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.
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!
Helping students succeed in math for over 15 years. Individualized attention makes the difference!