by Chuck Summers | May 2, 2015 | Math
Slow and Steady…
While aptitude may have something to do with your success in math, hard work and perserverance trumps any natural ability that you may have. There is a principle called the slight edge that teaches that idea in a big way.
Simply put, the slight edge says that with small incremental advances over time, you can achieve huge results. It also says that if you put in a little more effort daily than the average student in practicing math, you will be many times better than they are over time.
Say, for instance, your friend who is awesome at math, spends only 15 minutes a day on his math homework and none on practicing previously learned material. You, on the other hand, take longer to do homework, BUT you spend 15-30 minutes every day practicing what you have learned, and you will soon find that you will surpass your friend in math awesomeness.
This principle applies to everything you want to have success in. For example, if you only read 1 minute of night in a particular subject, you will have read 8000 words in a school year, while if you read 20 minutes a day, you will have read 1,800,000 words! That is a huge difference, and you will be becoming an expert in that field. Studies have shown that students who read every day for 20 minutes will have larger vocabularies, and much more success in school and life assuming the subjects are positive and practical.
Regards,
C00lnerd
by Rebecca Mayer | Apr 23, 2015 | Math, Teaching and Learning
The Socratic Method is a form of discussion based on asking and answering questions to stimulate critical thinking. When teaching a student a new topic, it is important to make them think about what they are learning rather than just firing information at them that they may or may not absorb. If you go about teaching as more of a discussion, then not only does the student retain more knowledge, they also feel more included in their own learning.
When using the Socratic Method with tutoring or teaching, asking questions to fuel the students’ thoughts helps them explore the topic further to reach a better understanding. In addition to this, asking questions that require more than a yes or no answer will help the student create their own thinking process to figure out questions rather than you just telling them the answers. This way, when they end up in a situation where they don’t have your help, say when taking the test, they will have already established their own process for solving the question and won’t feel lost without your guidance.
Another important aspect of the Socratic Method is checking students when they get answers wrong. Rather than just telling them they’ve arrived at an incorrect answer, ask them why they think it’s incorrect and what they think they did wrong. This will help them later to be more aware about when answers are wrong so that when taking a test, they will be able to see their mistake easier and know how to fix it, or they will remember correcting their mistake during tutoring and won’t even make it. Teaching about wrong answers is just as important as right answers. If a student is just constantly told that they are getting incorrect answers, they won’t be able to understand where they make mistakes or how to get them right.
Question asking is an effective way to keep students aware of their learning and to let them be a part of it. They feel more involved, like they are even teaching themselves a topic. It is much easier to remember something if you came up with it on your own instead of someone simply telling you step-by-step how to do it.
by Nicole Dowling | Apr 18, 2015 | Math
Finding Your Way…
Calculus 1. Check. Calculus 2. Check. Calculus 3. Check. Mathematical modeling. Check. Linear algebra. Check. Modern algebra. Check. Differential equations. Check. Probability & statistics. Check & check. …I have only three “checks” left before I receive a piece of paper saying I’m a somebody in the political world.
At least that’s the mentality I had for awhile before I realized why the heck I’m putting myself through a mathematics degree…
We all go through that BiG QuEsTiOn phase in our lives; that moment when you realize the thing you’ve been forcing to work for so many years is actually not the right path for you. And that’s okay. But it’s taken me about a year to accept my change. This is a personal story.
My freshman year in college my mind was so..well..fresh, so ready to soak up All The Maths! My interests were all over the place: fractal dimension, fluid & air dynamics, physics, graph theory, topology, sacred geometry, knot theory. I’ve been fascinated with how this world fits together and, more impressively, the constant dance of each system moving as a whole. I wanted to learn it all! I even stretched into areas like molecular structures, artificial intelligence, philosophy of mathematics, cause & effects of human behavior, sociology, economics, anatomy. ANYTHING that incorporated mathematical thinking in some form or fashion. But by the time I was a sophomore I barely had any energy left to breathe! So I made it by doing the bare minimum for a while. Perhaps it’s not the best decision to present your faults, but from time to time it shows us all that we are just…human.
So what happened?
Well, all my interests has one underlying pattern: analyzing theoretical possibilities at its most fundamental level. AKA, the infinite! No wonder I was drowning. I love exploring possibilities, but I am not a theorist. Maybe one day, but not yet.
Now I still consider myself a child of wonder when it comes to mathematics, but its not all rainbow daisies and frolicking unicorns. There’s hard work involved. There’s pain and sweat and tears involved. My relationship with mathematics was on the rocks and I thought about breaking up with it for an insane moment there. So I took some time away from the usual, I took time to myself for awhile and not what mathematics demanded of me. I matured more during that time, this time, than I ever had/have before. I am pleased to say that our relationship is so strong that I couldn’t possibly live my life without it. So we made up (good thing too because that graduation date is approaching), but there were conditions. Instead of beating myself up for not being the theoretical analyst I thought I was preparing to be in grad school, I took the path as a mathematical communicator. I am a mentor for those who cannot see the connections I can; I have a gift of visually expressing these fundamental concepts that are so important in logic. Sometimes all it takes is a new approach, a different way of looking at something that was seemingly so complicated to understand why it is what it is. I am just another piece of the puzzle, but an important one. We have the ability to connect ideas in milliseconds with our advancements in technology, but we need to know how to use our tools. Like my crazy professor says, “The day they make a calculator that can do mathematics I want to be first in line.” Anyone can compute, but it takes a special care to do MaThemaTics.
by Katie Boswell | Apr 11, 2015 | Math, Teaching and Learning, Testing
A Little Gold Star
How many of you parents remember the work you would do for one of those little foil stars? I can remember practicing a song on piano over and over in hopes that it would gain me that tiny little seal of confidence. And when I did earn one, the next week I’d practice twice as hard because I knew I could earn one and had to prove myself once again.
What was it about that star that made me work? It certainly wasn’t it’s monetary value or glamour. It was the pride that came with knowing I could do something. Every other week I accomplished my songs, but that week, I was a star!
Do you know the role your positive words play in your students’, friends’, coworkers’, spouse’s, tutor’s lives? Your role is huge in your child’s education, even if you never look at a piece of homework. Encouraging them to score their best, without berating them over less than stellar grades can make all the difference in the world. I would never be where I am today without my mom telling me how proud she was of my grades, piano playing, crafting, etc. Now I was never good at cleaning my room, so she chose not to focus on that flaw, as she knew I could make it to adulthood with clothes on the floor, but I couldn’t without my education.
As MaThCliX test prep coordinator I spend quite a bit of time encouraging students to use their own abilities. I find so many of the skills a student needs to excel on the ACT and SAT are within them, they just don’t trust their instincts and chances are, someone along the way chose to point out all of their mistakes and not their strengths. I am not at all saying students do not need to know their mistakes or to work on where they struggle (that’s why we’re here!), but the approach is key. A conversation started with confirmation of what is done right, is going to be received a whole lot better than one that begins with everything someone fails. I see students with the same abilities and different confidence levels score drastically different.
I want to close with some tangible ways you can encourage your children, coworkers, peers:
1. Commend good behavior
2. Spend more time with praise than discouragement
3. Work on things like vocabulary together as a family, make it fun, a joke even and laugh together when you use it!
4. Talk about areas of weakness as how you can improve, rather than focusing on it being a poor area
5. Don’t use powerschool only to ground your child, but also as a bragging point
6. Ask your child’s tutor what they did well, so you can discuss
7. Keep in mind, we all have different skills and abilities. If one child isn’t doing what another did, encourage them to do THEIR best and do not compare to others!
by MaThCliX | Apr 2, 2015 | Math, Teaching and Learning
When I was a graduate student, I was very serious about my work and committed to making A’s and doing my best. While taking a graph theory course, I remember working hard daily to learn and Learnunderstand the many proofs coming at us each week. I knew that I would never be able to reproduce any of these proofs on a test if I didn’t learn them and understand each step involved. To help me with this endeavor, I purchased the poster-sized Post-It Notes and carefully wrote out each proof in different colors. I hung them all over my apartment walls; they became my wall art for the time being. I studied them day and night as I spent time at home. I practiced writing them out on my own to see if I truly understood it and to discover what I might not understand. I think it is safe to say that I put forth a great amount of time, effort, and sacrifice. However, it paid off because I made very high A’s on all four tests and was exempt from having to take the final exam! In addition, I can honestly say I learned the content of the course.
I currently teach college algebra and while helping my students get prepared for their upcoming test, I was telling my students the above story about my efforts in graph theory. I was using it to demonstrate that to learn something we must work and put forth effort. Afterwards, one student even made the comment, “You’re like someone on the Big Bang Theory or something!”. Of course I laughed and took that as a compliment.
It occurred to me, at that very moment, that there are so many students out there who haven’t a clue what it means to work hard. It may sound simple, but for me, it was one of those “a ha” moments—-Learning requires time, effort, and sacrifice and it is every bit worth our time, effort, and sacrifice! The knowledge and experience that we gain and the discipline it takes to acquire it is invaluable and can build our character in ways nothing else could. I look back on my college days of hard work and stress and many moments of confusion and cherish it as a special time that shaped who I am today.
I encourage all students working towards a worthy goal to know that it will all be worth it in the end! Keep going!
by Aaron Sandlin | Mar 2, 2015 | Math, Teaching and Learning
One of my math professors always insisted on showing us around thirty minutes of why a concept works and how to get the formula that we use in the final product. Once he showed us the short cut (formula) the work went from ten minutes of calculating to ten seconds. Back then everyone groaned about the “waste of time” but now that we are free of his tyranny, we are coming into contact with the “formula people”. They are the folk who panic every time they have to use an old concept in a new way. Why are they so unsure? It is because they were told to take the math on faith. They were taught that “It just works” and that was okay for them. My math mentor would routinely go through some fake absurd process on the board and watch the majority of the room follow his false trail. He awarded bonus points to anyone who rightfully challenged him by understanding the concept and working it out for yourself. The sad thing is that for my entire education until now the teachers taught instead of mentored.
It wasn’t until I was 29 yrs. old that I finally experienced why any number raised to the zero exponent is one. See my short video explanation, Powers of 0 and 1. I had been told that it was one and sent on my way, just relying on my memory to retain that knowledge. After a long gap in school between high school and college, I had forgotten even that simple rule. I have often heard that math is not like riding a bike and I have said it myself. You have to keep it up or the knowledge melts away. Could we be wrong? When I think back to my trigonometric identities, I can’t remember them! BUT, I remember one concept that was experienced and I can reliably derive the rest of the identities from that one branch. Think about bikes for a minute. Did you get tested on the methods of balance? Were you drilled on the names of a bicycles parts and their purposes? Was everyone made to ride on standardized bikes and had to all learn at the same pace? Do you recall the physics class you had to pass in order to take your training wheels off? How is it that just about anyone who ever learned the difficult task of riding a bike can go for years without practice and still retain the skill? It is because we all experienced the process of learning instead of memorizing the concept. I bet a shiny nickel that anyone who had never learned how to ride a bike, but had studied it in a book, would not remember the necessary information needed to describe the process to someone else. Years ago I had memorized the algorithm for solving a Rubiks Cube. Give me one today and I can’t do it! I failed to develop the fundamental experience necessary to achieve mastery of that skill. If you want to learn mathematics instead of memorize formulas, you need to know the why that sadly is too often left out in s foolhardy quest for time and effort savings. So the next time a “teacher” asks you to memorize a formula, be brave, and ask “why?” and turn them into a mentor.
by MaThCliX | Mar 2, 2015 | Math
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.
by Nicole Dowling | Feb 25, 2015 | Math, Teaching and Learning
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.
by Rebecca Mayer | Feb 19, 2015 | Teaching and Learning
I am new to tutoring and I have learned many things during my start. I have learned that different students need different types of teaching and different ways to grasp topics fully. It is generally important, for all students, to make sure they are confident in what they are learning. Knowing your student is an important aspect of tutoring. Using differentiated instruction, you are able to learn what your student needs and adjust to provide them with tutoring specific to them.
Differentiation is giving students multiple options for absorbing information. As you teach a certain student, you should observe how they respond to your methods and start to understand differences and similarities among students in order to respond to a variety of student needs. This way, you are able to modify the content you teach and the process you teach it to offer them a chance at full understanding. Since every student is different, this process will be different every time you teach. I have learned that when tutoring different students, you have to learn how to tweak your method so it is effective for all of them, since the same method that helps one student understand something might be completely confusing to another student.
An important thing to remember when varying teaching methods is to continue to assess how the student is responding and to make sure that you are always effective in the way you teach. If you use the same method for a student every time you tutoring them, you leave no room to realize if they need an adjustment or if they stop understanding something fully. For example, if a student works really well when they can work out problems with you so they can make sure they follow all of the steps correctly, eventually they will gain a more concrete comprehension of what you’re teaching and they will need you to draw back and let them solve it on their own. It is essential that, as tutors, we are able to see when this happens and know when to let them do things by themselves instead of using you as a crutch.
Also, once the student gains a better grasp on the content, they should be pushed further to challenge their understanding and go deeper into the topic rather than sticking with what the “book” wants them to know. If they expand the range of their knowledge, they will be more confident to do the simpler things.
No two students learn the same way or have the same abilities or needs but they are all working towards the same understanding or goal. They have to reach the same place but the method or path they use to get there might be completely different. It is important that we learn how to send them down the right path by structuring a teaching style suited for each individual student’s needs.
by Tracy Porter | Jan 20, 2015 | Math
I 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!
