Some curriculums emphasize a process oriented approach through practiced repetition while others aim to give students an experiential approach to learning through a self-discovery of math's underpinnings. Both methods can leave students lacking the skills to effectively use math. If your student finds themselves feeling like a machine cranking out problem after similar problem make sure they are doing more real-life application exercises followed by doing some writing on why a given process yields a given result. On the other hand, if your child has a general sense of the magnitude of numbers, spatial relationships, and the connection between similar figures make sure they know their multiplication tables, can add/subtract/multiply/divide fractions, as well as graph lines, etc. In conclusion, you want to aim for a balanced approach: an overall understanding of why math works the way it does as well as having the process-oriented skills to execute and solve those math problems. The next time you tackle your homework problems give those challenge problems a try. They stretch your mind and often tie together the concepts you have been learning up to that point. Just think how easy the regular problems will seem once you master and understand some of those section 'C' problems. Some of the students I meet with want to know how to tackle all the challenge problems and others prefer to avoid them if possible. To this latter group, I encourage you to try and do a tougher problem once in awhile to build those mental math muscles. Oftentimes these problems will answer for you the question, 'Will we ever need this? and 'What is math used for?' In conclusion, keep on studying and finish off this first quarter strong! This could be my shortest blog yet. Practice, then practice some more! Experience with the test, in my opinion, will help you more than anything else. If you take a number of timed practice tests on your own and see which problems you are missing I can show you how to approach and solve those problems. When you see similar problems you will know how to do them. Remember, the ACT is a concept based test not an intelligence based test. Also, you may find it interesting to know that the entire test can be done without a calculator ...but of course you are free to use one as well. My highest recommendation is to start taking practice tests on your own, see which ones you are missing, review those concepts and repeat. I could tell you all kinds of neat tricks like picking the letter b when you don't know the answer but at best these strategies will likely only add a couple of points to your score. If you are reading this you want to see a jump of 5 or more points, right? Many students resist doing additional work over and above their normal homework load so figure out what type of weekly time commitment you can make and commit yourself to it. It's a new school year which means most every student has gone up a grade level and a math level. Every athlete knows that when you go from middle school sports to high school sports to college to Olympic or Pro each is a big step up and requires a whole new level of mental and physical fitness in order to be competitive. Math is the same way. Your teacher will have higher expectations of you this year and will take for granted that you know all the concepts learned from previous classes. The first days of school pay extra attention to the format of the class: Is homework graded? When are the tests? Are there pop quizzes? How are points earned or lost? Notebook quizzes? Participation points? Group quizzes? Use this information to guide you in your strategy to maximize your performance. Try a little bit more this year and start off strong by studying to get an A on that first quiz or test. In this way you are encouraged to continue and you are not spending the rest of the quarter trying to boost up your overall average if you start off with a low score. Ask your teacher questions when you don't understand and for clarification. Last but not least enlist the help of a good tutor early as good tutors are generally in demand and book up early! In learning to read, beginning readers "sound out" what they are trying to read. In this way, they gain confidence that they can read any word that they come across but they also gain confidence in themselves. Similarly, in math, students need tools to help them solve problems as each problem is different from the next. Talking out loud or to oneself about what should be done first, second, and third helps in thinking the problem through gives the math student a starting point to get over the hump of "not-knowing." What I often find when working with students is that they do in fact know more than they realize or give themselves credit for and, with a little prompting, are able to verbalize what needs to be done. What I aim to do is give students the encouragement and the tools to convince themselves to begin the problem with confidence and to talk themselves through the steps. There is a saying, "to teach is to learn." This can be used to a students advantage by the student actually teaching another person how to solve a problem or even to pretend that they are explaining to someone how to solve a problem in every minute detail. This helps them to examine each step more closely, see which steps need clarification, and cements their understanding more deeply. Henry Ford's often quoted saying of, "Whether we think we can or we think we can't, we are right." is appropriate here because what I have learned through teaching is that often a large part of my tutoring is aimed at getting students to agree with me that they are good at math.
Math is a very useful and practical subject however the solving of math problems can start to become quite abstract as you go on in math. Usually In daily life we don't cross paths with a right triangle sitting all out there on its own, the variable x, or a negative number(let alone an imaginary one (i)). Which is why I say 'make it real' for you. Pretend x represents the number of x-ray machines, triangles represent mountains or ski slopes, and well 'i' that's a tougher one but it's a short hand for the square root of -1. When learning anything you want to tie it in with something you already know and understand. If you try to build on a foundation of half understood concepts that's where the abstraction seems like we were speaking English last year then we switched over to Greek and now it all looks like Hieroglyphics, right? So if you need to back up a few steps and fill in the gaps and make these ideas real for you. One last idea is don't be afraid to actually use math in your life. If there is something you'd like to figure out that requires math- go for it. If you get stuck ask your teacher for help. One thing I see off and on is students who are overly tired. Sometimes students are tired after school, sometimes it is early in the morning, and still others after eating. Being tired makes learning math so much tougher. Pay attention to when you are most alert and awake and focus on doing your math studies then. Everyone is a little different but you want to get the most benefits from your time spent. With the longer days the tendency to stay up later is also present so make sure you are getting enough rest so you can finish the year strong!
The concept of apprenticeship is an interesting one as it's different from sitting in a classroom learning carefully planned out lessons. Rather you learn a lot by watching, absorbing, doing, and asking. You are learning not necessarily by being 'taught' but by seeing someone model what you are trying to learn. What does this have to do with math tutoring? Well, one time I had a parent insist that I try and help a nephew as I had helped two other family members and she wanted me to do what I could for him too. It was quite a distance and I tried to politely decline but she insisted, ' just meet with him whatever it takes.' So to make a long story short it turned out that this student was already an excellent math student, had scored a 35 on the ACT, and was being actively recruited by many universities...what could I possibly offer? We talked about school, colleges, jobs, goals, etc. for an hour without hardly a mention of mathematics, yet they were so happy I came over? Why? I happened to mention that he should 'shadow' some people whose careers he was thinking about pursuing and he and his parents had never thought of this possibility. We all learn math in school but for most this is just a means to a different end. This summer think of what that 'end' is and consider interning, volunteering, shadowing or working in an career you are interested in even if without pay. The experience will be invaluable!
I'll share another story about a student I worked with for a couple of years. Her parents had her contribute $5 of her own money to the tutoring sessions and her parents paid the remainder. This student was a Junior and Senior while I worked with her and she had a part time job so she had a source of her own money. Although the parents could have just as easily paid for the tutoring I believe she wouldn't have gotten the same amount out of it. She had a sense of ownership and she wanted to make sure she got a good return on her investment. When we met she knew what she wanted to work on and what questions she wanted answered. She was efficient with the time because now it was 'her' time and now it had 'value' for her. Hmmm, maybe this would work for you too?!
When most students think of the final exam they shudder at the thought of what amounts to not just a test but a comprehensive one at that covering sometimes 6 or more chapters. Before you panic, or worse yet give up before you start, realize what an opportunity this can be. Finals can be anywhere from 10% of your grade in middle school to 20% in high school to 50-60% in college! However, if you score well this can oftentimes mean a jump of one whole letter grade. The final usually differs from the chapter tests in that it doesn't go into the same depth. There is limited time to test on everything covered during the semester so it is the MAIN concepts that are tested. Start going over your old tests and quizzes NOW to fill in gaps in your understanding. Oftentimes, what seemed difficult before will be easier now that all your other math skills have been improved. Lastly, math as a whole is cumulative. Not just chapter to chapter but from year to year. So taking adequate time to study for your final will SOLIDIFY what you have learned and set the stage for a successful year next year in math as well. Make it a good one!
|
Mario DiBartolomeoHelping students succeed in math for over 15 years. Individualized attention makes the difference! CategoriesArchives
August 2023
|