MaTh as One Whole Truth

Math Truth

When working with students I often get asked the question, “How do you know all of this?” or “How do you do math so well?”.  I feel the answer to these and similar questions is just as simple as it is for anyone learning to do anything.  When you study something thoroughly enough, you begin to piece everything together as one whole truth, if you will.  In other words, when we focus on math as one whole truth and refrain from getting caught up or lost in the steps and procedures and forget what we learned, we begin to understand how each lesson (or piece of truth) is preparatory for the next.  Think of it as a cake with infinite layers and each layer necessary before the next.  If a layer is missed, then the next layer will not fit quite right.

I am not sure why, but I notice far too often, that students “learn” math, take a test, and then forget it.  When you show them or discuss a concept that they already “learned”, they often act like they have no clue what you are talking about.  At some point, they must approach math as a whole subject and put the lessons together. 

For example, think of a knitting a sweater.  One might knit an arm, front, back, etc.  At some point, in order for the end result to actually be a sweater, it must be all pieced together. 

Or, one can compare it to learning to drive.  A new driver might study operating car controls, learning laws and road signs, parking techniques, interstate travel, backroads, night-time driving, etc.  Any one of these lessons standing alone will not create a skilled driver.  Nor will doing any of these things just once or twice.  It’s in the actual piecing together of the skills and practice of driving in each area, that one becomes a skilled driver.

So it is with mathematics.  To my elementary students, learn what you are doing now very well, because you will never stop using it in the progression of your mathematics study.  Middle school students, what you are learning now is preparatory for high school mathematics.  High school students, by now I hope that you are starting to piece together this beautiful subject of truth called mathematics!  What you are learning is a culmination of all of your earlier years and preparatory for you to advance in further mathematics.  There is always more to discover and learn and the further we go, we begin to see the subject as one whole truth.  Our perspective and understanding is enhanced.

Thus, I would suggest as a final answer to these opening questions is that I have learned to understand math and not just memorize it.  So, I approach it by applying all truth that I know and putting the question in context, then solving.  I have spent much time doing and practicing and that is “how I know all of this”!  Anyone else can, too.

Student’s Point of View

Effective Teaching Style

Have you ever thought about your teaching from a student’s point of view?

Now that I am a senior at Kennesaw State University, I have experienced a plethora of time in the classroom. What makes a class period more enjoyable? How do we, as students, get involved EVERY time we enter the room? As many of you have probably noticed, there are effective ways that teachers teach…and not so effective ways. Lets be honest, when the teacher isn’t engaged in the topic he or she is monotonously speaking about, then why should the rest of the class be? What a waste of time for everyone. And let me share a secret: learning takes time.

How many have been frustrated with a teacher that doesn’t teach well, or worse, doesn’t teach at all??? Responsible students are, then, forced to be both the teacher and the student. And we’re not even the ones getting paid! Math that. Or how about this scenario: learning something wrongly and then having to go through the painstaking process of breaking that bad habit by UNLEARNING that something, only to have to go through even MORE practice to set the new good habit in its place. Whew! That’s an awful lot of work that could have been avoided simply by effective teaching.

Please enjoy the following experience from a fellow student, me:

I loved going into my Real Analysis course because my professor would get so enthusiastic about his subject that he spat everywhere when he went off on a tangent. (Ha, math jokes.) Sitting in front of his laptop, he would write his lesson right before our eyes. “Mathematics should come from the heart,” he would nearly whisper as he was deciding on which way to prove something. He emphasized that great mathematical writing comes from good grammar: “Mathematics is hard enough when written correctly. Proper grammar makes the math easier.” His tips on proof-writing bleed into all areas of my life because quite frankly I have little skill in the matter. But I digress.

Some days I just wanted to listen to a good story after a long day of rigorous studying, and his class was just the relaxing break I needed. As it always should be with learning: first, soak in new material; then, play around with it in one’s personal time. “The learning happens outside of the classroom, when you DO the mathematics” as my professor would say. For this reason he records all of his lectures with a video & audio software. Actually, he requires that NO ONE take notes.

How many have tried to fiercely write all of what the teacher said or wrote on the board? So much room for error: what with constantly looking up and down and up and down, or comments meshing into each other, or not hearing everything because you were too worried about writing down the previous thing… Whew. My hand hurts just thinking about it. However, with a recording you have the notes you need, VERBATIM. A recording also sets the standard for the teachers to be professional and not slack off, because no one wants to look bad on camera ;)

~Now teachers here is a question for you: Would you want to be a student in your own class? ReadRebecca’s blog for more on this topic.

The Basics

math basicsI have been teaching math for many years now and have taken more college math courses than I can count on my hands and toes!  I remember being in the 3rd grade and winning the times tables game every time as we raced around the room.  I have never struggled with fractions and computing arithmetic, nor needed to rely on my fingers to figure out problems.  Is this because I have a “math gene” or I am a math whiz or some genius?  The answer is no!  So, why am I “good” at math and why have I always been this way?  The answer is simple and I try to teach my students this continuously. 

Think of math as a never ending gigantic cake with an infinite amount of layers, where each layer is necessary and preparatory for the next one.  Each layer represents a skill that must be mastered before adding a new layer.  So, in terms of the cake, I have mastered each layer!  Well, how does one master each layer?  I answer this question frequently…three most important things…I look for patterns, make connections, and I practice.  Many students think that doing a few problems or watching the teacher do problems is sufficient.  To this I say, NO, NO, NO!  It is in the doing of the mathematics where the learning takes place.

So, what about all this talk about getting kids away from learning basic math facts, like times tables?  The argument is that with computers and calculators, the need for higher level thinking is more important than just producing an answer.  While I believe there is truth to this and could write a quite a bit in agreement with that statement alone, I certainly do not want to discount the importance of teaching youngsters to compute!  There is evidence that suggests that students are not learning how to compute.  I see it daily in my student interactions.  Research suggests that youngsters who have not mastered whole-number arithmetic by the end of the fourth grade are at risk for becoming remedial math students.

I completely contribute my mathematical success to having a solid foundation with basic skills.  Arithmetic is the starting point in mathematics and basic skills are necessary to advance in mathematics, which includes critical thinking, problem solving, and communication of mathematics…All things computers cannot necessarily do!  Without a foundation of arithmetic and basic skills, students will not be prepared to progress to algebra in middle school, middle schoolers will not be prepared for advanced mathematics in high school and our high schoolers will go off to college ill-prepared to be successful in mathematics and in the workforce.

In my opinion and from all my experience and training, the better a child learns all the basics and recognizes patterns and makes connections, the better prepared the child will be for the next layer, and so.  Every layer in mathematics is important.  It is all part of one great whole!

Mathematics in the World

math in the world quoteThinking de about a career in mathematics may lead some people to think only of math and leave out the other three fields empresa in which math is a cheap mlb jerseys critical player. These fields are science, technology, engineering and mathematics and they are acronated as the word STEM. All of the hundreds of careers that fall under the STEM banner are How laid on wholesale nba jerseys the foundation of fotograflar? mathematics. I want to become an electrical engineer Vision and then progress towards quantum physics with a research scientist career for cheap jerseys government research facility such as NASA, the National Aeronautical Space Agency, or cheap nfl jerseys for Prepare a university like the Georgia Institute of Technology.

Everyone that wants to advance our understanding of the universe, or find a faster or cheaper way to manufacture Slinkys must still study math first. If you want to be the person to find a way to verbally communicate with dolphins, first you must know math. If you want to be a financial professional like an accountant, actuary or market analyst, first you must know math. Math is the concrete that we build all manner of buildings upon. Yes, mathematics can be difficult at times, but that is it’s strength. Anything that is built on something easy will not stand against something hard. Any job you can think of as part of a business or field that has been developed or is maintained by people who have the strong concrete foundation of math. Do you work at McDonald’s? Someone used math to find out how to efficiently feed millions of people in a way that is predictable, enjoyable, and not costly. Are you a game warden? Someone used math to map migration paths for the animals you need to be protecting and they used mathematical population growth models to determine how many hunting licenses to issue which fund your position. Geologists might even save your life by using math to correctly predict and warn of a volcanic eruption in your park. Are you a truck driver?  Without engineers designing strong bridges to open up more shipping routes or more fuel efficient trucks, your company would not have the ability to hire as many drivers.  Can you see how valuable someone skilled in math is to all of those who are employed in various fields? That value comes with a hefty price tag. The skills of those well versed in mathematics are in short supply and the demand is strong and in every corner of the  economy.

How to DO MaTh

Carlie Working

How to DO MaTh-

1. First, GET ORGANIZED.  You need a place for your MaTh!  Put together a notebook that includes a place to write down assignments and important dates, a place for notes, homework, and returned papers.  Keep it in sequential order and know where everything is so that you can refer back to it.  There must be order in the chaos of learning!

2. In Class, take notes.  Ask questions.  Do your homework and and all assignments.  Compare with other students, if necessary.  Make marks by questions that you did not understand and ask about those problems.  Correct any mistakes that you find and understand what you did wrong.  Once you have done it enough and you think you understand, try teaching and explaining to someone else.  If you can teach it, then you can be more confident that you actually understand it.

3. TAKE THE TIME TO BE NEAT AND COMPLETE.  Many people think that MaTh is just about the answer.  However, the process is often just as important and so, that is why students always hear “Show your work”!  Write the problem down, show each step and circle or box your answer.  This will allow you to go back and see your work, as well as your teacher or others.

4.  STUDYING IS DOING!  PRACTICE, PRACTICE, PRACTICE.  Do not think that if you understand what your teacher is doing and can follow along that you, too can do it.  Also, do not think that if you can do one or two problems that you have done enough and do not need to do anymore.  Learning MaTh means DOING MaTh!  You must do it for yourself repetitively.  That is how the connections of understanding are made and that is how you know if you can actually do it on the test.  MaTh is not a spectator sport!

5.  Understand TWO things:

1) Learning MaTh is like a giant snowball rolling down a hill.  It gets bigger and bigger.  In other words, once you learn it, it stays and you will use it in the future.  So, there is no place for learning MaTh just for a test and then thinking you can forget it.  It is a collection of skills that build into a giant “snowball”.

2) Everyone can DO MaTh!  There is no such thing as not being able to do MaTh because your parent wasn’t good at MaTh.  Confusion and struggle are normal parts of learning.  They are not going away.  However, determination and persistence will carry you through to success.

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MaThCliX Story and Vision

Ellie Working

MaThCliX Story and Vision-
On October 28, 2014, I had the opportunity to speak at career day at Woodstock Middle School and E.T.Booth Middle School, both in Woodstock, GA. Thanks to the Cherokee County Chamber of Commerce, I was honored to be a part of this special day and share my love and passion for mathematics, learning, and business with so many young minds. I spoke to 12 different groups of 8th grade students throughout the entire day and basically gave the same presentation each time. I had it down by the end of the day!

I shared with the students my story and how MaThCliX came to existence. The name “MaThCliX” came about around the year 2000, when I was an undergraduate math student at Georgia State University. As a college student, I did a lot of tutoring and would always hear people making comments like, “I’m just not good at math”, “My parents weren’t good at math”, “I never really understood math”, “I had a bad teacher and could never get math to make sense”, etc. I realized quickly that there was a large amount of the population who just had this fixed “attitude” toward math. I knew that these things were things that could be remedied, if only math were taught in a manner that each student understood and if the student practiced math correctly. It then became my thought that I wanted to make math “click” for others.

Another play on the word “click” comes in the version of “clique”. At the university, the math majors tended to stick to together and I guess you could say we formed a “math clique” as we worked intensely to study and prepare for exams, learn and understand proofs, and work countless math problems.

So, why the capital M, T, C, and X? Why Clix and not clicks or cliques? Well, I chose to use clix because it seemed to be a fusion of the two and is shorter and a bit catchier. The M is capitalized because it is the name, the T is for my name, Tracy, the C is for my first daughter, Carlie, and X is for the most popular math variable, X! It may sound complicated but I thought it gave the name a “cooler” look and if it were to be on signs, t-shirts, brochures, etc., I wanted it to look appealing.

So why the two slogans “A place where students DO math” and “Math Problems Solved”?

I wanted MaThCliX to be a place where all students can come and be part of a math family, if you will. I wanted to create a math home. A place where students can come and have their math needs met, whether it be working on homework, skill building, enhancing understanding, etc., all of which enable students to eventually DO math. I follow the counsel of Maria Montessori who said, “The greatest sign of success for a teacher is to be able to say, the children are now working as if I did not exist.” This is when I know that students are “doing” math.

What is your math problem? For some it may be a failing grade, for some it may be a gap in learning, or some may literally be stuck on solving a math homework problem. Whatever the “problem” may be, MaThCliX is a place where any student’s math problem can be solved! I want everyone who walks through our door to feel comfortable, welcome, and at home and when they leave I want them to feel that their time was well-spent, their minds were enlightened, that the math “clicked”, and they are one step closer to their academic goals and on their way to success in the classroom and the world. I want our students to feel proud and happy to be part of MaThCliX, or our “math clique”.

I invite all students to come an experience MaThCliX!