Math Super Powers
Want to know how Math Powers work? Read Math Super Powers.
We Need 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.
Math Manipulatives
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!
Pinewood Derby
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.
Image courtesy of Curiosa Mathematica
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.
Factoring Polynomials
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.
How do You Eat an Elephant?
The old adage asks, “How do you eat an elephant? One bite at a time.” Here are some great ideas for making all those things you need to get done a lot more achievable.
Many thanks to author Maria Gracia for the basics of the list.
- GOALS– set realistic goals at the beginning of the school year (also semester, week, day, study period, etc). Write them down and keep them visible.
- AVOID THE RUSH– My dad always figures in “oops time” to every plan. If he thinks something will take 30 minutes, he’ll budget 45 minutes, in case something comes up unexpectedly. The same applies to time spent on homework and school projects. Plan for the unexpected.
- AVOID CLUTTER– At the beginning of the school year, there is no clutter yet. Don’t let it build up. Create separate folders for classes,for things that need to be signed,for tests and papers that have already been graded, etc. As things become outdated, move them to a separate file immediately. Avoid the paper build-up.
- MAKE TO-DO LISTS– Whether it’s a list of things to grab from your locker before you leave school, a list of what homework needs to be done that day, or a list of questions to ask your teacher about your math, lists help you to know exactly what you are doing and what’s still to do.
- EFFECTIVE STUDY AREA– Designate an area that is quiet and well-lit to do your schoolwork. If you can’t find a quiet place at home, go to the library. Study sitting at a table or desk, since getting too comfortable in a chair or on the bed may make you drowsy.
- AVOID OVERLOAD– While extra-curricular activities are a fun part of growing up, taking on too much may mean not having time to get everything done.
- USE A PLANNER OR CALENDAR– Write it down. Make sure that everything you need to do is on one calendar instead of separate social, school, and sports calendars to avoid the risk of scheduling conflicts and missed appointments. You may consider color-coding events such as marking all the tests in yellow, all the projects in blue and so forth.
- BREAK IT UP– Break up big assignments into smaller pieces that are more manageable. If you have 3 chapters to study, study one each day for 3 days instead of trying to do everything at once.
- EAT YOUR BROCCOLI FIRST– Eating your vegetables before dessert gives you something to look forward to. Likewise, doing the hard stuff first makes the rest of the work feel easier.
What does a math tutor do?
MaTh TuTor. Sounds like a pretty straight forward job, right? Just reverse the words, and you get it: we tutor MaTh. But there is so much more. Not only do we tutor MaTh, we care, we create, we adapt, and most importantly we DO MaTh. But why do we do it all? Because we believe that a world where everyone understands MaTh is a wonderful place. So, how do we do it? Well that’s what I’m here to tell you!
Do you know how many students the average public high school teacher in Georgia has? The average class size is 25.4; if each teacher has 5 classes that makes a total of 127 students per teacher. This makes it fairly complicated for the teacher to ensure that each student gets the attention they need. This is where the MaTh tutor comes in! We care for the individual student. When they succeed, we succeed. We assess each and every student we have on an individual level. We look at their personality type and their learning style to determine what they need to succeed. It’s our job to care for and cater to every student to the best of our ability. It’s part of our job, and we love it because knowing and seeing a student’s progress is extremely gratifying.
Enrichment and practice are two things that are incredibly important to learning and succeeding in MaTh, and as MaTh tutors we are dedicated to both of these things. This is why we create. We create games, worksheets, instructional videos, interactive projects, reward systems, all in the pursuit of our student’s success. Not only are these things helpful to us, they benefit our students. MaTh games are a wonderful way to get the student involved and excited about MaTh. Instructional videos help students who need instant access to information on a specific MaTh topic. Interactive projects build teamwork and leadership skills. Our reward systems encourage our students to constantly improve, and to not only get the grade, but to reach another goal that may be more rewarding for them personally.
Every student is different. They learn at different paces, they are encouraged by different things, and they all have different interests. Being MaTh tutors we deal with almost all types of students, and sometimes we come against a challenge. But we adapt. If we have a problem, we have the time to step back and look at our student to see what we can do better. Why is this student struggling with a specific topic? What can we do to make it better? What can we do for this student to ensure that they succeed? These are the questions we ask ourselves when a problem arises. These are the questions that we take the time to answer to ensure the student’s success.
MaTh. It’s a unique subject that many students abhor. But why? It’s all around us. From the food that we eat to the technology we use, MaTh is the basis for most of the modern world. As MaTh tutors we are determined to encourage students to not only succeed in MaTh, but to enjoy it, explore it, and appreciate it. So not only do we tutor MaTh, we live it, love it, and make the world a better place with it.
Keep Your Momentum
K
eep Your Momentum!
By now, we are several weeks into the semester. This is about the time that people tend to start slipping from their goals. They lose stamina. Notebooks that began the semester neat and organized are now becoming messier and messier. Don’t fall into this trap! Here are some ways to keep going strong this semester:
1. Keep Practicing Every Day
Especially with math, it is extremely important that you keep practicing every day! Don’t think that because things seem easier in the beginning, it’s okay to not work as hard now. Even if you think you have a good grasp on the material, keep coming to MaThCliX. Working with other people helps you more than you realize.
2. Get Organized…Again
If you are starting to notice that you are becoming less and less organized as the semester is going on, take a break and organize everything again. Staying organized throughout the semester makes studying for finals much easier when you make it to the end of the semester. You also avoid unnecessary stress when everything is in order the way it should be.
3. Remember Your Goals
Remember the goals that you set in the beginning, and remember why you set them. Evaluate your progress so far. Are you still on the right track? Are you still doing what you need to in order to reach your goals? If not, that’s okay! You can still make the changes you need to in order to reach your goals. In fact, it is easier to make changes now than waiting until right before the final.
4. Remember to Rest
It’s okay to take a break sometimes. Don’t use this as an excuse to slack off, but if you are working diligently towards your goals, it is okay to take a break to regroup and refresh yourself. Taking time to rest will help you avoid becoming too overwhelmed and will help you avoid becoming burnt out from working so hard in the beginning.
Don’t lose heart! It may take work, and it may take stamina, but you can reach the goals you have set! Don’t get too comfortable. Just remember to keep on trying, and you will find that you will achieve your goals.
Off to a Good Start
Off to a Good Start!
Having a break from school is a good thing. You have a chance to catch up with family and friends and to catch up on sleep. However, being away from school for multiple weeks can take you out of the right mindset and put you in an unproductive mood. It can be difficult to get back into the swing of things and if you don’t adjust fast enough, it can negatively affect your grades. If you mess up on the first couple of assignments or the first test, it definitely won’t be good for your overall average in the class. However, that is not all of the damage that it will do. It could also make you less confident in your ability to succeed in the class, which could discourage you and potentially lead to additional bad grades in the class. Also, if you fail your first test, you probably did not learn enough of the material. In subjects such as math and science, the new material builds off of previous material. Therefore this could hinder you on future assignments and tests. Plus, most finals are cumulative, so if you didn’t do so hot on the first test, then you might lose some points when you encounter the same material from the first test on the final. So, I’ve just ranted on to warn you about the terrors of slacking off at the start of school.
Now let me give you some advice on how to start this next semester and year off with a bang.
1. Goal setting: Having goals is important because it gives you something to work on and to aspire to. If setting goals isn’t your thing or you are having trouble developing some, that’s ok, because we got you covered. For the start of the semester, here at MaThCliX, we are working with students to develop three S.M.A.R.T (Specific, Measurable, Achievable, Relevant, Timebound) goals for the semester. So if you haven’t already, try to come by in the next week or so, and we’ll make sure to set you up with goals that will keep you focused and on track throughout the semester.
2. Enough sleep: Not getting enough sleep can cause problems with our mood and ability to function. Because of this, I would say sleep is a crucial factor when it comes to functioning at school. It’s not an easy task to go to bed early every night. Today in our modern society we have a lot of fancy devices that get our attention before bed. However, whether this coming week is your second week of high school or first week of college, try to put away your smartphone and go to bed at a decent hour. You will find yourself with more energy throughout the day which will hopefully take you out of denial that the holiday break has ended. Furthermore, by seeing the positive effects of going to bed earlier, you might find yourself more inclined to not stay up really late in the future, and going to bed early might formulate into a good habit.
3. Priorities: Setting your priorities straight is pretty important to say the least. What I would advise you to do is to make a list of activities that you do during your week (whether hobbies, school assignments, etc.) and rate them from 1-10, first on importance, then based on how urgent each activity is. For example, playing video games is not that important and isn’t urgent. So I would give it a 2 for importance and a 1 for urgency. However, having a test tomorrow is, so I would give it a 10 for importance and a 10 for urgency. If you do this for every activity you do in a week (or month, you can set whatever time interval you need), it will give you a pretty good idea what you should focus your attention on and what you can save for later.
In conclusion, if you set goals that you can pursue, get enough sleep, and set your priorities straight, then you will be setting yourself up to succeed.
Get Moving
Get Moving!
If someone asked me what I feel is most lacking in those that I tutor, my response would be one word: “Confidence.” I have not found a single person, ever, that I could honestly say was not smart enough to “get it.” What I usually find is smart people who have convinced themselves that they cannot do it. An occurrence far too common in tutoring, especially in math tutoring, is that students give up far too easily on themselves. They lack confidence in their capacity to solve their own problems. One of the most valued skills in business, so I’ve been told, is the capacity to assess and solve problems. A key component of this skill is acting and doing all we can before asking for help to do what we can’t do. In what follows I hope to suggest ideas that will improve our ability to act and do what we can for ourselves before we seek assistance.
What seems to happen with all of us is that if something looks hard we automatically assume that it is hard, panic and give up before we even begin. Instead of doing that we need to simply begin with confidence. We do this by first making sure what we are being asked to do. It seems rather obvious, but what we begin with is reading the question. When people ask me for help, usually I’ll ask them if they have read the question. Far too often the answer to that question is “No, I haven’t.” More than a few times, after we have read the question they’ll say “Oh, I do know how to do this.” Problem solved. So one thing that is a part of doing all you can is reading the question. Simple, but it works.
I have also found that many students, when they read, do not understand the question because they do not understand the words the question is using. I’ve personally had this problem more than I care to admit. I remember once when I was reading a physics article that used a certain word multiple times. Because I did not know the meaning of the word, I wasn’t really sure what they were talking about. After some time, I went back, learned what the word meant, then re-read the article. When I did that, it became clear to me what was being said. So if in reading the question you find words that you do not know, look up the definition. It doesn’t matter if you search for it in your notes, your textbook, and a dictionary or ask somebody, if you don’t know it, find out! That is one thing you can do.
After reading the question and making sure we know what it is asking, we may find, that we still do not know how to do the problem. Does that mean we have done all we can and can ask for help? No. Not yet anyway. When I first started tutoring there were quite a few math problems that I did not remember how to solve. What I’d usually do is ask the person to see their notes. I’d quickly look them over and more often than not, I’d discover how to solve the problem. I’d suggest doing likewise. If you have read the question and know what it is asking but still do not know how to do it, look in your notes! The answer is almost always there.
If we’ve reached this point and we still cannot understand then we need to ask for assistance. You may wonder why you need to expend so much effort if you’re probably going to ask for help anyway. Well I’ll answer that by saying it’s quite a bit easier to steer a moving car than it is a parked car. If you’re already moving in some direction, any direction, all that any tutor would ever need to do is help you steer. The same is true in any pursuit in life.
In all that I’ve said, I’d like to add a caution. Rarely does your best effort cover all that you will need to do in math, or in life. Do not hesitate, ever, to ask a question or seek help. If you need help, ask for it! Just make sure you’re doing your part!