But there's always MORE math! That's what I told one of my students a month ago, and I meant it. I've dealt with math in every role from student, to teacher, to tutor and I can honestly say that the more I learn, the more I'm sure that I've barely scratched
the surface of what's out there. A scary thought considering I've been educated in the subject for nearly 25 years. So what is a high school student to do these days with so much scary math out there?
I have one piece of advice: focus. That does NOT mean fixating on every minor detail you come across in order to then extract meaning from each individual piece of information and then put it all together at the end. That's not focusing, that's suffering.
Nobody learns the ABC's all at once. Neither should you attempt to do it with math.
In order to focus, it helps to (temporarily) ignore the minor details and devote your attention to "the big picture." You want to quickly identify and...
I can't count how many times I've sat and watched a student erase half a page of her hardest math work just because the end result didn't come out right - or because it didn't fit neatly on the page. I'm not sure if this is a new thing, this preoccupation
with making one's homework look nice and flow perfectly from Point A to B. But it makes me sad to see my students erasing some of the most important records in their academic lives.
Mistakes are not failures. Mistakes show you how hard you worked, how far you got and exactly where you went wrong. They are beautiful pieces of your mental history. They show you what kinds of things you need to watch out for in the future. Do you
often forget to distribute your negatives? Do you get exponent rules mixed up? Maybe you're not so great at remembering when to rationalize the denominator. Whatever your personal "weaknesses" are, they are uniquely yours. Acknowledging...
"I don't need to learn math because I want to be a truck driver". I love hearing that or similar comments. Especially from a 12 year old. How does a 12 year old who never drove a car know he wants to be a truck driver? There is nothing wrong with being
a truck driver. Some truck drivers make over $100,000 a year. Many office workers fantasize what it would be like to be on the road away from the drudgery of the cubicle. However, being a truck driver is hard work; which is why it pays well (sometimes). You
never see your family, have few friends and face real dangers. But does a truck driver need math?
I would say yes; some are immediately apparent, some are not. The immediately apparent reasons are truck drivers need to have a good understanding of weights and heights. How many times have we seen that truck hit a bridge because the driver did not realize
his truck was too high? How many trucks have crashed because the weight of the freight was...
Rather than droning on about each subject in math at this point, I'm going to make a shift. I'm currently engaged in a conversation with a friend, and my most recent reply to him expresses my opinion on how math is being taught today:
...The beauty of math is something that I have seen most of my life, and it stands in my mind as one of my fundamental motivations for studying math.
As a person with that emotional tie to math, I realize that many students would find it difficult to identify with my assertion that math is beautiful. As a result, I often take a stance that might be a little self-protective, and offer an answer that seems
to be weaker but more universal.
In short, some aspects of math are of universal benefit, such as the skill of basic calculation, or the benefits of mental exercise. There are some benefits that apply only to a portion of the population, such as the ability to factor polynomials, or to find
missing sides of triangles...
One of the biggest frustrations for students is getting something wrong that they know how to do. What is usually the problem? Careless errors. Do students really care less? Probably, they care less for writing everything down step by step. They care
less about labeling the formulas. They care less about thinking about why they keep making that mistake. For some reason, I have found that students have the perception that smart people don't write stuff down. Students believe that "smart" people hold it
all in their heads. Well, here's the real deal. Smart people write almost everything down with meticulous attention to detail. They know that the "blackboard " in their head gets erased quickly. There's nothing more frustrating than trying to figure out what
you did wrong when you don't have a record of what you did. I call it the dance in your head that leads nowhere! What's the cure? If you believe that your student is being careless...
I wanted to share something with everybody which seems obvious to me, but I'm not sure everyone is on the same page.
Have you ever had a terribly boring school teacher?
I bet you have because we all have at some point!
It doesn’t mean that these teachers are all uneducated in their subject, (although they might be…) it just means that either:
A. They aren’t involved enough in their field to have passion for it
B. They don’t know how to transmit that passion to students effectively
To be able to have fun or at least gain respect, understanding, or interest in a subject -
the subject must be presented in an interesting way.
It seems obvious when you put it that simply, but some or most teachers don’t care enough to even pretend to be excited, passionate or involved in their field.
This makes learning from these teachers very difficult, especially if the students are self-sufficient learners.
——That is where...
A question that I have heard many times from my own students and others is this: "When am I ever going to use this?" In this post and future posts, I'm going to address possible answers to this question, and I'm going to also take a look at what mathematics
educators could learn from the question itself.
Let's look at the answer first. When I was in school myself, the most common response given by teachers was a list of careers that might apply the principles being studied. This is the same response that I tend to hear today.
There is some value in this response for a few of the students, but the overwhelming majority of students just won't be solving for x, taking the arcsine of a number, or integrating a function as part of their jobs. Even as a total math geek, I seldom
use these skills in practical ways outside my tutoring relationships.
Can we come up with something better, that will apply to every student? I say...
Since it's Thanksgiving week, let's think about pie for a second. No, not mathematical pi, just actual real edible pies. For Thanksgiving I'm in charge of making dessert, so I'll be bringing two pies, one pumpkin and one apple. Let's say that I sliced the apple
pie into 12 pieces, and the pumpkin pie, since it held together better, into 18.
Fast forward to the end of the evening. My pies were a big hit, and I have almost none left. In fact, all I have is three pieces of apple and four pieces of pumpkin. I want to combine the remaining slices into a single pie pan, so that they take up less space
in the fridge. How do I figure out if my remaining pie will fit in one pan?
Well, let's start by writing down the remaining amounts of pie in the form of fractions. Remember, one of the definitions of a fraction is parts of a whole, so let's apply that definition to figure out our starting fractions.
The apple pie was cut into 12 pieces, and we have three...
This is my all time favorite website for Math worksheets.
The primary student baseline communication skills a student should learn from their tutor are the following:
Precise use of vocabulary
Express complete thoughts
Interpreting and following instructions
These baseline communication skills are common in academia, particularly Mathematics. Any behaviors, thoughts, attitudes, philosophies, etc. that hinders these baseline communication skills presents learning hindrances for the students and tutors.
Let me know your thoughts.
Purpose: This series shares tips on how to identify, manage, and overcome Mathematics Negative Self Talk (NST). We cannot avoid NST totally because the NST about Math skills in general is a widely accepted habit.
So what is Mathematics NST anyway? Mathematics NST is when we speak in our minds or to others about an inability to learn, do, and/or understand Mathematics in general. Focus here is what we cannot do or have never done in Mathematics. For example, "I hate
Math." "I can't do Math!" "This is too complicated!" " I could never do Math!" "My parents aren't good at Math either." "What can we use Algebra for anyway?" "The teacher is confusing me." The NST phrases list is endless, but also popular in today’s
Downside of NST: NST in Math is simply a bad habit of thinking and attitude. This habit limits learning...
When is it a good time to look for a tutor? Some students wait until a big exam comes up, and do lots of cramming at the last minute. While that strategy may work for some, others may need to take a different approach.
What if you need to take a mathematics or physics course and you know you will have difficulties? Maybe the course is really advanced or it is not one of your best subjects. The best approach would be to work with a tutor on a regular basis throughout
the semester. They can help you with any misunderstandings that may come up along the way, and help prevent you from falling behind in the course. This also ensures that you get the individual attention that you may need.
There are many situations in which a student or parent might want to seek extra help with math.
Does the student often need to retake assessments? As a teacher, I like to offer make-ups because I want my students to know it's more important to learn the material than to move on before they're ready. Needing to
frequently retake assessments means that the student needs to reevaluate how they are preparing. Often, getting a tutor can help them figure out how to best study independently.
Does the student freeze during assessments? Does their mind go blank? Or do they think they did well but it turns out that wasn't the case?
It's possible the student has test anxiety and needs to build their confidence. Talking through the material with someone is one of the best ways to alleviate that anxiety.
Does the student have a difficult time staying caught up with the material? Do they feel like they always get it after the test or quiz but not before?
One of the first things you notice in algebraic expressions (besides the sometimes haphazard mix of operations) are numbers that appear with a smaller number above them (like this 54). These smaller numbers are called exponents and, in this
post, I'll give a basic rundown of what they represent and a few basic rules that you will need to follow when dealing with them.
So, you're probably thinking, what do exponents represent anyway. In short, it's a special way of writing a special form of multiplication. I know it sounds hard to grasp, so I'll give you an example:
- Let's look a 3*3. Of course we know it as 9, but in dealing with the order of operations writing a number multiplied by itself may be combersome if you already have several parentheses in the expression. so the way that 3*3 would be written is 32
as your multiplying 3 by a second 3.
But what if you want to represent 4*4*4 or need to multiply 10 5's? Simply count up...
In my experience both as a student & tutor in various math disciplines (especially algebra) I have encountered many students that struggle with the subject. Some students have never been exposed to the material in over a decade; others avoid it like the
plague & yet others struggle with test anxiety. Based on what I have seen I have a few pieces of advice that warrant sharing. Hopefully this will help the students that struggle with it as well as offer tutors some guidance on dealing with the most difficult
(1) There is a definite emotional aspect in any subject that involves numbers. Math brings out the emotions of frustration & fear (or some combination) in those that struggle with it. The frustration comes from not being able to understand the concepts, while
the fear results from failing a test or assignment. In either case, these emotions drastically affect the student's thinking to such...
Hi Everyone! As the school year kicks into full swing, its important to monitor your child's progress. Some schools are great at doing this, and some... not so much. It is up to you as parents (or students!) to take control of your student's education
and make sure they are at least on track, but hopefully excelling. That's all for now, take care!
I recommend Wolfram Alpha to all of my math and physics students, and to many others. It calls itself a Computational Knowledge Engine which doesn't do too good a job of describing itself but it is very useful as i'll explain below. It does quite a number
of things that aren't comparable to other search engines.
First, one of its central components is based on Mathematica which is a mathematical programming language. Because of this it can solve problems in algebra, geometry, calculus, statistics, matrices and many other subjects. This is largely what I use it
for; as in if I want to quickly solve or check a problem. If i can't remember exactly what the half angle integration of tangent is, or if a problem results in an answer to large for my calculator to display.
Second, it has large data sets available to it. These vary from current and historical weather data, i.e. what is the current temperature/chance of rain and what was the temperature...
I am excited to begin a brand new school year. There are always anxieties students face. There are tests. And projects. And the teacher who wears the purple pants three times per week.
But now we have ways to search for the best tutors. I cannot wait to see who will find me. I cannot wait to meet more students, help them study for tests, projects, and vent about their old-fashioned, purple-polyester-pants-wearing teachers who need to
slow down the pace.
I want to help with all of that. I want my tenth year of tutoring to blow the red socks off the teachers with purple pants! Let's do this!
Don’t be stubborn: its The Monty Hall Problem. This is one of the least generally understood problems of all time. My hypothesis: the reason most people fail on The Monty Hall problem is that it isn’t straight, and it involves changing plans.
If you don’t know, the way this works is that you are on a game show and must find a prize behind one of three doors. You pick a door and then The Game Show Host reveals that the prize is not behind one of the two remaining doors. With due intellect your supposed
to reason that it is always advisable two switch your selection.
What isn’t understood during the time the game show hosts open the door is that he will never open a door that has the prize in it. He will always open a null door. Vital information is encoded by the pact the game show host has with the producers and it moves
in the transaction between the game show host and you. Think of it as the elements of America being encoded to the writing and voice of Stephen...
In math you learn new terminologies and many significant things pop up. Guys, do you ever dream about analytical calculus? No? Well, why not!
As a high school student you learned algebra and pre-calculus and those are great, but you can really figure that there is more to math than just that. I assume you were dazed and confused. That's okay. Perhaps though you enjoyed your subjects. That is
There, you must try to learn analysis, because it is the most-funnest part of mathematics! Do you think I'm wrong? Well, begin with a subject like real analysis. During your study of analysis, you learn about continuity, metrics, and integration. I would
like to know more about metrics.
The weird thing is that math is everywhere. Sorry, but I like math because of this fact.
It takes a real scholar to learn math. Got me wrong? Gals sometimes support the most advanced mathematical conclusions. You can make their notions...