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## Geometry Blogs

I had a student who submitted a request to get assistance with basic Algebra skills in preparation for an exam. She highlighted the skills she needed assistance with and had a set schedule that she wanted to adhere to for the tutoring. Being the person that I am, I still wanted her to take a skills assessment so that I would know where to begin and what concepts she had yet to learn. For any new student or tutor, the pre-assessment is something that is needed! It is an integral part of learning. Since a tutor's time with any student is short, the best way to maximize the results is through a skills assessment. The assessment is not long and should only take, at most, 5-10 minutes. However, within that time the tutor is able to observe where mistakes are being made, comprise a lesson to help re-teach those skills, and possibly have time to teach higher order skills within that subject. I will state that the pre-assessment helped me tremendously with my student. Not... read more

Reading Formulas can make or break how a student comprehends the formula when alone - outside the presence of the teacher, instructor, tutor, or parent. Formula For Perimeter of Rectangle:  P = 2l + 2w How To Read:  The Perimeter of a Rectangle is equal to two (2) times the Length of the longer side of the rectangle (L) plus two (2) times the Width of the shorter side of the rectangle (W). When is reading formulas like this necessary?  At three particular moments, reading this formula in this manner can be effective.  When students are initially learning what the formula means When student are learning what it means when they should already know (remediation).  When students want to remind themselves (basics learning study skill habit) Remember, Formulas at their introduction are complete statements or thoughts.  Students cannot and will not recall complete thoughts or statements... read more

Suppose, one have two parallel lines given by the equations:   y=mx+b1 and y=mx+b2. Remember, if the lines are parallel, their slopes must be the same, so m is the same for two lines, hence no subscript for m. How would one approach the problem of finding the distance between those lines?   First, if one draws a picture, he or she shall immediately realize that if a point  is A chosen on one of the lines, with coordinates (x1, y1), and a perpendicular line is drawn from that point to the second line, the length of the segment of this new line between two parallel lines give us the sought distance. Let us denote the point of intersection of our perpendicular line with the second line as B(x2,y2).   What do we know of point A and B?   First, since A lies on the first parallel line, its coordinates must satisfy the equation for the first line, that is,   y1=mx1+b1       (1)   Same... read more

Proof of the Assertion that Any Three Non-Collinear Points Determine Exactly One Circle This is an interesting problem in geometry, for a couple of reasons. First, you can apply some earlier, basic geometry principles; and secondly, you can choose two different strategies for solving the problem. The basic geometry underlying: any three non-collinear points determine a plane, somewhere in 3D space. Once that has been done, imagine that the plane has been rotated into the x-y plane, which will make the problem much easier to solve! The two strategies for solution are: (Proof A) actually solve to find the circle. This is equivalent to finding the center of the circle (finding the equation of the circle is simple from there). But, you actually have to do some math to get this! If, while doing this, there is no possibility to obtain other values for the coordinates of the center of the circle, you have proved the assertion as well as obtained a method (and perhaps... read more

Here are 3 tips to help you solve geometry problems involving shapes: (1) Understand the definitions of the shapes your questions ask you about. To help understand the definitions of the many shapes with fancy names, make flash cards with drawings of the shapes and study these cards 5 to 15 minutes at a time a few days in a row until you understand and remember the definitions of the shapes. (2) If you are dealing with two congruent (= same exact shape, angles, & size) or similar (same shape and angles, but different size with sides of shape A proportional to the sides of shape B) shapes and the questions seems very difficult, try re-drawing one of the shapes carefully so that the angles of the two different shapes that are equal to one another are in the same orientation, and then try again to solve the problem. Make sure that the sides of the two shapes that are proportional to one another are also oriented similarly. (3) To find out if two triangles are... read more

The majority of the students that I have often have the same problem -- they aren't grasping the information fast enough or they aren't really able to follow the lessons a teacher gives.   Sometimes, teachers aren't adaptive to every learning style for each student in their classroom.  However, know that each student has the capability to learn math on their own.  It is just necessary to have key characteristics to make it successful.   Every math student should have: patience motivation adaptability organizational skills open communication between themselves and their teacher (inside and outside the classroom) breaks!! :)   Study Tips Always try to study outside of your home or dorm room. In our minds, those are places that we relax at and it can be difficult to turn your mind off from the distractions to study. Public libraries, universities, coffee shops, and bookstores are the way to go... read more

Hello Students!   Start this year off strong with good organizational and note taking skills. Make sure you understand the material and are not just taking notes aimlessly. Try to take in what your teacher is saying and don't be afraid to ask questions!! If you start taking the initiative to learn and understand now, college will be a much more pleasant experience for you. Trust me!   Stay organized and plan your homework and study schedule!   Quiz yourself!   Study with friends!   READ YOUR TEXTBOOK! :)    Remember, homework isn't busy work and a chance to copy down your notes, it is part of the learning process. This is especially important with math, as it builds on itself and understanding the basics will make the other subjects easier!   Have a fantastic and fun year!

Several of my current Geometry students have commented on this very distinction.  This has prompted me to offer a few possible reasons.   First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal two-column 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 2-d and 3-d 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... read more

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

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... read more

I hear a lot about math teachers from my students, and while every teacher is unique, some comments are repeated over and over. By far the most common one I hear is that their teacher didn't really explain something, or was incapable of elaborating when questioned and simply repeated the same lecture again. As a tutor, my first priority is to make sure the student understands the material, and if they're still confused, to find another way to explain it so that it makes sense. In order to do that, I need to have a thorough understanding of the concepts myself, so that I am not simply reading from a textbook but actually explaining a concept. In my years of tutoring math, I've developed a point of view and approach to math that I refer to as “teaching the concept, not the algorithm.” An algorithm is a step-by-step procedure for calculation. The term is used in math and computer science, but the concept of an algorithm is universal. I could tell you that I have an algorithm... read more

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... read more

Nailing an 800 on the math portion of the SAT can be a tricky feat, even if you are steadfastly familiar with all of the requisite formulas and rules. A difficult problem can overwhelm even the most prepared individual come test day. Time constraints, test surroundings, and the overall weight of the exam can unnerve the most grounded students. So what do you do when panic strikes and your mind draws a blank? How do you re-center yourself and charge forward with ferocity and confidence? What you do is this: write everything down from the problem. This is the most important part of the problem solving process. As you peruse the question, write down the pertinent data and establish relationships by setting up equations. This exercise will help you see solutions that were previously difficult to decipher. As you work on practice tests and sample problems, you must work diligently to form a solid habit of writing down important bits of information as you plow through... read more

As you may know, I am a big fan of the well-known author and brain specialist, Dr. Daniel Amen. He mentions in several of his books that Physical Exercise is good for the brain. I have read of research studies that showed a clear correlation between IMPROVEMENT in students' test scores in math and science, and their level of physical activity (for example, when math class followed PE class, the students had significantly higher scores). Maybe we should schedule PE before all math classes in our schools. What do you think about that idea? This morning I read an online article on the myhealthnewsdaily site, entitled "6 Foods That Are Good for Your Brain," and another article about how Physical Exercise helps maintain healthy brain in older adults too. The second article, "For a Healthy Brain, Physical Exercise Trumps Mental Workout" was found under Yahoo News. The remainder of this note is quoted from that article: Regular physical exercise appears... read more

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 one-on-one instruction that is more personalized. A tutor will help bring the subject to life and engage the student. A good tutor will... read more

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... read more

Willpower is unique to humanity. It is the keystone characteristic that is directly responsible for our technological advancement over the last several hundred thousand years. Willpower can be defined as the capacity to restrain our impulses and resist temptation in order to maximize our long-term success. It is the expulsion of energy to fight off innate survival based urges to exponentially increase future advantages and benefits. It is the driving force behind all civilizations, and it is what prods humankind forward to learn and grow. When we turn down a bite of cheesecake, step away from a mind numbing reality sitcom, or push off a nap to get some work done, the credit goes to willpower. It is this ghost like aura of control and discipline that we rely on to extend our existence and maximize our accomplishments. When we watch highly successful individuals exercise routinely, read voraciously, and work tirelessly, we are impressed with their ability to resist... read more

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!!

This week in geometry one of my students is learning about the different "centers" in a triangle (orthocenter, circumcenter, incenter, etc), as well as the midsegments theorem and triangle inequalities.  To help him visualize why all of these things are true, I had him cut out an acute triangle, an obtuse triangle, and a right triangle and use these to illustrate the concepts.  For triangle inequalities, we worked with different lengths of string to see why some combination of leg lengths and some do not. These are both quick, easy ways that help students understand beyond the words and definitions what we are talking about!