by Rebecca Mayer | May 4, 2016 | Math
Being a student is hard, stressful, and time consuming. This is a small list of the most important things I have discovered over time that I believe are the most beneficial things a student can do to be successful, without all the stress.
Time Management and Procrastination
Time management is a big part of high school success. Having a lot of homework to do and the motivation to do it will only get you so far unless you plan out the time to actually complete the assignments. High schoolers are notorious for busy schedules, being a part of sports and countless clubs, students often find it hard to set out time to do homework. This is when procrastination becomes a big problem.
Waiting until the last minute to complete homework is how bad grades appear because the work is not the best it could be. Creating a weekly schedule that lays out when all due dates are and when you have time available for doing work can go far when trying to be successful.
Start out each night with the things that are either due the soonest or the hardest and most time consuming. You don’t want to start with the easiest thing and then not have the motivation or time to complete the rest. Setting out enough time to complete all assignments well is the first step to getting good grades.
Note Taking
The main problems students have with studying for tests are that they don’t understand the textbook or the online notes that the teacher provided. The issue is that the words in the textbook are about as complex as the information gets, and you might not understand all the words it uses or all the material.
Bringing a notebook to class and some colorful pens will help with note taking in class. Don’t write down exactly what the teacher says, instead reword it to be in your own words. This way, when you’re studying, you will know exactly what the paper says and studying your own notes will help you remember what the teacher taught.
Use whatever note style best suits you, whether it’s bullet points or drawing a lot of pictures. Also, using colored pens and highlighters all over the paper will help you remember the material more on the test. Usually, when I read a question on a test, I am able to picture where it was in my notes.
Organization
It is very easy to let that school binder get bogged down with all of the papers students get daily. This makes it very easy to lose assignments, misplace papers, or crumple them. The best way to keep your binder organized is to put in colored pocket dividers, one for each subject.
I like to coordinate the colors of the dividers in my binder with the notebooks and folders for each class, so math has a green divider and a green notebook. This way, when I’m in math, I can flip to the green divider and all of my worksheets will be neatly placed in the folder, not shoved into my backpack. Then it’s easy to reach for the green notebook to be prepared to take notes and turn in homework.
Doing homework after school is also easier and less time consuming. When you’re able to grab an assignment out of a colored folder, where you know it will be, it makes it easier to start that homework and get it done.
Get to Know the Teacher
Or maybe I should say let the teacher get to know you. Sitting in the front of the classroom is one of the main signs to a teacher that a student is in their classroom ready to learn and succeed.
Asking questions in class can make the teacher feel like you care about their class and the subject, and most importantly, that you believe the teacher can successfully teach you, and you value their opinion about the topic.
Going to your teacher’s tutoring sessions can also help the teacher get to know you. When studying the night before prepare a list of questions you have, so you can make the most of the teacher’s time during sessions.
Getting to know the teacher and spending time showing that you care about their class will help you because the teacher will be more willing to help tutor a student that they like, and that they know cares.
Stay Positive and Motivated
Getting a poor grade on a test is not the end of the world. It is all part of the learning experience.
When you do bad on a test in a certain class this tells you that you need to study harder for the next test in order to do better. The point of learning is to improve your skills and knowledge, not to start out a pro at each subject.
A bad grade on the first test of a class will not make or break your high school career. All the grades will get buffered out by the tons of grades you receive throughout the semester, so there is no need to stress about the very first grades you get. Do not let bad grades discourage you from continuing to try the rest of the year, and stay motivated to get a better grade on the next test!
Attempting to complete all of these success tips every day when you go to school, even just a couple at a time, can change your grades and the way you go through your education. It will certainly help your grades, and you will have a great learning experience.
by Chuck Summers | Apr 19, 2016 | Math
How to Reprogram Your Brain
You no doubt have heard 
the expression, “You can’t teach an old dog new tricks.” Well, it turns out you can. The human brain is quite elastic and can be molded and changed, even in older people.
Imagine a ski slope that has a fresh fall of snow. At first the slope is a dream come true because you have full control, and the slope is not too fast. As time goes on and more people use the slope, the grooves get deeper and faster because of ice build-up. You have less freedom to veer from the path, but you can go faster.
The Brain is similar in that you can purposely increase the speed of processing. The synapses that provide the connections within the pathways will shrink the gaps with more use. This will also add more synapses for the purposes you program your brain to do. This applies to whatever you want to learn, whether it be math, history or a language. Brain washing techniques use this to reinforce ideas that are being promoted, but you can purposefully do the same to yourself. It is no mystery that when you focus on a topic and repeat exposure to it over and over that you will master the subject.
In a study at Harvard Medical School it was found that not only was repetition of a particular task necessary to rewire the brain, just the mere thought of doing the task also had a similar result! Check out this article from Time: https://content.time.com/time/magazine/article/0,9171,1580438,00.html
“Mental practice resulted in a similar reorganization” of the brain, Pascual-Leone later wrote. If his results hold for other forms of movement (and there is no reason to think they don’t), then mentally practicing a golf swing or a forward pass or a swimming turn could lead to mastery with less physical practice. Even more profound, the discovery showed that mental training had the power to change the physical structure of the brain.
This is great news for those of us who think they aren’t smart or strong. Because we CAN teach “an old dog new tricks”. The neuroplasticity of the brain extends even into old age. Even with damage, such as a stroke:
“If a stroke knocks out, say, the neighborhood of motor cortex that moves the right arm, a new technique called constraint-induced movement therapy can coax next-door regions to take over the function of the damaged area. The brain can be rewired.“
There is a verse in the Bible that is useful in understanding this effect:
Philippians 4:8-9 (ESV)
8 Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is commendable, if there is any excellence, if there is anything worthy of praise, think about these things. 9 What you have learned and received and heard and seen in me—practice these things, and the God of peace will be with you.
The impact focused thought can have on your life is amazing. When you think on good things as the verse says, your brain rewires itself to be much more open to such things and less so towards others. If you want to have a positive outlook, fill your mind with positive thoughts. The inverse is also true, when you think “unhappy thoughts” you will bring these thoughts to fruition, and your brain will actually make it easier to have such thoughts in the future.
So what does this have to do with learning MaTh? For one, if you start training your mind to think in mathematical patterns, even simple ones, then your brain will rewire and accommodate your efforts. Practice with simple math puzzles and logical problems. If you don’t know where to start, we at MaThCliX can help. It will expand your mind and help you to learn other similarly patterned subjects. Attaching positive emotions to the process will also help your brain rewire It is more difficult to learn something you don’t like. There is a saying among motivational speakers: “If you think you can, or you think you can’t, either way you are right”. It seems that there is a physiological explanation for this phenomenon.
Reprogramming your brain for success is possible with focused effort, but you can do it!
by Melody Hailstone | Apr 19, 2016 | Math
Take Note
Remember being in class and the teacher warns, “This will all be on the test.”? Suddenly there’s a mad scramble for paper and pen, and you begin to frantically piece together what the professor just taught. Many of us have been there. Many still wait for some signal to take out their paper, but good students prepare for note-taking, write down key concepts, and review their notes right away.
Often a teacher will assign reading before a class so that the students are ready to discuss the concepts during the presentation. Taking the time to read the prep work in advance will give you an overview of what is being taught and help to direct your note-taking. You will be more prepared to understand principles and to ask good questions. A little time in advance will save time later.
There’s a difference between transcribing what the teacher is saying and actually taking notes. It isn’t necessary to get everything down in written form. In fact, trying to get each sentence may distract you from understanding what’s being taught in the first place. Remember that notes are an abbreviated version of the concepts. Consider organizing your notes into sections, with a place for questions and a place for a summary. Cornell note-taking suggests 3 sections: one down the left side of the page for cue words, main ideas, or questions; a main section for general information, diagrams, dates, key information, and formulas, with space at the bottom for a summary of your notes. Remember to date the page and provide page numbers to keep your notes in order.
After class, take some time to look over your notes and create a summary, identifying and defining abbreviations and acronyms. Giving it one more look before you move on to something different may give you the pause you need to correct something, make that handwriting legible, or add more information for a better grasp of the subject matter.
Some debate the virtues of taking notes directly to the laptop, with its efficient speed and navigation versus putting pen to paper. Many find that notifications from social sites and email are distractions or temptations to lose focus, while others can type much faster than they write. Whether you go for the modern approach or are comfortable with your low-tech, tried and true written page, keeping top-notch notes makes for sage scholars.
by Hanna Fleeman | Mar 29, 2016 | Math
With Spring Break fa
st approaching, you might begin to wonder, where do math tutors go on vacation? Times Square of course! Personally, I always prefer the beach, somewhere I can relax, read a book, do some math in the sand. But what about those who are completely dedicated to knowledge? Those mathematicians that not only DO MaTh, but explore the proof and people behind it. Where do they go on vacation? Where do they spend their free time? Now you may be thinking, “Well it’s obvious! In a lab! In the library!”, but mathematicians are people too; they strive to travel, to explore, to discover.
Some may think that the only place a mathematician can discover new things is in the infinite limitlessness of space, but trust me, not everyone wants to (or can) be hurled into space by a rocket traveling 20 times the speed of sound. In the future perhaps, but today? Not so much. So where do they go? Well, why not back to the place where a principle of math was discovered? Why not go see where Pythagoras lived? Or Galileo? Visit Einstein’s or Fibonacci’s hometown? So many people from artists to physicists draw inspiration from the things around them. What inspired these great people might do the same for the mathematician.
Let’s focus on Pythagoras to begin, since I believe most people are familiar with his most famous Pythagorean Theorem. In history he is known as the first pure mathematician. Born in 570 BC, Pythagoras traveled through Egypt, Italy, Greece and some say even India. He studied under Anaximander, and he was known to be an influence on Plato and Euclid (among many others). Can you imagine taking a pilgrimage through these places? As we are all aware, we may not be able to see exactly where he was because he lived so long ago, but a trip to see the Pyramids and a walk through an ancient Greek town might be just enough to inspire greatness.
How about Fibonacci next? Have you heard of the his famous sequence? In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, and as most mathematicians know it is pretty phenomenal, particularly because it can be found all throughout nature. You can see more about that here: https://www.youtube.com/watch?v=ahXIMUkSXX0. It’s extremely interesting, and not just to MaTh nerds. Fibonacci was born in 1170 in a town called Bugia on the coast of the Mediterranean Sea. He traveled extensively with his father (a wealthy merchant) around the Mediterranean Sea where he learned the Hindu-Arabic system and the arithmetic that accompanied it. He was a great influence on modern mathematics, introducing the Hindu-Arabic numerals (digits 0-9 and place values) in his book Liber Abaci, thus replacing Roman Numerals system throughout Europe. In the 19th century he was immortalized in stone with a statue now located in the Piazza dei Miracoli (where the Leaning Tower of Pisa is located). Now wouldn’t Italy make for an inspirational trip? You could even learn about a little bit of failed architecture.
Next, let’s find someone a little more modern: Einstein. And I know what you’re thinking, he’s a physicist, but math is a huge element of physics, so let’s just see what we can find. Born in Germany in 1879, he lived most of his early life in Munich, but he also traveled a lot (which is becoming synonymous with many famous mathematicians). He worked and researched in Italy, Austria, Switzerland, and the United States. Quite a road trip, right? It would be almost impossible for me to summarize Einstein’s papers here, especially since a lot of his theories are still in the works of being proven today, but I will leave you with this, Einstein was an incredible person, intellectually and personally. He felt a great deal of responsibility for Germany’s actions in WWII, and without him the Manhattan Project may have never come to be. I believe a pilgrimage to his hometown, the universities where he taught and researched, and his home in Princeton, NJ would be an amazing experience and inspiration.
All of these intellectuals lived (somewhat) just like us. They grew up with hardships and challenges and out of that came something beautiful. They answered (and created) some of this world’s greatest questions. So on your next vacation (mathematical or not), look around and wonder, “What can I learn here?”. Who lives there? Works there? Could the place inspire greatness? There is always something to discover. And who knows, you might just discover something great.
by Amanda Fagan | Mar 29, 2016 | Math
Why Math and Science Go Together
Many students wonder why they have to do math in their science classes. They are completely different subjects…. aren’t they?
The reality of this question is that math itself is a science. Mathematics is defined as “the abstract science of numbers, quantities, and shapes, and the relations between them.” This might seem strange to some people. Isn’t science the biology, chemistry, and physics we learn in school? It is, but in a more general sense science is knowledge about or study of the natural world. Science is a systematic way of learning. The systematic approach to learning is what we know as the scientific method.
Think of any way you do a math problem. For example, imagine how you would find the zeroes of any quadratic function by using the quadratic formula. You work one step at a time to plug the coefficients from the equation into the quadratic formula and then to simplify. After finding the zeroes, you can then plot them on a graph. Every algebraic expression is solved in a systematic fashion- the same way any scientific problem would be solved. Any math problem is solved one step at a time.
Now, compare this to the scientific method. The scientific method begins with a question, which leads to a hypothesis. This hypothesis is then tested in an experiment. Following the experiment, you analyze the data and draw conclusions. Everything is done one step at a time. It doesn’t make sense to analyze the data before you conduct an experiment, just as it doesn’t make sense to plot the zeroes of a quadratic function before you have fully solved for them.
There is also quite a bit of research in math that involves the scientific method. Mathematical research is the reason we have formulas that we can use to begin with. There would be no explanation of why these formulas work without science. Many of the people who shaped the early history of mathematics also shaped the early history of science. For example, early Indian mathematicians are responsible for the beginnings of algebra as well as many major astronomical observations. Chinese mathematicians invented the abacus, which was an early counting machine. These mathematicians were also used for solving practical problems in engineering and business. The Greek philosophers Pythagoras, Plato, and Aristotle were responsible for much of the world’s early conceptions of the universe. They also began the conception of numbers as elements of all things in the universe, making mathematics a respected field of study.
by Ty Hilton | Mar 8, 2016 | Math
Want to know how Math Powers work? Read Math Super Powers.
by Rebecca Mayer | Mar 3, 2016 | Math
Math is very important in everyday life, more necessary than some may think. I often hear students complaining about how they do not think they will ever need to know any of the things they are learning in math class and how it is a waste of their time. It is more relevant to your life than you may think. Whether you are baking a cake with a recipe or deciding how long it will take for you to drive to your friend’s house, math is hidden in daily tasks and often goes unnoticed, but not unused.
Trying to decide how much your lunch will cost? Math.
Setting an alarm in the morning to have enough time to drive to school? Math.
Many basics everyday activities depend on math and would be very difficult to figure out without it. Some people have the false impression that only complex jobs like engineering and accounting rely on math, however, a lot of different jobs include math. At least every employee has to know some math to understand their salary, wages, and hours, even when working at a job that seems completely unrelated to math. It is easy to overlook the necessity of math in our everyday lives because it becomes a habit, however in order to form these habits, everyone needs some extent of math knowledge to make these daily tasks involving math second nature.
Math is also important in other subjects and can be helpful to understanding things in science, English, and even the arts. There are many numbers and calculations involved in different sciences, like chemistry and physics. Studying the movement of objects, chemical reactions, or reading charts, graphs, and data all require one to know some math concepts. In English, poetry has a meter, or beat, and a certain number of lines, stanzas, or syllables that is easier to understand with knowledge of math.
Many students think that their high school math class is a waste of time and that since they are going into a career as a history teacher or a writer, whatever the case may be, that they do not need to pay attention or care about math. Of course, it is not necessary that everyone be as ecstatic about math as I am and wake up loving it every day, but everyone should be willing to learn it to an extent because of how much it is used in everyone’s life, regardless of careers. Knowing at least some basic math concepts is very helpful to have a simpler, easier life. Having to pull out a calculator every single time you go to the store and wonder how much change you will get can get annoying and time consuming and it is just easier and faster with a basic concept of math.
by MaThCliX | Feb 23, 2016 | Math, Teaching and Learning
Do Math Manipulatives Help Our Students Learn?
What are they?
A math manipulative is an object that is used in the teaching of mathematics that allows students to perceive the idea or concept they are learning through touching and moving the object. These manipulatives can range from anything like dice or money to pattern blocks, two-color counters, and even playing cards or dominoes.
What age groups?
All ages can benefit from the use of manipulatives while learning math. Math manipulatives are most commonly used in the early elementary ages or younger. Once students become more capable of abstracting concepts (older elementary, middle, and high school), teachers seem to have students spend more time doing math with paper and pencil, and less with hands on methods.
What are the benefits?
The use of manipulatives in the learning of mathematics allows students to represent math in multiple ways. More senses become engaged, including visual and tactile, which keeps a student more attentive. They are able to “see” math, which reinforces the conceptual understanding. This lays the groundwork for the mechanics that they will use later and allows the rules to be more meaningful and make sense, which in turn, will be less for them to “memorize”. Seeing math allows students to expand on ideas and uses of math in the world around them.
Why aren’t teachers using them?
Three reasons that math manipulatives are not used as often as they could, is time, money, and lack of knowledge. Developing the concept with a manipulative may require more time and so often, our teachers are burdened with getting through the material. While many math manipulatives on the market can be costly, not all manipulatives are expensive, but having enough for a class set could get pricey. Each math manipulative can be used to teach a variety of concepts. Often teachers may not know how to teach various concepts with these tools, and so they just do not get used. There are many companies out there that do trainings with their manipulative for teachers to learn.
This blog has an ultimate list of math manipulatives that can get you started!
by Chuck Summers | Feb 22, 2016 | Math
Pinewood Derby Physics
Have you ever seen a pinewood derby race, a race that is held every year in many Cub Scout dens? I have worked with my grandson to enter one a couple of years, and being the engineer that I am, I wanted to use my knowledge of math and physics to perhaps win the race.
We tried to add weights to the car, decreasing the friction of the wheels (it is illegal to use ball bearings), and experimented with the shape of the pinewood derby car to give it a more aerodynamic shape. All of these things help to one degree or another, and all are well known in the Cub Scout community as a simple search will prove (https://www.wired.com/2010/12/pinewood-derby-physics/).
Tautochrone Curve (or Brachistrochrone Curve)
There is something that can affect the speed of an object down a pinewood derby track and that is the shape of the track. You would think that the shortest distance would give you the fastest time (We all know that the shortest distance between two points is a straight line). But in the real world with gravity pushing an object down a slope, the distance takes a peculiar shape, called the Tautochrone curve (also brachistrochrone curve), shown in the graphic above. The next simulation shows this.
Another strange property of the curve is that regardless of where an object is placed on the curve, the time required to reach the end is the same. The first illustration shows this, and is totally unintuitive.
The curve is a form of a cycloid (see https://en.wikipedia.org/wiki/Cycloid), that is the path a point on a wheel makes when it rolls on the ground. There is a lot of math involved in the description (but not too much for a student familiar with trigonometry).
The point to all this is that math is fascinating and has a lot of amazing applications for the student with an inquisitive mind. There is a lot of history behind the study of the cycloid, as noted from the wikipedia article cited above shows, so there is an endless supply of interesting applications of math and a lot of unsolved math mysteries for those who want to make a difference.
by Karl Mattle | Feb 18, 2016 | Math
Factoring Polynomials: Learn It or Die!
Ask any adult if they know how to factor a polynomial. Most will say “What?”. Some will say “I learned that in high school, but I couldn’t tell you how to do it now”. If you happen to be asking an engineer or a scientist, they’ll probably say “Sure! It’s fun, but not really useful”. So why do we, as math educators insist that students must not only know how to factor polynomials but must master the subject as if their very lives depended upon it?
Most math educators would agree with the engineer’s first statement. It is fun. But why is it fun? The answer is that it is a puzzle, a mental exercise that yields satisfaction when solved. But let’s examine its utility. Factoring polynomials does lead to the Fundamental Theorem of Algebra (Wow! That sounds regal). It does lead to completing the square to solve a quadratic polynomial, which, in turn, leads to the quadratic formula. Are some adults required to solve a polynomial equation? The answer is yes. engineers, scientists, actuaries, programmers, and others are sometimes required to solve polynomial equations. But rarely is the solution even rational, much less an integer. Since the solution must be approximated, the clever maneuvers learned in high school are not applicable.
So why bother to teach factoring at all? The answer is that we, as educators, have been charged with teaching our students to think, to enjoy thinking, and to trust the results of their thought. We cannot possibly teach our students everything they will need to know to be productive citizens. But we can train their minds to empower them to figure it out. Factoring polynomials should be taught once, early in the math curriculum, not as a useful life skill, but as mental exercise to hone the mind. The trend in math education is to offer students various gimmicks or procedures (the X method, slide and glide, etc.) to allow students to factor a polynomial without really thinking about it. The mind is not honed. The procedures are robotic and forgotten as soon as they are regurgitated on a test.
That being said, here is a link to a great way to factor a polynomial.
