What I see daily is parents who are very cognizant of the fact that to get their children into the top universities top grades are a definite priority. Toward that goal I help students with test taking strategies, memorization techniques, and alternative problem solving approaches. But what I also strive to include is a deeper understanding of how math works so that what is learned is not promptly forgotten. Again, math's cumulative nature requires retention and an understanding of the pieces to the greater whole. To help in this regard, I utilize and encourage lots of visual diagrams in my tutoring so that a specific process is not just repeated to solve problems, but rather a picture of what is actually being described can be seen, interpreted, and remembered. The temptation is often there for students to hurriedly finish through many subjects of homework without thoroughly grasping the meaning of what they are doing and why I say, "to improve your grades you also want to deepen your understanding."
This is a common question that I get a lot, especially amongst juniors in high school that are in Pre-Calculus and feel burnt out from years and years of math classes. They are approaching their senior year and they are tempted to just take some easy(or easier) classes and just slide through their last year. The name "Calculus" alone makes some students shutter at the thought. After all, they think, "I can take more math classes in college." Unless, students are clearly going onto be a mathematician, engineer, or physicist for example they reason that they have little need for more math. Here is where I give them my, usually unpopular, opinion on the matter. First of all, I tell them that the name of the class(Calculus) is more intimidating than the class actually is. Also, it is just the next step along the path they have already been traveling. In addition, many universities require that students complete up through Calculus 1 even for seemingly unrelated degree programs. Furthermore, you may decide to change your course of study. Completing a math program up through even the first Calculus course gives you a solid math background whichever direction your studies take you. Also, while you are still in high school you stand the best chance to really learn, digest, and absorb Calculus. At college your class meets twice a week, you usually have little to no interaction with the professor, and are left to figure out a lot of the math on your own. Conversely, in high school you attend class on a daily basis and can take the information in bite size manageable pieces that you can more readily understand and retain. Think of it this way: If you were running a marathon and had completed an amazing 25 miles, would you walk the last mile? Similiarly, you are about to round out a comprehensive and cumulative math sequence. Don't stop now, the finish line is in sight and even if you don't ever use Calculus again you can always tell people you took Calculus...and yes it will sound impressive.
After working with many students I notice that students often tell themselves they are either good at math or not good at math. It is as if they have a relationship with math that is either "friendly" or "not-so-friendly." What I would like to share with you here is that math is actually neutral towards you. All of the math that students are studying at the middle school, high school, and even undergraduate levels has already been discovered, analyzed, predigested, and systematized between 300 years ago all the way back to thousands of years ago. So its not like mathematics somehow plays tricks on you when you are taking a test and changes its mind how it is going to operate that day(although it may seem that way sometimes). But rather, math is like a loyal friend that you can always count on in a consistent reliable way. I tell students, "when you don't understand something it is difficult, but when you understand then - it's super easy right?" Furthermore, even though some students say that they are bad at math, the fact of the matter is that the math that they understand they are really good at it...it's the math that they don't understand that is perceived as the antagonist to their good grades. So our work begins with building on the excellent math skills that students already have and adding to them...and well, it couldn't hurt to think of math as that good friend.
Midterms are here and I often get calls from parents wanting help for their child for the first time. Sometimes these students have fallen so far behind after 15 weeks of school that one session with me will not allow them to bridge the gap in their understanding. Fortunately the parents recognize this also and ask me what they can do at this stage of the game. This is where I say, "to go forward go back." What I recommend is that students, in addition to keeping up on their current material, take the time to review problems from each chapter starting with chapter 1. This can be a daunting task, but most textbooks have a section at the back of the book entitled, "Extra Practice." This section has 1-2 pages with the key problems that one should know how to do from each section of the chapter. I recommend making a daily commitment(Saturday and Sunday included) to do say 10 problems. By the end of the week you will have completed a chapter or two and by the end of a month you will have completed the entire first semester's material. You can have a parent, teacher, friend, or tutor help you with the ones you don't understand. Again, this is not my most popular recommendation which is why when I mention it to some students I never see them again. However, I want you to succeed, so I suggest breaking this down into very small manageable steps so it won't take much extra time per day and you will be building the foundation for success in the second semester and beyond! You can do it!
When you see a math tutor you want to get the most benefits possible. After working with many students here are some suggestions based on the students that get the most out of tutoring and how you can too.
These are 10 suggestions from some of the students that get the most out of their sessions with me. Pick out a few or even all of them to start maximizing your benefits too!
This is a good question? Your child goes to class, maybe even sits in the first row, does their homework, yet still struggles or does not get the results desired. Unless the student is actively involved in asking questions or seeking help on missed concepts, due to the cumulative nature of math, they could still be coming up short. A tutor works - individually - with a student literally looking over their shoulder to see if and where they are making mistakes and can fill in gaps even if from previous math courses. Sometimes, students are shy or reluctant to ask questions and a tutor can ask the key questions to get them thinking and understanding. Also, when a tutor works with a student a lot of material can be covered relatively quickly helping a student either to catch up or get a nice head start on the upcoming week's material. I generally work with students weekly and, depending on the student, we sometimes are able to review a number of sections of a chapter equating to a few days to a week of material covered in class. A tutor is also there to encourage a student and to help them gain self confidence. When I first started tutoring I did some work for a retired teacher that had taught for over 30 years. I asked her what she thought was the most important thing when working with students, in other words after 30 years what was her 'secret'? What she told me essentially boiled down to 'positive reinforcement.' I have incorporated her insights, focus on the positive, believe in the students I work with, and encourage them. Students are relaxed when they get help from me and get good results because of the positive learning atmosphere I create and the high self esteem they build when they see themselves more easily reaching their goals.
I say that midterms, and finals for that matter, are difficult yet easy for the following reason: These types of assessments require long term memory(the bad news) yet generally do not require the same depth of understanding(the good news). These tests are usually weighted more heavily than regular tests so this creates an opportunity to really boost your grade.Generally, the central concepts are focused on so if you understand the basic types of problems from each section you stand to do very well. Go back and focus on the material you covered at the beginning of the semester as those are the problems that are least fresh in your mind and review toward the more recent chapters. Circle or write down the problems or concepts you don't understand and enlist the help of your teacher, online resources like YouTube, or a math tutor. Good luck on your test!
1. First go over problems you don't understand or are still shaky on. You don't want to spend your valuable time going over topics or questions you already know.
2. At the end of every chapter there is usually either a Chapter Review a Chapter Test or both. Also, at the back of the book there is usually a section entitled Extra Practice. Pick a problem from each section and make yourself a mini test. Then go over which ones you missed and do more of that type. Then go back and make yourself another one of these practice tests and repeat until you are confident.
3. To take it to the next level make up your own problems and then solve or attempt to solve them. Try to challenge yourself by pinpointing your weak areas.
Does your child dislike fractions? Do they reach for a calculator every time they see one of these / (i.e. a fraction bar)? The problem with converting every fraction to a decimal is that your final answer will be a rounded answer - not exact. The other issue is that much more time is spent in avoidance of what is and always will be there(fractions) instead of acknowledging that "I need some help with how to work with fractions." I see this frequently with students, not just with fractions, but in other areas as well. In the short term it's just easier for students to avoid or gloss over trouble areas then to learn some alternative ways to problem solve in math and this is where a tutor or teacher can help a student have that "ah ha!" moment which can allow for a student to experience leaps and bounds in their progress.
Why do I mention this? It's easier to spend a little extra time to stay on top of your math and math class then to let yourself fall behind and then try and catch up. It's not that a person cannot catch up, it's just that it is easy to get mentally defeated when your teacher slowly starts to throw in a little Greek(think alpha, beta, delta, and theta) to the classroom conversation and it all seems well.. a little "Greek" to you too! Try and keep up with the overall concept of what you are doing in class and then get some extra help from your teacher, online, or elsewhere to help you fill in the blanks.
When you are learning math tell yourself to "hold on" to what you are learning. Take that extra second to imprint it on your memory because math has a way of spiraling back around to similar topics but at a more advanced level. This way you won't have to re-teach yourself what you already knew before.
On the upside, going back to the fundamentals(as mentioned in a previous blog) and getting the basics down will reap dividends in making all the arithmetic of solving problems easier and have you spending less time on your homework and allowing you more time to focus on the harder test problems or ACT.
Helping students succeed in math for over 15 years. Individualized attention makes the difference!