Today, the future depends on you as much as it does on me. The future also depends on educating the masses in Science, Technology, Engineering, and Math, otherwise known as STEM. As a new tutor to WyzAnt, I hope to instill the importance of these subjects
in student's lives, as well as, the lives around them.
Besides the fact that, "the average U.S. salary is $43,460, compared with the average STEM salary of $77,880," (Careerbuilder) these subjects are interesting and applicable to topics well beyond the classroom. Success first starts with you; I am only
there to help you succeed along the way. STEM are difficult subjects. Yet when you seek out help from a tutor, like myself, you have what it takes to master them.
Please enlighten me on students looking to achieve and succeed rather than live in the past and think I can't as opposed to I can. We can take the trip to the future together, one question at a time
This week's Math Journey builds on the material in
The Function Machine. If you have not yet read that journey, I suggest you do so now.
In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered
pair on a coordinate plane. Plot enough pairs and a pattern begins to emerge; we join the points into a continuous line as an indication that there are actually an infinite number of pairs when you account for all real numbers as possible x values.
But plotting point after point is a tedious and timeconsuming process. Wouldn't it be great if there was a quick way to tell what the graph was going to look like, and to be able to sketch it after plotting just a few carefullychosen points?
Well, there is! Mathematicians look for an assortment of clues that help to determine the shape of a...
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I was a fairly typical young person and, like my peers, counted down the days until summer. My mother was a math professor, so I never stopped doing math during the summer, but felt like other parts of my brain became a little mushy in the summer. Come September,
it was difficult to get back into the swing of writing papers and studying history and memorizing diagrams. I was out of practice and lost my routine. As an adult, I have almost continually taken classes, because I enjoy learning and find that from class to
class, I need to maintain a routine, i.e. a study area and a time of day that I complete my assignments. I have also found that reviewing material a week or two before the course begins helps me to start the class with more confidence and competence. I am
a big believer in confidence fueling success and I wonder if younger students practiced assignments in the week or two prior to return to school, if that confidence would help the transition to the school year...
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Probably the hardest thing about doing word problems is taking the words and translating them into a workable mathematical equation. For this reason many students fear and hate doing them. It can be confusing to know where to start and how to go about figuring
out the answer. However, there are ways of breaking down a word problem that makes it clearer and easier to solve. The following is a list of helpful hints and strategies in tackling these challenging word problems.
1. Remember that when you are doing a word problem you are looking to convert the words into an equation, so read through the entire problem first. Don’t try to solve the problem when you’ve only read one sentence. It’s important to completely read the problem
in order to get the whole picture and effectively translate and solve the problem.
2. Go back to the beginning. Reread the first sentence. Write down what you know and what you don’t know. Use variables to stand for the unknowns and clearly label...
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Several of my current Geometry students have commented on this very contrast. This has prompted me to offer a few possible reasons.
First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal twocolumn proof variety) that involve stepwise, deductive reasoning. For many, this is their first exposure to this type of thought process, basically
absent in Algebra 1.
Second, a large part of Geometry involves 2d and 3d visualization abilities and the differences in appearance between shapes even when they are not positioned upright. Still further, for a number of students, distinguishing the characteristic properties
amongst the different shapes becomes a new challenge.
Third, in many cases Geometry entails the ability to form conjectures about observed properties of shapes, lines, line segments and angles even before the facts have been clearly established and stated...
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It is the mark of an educated mind to be able to entertain a thought without accepting it. (Aristotle)
This quote provokes me never to accept the status quo and always challenge assumptions. It is the thought that through education we never stop learning or seeking after truth and knowledge.
I am happy to announce that all my students have passed the NY State Regents examinations, except one student. The subjects varied from Algebra 1, Algebra 11/Trigonometry, English, US and Global History and Living Environment. I am so proud of them.
Most of these students are students who struggled quite a bit. It was a long journey but one I would do again.
I am very proud of them as most of them will be graduating this year. The NY State Common Core examinations are next.
Factoring can be quite difficult for those who are new to the concept. There are many ways to go about it. The guess and check way seems to be the most common, and in my mind, it is the best, especially if one wants to go further into mathematics, than
Calculus 1. But for those just getting through a required algebra course, here is another way to consider, that I picked up while tutoring some time ago:
If you have heard of factor by grouping, then this concept will make some sense to you. Let's use an example to demenstrate how to do this operation:
Ex x2 + x  2
With this guess and check method, we would use (x + 1)(x  2) or (x + 2)(x  1). When we "foil" this out, we see that the second choice is the correct factorization. But, instead of just using these guesses, why not have a concrete way to do this.
Let's redo the example, with another method.
Ex x2 + x  2
First...
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My recommended strategy to Students at all academic levels for learning and successfully passing the course at all modalities (online, onground) is the culmination of at least ten years of teaching and tutoring statistics at the undergraduate, graduate,
and postgraduate levels in business, management, sciences, social studies, and psychology. It consists of the following:
1. The first is to learn how to overcome fear and anxiety from the unknown and look at tutoring as a prudent investment to your immediate future and success. Engage the tutor from the start of the course and don't prolong the decision because of the complexity
and quantitative nature of the subject area. This component of the overall strategy is to keep the weekly normal pace and retain basic real life knowledge for ongoing participation in the political and economic process of the National affairs and StateoftheUnion.
2. Academic Reading Materials and Study Guides encompass three distinct sections...
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The first thing to do when teaching a frustrated student is to listen to, and acknowledge, their frustrations. Let him or her vent a little. If you're working with young children, they probably won't even realize or communicate that they are frustrated.
Therefore, the first thing to do is say "you're very frustrated with learning ________ aren't you?" If you are in a group situation, take the student aside to talk to him or her about it so he or she doesn't become embarrassed.
One of the best things you can do when teaching frustrated students is to watch them oneonone in academic action and observe every little detail when they think, write, and speak. Often, students are lacking very particular, previous basic skills. By watching
them work, you can identify where they are going wrong and notice common patterns. For instance, I have tutored many algebra students whose frustration stemmed from an inability to deal with negative numbers. Once this problem was...
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I recently responded to a question on WyzAnt's “Answers” page from a very frustrated student asking why he should bother learning algebra. He wanted to know when he would ever need to use it in the “real world” because it was frustrating him to tears and
“I'm tired of trying to find your x algebra, and I don't care y either!!!”
Now, despite that being a pretty awesome joke, I really felt for this kid. I hear this sort of complaint a lot from students who desperately want to just throw in the towel and skip math completely. But what bothered me even more were the responses already
given by three or four other tutors. They were all valid points talking about life skills that require math, such as paying bills, applying for loans, etc., or else career fields that involve math such as computer science and physics. I hear these responses
a lot too, and what bothers me is that those answers are clearly not what this poor student needed to hear. When you're that frustrated...
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My recommendationa:
Vi Hart, website: vihart.com
Sal Khan, https://www.khanacademy.org/math/algebra
Mamikon Mnatsakanian, www.its.caltech.edu/.../calculus.html
As the school year ramps up again, I wanted to put out a modified version of a Memo of Understanding
http://en.wikipedia.org/wiki/Memo_of_understanding for parents and students. It seems each year in the rush to get through the first weeks of school parents and students forget the basic first
good steps and then the spiral downwards occurs and then the need for obtaining a tutor and then the ‘wish for promises’ from a tutor. Pay attention to your child’s folder or agenda book. A student is generally not able to self regulate until well into high
school. Some people never quite figure it out. Be the best person you can be by helping your child check for due dates, completeness, work turned in on time. Not only will this help your child learn to create and regulate a schedule, it prevents the following
types of conversations I always disliked as a teacher ("Can you just give my child one big assignment to make up for the D/F so they can pass"; "I am going to...
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Let's use our imagination a bit. Picture yourself in math class (Algebra I to be exact), minding your own business, having fun playing with the axioms (aka rules) of algebra, and then one day your teacher drops this bomb on you:
"Expand (x+3)(x1)"
And you might be thinking, "woah now, where did come from?"
It makes sense that this would shock you. You were just getting used to the idea of expanding 3(x1), and you probably would have been fine with x+3(x1), but (x+3)(x1) is a foreign idea all together.
Well, before you have much time to think about it on your own and discover anything interesting, your teacher will probably tell you that even though you don't know how to solve it now, there is a "super helpful", magical technique that will help you…
FOIL
For those of you lucky enough never to have heard of FOIL, I will explain. FOIL stands for First Outside Inside Last and is a common mnemonic...
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Should I get a tutor? Will it help my child? These are some of the most common questions posed to tutors by parents of students struggling in school. Tutoring can be expensive and difficult to schedule so parents must decide whether the time and money will
be well spent. Instead of relying on a crystal ball, use these factors to help make the decision.
1. Does the student spend an appropriate amount of time on homework and studies?
While it can help with study skills, organization, and motivation, tutoring cannot be expected to keep the student on track unless you plan on having a session every night. If you can make sure the student puts in effort outside of tutoring, she will be more
likely benefit from it.
2. Does the student have difficulty learning from the textbook?
If this is the case, the student will probably respond to oneonone instruction that is more personalized. A tutor will help bring the subject to life and engage the student. A good tutor will...
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Do you think is factorable?
In general, the sum of two squares is not factorable, such as .
However, there are special situations in which the sum of two squares is factorable, like the one in our title.
You don't believe it? Let's try it.
The trick here is to add an extra term to this polynomial, with a purpose of completing the square.
Usually, when we complete the square, we will add a constant term to a quadratic expression, and subtract that same term at the end of the expression. But this time, we are adding the "middle" term. (Of course, we will need to subtract it at the end so that
we don't change our original expression.)
+

Here we can group the first three terms of the expression:
Write the grouped terms as a perfect square:
Now, do you recognize this is the difference of squares?
Difference of Squares
To use the difference of two squares formula, we can write...
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Whenever you complete a math problem, it is paramount to go back and double check your work. Remember, no one is perfect and mistakes will be made from time to time. The first step is to always ask yourself "Does this answer make sense"? For example, if
you're working on a geometry problem and you're trying to calculate an angle of a polygon, and you determine the answer is 110°, look at the angle and ask "Does this answer makes sense, does this angle look like it's greater than a right angle or a 90° angle"?
If not, you know you've made an error and can go back to find the mistake. You can do it!!
Writing Expressions Involving Rate of Change
These realworld problems can be best translated when broken down into their components (variables and operations). When you see the words “is” or “are”, this is the points where you setup the equality. Whenever you see the word “per”, “each” the implication
is a multiplication. This indicates the rate of change between the variables.
The general format for these problems is:
Dependent Variable = Fixed Value + Rate of Change * Independent Variable.
The fixed value is generally a fixed value which does not change. Most commonly, it will be the initial value in a situation.
Example 1:
“Mark is purchasing a new computer. The cost of the computer is $2400 after tax. He will make monthly payments of $150. Write an equation which describes the balance on the account after any given number of months”
Variables present: balance and number of months.
The rate of change in this case is the $150 per...
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Recently I had the opportunity to meet with a parent/business owner who hires/places tutors for high end families in my area. It was a wonderful opportunity as once again I heard the mantra, "Parents just want the grades to go up." I asked what this meant,
how I could measure it (quantitatively and anecdotally) and if this was indeed proof of my skills as a tutor or a momentary 'save' on a reversal of fortune. This parent does not use Wyzant. I was hard pressed to accept from this parent the reason I wasn't
being contacted by high end parents for tutoring was my lack of guaranteeing grades would go up, a promise I can not make in good faith as there are too many factors involved. Honesty and integrity should be important, not my sales ability.
In my years as a teacher and tutor, I have found once I have parents on board, the rest is EASY. Parents are the elephant in the room and I can run myself ragged (knowing full well very little if anything changes without parental...
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When both writing down and reading the algebraic expressions, the binary operation (including addition+, subtraction, multiply*, divide/, exponential^) follow a conventional order:
0) Parenthesis, including {}, [], ()
1) Exponent, multiply and divide
2) Addition and subtraction
The ordering is 0)>1)>2). Then there is no ordering within each group, eg multiply and divide are at the same level of priority except that 0) comes in such as a parenthesis.
Let's take a look at one quick example: 3+(82)*6.
First compute (82)=6;
Then compute (82)*6=6*6=36;
Finally compute 3+(82)*6=3+36=39.
Another example: 3^2+3/(52)
First compute (52)=3;
Then do 3/(53)=3/3=1;
Next compute 3^2=3*3=9;
Finally add 3^2+3/(52)=9+1=10.
Hope it helps!