I think technology is making us all a little short on attention and patience too! Lately, what I've been seeing are students who 'don't do' story problems. Whether these story problems are in their math homework or even on the ACT. Are story problems more difficult than regular problems? Maybe a little bit, but after all, math problems in real life are actually story problems, right?! What I recommend is to work with a lack of patience or short attention span and just plow right through those story problems. That's right! Read as quickly as you can through the problem without pausing at all. Even read quickly through the multiple parts a, b, c, and d too all in one go. If you feel yourself getting weak, light headed, or bogged down, go even faster. Get yourself over the initial hurdle...then go back and find out what the question is asking you to solve for(hint: it's usually asked in the last sentence). Then, draw a diagram if applicable, identify your variables, write an equation, then solve. Done! Here is a concise list of must know topics for doing well on the ACT: 1. Slope formula 2. Distance formula 3. Midpoint formula 4. Equation of a circle 5. Equations of lines (parallel and perpendicular) 6. Area and volume formulas of common shapes 7. Pythagorean theorem and Pythagorean triples. 8. Functions 9. Rules of exponents 10. Factoring 11. Probability 12. Averages 13. Proportions 14. Trigonometry(soh cah toa) 15. Special right triangles 30-60-90 and 45-45-90 16. Multiplication counting principle 17. Percentage problems 18. Fractions 19. Graphs of lines and inequalities 20. Reading and interpreting charts and diagrams. The key to doing well on the test is RECOGNIZING what the problem calls for and knowing which of the concepts above to apply. This is where experience makes all of the difference. I tutor students on the math section of the test and what I do is have them take a number of ACT tests on their own and then after each time we go over the ones that they miss and I point out what concept is DISGUISED in the problem and a more direct way of solving it. The experience gained is very valuable but it is experience that has to be gained by the student themselves through EXPERIENCE with the test and wrestling with the problems and learning when to apply the various topics mentioned above. This I feel is the best way to spend one's time in preparation for the math section of the test. Again, I am very familiar with the test and have helped many students improve their score but there isn't any secret beyond knowing the key topics and taking a lot of practice tests and have someone point out what to look for and apply to the ones that you miss. Someone just informed me today that their score went up a full 7 points since I started tutoring them. They put in the effort and there is still room for even more from this particular student. I work with a lot of students on a daily and weekly basis and students often impress me with their high level of efficiency. From how quickly they can locate something in their book or notes to how they prioritize what they don't understand and want to work on in the sessions. Math may not be their favorite subject, but their laser like focus, level of intensity, and willingness to jump right into the heart of it all allow them to quickly overcome any obstacles that may be in the way of their understanding. Not to be confused with hastiness though. Some students may want to hurry through their homework, assignments, and quizzes to be 'done,' but this is something entirely different. It's a willingness to engage fully with math and learning in general with the speed and attention with which teenagers type text messages or play video games. They work at their own pace yet they are challenging themselves and adapting to subtle nuances and variations and integrating these into their understanding like a giant snowball expanding with each successive turn. See if you can cultivate an efficient approach to learning. It starts with a willingness to learn something, right? Being organized helps too. Followed by asking questions on sticking points helps to continue propelling oneself forward. Lastly, being reflective. Pay attention to how your time is being spent. How could it be spent better? Tutoring also can be part of an effective efficiency plan, especially when added to a student's own class and individual efforts. When I work with students I am cognizant of the fact that I have a limited amount of time to convey a math concept or idea. A student will ask a question or may make a misstep in solving a problem and I know that once I start talking I only have their attention and open-mindedness for a short amount of time. This is for a number of reasons. One reason is that some students just want to know the answer to the current question that they are working on and not necessarily anything more. Another reason is some students have limited patience and/or attention span. A third reason is that some students can get bogged down by too much information. So what is a tutor to do? I am careful to choose my words and examples carefully so as to make maximum impact in the short amount of time that I have their attention and open mind. I aim to answer their questions plus give them a little more to deepen their understanding and improve their math skills.
We could fill up volume after volume discussing this topic but still let's go into it a little bit here. I periodically ask students how they are doing in their math class and what grade they are getting. Sometimes the answers to these questions don't seem to match. A student may say, 'I'm doing good.' What grade are you getting? 'B-' is the response. Some students are just coasting by and not putting in a good effort and seem to casually accept a B- as good 'enough' though they know they could achieve higher. On the flip side, some students are taking an advanced math class or honors class and are working their tail off and earn every percentage point of that B- and are discouraged. There are so many factors that determine what grade a student may get that I wouldn't rush to make any self judgements such as 'I'm not good at math' or 'I'm not A material,' etc. Math is a collection of topics. Some like Geometry you may enjoy while others such as Probability you may abhor. One chapter you may completely ace and with the next you may have quite a struggle. Some teachers make math easy for you to understand and you may resonate with their style of teaching while others you may not. In spite of everything you need to ask yourself if you are putting in your best effort and if there is a way you can improve or are you doing your best already. When the grades come in you can see if you want or need to change your approach. Parent-teacher conferences have come and gone, Progress reports have come and gone, and now some students have math grades very different from their other classes - but not different in the good sense of the word! At this point some parents will ask me, 'Can you talk to_____(my son or daughter).' Naturally, parents want their child to get the best grade possible and I too want them to get the best grade possible but the talk that parents have had with their child hasn't yielded the desired results so I'm called in for back-up. I know from working individually with hundreds of students that if I come down on them too hard they will shut down, get more stressed and/or resistant and learning becomes that much more impeded. If I am too soft with them they can be too lax in their efforts and not achieve their potential. So I have come to think of this as 'the pep talk.' I review with the student what their approach to their class has been up to that point: how much time do they spend studying, do they ask questions in class, are they actively participating in their class or are they relying too heavily on their tutor as a substitute for their class and their own individual effort. I emphasize that I believe that they can be doing better with a refocused and fine tuned approach. I also ask them about their college and career ambitions and explain that they will need a higher understanding of math to get where they want to go. I aim to make them feel empowered and to realize that they are doing this for themselves and I'm there to support them in their efforts but they need to take charge of their learning. I focus on where they can improve and tell them they can do it. Each pep talk is slightly different given the situation but my goal is to emphasize the positive and encourage students to keep going forward in the right direction. I am not a counselor, life coach or anything like that so I just stick to helping students the best I can with their math, but occasionally, after knowing a student and family for awhile I will be asked to say a few things along these lines and I'm happy to do it. If you feel you or your student needs a pep talk, let me know. I am still working on my best-selling motivational self help book so it will be mostly just words of encouragement, ie a 'pep talk' - but that may be exactly what your student needs. Tutoring is not a magical pill that a student takes that cures all their math ills without any effort on their part. (Could you imagine how great that would be!) Rather, tutoring is a lever that one applies to amplify one's own efforts. The famous mathematician Archimedes is often quoted as saying, 'give me a place to stand and a lever long enough and I will move the whole world.' You can think of the tutor as the fulcrum and the amount of effort the student puts in both during their tutoring sessions as well as on their own as corresponding to the length of the lever. No effort no results, lots of effort spectacular results. Again, because what tutoring does is a-m-p-l-i-f-y ones efforts. Some of the students I work with are actually very good at math yet they and/or their parents like to have someone with which they can work to keep their skills strong and to keep improving. People that know how to do yoga or lift weights certainly could do their workout at home yet many of them still choose to go to a studio or gym. Why? These people find that at a studio or gym there are trainers there that make sure they use good form, that they push themselves a little further than they normally would and to help them adjust if they are making mistakes. It is the same with some of the excellent math students I work with. They want to know how they can be faster and more efficient. They want to know alternative ways of problem solving and how to go beyond their present level of understanding. I give these students a little tune up and a little push to stretch their math minds a little further. In short: a math workout!
There are various types of questions that math students ask me and one could qualify them into various categories.. There are the almost rhetorical type questions such as 'what do we need to know this for?' Or 'Do you ever need this in your daily life?' These questions are often posed because students are struggling or are resistant to the practice required to understand and to continue moving forward in math. The next type of question deals specifically with the specific topic at hand. The third type seeks to understand the underpinnings of math: why it works, how it came about and so on. I had a question of this type the other day. A student was asking where the concept of degrees came from and we discussed it's possible roots in that there are approximately 360 days in a year and that the earth moves approximately one degree each day around the sun. A fourth type actually aims at advancing math itself! I've had some of these questions, where students actually aim to come up with new mathematical formulas and they run them by me. |
Mario DiBartolomeoHelping students succeed in math for over 15 years. Individualized attention makes the difference! CategoriesArchives
August 2023
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