I sometimes hear from students about how they have a bad math teacher. What makes him or her a bad teacher? Sometimes students don't like how much homework they are assigned, or how strictly the teacher runs the classroom, or that the tests are too difficult. Oftentimes, a student might not care for the personality of the teacher and there exists a personality conflict. Now if for some reason the teacher does not know the material that they are supposed to be teaching that is another story and I would see if it is possible to switch to another teacher. However, many times what is required is a shift in how you perceive the teacher. Try changing your perception from a me vs. them mentality to one of thinking that the teacher is truly on your side and looking out for your best interests. They are assigning lots of homework because they want you to really learn the material and get lots of practice. They are giving you difficult tests because they want you to challenge yourself to take it to the next level and be prepared for the next math class. They are running a "boot camp level" discipline in class because they want to make best use of the class time and they want it quiet so everyone can hear and get the most out of it. Occasionally, a student may have gotten off on the wrong foot with a teacher and the teacher may actually perceive a given student as a "trouble-maker" or "lazy", etc. If you feel your teacher has a poor image of you try going to the teacher and saying something simple like, "I wanted to let you know that I'm turning over a new leaf and I'm going to be putting more effort into this class and I really want to do well." Then follow up that statement with action by participating in class, giving the teacher your full attention instead of socializing with classmates, and by putting in more effort. All of these suggestions can turn what would be a disaster into a learning opportunity for you.
One of the many reasons that tutoring is effective is because you are learning math from another perspective. You are hearing and seeing the same topics you learned in class but perhaps in a different way that may resonate with your way of thinking better. Similarly, I recommend taking advantage of the many sources available to you to help you learn. You could watch a You Tube video on a topic. You could read the book's explanation. You could ask a friend how they do a certain type of problem. You could go to Barnes and Nobles and pick up one of the many study guides available. There are so many resources, many of which are free, to help you. So, if you are not understanding something take the initiative to find out another way to achieve the grade and understanding you want.
When solving any math problem you first want to concretely identify what you are trying to solve. Then, you go about constructing a plan for solving it. This may sound obvious but as you go on in math the problems progress from 1 step to 2 steps to 20 steps and if you don't break down your plan into small workable steps that fit into the greater whole of solving the problem it is easy to get lost in the minute details. Similarly, not every student that I work with has as their goal to be an aerospace engineer or a mathematician. However, if they have a plan for what they want to go on to study, major in, or a specific career path they can see to what extent their math classes play a role in achieving their goal. A technique I share in helping students with Geometry proofs is the concept of taking what you are wanting to prove(your last step) and working backwards to your givens(your first step). In other words, if you know where you want to end up and you know where you are now you can tunnel from both ends to clear a path towards your goal. So in conclusion, making a plan, working the plan, realizing that understanding math is part of that plan all will give you that extra edge to help you solve your math problems...and achieve your goals.
Some students are good at math until it comes to the dreaded story problem. They have conditioned themselves to give up on it before they have even begun. Here are some suggestions that can help you be successful with story problems.
1. Read through the entire story problem quickly to get a sense of what is happening but don't be tempted to hesitate or pause on individual words or sentences. That is why I say read through it quickly.
2. Go back and ask, 'what am I being asked to solve for?'
3. Draw a diagram if possible and label it with the appropriate dimensions.
4. Write an equation or inequality to solve the problem.
5. Solve it.
6. Do a 'reality check' on your answer to see if it makes sense.
Again, the way to get really good at something is to do it a lot. It's no different with story problems. Keep doing them as often as you can until you start to enjoy the challenge. Oftentimes what is being asked is not that difficult. Textbook writers are just aiming to give you a real world application of math. After all, in daily life aren't all math problems actually 'story problems?'
In agriculture or gardening there is the concept of the three sisters. When corn, beans, and squash are grown together they mutually help and support one another like three sisters. One could think of negative numbers, fractions, and multiplication tables as a sort of three sisters as well. These mathematical three sisters are mutually interdependent and interact with one another in virtually every math problem. If your son or daugher is between 5th and 9th grades or older and they struggle with math, ask them if they know these three concepts:
1. All of their multiplication tables up to 12 x 12.
2. How to add, subtract, multiply, or divide using positive and negative numbers.
3. How to add, subtract, multiply, and divide fractions and mixed numbers.
Oftentimes, students never really master these concepts and when they go on in math they are constantly faced with these three and are then stumped by problems that have these components to them. When helping students if I find that they don't know one, two, for even all three we take a little tangent and I explain how to understand and work with these sisters and give them some practice to do on their own until they've got it down. So ask your child about these three concepts...but don't mention the three sisters because they won't know what you are talking about. That analogy is really just for gardeners.
There is a positive correlation between teachers' higher expectations and higher student achievement. In other words, the more teachers expect from the students in their class the more the students rise to those expectations. I'm often asked by parents whether they should have their son or daughter go into a "lower level" math class than the one they are in. Most of the time I say that they should stay in the level they are in or go into a more advanced class not the other direction. Here's why: Not only are you in a more advanced class with higher expectations which will allow you to achieve more but you are often surrounded with students that are more interested in learning the subject matter and thus are placing yourself in a more conducive learning environment. Occasionally for some students this would be too much to ask of them, but for most they find that they just needed some incentive to step up their efforts, rise to the challenge and start to see that they themselves can be high achievers. Additionally, in the long run, I would rather see a student get a B in a more challenging course than an A+ in an easy class where they are repeating topics they have already covered. When students transition from elementary to middle school, or middle school to high school, or high school to college there is sometimes a subtle or not so subtle resistance to the increased expectations and time requirements to succeed in math. So, after going through the "growing pains" of these transitions then look forward to the growth.
Oftentimes, one can avoid having to memorize in math if the underpinnings of a given process are understood. This is always the preferred method, however, for convenience there are many formulas that are used to make solving problems simpler without having to recreate the wheel each time. Below are some techniques you may find useful. Feel free to comment if you have additional techniques you'd like to share.
1. Whenever you are solving a problem that requires a formula - write the original formula down in it's entirety without immediately substituting in values for the variables. After doing problem after problem this way you will have inevitably impressed the formula into your memory banks.
2. As mentioned in a previous post, you can always go the flash card route. Write the formulas on 3x5 cards, put them in your pocket or backpack and go over them multiple times throughout the day until you've got them down.
3. You can repeat the formulas out-loud over and over again so you are audibly hearing them repeated. Some people learn better by seeing, others by hearing.
4. Maybe you are more of a tactile learner. You could trace with your finger or your whole hand the formula in the air or on the table. If it is a geometry formula involving a shape you could make a 3 dimensional replica and hold and look at it from every angle while seeing each dimension required in the formula.
5. Perhaps you are artistic and like to make a little rhyme, song, or rap of the formula to help you remember it. I've had students sing me so many different renditions of the quadratic formula that I'm always amazed...and it works.
In conclusion, I'd just like to say that if necessity is the mother of invention then repetition(which all the above techniques require) is the daughter or granddaughter. Mathematicians created these formulas and we are now learning to appreciate, learn and use them. And hopefully some of you will go onto discover new ones as well...and p.s. you get to name the formula whatever you like...or name it after yourself if that suits you!
I used to think that the best study environment was the quietest with the least amount of distractions. However, after many years, I have come to believe that a mix of different study environments is the best. Let me explain. When I was in college I used to seek out the most remote, secluded, and quiet places on campus to study. There were times that it was so quiet that I actually started to become distracted by the incredibly loud sounds of my breath and even my own heart beating! (I know...funny. Right?) Overall, having a really quiet place to study is beneficial but the downside is that one becomes habituated to needing a quiet environment to concentrate. In daily life it is almost never quiet. The person next to you might be continually talking to himself, coughing, or foot tapping while you are taking a test. You don't want these little things to affect your grades or your ability to focus. So, what I suggest is to condition yourself gradually to different levels of cacophony and distractions to hone your ability to concentrate. This is an invaluable skill that will not only improve your math scores but is something that will yield benefits your entire life. Happy studying!
I often hear students say that they "get it" in class but when they go to do their homework they draw a complete blank. Or similarly, a parent will tell me that their son or daughter does well on the homework but not on the tests. Both of these scenarios usually point to math being treated as a "spectator sport." It's easy to watch a teacher explain on the board how a problem is solved but until you actually "wrestle" with it yourself you won't build the mental math muscles needed when it comes to the test or real-life applications. So in addition to paying attention in class be an active listener and try and anticipate what the next step is while the teacher is explaining and if your hunch is incorrect use that to learn from. Most importantly, work the practice problems. Do the easy ones first but then challenge yourself by doing ones that look "impossible" to make you think and build those mental muscles. When I work individually with students I ask them how they would "tackle" certain problems. Then I may adjust the problem slightly and ask them what they would then do in the modified situation, etc. I will show some examples but I want the student to have the experience of it themselves and feel the anguish of defeat followed by the feelings of victory and success! So get off the bleachers and get into the game - you can do it!
There are 3 types of study partners that are good to have. First, studying with a fellow classmate who knows more about the math you are studying than you do can help you fill in the areas where you are weak. The downside to this type of study partner is that they can easily leave you in the dust struggling to keep up if they are much more advanced at math than you. The second type of study partner is where you know more than your classmate and you are helping him or her to understand the material better. This is a good type of partner to have because it solidifies your understanding and helps you to better remember what you have learned. The shortcoming here is that you may not be learning anything new. The third type of study partner is you yourself. You sit down and work through problems and see where you get stuck or are not as confident. The challenge here is that you may be making mistakes and not realizing it or not knowing if and when there is a better way to approach certain problems. Overall, it is good to experiment with a mix of all three types of study partners as they all have their strengths and weaknesses and see what helps you the most.
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