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.
