Study Skills for Mathematics. Dr. Lisa O Keeffe August 2012

Transcription

1 Study Skills for Mathematics Dr. Lisa O Keeffe August 2012

2 Study Techniques for Mathematics Study outside of class regularly Work on maths every day. (recommended 2 hours study for each one hour lecture) Read the textbook or lecture notes* Take good notes in class** Make summary sheets. Make a list of important theorems, properties, formulas and vocabulary Make a list of the important course objectives Review these lists every day. Practice all problemsuntil you have mastered the ability to solve and check them. Be aware of what topicsyou know well, which topics need more practice and which topics you don't know at all. Continually review: Review material from the beginning of the semester throughout the entire semester

3 Study Techniques for Mathematics Take breaks. After a period of concentration, take a break for relaxation or to work on other subjects. Return to problems that you could not complete previously. Utilize campus resources Math Learning Center: tutors, software, screencasts, textbooks etc Study in a proper environment Quiet. You need to be able to think deeply to learn mathematics. A nosiyenvironment will create obstacles to your concentration and create distractions to focusing on the problems at hand. Have plenty of rough paper, graph paper, etchandy, a scientific calculator Well-lit: Make sure there is good lighting while reading and studying. Study groups

4 Reading a Maths Textbook or Lecture Notes Read the title and the learning objectives Skim the section to be read Highlight important sections, questions and examples Read the text: Read in an environment with few distractions. Highlight important material. Pay close attention to material that the textbook author has highlighted Remember: reading a math textbook is not like reading a novel, you need to go slowly and often re-read material to understand the ideas being presented. When you get to the examples, go through and understandeach step. If there are missing steps, fill them in yourself. Study the examples carefully, as they will serve as models for homework exercises and test questions. Mark concepts and words that you do not know. Make a list of these areas of confusion. Look up unknown or ask someone about unclear concepts or vocab

5 Reading a Maths Textbook or Lecture Notes Make lists of important ideas. keep lists of definitions, theorems, formulas Each time you read a section in the math textbook or notes, add something to these lists. Have the lists in front of you as you do your homework. Review these lists daily. If you do not understand the reading material, follow these points until understanding arises: Go back to the previous page and re-read the information Read ahead to the next page to see to where the author is going Study all graphs, diagrams, charts and examples used to illustrate the concepts. Read misunderstood paragraphs aloud to engage your other sensory organs. Refer to your notes from class on the same material. Refer to another math textbook. You might find explanations and/or examples that make more sense to you. Use screencast and website recourses to help with your understanding. Define exactly what you do not understand and ask someone. Reflect on what you have read.

6 Note Taking 1. Listen 2. Write 3. Review 4. Reflect

7 Note Taking 1. Listen Come to class with a positive attitude; this will help you focus, concentrate and get the most out of the lecture. Sit close to the front of class as possible to improve your concentration and vision. Stay focused on the content of the lecture. Do not be distracted by classmates or daydreams. Relate important points to concepts you already know. Ask the instructor for clarification, if you don't understand. Listen for words that signal important information.

8 Three tips for good listening: Anticipating the next point Good listeners try to anticipate the points a speaker will make in developing a subject. If they guess right, the speaker's words reinforce their guesses. If they guess wrong, they'll have to do some thinking to discover why they and the speaker failed to agree. In either case, their chances of understanding and remembering what was said is nearly double what it would have been if they had simply listened passively. Identifying supporting material Good listeners try to identify a speaker's supporting material. After all, a person can't go on making points without giving listeners some of the evidence on which the conclusions are based, and the bricks and mortar that have been used to build up the argument should be examined for soundness. Recapitulating With the tremendous thought speed that everyone has, it is easy to summarize in about five seconds the highlights covered by a speaker in about five minutes. When the speaker stops to take a swallow of water or walks over to the blackboard to write something or even takes a deep breath, the experienced listener makes a mental summary. Half a dozen summaries of the highlights of a fifty-minute talk will easily double the understanding and retention of important information ( Academic Skills Centre, Dartmouth College 2001)

9 Note Taking continued 2. Write Bring pencils and paper to class and take math notes in pencil, not pen. Always use the same notebook to take note for your math class. Date each notebook entry. Keep your math notes separate from notes from your other courses. Copy down everythingthat the instructor writes on the board. If the instructor takes the time to write something, it is important. Take notes, even though your understanding may not be complete. Develop a good note-taking system. Ideas for note-taking systems can be found here.

10 Note Taking continued 3. Review Review and reorganize your notes as soon as possible after class. Write clearly and legibly. Rewrite ideas in your own words. Highlight important ideas, examples and issues with coloured pens. Review your class notes before the next class period. Ask questions during office hours or the next class period if there are items that are unclear. Review all your notes at least once per week to get a perspective on the course. 4. Reflect Think about what you have written and connect it with other maths concepts. Begin to remember definitions, procedures, concepts, theorems and formulas that are in your notes. Compare your lecture notes to the ideas, explanations and examples in the textbooks