I think there is a part of all of us that likes extremes. We all "ooh and ahh" when someone completes a marathon, or goes on an all raw food diet, or pulls an all nighter to cram for an exam. However, it's the little things done regularly day in and day out, or week in and week out, perhaps seemingly insignificant but which really add up to the tangible results that we seek. (Uh oh, prepare yourself, here comes the segue to studying and succeeding in math.) Math, unfortunately, is not just one class. Wouldn't that be great if it was? Imagine telling your friends: "I took that class, it was really easy, I Aced it!" Alas, we have to keep working at it. Each year we have to build on what we have learned previously. Luckily, throughout the math curriculum we keep cycling back around to revisit past topics at a more advanced level but also giving you the chance to pick up things you didn't understand or only understood very shallowly. If you have given yourself the idea that you aren't good at math perhaps it's because you(currently)don't really understand what is going on with all those numbers, symbols, diagrams, etc. Maybe you don't understand what is being asked or don't know where you have been or where you are going next with the math you are learning. I argue that math is like a large tree with many branches but what most students are actually learning is the main "trunk." We start at the base of the tree and learn the math language it's symbols, operations, etc. Then we learn applications(i.e. story/word problems). We do go down some of the large side branches to give you the ability and appreciation of how to use math in different ways but we generally return to the trunk in short order to go onward and upward. Aim to really know the trunk of the math tree. When students get their tests back the reason they often get a lower than expected grade is not because they didn't understand the new concepts its that they made the errors that should have been mastered lower down on the "trunk." So before I go off the deep end with this analogy creating a forest out of every subject let me just say that there are no secrets, per se. Practice a little bit every day or every week. Build on what you know, if you miss something go back and fill in the gaps. Remember that the math skills you take for granted you had to learn at one point and the math you don't understand now you can learn the same way too. You can continue to improve your understanding, skills, and efficiency. Seek out help from friends, classmates, parents, teachers, and a tutor. They can help you to see things from different angles, approaches, etc. to help make math understandable, easier and your own. If I can be of assistance to you let me know. Practice for the ACT don't just take it, study for your tests, take it seriously(but not too seriously, a relaxed but focused mind learns better) have fun, realize at this stage we are not coming up with or discovering math we are just learning what mathematicians discovered hundreds of years ago and wanted to share with everyone!
Some teachers will take your paper, tear it up, and throw it in the trash if it is done in pen! Wow! I know that sounds harsh but you should only have to do your math in pen once to realize that pencil and eraser are the way to go. I'm not sure why students like using pen. Perhaps pens glide more easily across the page, or create darker print, or maybe it just feels like a more grown up thing to do. In any case mistakes in math are inevitable and being able to correct the small typos or even to start a problem completely over is the purpose of pencils. What I recommend is using a pencil and eraser that are easy and enjoyable to use. Some mechanical pencils have lead that is so fragile that the lead constantly breaks. Some erasers are so hard(usually the pink ones) that instead of erasing they just make a mess of things. So get some decent writing(and erasing) utensils that will make doing your math more enjoyable and save the pen for brainstorming your big ideas on the back of envelopes and napkins! One thing I notice successful students do is that they 'sum it up.' What I mean is that they say in their own words not only how to do a particular problem but also how it fits into the greater whole of the chapter or concept they are learning. They will bounce their ideas off me by saying something like, 'so basically what we are doing is learning techniques to show how different series converge or diverge through these various tests, is that right?' Then they will follow up their summary with other questions such as, 'why is knowing that useful?' and a dialogue ensues followed by further clarification and a deeper understanding. Furthermore, this whole process usually diminishes or eliminates the intimidation factor of a new and challenging concept down to size. It helps with remembering it also because you have made it your own by relating to it with your own lexicon. So, don't hesitate to do a summation with yourself, your teacher, a fellow student, a parent, sibling, and/or a tutor to help you grasp those math concepts! It's ironic that as I write this that I, myself, am off sick. Math is one of those classes where almost every day a new concept is covered. Miss a day and one can quickly find oneself swimming against the current to catch up. Whether it is orthodontist appointments, student government meetings, sickness, missing the bus, making up tests/quizzes, and/or traveling sports teams if you are not there you are adding a degree of difficulty. Sometimes these events are unavoidable, but if math is one of those classes that you struggle with, make it a point or rather your goal to have 100% perfect attendance! Schedule those braces appointments at a time that doesn't conflict with your math class. Also, make sure to go to bed early and get extra sleep so your immune system is at it's best to keep you from being off sick. If you have to make up a quiz or test see if you can do it before school, after school, or on your lunch break. You get the idea...make it your top priority to be in that math class seat when class starts ready to learn every day whatever it takes. Now, if for some reason you know you are going to miss, make it a point to get the materials, assignments, and/or worksheets before you are off and start working on them that same day so that when you get back you can seamlessly rejoin the class. So there you have it - being there is the first 50%...for tips on mastering the other 50% read some of my past blogs.
This seems to be the question on the mind of many a parent and student alike. Which one to take? Well it all depends what your aspirations are and what your college degree program is like. If you are going into engineering, business, the sciences, and/or math then by all means press on and take Calculus. If you have a full schedule and don't want to be too overwhelmed then just go for the AB Calc. This class will cover less material and at a slower pace. If you are up for it and can devote the time to your studies the BC Calc will put you in a good position to pass out of two full semesters of college calculus i.e.Calc 1 and Calc 2. Now if your schedule is full of other AP classes, extracurriculars, and/or higher math is not needed for your college degree then by all means take AP stats. But, keep in mind everything you have been learning over the past 4 years or more has been preparing the ground work for you to take Calculus so don't bail out now unless you have some good reasons(see above)! If you are not getting the results you want I encourage you to try something different. It may be something big or it may be something small. Here are some ideas I have been ruminating over the last few days:
1. If you feel you are totally lost it may help to get a map. A number of calculus students and parents have contacted me this year because they or their student feel totally lost. Sometimes I know it is easy to get confused in the minutiae of infinite details so having an overview and understanding of how all the pieces fit together can be invaluable. The Idiots Guide or Dummies Guide to Calculus as well as others like these are resources that can give you that perspective of what Calculus is, how it works, and how all the pieces fit together. 2. Make it a goal to ask your teacher 1 question every day. Whether it's before class, after class, during class, on your lunch hour, before school, or after school 1 question a day every day can help you turn things around or accelerate your understanding if you are already doing well. 3. Help others. Try and help explain a difficult concept to one of your friends and classmates. You will either solidify what you know or quickly realize there are some aspects of that concept you need clarification on as well. Ok, so that's a few ideas and I'm sure you can think of many more as well, but try and do something new and improved to help you succeed in Math! If you would like me to write about other topics or answer any other questions please comment below and I'll discuss them right here on the blog. Until next time - keep studying! It's the SuperBowl today, but that's not the game I'm referring to....rather, Second Semester Math. The holiday break has ended, finals/midterms have come and gone, and we've had a number of snow days this year. All of these have given students a well needed mental rest but now it's time to refocus your efforts on where you'd like to see your grades come the end of the year and to build a nice foundation of understanding that will be needed for next year's class due to the cumulative nature of math.
My favorite technique for students is getting a head start and staying ahead of the game. Imagine you are running a race and you fly off the starting blocks, sprint down the lane, but get this....the starting gun has yet to even go off! When it does finally fire you settle into a steady pace even saving a little extra energy for the sprint at the end. And, there is no penalty for doing this....in math that is. When students take advantage of this I see changes in their confidence level, their grades, and a sense of relief and even enjoyment when it comes to their math class. A student yesterday told me that their teacher said jokingly to him, "stop raising your hand...give the other students a chance!" He was so proud when he told me this and that he knew what was going on in class and that it was now so much easier. I always try and spend some time looking ahead at upcoming material with students to help give them this head start but students can do this for themselves as well. Just take a few minutes and "speed read" the section ahead of class. You don't have to understand everything you are reading, just skim it spending a few extra moments on the formulas in the boxes, bolded terms, italicized sentences, etc. Give this a try and let me know what it does for you! Retention seems to be a challenge for a number of students whom I see. Topics are covered in a given chapter then quickly forgotten. This is of course a big mistake. I suggest to students that they mentally tell themselves to 'hold onto this information.' Another suggestion is to keep a running formula sheet in their binder somewhere that can be continually added to as new formulas or topics are learned. When adding new formulas you can quickly review recently and not so recently learned ones. On the Math section of the ACT, topics through Algebra 2 are covered and many students have already forgotten a large part of what they learned in Geometry. So, a large part of being successful in math is not just learning new material but rather holding onto the old. Why is it so difficult to remember? When I think of other subjects such as Biology, for instance, there is many times more facts to remember than in math. Part of the reason I believe it is hard to remember is because new facts are shallowly understood as well as not tied into previously learned concepts. This is why I focus on understanding why and how something works as understanding trumps memorization every time. You can often quickly figure out a problem even in the absence of a given formula if you understand how and why a formula works. So work on deepening your understanding and see how what your leaning in math ties into the greater whole of Math. Also, the holiday break is quickly approaching-this may be a good time to take some practice ACT tests and get in some quality practice. You can break up the test and do a part every few days, then by the end of the break you will have completed a few tests. Happy Holidays. There has been a positive movement to reduce/recycle/reuse that I have seen taken to heart by the students I work with. However as students progress in math they need to let go of previous ideas held about fitting each homework assignment onto a single sheet of paper. I remember my 10th grade math teacher Mr. Saltzman who wouldn't accept any assignment unless there was a blank line between each problem, no writing in the margin, and two empty lines at the top and bottom of each page. Contrast that image with what I often see: students trying to do a 6 step problem all on one horizontal line, no space between problems and/or small illegible writing. When you go shopping for those notebooks at the beginning of the quarter, semester, or year pick up the 5 subject-perforated-college ruled ones. These hefty notebooks are not to be used for 5 different subjects but rather dedicated just for math. In this way you can stretch out and allow yourself plenty of physical and mental space to complete those assignments. Furthermore, you will have the space to be more organized and can see where you are making errors and correct them. Then at the end of the year if you choose not to save your notebooks you can always RECYCLE them! The first quarter has come and gone, grades are posted and the dust has settled. Where does your child stand? Lower marks than you had hoped? I've been asked by a number of parents lately to convince their student that they can and should do better. This is a very tricky situation more so than most parents realize. Why? Many students are working at their capacity, others are very sensitive to anything perceived as criticism, and still others may already be resistant to receiving outside help. All of these reasons and more put me in a very precarious situation. If I press too hard students may shut down never again to be very receptive to the help or advice I offer. Press too little and parents may be unsatisfied with the service I offer. What to do? I always go back to what I feel works which is the following: I encourage, then encourage some more. When a student is successful I praise them, when they are wrong I offer suggestions for improvement. I want students to look forward to their tutoring sessions not dread them. My aim is to increase self confidence and mathematical competence through my unique approach which is different from perhaps a boss', coach's, or even a teacher's approach. I received a nice testimonial last year from a family who praised me for, 'Creating a conducive space for learning.' which is actually what I consciously aim to do through building a repoire with the student, gaining a student's confidence in my teaching style, etc. All of which can be easily lost through a well meaning but too heavy duty an approach. If you are looking for someone who can help your child navigate Mathematics with an accentuate-the- positive persuasiveness I'd be happy to help. Mario shares his various math teaching insights gained through his many years of individualized tutoring on his blog at www.mariosmathtutoring.com He can be reached through his website to schedule private tutoring sessions. |
Mario DiBartolomeoHelping students succeed in math for over 15 years. Individualized attention makes the difference! CategoriesArchives
August 2023
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