Here are some tried and true strategies for improving math comprehension and grades. Happy new year!
Steps in Math Comprehension, Application, and Mastery OR How to Get the Most Out of Your Tutor
Those individuals who get the most out of life are those people who understand their own role of personal responsibility in that life.
Resource #1: the math teacher
1) Take notes in class. Even if you don’t understand what the teacher is saying, write it down. Later, go over the notes with your textbook. If you still don’t understand, approach the teacher by showing him/her what you’ve written, while you express your concerns regarding your lack of understanding. And respectfully ask if the teacher can explain the concept/term/whatever to you. TEACHERS REALLLY APPRECIATE STUDENTS WHO MAKE A DILIGENT EFFORT AND WHO LISTEN AND TAKE IN-CLASS NOTES.
Do not lull yourself into a false sense of apathy by thinking that what your teacher is saying or writing is something you already know.
A good “rule of thumb” is that if the information is important enough for the teacher to write on the whiteboard, smart board, blackboard, overhead projector, power point, etc. it is important.
Do not lull yourself into a false sense of apathy by thinking that what the teacher is writing and/or saying is already in your text, so you don’t need to write it down. Every time you use your visual, hearing, and writing skills you are literally taking that information and putting it into your brain with deeper and deeper levels of comprehension. And the text is not always that easy to understand, either.
If you have been fortunate enough to get a hand-out/graphic organizer made by the teacher, and he/she is explaining it in class with or without overhead projection, take notes on the hand-out by writing explanatory information in the margins and/or on the back. Do not expect the handout to do the work for you. It is nice to have, and your teacher has taken his/her own time outside of the scheduled teaching day to do it, but it won’t jump through your ears and into your brain. You, the proactive achiever, can make that happen without a trip to the emergency room.
2) Ask questions when appropriate. If your teacher has specified a time during class for questions, ask them. Make a list of questions that you cannot always have immediately gratifed, and cross them off as you or others get the questions answered. Always raise your hand and ask politely. Be specific in your question; do not use terms such as “things” and “stuff”. If you are not sure about the name of a term, try to find it in your text (if possible), and ask the teacher to clarify the term or concept.
If you do not have time in class, or if the teacher has not called on you when you’ve had a question (despite your excellent etiquette), make arrangements during the same class to see the teacher outside of class to clarify whatever you do not understand. (Every morning after calculus class, my professor has a “pool” of students--that sometimes includes me--standing around him, waiting for their turn to ask questions; and he does allow questions during class, as well.)
Resource #2: the textbook
3) Read/take notes on the textbook. The same day that your teacher has covered the content in class, read the textbook and take notes on the text. The longer you wait to cover the material your teacher has covered in class, the less comprehension you’ll have on that material, regardless of how well you did or did not understand the material when the teacher was going over it in class.
When you read the text at home, compare the text and the notes you are taking with the notes you have from class, and combine them. Ask yourself if it all makes sense. Sometimes, the text is easier to understand than the teacher, and sometimes the teacher is easier to understand than the text. Use both! Fill-in or even rewrite any class notes with your textbook notes. The outcome should be a cohesive set of notes on the current material that you, the student, understand and can use for reference and study. Remember, every time you listen, read, and write, the information is further clarified and refined within your brain in ways that even the most sophisticated of scientists do not understand.
Resource #3: homework
4) Do homework after reading text and taking notes. Although considered by some to be an archaic form of torture that somehow trickled into the 21st century, homework, like tests, can be used as a tool to increase comprehension and to assess what and how well you understand concepts.
It is important to attack the homework after you have comprehended the text and your notes because that is when your understanding is at the highest it can be at that point in time. When you try to get homework done without the preparation, it leads to further confusion, bad habits, and even having to redo it. Remember, it takes an average of 7 repetitions in order for basic comprehension to take place, and an average of 27 repetitions to undo any miscomprehensions.
As you do your homework, put a small mark next to, or make a list of any homework problems that you could not do or were unsure of. If you have time, try doing them later after a break and after reviewing your notes and/or text. If you still cannot do them, ask your teacher for help the next day in class. If you are still having trouble, try the problems once again when you are not tired and/or hungry. If you are still unsure or are not getting a correct result, save them for the tutor by adding those specific problems to the list of unanswered questions that you can ask your tutor.
Resource #4: the tutor
5) Clarify questions/material. From the list of questions that you have diligently been seeking assistance for during the week, ask for clarification on anything you were not able to completely understand or were not able to get answered. The tutor can help to locate the information in your text or can bring extra materials/information that can aid in comprehension.
Then review work with the tutor in order to achieve mastery.
Since tutoring is limited in its time, the tutor can suggest ways for you to get more out of all of your available resources.
Keep work/hand-outs that the tutor has given to you in a separate binder. Use those materials in combination with your textbook and notes when you are doing homework and/or studying. These materials are more condensed and specific than your text or notes, and are updated and refined on a regular basis to facilitate deeper comprehension and expedience in doing homework/study. Whenever appropriate, make copies and file any helpful graphic organizers/hand-outs into your math binder that you use for school. In this way, materials are integrated for optimal comprehension and achievement.
1) Take notes in class. Even if you don’t understand what the teacher is saying, write it down. Later, go over the notes with your textbook. If you still don’t understand, approach the teacher by showing him/her what you’ve written, while you express your concerns regarding your lack of understanding. And respectfully ask if the teacher can explain the concept/term/whatever to you. TEACHERS REALLLY APPRECIATE STUDENTS WHO MAKE A DILIGENT EFFORT AND WHO LISTEN AND TAKE IN-CLASS NOTES.
Do not lull yourself into a false sense of apathy by thinking that what your teacher is saying or writing is something you already know.
A good “rule of thumb” is that if the information is important enough for the teacher to write on the whiteboard, smart board, blackboard, overhead projector, power point, etc. it is important.
Do not lull yourself into a false sense of apathy by thinking that what the teacher is writing and/or saying is already in your text, so you don’t need to write it down. Every time you use your visual, hearing, and writing skills you are literally taking that information and putting it into your brain with deeper and deeper levels of comprehension. And the text is not always that easy to understand, either.
If you have been fortunate enough to get a hand-out/graphic organizer made by the teacher, and he/she is explaining it in class with or without overhead projection, take notes on the hand-out by writing explanatory information in the margins and/or on the back. Do not expect the handout to do the work for you. It is nice to have, and your teacher has taken his/her own time outside of the scheduled teaching day to do it, but it won’t jump through your ears and into your brain. You, the proactive achiever, can make that happen without a trip to the emergency room.
2) Ask questions when appropriate. If your teacher has specified a time during class for questions, ask them. Make a list of questions that you cannot always have immediately gratifed, and cross them off as you or others get the questions answered. Always raise your hand and ask politely. Be specific in your question; do not use terms such as “things” and “stuff”. If you are not sure about the name of a term, try to find it in your text (if possible), and ask the teacher to clarify the term or concept.
If you do not have time in class, or if the teacher has not called on you when you’ve had a question (despite your excellent etiquette), make arrangements during the same class to see the teacher outside of class to clarify whatever you do not understand. (Every morning after calculus class, my professor has a “pool” of students--that sometimes includes me--standing around him, waiting for their turn to ask questions; and he does allow questions during class, as well.)
Resource #2: the textbook
3) Read/take notes on the textbook. The same day that your teacher has covered the content in class, read the textbook and take notes on the text. The longer you wait to cover the material your teacher has covered in class, the less comprehension you’ll have on that material, regardless of how well you did or did not understand the material when the teacher was going over it in class.
When you read the text at home, compare the text and the notes you are taking with the notes you have from class, and combine them. Ask yourself if it all makes sense. Sometimes, the text is easier to understand than the teacher, and sometimes the teacher is easier to understand than the text. Use both! Fill-in or even rewrite any class notes with your textbook notes. The outcome should be a cohesive set of notes on the current material that you, the student, understand and can use for reference and study. Remember, every time you listen, read, and write, the information is further clarified and refined within your brain in ways that even the most sophisticated of scientists do not understand.
Resource #3: homework
4) Do homework after reading text and taking notes. Although considered by some to be an archaic form of torture that somehow trickled into the 21st century, homework, like tests, can be used as a tool to increase comprehension and to assess what and how well you understand concepts.
It is important to attack the homework after you have comprehended the text and your notes because that is when your understanding is at the highest it can be at that point in time. When you try to get homework done without the preparation, it leads to further confusion, bad habits, and even having to redo it. Remember, it takes an average of 7 repetitions in order for basic comprehension to take place, and an average of 27 repetitions to undo any miscomprehensions.
As you do your homework, put a small mark next to, or make a list of any homework problems that you could not do or were unsure of. If you have time, try doing them later after a break and after reviewing your notes and/or text. If you still cannot do them, ask your teacher for help the next day in class. If you are still having trouble, try the problems once again when you are not tired and/or hungry. If you are still unsure or are not getting a correct result, save them for the tutor by adding those specific problems to the list of unanswered questions that you can ask your tutor.
Resource #4: the tutor
5) Clarify questions/material. From the list of questions that you have diligently been seeking assistance for during the week, ask for clarification on anything you were not able to completely understand or were not able to get answered. The tutor can help to locate the information in your text or can bring extra materials/information that can aid in comprehension.
Then review work with the tutor in order to achieve mastery.
Since tutoring is limited in its time, the tutor can suggest ways for you to get more out of all of your available resources.
Keep work/hand-outs that the tutor has given to you in a separate binder. Use those materials in combination with your textbook and notes when you are doing homework and/or studying. These materials are more condensed and specific than your text or notes, and are updated and refined on a regular basis to facilitate deeper comprehension and expedience in doing homework/study. Whenever appropriate, make copies and file any helpful graphic organizers/hand-outs into your math binder that you use for school. In this way, materials are integrated for optimal comprehension and achievement.
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