How To Study Math

1. Slide #1 How To Study Math "The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder BCC Cocoa Math Lab Coordinator: Denice Lewis

2. Before We Get Started . . . Slide #2 • Introductions • On the sheet of paper, • Answer the question “I’d like to learn, ___________________”

3. What are we going to Cover in this session Slide #3 • Planning the journey • Assess where you are currently • Determine what you would like to accomplish • Figure out how to get from A. to B. • Taking the trip • Learning the Language of Math • Learning how to read a Math book • Discovering your resources • Building a learning circle "One person's constant is another person's variable." -- Susan Gerhart

4. Where are you now? Slide #4 • Do you know what your internal and external variables are? • Internal variables • Do you know your learning style? • Do you experience math anxiety? • Do you go through text anxiety? • Do you have a math learning disability? • External variables • What are you trying to juggle at the same time? • Family/friends • Work • School • Any thing else?

5. How do I Know What My Learning Style is? Slide #5 • What is a Learning Style? • A learning style is an individual's preferred means of acquiring knowledge and skills • Handout, “What are my Learning Strengths?” • Time Limit: 10 minutes “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” --  John Louis von Neumann

6. Do you have . . . ? Slide #6 • Math anxiety is a learned emotional response to one or more of the following: 1. Participating in a math class 3. Working through problems 2. Discussing mathematics 4. Listening to a lecture • Test Anxiety “ If your anxiety is a direct result of lack of preparation, consider it a normal, rational reaction. However, if you are adequately prepared but still panic, "blank out", and/or overreact, your reaction is not rational. While both of these anxieties may be considered normal (anyone can have them) it is certainly helpful to know how to overcome their effects.” • Math Learning Disability • If you have problems with basic math e.g. adding, subtracting, dividing, etc. you may have a math learning disability. • If you are having problems in Algebra, you may have an issue with reading, writing, language, or sequential processing. Information courtesy of http://www.lemoyne.edu/academic_advisement/academic_support_center/mathanx.htm and http://www.couns.uiuc.edu/brochures/testanx.htm

7. Math Anxiety Web Sites Slide #7 • http://www.mathacademy.com/pr/minitext/anxiety/ • http://www.mathpower.com/anxtest.htm • http://mtsu32.mtsu.edu:11064/anxiety.html • http://www.math.com/students/advice/anxiety.html “What we know is not much. What we do not know is immense.” --Pierre-Simon de Laplace

8. Test Anxiety Web Sites Slide #8 • http://www.studygs.net/tstprp8.htm • http://www.healthyplace.com/communities/Anxiety/treatment/test_strategies.asp • http://www.couns.uiuc.edu/brochures/testanx.htm • http://www.testtakingtips.com/anxiety/index.htm • http://web.mit.edu/arc/learning/modules/test/testanxiety.html • http://www.sparknotes.com/testprep/books/newsat/powertactics/strategies/chapter4.rhtml • http://www.howtostudy.org/resources_skill.php?id=16 • The “How to Study” website presents several links to other websites that reference test anxiety. Certain links may require additional time, information, pre-tests, etc. “Obvious' is the most dangerous word in mathematics.” --Eric Bell Temple

9. What do I do if I have . . . ? Slide #9 • The Office of Students with Disabilities (OSD) is here to help you. If you have a diagnosed disability or other questions, please contact Chris Pierce (OSD Disabilities Services Specialist, 433-7295). • NOTE: OSD is located in Building 9, Room 108. • If you have any questions regarding learning disabilities, please contact Nancy Malta (Learning Specialist, 433-7297).

10. What are all the external variables that you’re juggling? Slide #10 • Handout, “What are my external variables?” • What are all the things and who are all the people that you commit time to? • Time Limit: 10 minutes "Don't say you don't have enough time. You have exactly the same number of hours per day that were given to Helen Keller, Pasteur, Michelangelo, Mother Teresa, Leonardo da Vinci, Thomas Jefferson, and Albert Einstein." -- H. Jackson Brown

11. Using a personal example Slide #11 Denice’s scheduled for Fall 2006 NFL NOTE: These times do not include running errands e.g. shopping (grocery, etc.), car maintenance (gas, oil change, wash the car), cooking etc., etc.!! NFL

12. Setting Priorities . . . Slide #12 • Where are you now? • Now that you know . . . • Your current state • Why you feel tired • Why there just doesn’t appear to be enough time in one day  • It’s time to set some priorities . . . • Keep in mind that for every hour you spend in the classroom, you’ll spend 2 to 4 hours outside of class.

13. What things are important to you? Slide #13 • On a blank sheet of paper, list the people, places, things, goals, etc. that are important to you. • Time Limit: 3 minutes

14. Plotting Your Course Slide #14 • What grade do you want to make in your Math class? • “A” • “B” • “C” • “D” • “F” • It’s time to figure out “How do I get an “ ____ “ with all of the things that are on my plate and with my current personal priorities?”

15. How do You Plan to Study or Learn Math? Slide #15 • Handout, “What are your study and planning habits?” • Time Limit: 5 minutes “The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.” -- Aristotle

16. Definitions of Proactive & Reactive Slide #16 • Proactive[proh-ak-tiv] adjective  serving to prepare for, intervene in, or control an expected occurrence or situation, esp. a negative or difficult one; anticipatory: proactive measures against crime. • Reactive [ree-ak-tiv] adjective  1. tending to react. 2.pertaining to or characterized by reaction. 3.Electricity. pertaining to or characterized by reactance. • We’ll review a couple of different scenarios to see where you fit on the Proactive/Reactive Scale. . . . Proactive Reactive Do you plan for things to happen? Do things happened to you?

17. Are You Proactive or Reactive? Slide #17 • Handout, “Are you proactive or reactive?” • Time Limit: 5 minutes

18. If you’re proactive, You are actively endeavoring to learn. You know what you know and what you don’t know. You’re continually planning for success. If you’re reactive, You are taking a class. You don’t have a clue where to go or how to get there. You’re on your way to failure. Proactive Planning versus Reactive Planning (Summary) Slide #18 Why are you at BCC? Are you getting your money's worth? Are you a student or are you just taking classes?

19. Break time! Slide #19 • It’s time to take a 7 minute break. • Please be sure to be back on time!

20. In the Classroom Slide #20 • Make sure your awake and aware during class. • Get to know other people in your class. • Create a study group • Share notes • Take notes during class! • Be sure to at least write down legibly what information is covered in class. If writing is an issue, ask the instructor if you can bring a tape recorder to class. “For the things of this world cannot be made known without a knowledge of mathematics.” -- Roger Bacon

21. Outside of the Classroom Slide #21 • Read your book • Go to class • Review your notes • Do your homework • Go and get help when you need it Go to class. Read your book. Review your notes. Go and get help when you need it Do your homework. “I have had my results for a long time: but I do not yet know how I am to arrive at them.” --Karl Friedrich Guass

22. Making the Connection Slide #22 • You may be asking yourself, “Why do I need to know my preferred learning style(s)?” • Now that you know what your learning style is, it’s time to be proactive in the classroom.

23. The Auditory Learning Style Slide #23 • Learn through hearing • From a math perspective . . . • You may want to bring a tape recorder to class • Viewing DVDs or listening to audio tapes may be helpful • If you wish to enhance this style, you will need to sit away from noisy distractions such as the TV, open windows, or crowded areas. “Pure mathematics is, in its way, the poetry of logical ideas.” --Albert Einstein

24. The Visual Learning Style Slide #24 • Learn by sight • From a math perspective, • Graphs, charts, etc. may help you understand key concepts • Ask the instructor/tutor to graph it for you or demonstrate the concept visually • To enhance this style, • Review everything on the board • Pay attention to key points in the book while reading

25. The Kinesthetic Learning Style Slide #25 • Learn by doing • From a math perspective, • Do as many problems as you can • Have someone demonstrate to you different methods for solving the problem • To enhance this style, • Participate in class • Ask questions if you don’t understand how something was done

26. Take a moment Slide #26 • On a blank sheet of paper, write 2 things that you can do differently inside and/or outside the classroom. • Time Limit: 3 minutes

27. The Language of Math Slide #27 • Terminology • Definitions • Notation • Theorems • Factual Knowledge • Procedural Knowledge • Conceptual Knowledge • These are the things that you need to know in order to succeed in Math, feel prepared to take an exam, and basically, know what you don’t know. . . “In mathematics, you never understand things; you just get used to them.” --John von Neumann

28. Discovering the Language of Math (Terminology) Slide #28 • The first step in learning Math is understanding the words being used in Math. • If you don’t know what a polynomial is, could you “Factor the polynomial(s), circle the binomial, and underline the monomial.” given the following: • x2-9 • x2 + 2x + 1 • 2x “Since Mathematics is intermediate between natural and divine science, it is more certain than either of them.” -- Thomas Aquinas

29. Discovering the Language of Math (Definitions) Slide #29 • Next, you need to know what each word means. • Do you know what a derivative is? A polynomial? An integral? A matrix? • If you’re sitting in your Math class and it feels like your teacher is speaking another language, it’s time to review the terminology & definitions.

30. X X½ Discovering the Language of Math (Notation) Slide #30 • The language of Math includes words and symbols. • Understanding the notation that is being used is the next step in understanding the language of Math. • Do you know the difference between set notation and interval notation when calculating the domain/range of a function? {x | x ≤ 1 } ≈ (-∞,1]

31. Discovering the Language of Math (Theorems & Factual Knowledge) Slide #31 • Just like other languages, there are rules to Math. • Theorems (Pythagorean Theorem) • Properties (Additive Property: a + b = b + a ) • Equations • y = mx + b (Equation of a line) • y = ax2 + bx + c (Equation for a parabola) • Factual Knowledge is essential facts and figures that you’ve memorized • cos, sin, tan of 0, p/6, p/4, p/3, p/2 • x0=1

32. Discovering the Language of Math (Procedural Knowledge) Slide #32 • There are a number of different ways to solve certain Math problems • The more methods you know, the better off you are. • For example, to factor a polynomial, you could use the following: • Grouping • Completing the square • The AC Method • The quadratic formula • Plug and play • A combination of the above

33. Discovering the Language of Math (Conceptual Knowledge) Slide #33 • When you know the what, why, when, where and how behind any mathematical concept, you have reached nirvana and conceptual knowledge. • Example: • Not only do you know what a derivative is, you know how to calculate it for any given function. • You understand that the derivative is the rate of change of a function and gives you the slope of the graph at any given point. • You can discuss derivatives with your instructor. • Integrals come easy to you because you know reverse engineer calculating the derivative.

34. The Language of Math . . . Practical Application Slide #34 • If you feel as if the teacher is speaking another language, it’s time to review the Terminology and Definitions. • If it looks like the instructor is solving a problem using ancient script, it’s time to review the Notation. • If you find yourself missing problems because you don’t know the cos 45˚ํ or you forget your multiplication tables, is time to pull out the flash cards to memorize the Factual Knowledge. • If you can’t follow how the instructor solves the problem, you may want to check your Procedural Knowledge and what you know about Theorems. • If you’re in any math class beyond Pre-Calculus including Statistics having a Conceptual Knowledge of each concept/subject will enable you to solve problems more efficiently and effectively.

35. Reading for Understanding, I Slide #35 • Know the important sections in your book. • The Table of Contents outlines what information will be covered, in what order and what page you can find a particular topic. • The Index is a quick way to find information. If you’re looking for where polynomials are discussed, go to the index to find the page number. • The Glossary gives you the definitions of terms used in your textbook. • Most math textbooks have the answers to the odd problems in the back of the book. “There are no deep theorems -- only theorems that we have not understood very well.” --Nicholas P. Goodman

36. Reading for Understanding, II Slide #36 • Reading a math book is not like reading a fictional novel or a humanities textbook. You will be reviewing/reading each more than once!!! • Review your textbook to see how the author presents the information. NOTE: Some authors explain how to use the book in the beginning. • Are key words/terms bolded? • Are theorems, methods in separate squares? • How are example problems presented? • Review the section first to see what new terminology is being presented as well as to highlight any new notations used.

37. Reading for Understanding, III Slide #37 • After understanding what terminology & notation is being used, read through the section carefully. • Every word, dot, symbol, etc. counts!!! • If you don’t understand a word used by the author, stop and look it up in a dictionary. • When an example is presented, cover the answer and try to work it out on your own. • If you can’t, review each step of the example to understand the method being used. • If you can’t figure it out on your own, know your resources and get help. • Obtaining the student solutions manual may help you understand how to solve the problems. • Ask yourself, “Is my book working for me?” If it’s not, don’t be afraid to go to the library, a bookstore, online or even to your professor to find another book that will work for you.

38. Reading a Math BookWeb Sites Slide #38 • http://home.sandiego.edu/~pmyers/textbook.html • http://www.stonehill.edu/compsci/History_Math/math-read.htm • http://www.maa.org/t_and_l/exchange/ite3/reading_reiter.html • http://wc.pima.edu/~carem/Mathtext.html • http://academic.cuesta.edu/acasupp/AS/704.htm • http://www.newark.osu.edu/osunmathlab/pdf/handouts/howto/pdf/readmath.pdf • http://oakroadsystems.com/math/sdrdbook.htm • http://www.maa.org/t_and_l/exchange/ite3/TaalmanProblemzero.htm “Obvious' is the most dangerous word in mathematics.” --Eric Bell Temple

39. What other books can I use? Slide #39 • There are several books that were made to support education/learning. A few series are listed below: • Demystified series http://shop.mcgraw-hill.com/landingpage.php?template=testprep • Schaum’s Outlines http://books.mcgraw-hill.com/searchseries.php?series=Schaum's+Outline+Series&template=schaums • Schaum’s Easy Outlines http://books.mcgraw-hill.com/searchseries.php?series=Schaum's+Easy+Outlines&template=schaums • Dummies http://www.dummies.com/WileyCDA/Section/id-100171.html • Cliff Notes http://www.cliffsnotes.com/WileyCDA/Section/id-106156.html Pictures courtesy of the websites listed above.

40. Are there any free resources? Slide #40 • Always use your instructor as a free resource. • Visit the Math Lab (Cocoa Campus, Building 9, Room 106) for help or as a quiet place to study. • Learning Labs (Palm Bay, Melbourne, Titusville) on other campuses have Math tutors. NOTE: The hours vary per campus. • You can check out books for free at the library (BCC, public libraries, etc.). Also, in the Reference section of the BCC library, there are a number of math-related VHS and DVDs that you can take blank VHS tapes in and copy. • Also, if you are a registered BCC student, you can go online and use SMARTHINKING an online tutoring service.

41. Free Math resources online Slide #41 • Free math resources: Articles, Glossaries, Cheat Sheets, and more. • http://www.cliffsnotes.com/WileyCDA/Section/id-110127.html • Math and Science Articles • http://www.dummies.com/WileyCDA/Section/id-100170.html • The Math website • http://www.math.com/ • A number of professors have their lecture notes or other information online • Example: Bob Young, BCC (Palm Bay) http://home.brevardcc.edu/youngr/ • Google “notes on __________” e.g. “notes on algebra” and you’ll be surprised how many different websites appear!

42. Other online resources Slide #42 • The Study Guides and Strategies web site is authored, developed and maintained by Joe Landsberger as an educational public service. http://www.studygs.net

43. Building a Learning Circle Slide #43 • “No man is an island, entire of itself; every man is a piece of the continent.” John Doone • Get to know individuals in your class, friends/family members that were good in math, other professors, etc. • Know • Who you can go to for what type of help • Which individual explains things in ways you can understand • Who you can study with • Who to go to when you need to vent or need advice • Who to stay away from • Basically, you want to develop your own support group. • Don’t focus on quantity. Focus on quality. The quote was taken from http://www.quotedb.com/quotes/245

44. Reflection . . . Slide #44 • Go back to the initial paper that you wrote, “I’d like to learn ______” • Have we covered everything?

45. The floor is open . . . . Slide #45 • Are there any additional questions I can answer? • Are there any topics you’d like to discuss further in the time that we have? • One course that you may be interested in is SLS1101, Success Strategies for College and Life!!!

46. Dr. Amy Hendricks Dean Leroy Darby Quinn Hearn Nelia Lake Chris Pierce Nancy Malta Lisa Gill Mark O’Hara Penny Shannon Dr. Michael Gallo Marsha Lake Skip Downing Dr. Linda Krupp Erica Anderson All the students who have visited the Math Lab Fall 2006 Anyone that I may have missed . . . Thank You! My thanks . . . . Slide #46 All of this would not be possible without the following people:

47. Quick Tips (1) Slide #47 • Time Management • There are different tools available that will help you organize yourself, manage your time, and be proactive. • Planner • PDA • Etc. • It doesn’t help if you have a tool and don’t use it!

48. Quick Tips (2) Slide #48 • Time Management Websites • http://www.studygs.net/timman.htm • http://www.franklincovey.com/fc/index.jsp • http://www.ucc.vt.edu/lynch/TimeManagement.htm • http://www.couns.uiuc.edu/brochures/time.htm • http://www.managementhelp.org/prsn_prd/time_mng.htm • http://www.d.umn.edu/kmc/student/loon/acad/strat/time_manage.html

49. Quick Tips (3) Slide #49 • Test taking strategies • Your success in taking a test depends highly on your personal belief in your knowledge and ability. • If you think you’re going to fail, you’re on your way there. • Prepare yourself as much as possible. • Have a test taking strategy for timed exams. You are being tested on your knowledge of the subject area, time management, and how efficiently & effectively you solve problems. • As a result, do the problem you know how to do. • Circle the ones that you know how to do but will take considerable time. • “X” the problems where you have no clue. • Always go back and check your work for any arithmetic or other errors!!!!!

50. Quick Tips (4) Slide #50 • Web sites for test taking strategies • http://www.d.umn.edu/kmc/student/loon/acad/strat/test_take.html • http://www.testtakingtips.com/test/math.htm • http://www.ncsu.edu/felder-public/Papers/testtaking.htm • http://www.bucks.edu/~specpop/tests.htm • http://www.ucc.vt.edu/stdysk/stdyhlp.html • http://www.studygs.net/tsttak1.htm • http://www.mtsu.edu/~studskl/teststrat.html • http://euler.slu.edu/Dept/SuccessinMath.html • http://www.msjc.edu/math/mathcenter/handouts/oncourse/Test%20Taking%20Strategies.htm