situations as they start CCM 2 / Geometry! Good Luck!