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Math Center Tutor Training Manual Last Updated August 9, 2007 Table of Contents What is Tutoring? What Does a Math Tutor Do? …………………………………………………………………………...…..…….3 The Tutoring Session…………….…………………………………………………………………………...…...4 The Tutorial Creed……………………………………………………………………………………...….….......5 10 Benefits of Tutoring…………………………………………………………………………...…………..…...5 Math Center Procedures Math Center: A Guide for Math Tutors………………………………………..…………………………………………….6 Math Center Policies………………………………………………………………………………………………………..10 TutorTrac How to Register for NKU TutorTrac…………………………………………………………………………….11 Entering the Realm of NKU TutorTrac………………………………………………………………………….12 Tutoring Tips Questioning as an Effective Tutoring Technique………………………………………………………………..13 What to Do When You Get Stuck……………………………………………………………………………… 14 Tips for Tutors…………………………………………………………………………………………………...15 How to Promote Active Learning………………………………………………………………………………..16 Learning Styles Learning Styles…………………………………………………………………………………………………..17 Tutoring Tips Based on Learning Styles……………………………………………………………………...…18 Math Anxiety Some Causes of Math Anxiety…………………………………………………………………………………..19 Mathematics Anxiety Bill of Rights……………………………………………………………………………..20 Overcoming Anxiety……………………………………………………………………………………………..21 Math Test Anxiety Reduction Checklist………………………………………………………………………....22 Study Skills 21 Ways to Get More Done in Less Time……………………………………………………………………….23 Math Study Skills Inventory……………………………………………………………………………………..24 20 Tips for Academic Success…………………………………………………………………………………...25 Word Problems Differences between English Language and Math Language……………………………………………………26 Steps for Solving a Word Problem………………………………………………………………………………27 Natural Human Learning Process Summary of Natural-Learning Stages…………………………………………………………………………...28 Major Points about Learning…………………………………………………………………………………….29 2 What Does a Math Tutor Do? The tutor assists students as they practice, review or prepare material for class. This role includes helping students identify error, reminding them of mathematical concepts and finding additional practice problems. We always instruct students that are extremely behind to see their professors. Tutoring Do’s: Do always be on time for appointments and do your best not to have appointments run over. Do greet students as they come to the door and help them with logging in to TutorTrac. Do offer to help students who come in to the Math Center without an appointment if you do not have an appointment. Do exchange names with the student and take a minute to understand where the student is having problems. Do pay attention to the body language of the student. Do find out how the student’s professor would like a problem worked. Do help the student with note taking skills. Do help the student with test taking skills. Do help the student with overcoming math anxiety. Do go with the student to get clarification from a professor. Do let me know if you have any questions. Do be relaxed. It helps set people at ease. Do work your self out of a job. Tutoring Don’ts: Don’t be late or allow appointments to run over. Don’t ignore students when they enter the Math Center. Don’t do the problems for the student. Don’t do the problems the way you learned them. (Unless it will help the students to see it a different way) Don’t focus only on completing the homework assignments. Don’t work all problems with the student. Leave some for the student to do on their own and move on to other topics. Don’t “teach” the student a topic the professor has not covered in class yet. Don’t help a student with a quiz unless cleared with me or their professor. Don’t be afraid to say that you don't know the answer, or can't think of another way to explain it. Don’t criticize the instructor no matter how challenging the instructor or difficult his/her English for the student to understand. 3 The Tutoring Session How to begin a tutoring session: Have the student sign in to TutorTrac. Begin filling out the tutoring session form and ask the student what they would like to work on. Take the time to ask the student what they have been going over in class and what specifically the student has had problem with. Decide, with the student, the best plan of action. In the Middle: If at all possible, have the student work the problem. Only work a problem if necessary and then work one and allow the student to work a similar problem. Have the student tell you what they are doing, as they do it. Ask the student questions. Have the student think about what makes the problem different then other problems they have worked. Have the student think about what makes the problem the same as other problems they have worked. Once the student has mastered a topic, move on to the next. It is not necessary for the student to do all their homework with you watching. How to end a tutoring session: About 5 minutes before the end of the appointment, finish working the problem you are currently working on. Finish filling out the tutoring session form. Have the student log out of TutorTrac. Help the student with scheduling another appointment (if necessary). 4 The Tutorial Creed By Paul Ellis I. I will try to help you make sense of what you do not understand, but I will not be your instructor. II. I will try to show you how to find the right answer, but I will not just give you the answer. III. I will review with you the homework that you have completed so that you can see your successes and failures, but I will not do your homework for you. IV. I will help you learn how to read your textbook for understanding, but I will not explain to you something that you have not read. V. I can meet with you one hour per week (sometimes two, in special circumstances and with permission from the LAP) and help you achieve learning goals that we have set together, VI. I will always expect your best effort, and you should too! 10 Benefits of Tutoring By Paul Ellis 1. Successful work with others is a necessary skill for most careers. 2. Students learn strategies and habits for success by working with a peer role model. 3. Working as part of a team or community enhances students' motivation and confidence. 4. Students working with a tutor are free to ask questions as they come up, which they may be inhibited to ask in the classroom. 5. Ideally, the tutoring session allows students enough time to master an idea or concept. A tutor is in a good position to identify what the student still needs work on and when it's time to move on. 6. A tutor can guide a student to other available and appropriate resources (Supplemental Instruction (SI) / Structured Learning Assistance (SLA), Steely Library, Academic Advising Resources Center (AARC), Student Support Services (SSS), Financial Aid, Career Development Center (CDC), Health, Counseling, and Prevention Services, etc. 7. For students from non-academic backgrounds, the tutor functions as a bridge between the student's community and the academic community. 8. In a diverse setting like NKU, tutoring allows us to learn about each other's cultures, experiences, and languages in an accepting and supportive environment. 9. The tutor and the instructor have the same goals for the student, but the tutor can approach things from a different, often more individualized way. 10.Working with a tutor can provide a bridge into a learning community for students who have been used to working on their own. The environment in a tutoring center encourages collaborative work and support of fellow students. 5 Math Center A Guide for Math Tutors Center Goals The Math Center is designed to aid the developmental math students as well as the student in selected general studies math courses (i.e. 110, 111, 115, 205). The goal is to help the student develop the learning and study skills necessary to prepare for homework and tests as well as develop the problem solving skills that will allow the student to work efficiently, confidently, and effectively not only in mathematics but throughout life. Tutor Role The tutor assists students as they practice, review, or prepare material for class. This role includes helping students identify error, reminding them of mathematical concepts and finding additional practice problems. We always instruct students that are extremely behind to see their instructors. As a tutor, you should: Great all students that enter the Math Center, if you are with a student and there is no free tutor stop for a second and ask the student to wait. Help students register, set up appointments and login/out of TutorTrac. Show the student that you are interested. Start where the student is. Encourage the student to be an active learner. Model and promote effective study skills and support classroom instruction. Use student‟s notes, course textbooks, and solution methods used by student‟s instructor during tutoring session. WORK YOURSELF OUT OF A JOB Helpful Hints There are many common trouble areas that the tutor will begin to recognize when working with the tutees. Here are some hints for dealing with those problems before they become a major hindrance to learning. Try to determine exactly what kind of difficulties your student is having: Is your student able to remember basic skills? Does your student understand the text? Are the instructor‟s lectures causing problems? Does your student lack basic study skills? Does your student suffer from test anxiety? Negative self-talk (i.e. “I‟m stupid”, “I can‟t learn”, “I‟m too old”) is to be considered obscene and unacceptable. There is to be no waste of time in allowing students to qualify the question they are about to ask you with phrases such as “Can I ask you something?” or “This may sound stupid”. You are a tutor and are thus present to answer any question of the tutee relating to math. The tutee should be aware of this and feel comfortable in asking any question. 6 The tutee should keep his/her hand off the pencil until he/she has read the problem and understands the problem. If the tutor is working example problems, the tutee should follow along by listening, not by writing. The tutee should never be allowed to skip steps in working problems (no short cuts should be allowed). If you are working problems on the board, use colored chalk to color-code work. Positive and directional internal dialogue should be used, but concepts need to be understood and rote memorization should be discouraged. Always work on the opposite side of the hand the student uses (i.e. if the student is left-handed, work on his/her right side). Don‟t tell the student if he/she is right or wrong. Instead, let the student finish the entire problem, then if a question arises, ask, “What do you think?” “Is it reasonable?” “How did you arrive at that answer?” Use a sequential approach to problems to help the student build on what he/she already knows. Some students have trouble communicating with their instructors. Encourage the student to ask questions in class and to go see his/her professor during their office hours. Also, some courses have pooled office hours where a student can go to the office hours of another professor who is teaching (or has taught) the same course. The Textbook as a Learning Tool Students sometimes forget that the text is very important to their total understanding of the math problems they are working. Encourage the use of the Text. The MAH 095, 099 textbooks are color coded to aid the student in reaching a better understanding of each section of material covered. The following is a breakdown of those color codes for the Bittinger/Beecher textbooks. PINK - Section Objectives TAN - Margin Exercises ORANGE (arrow in box) - Rules GRAY - Calculator Spotlight Most textbooks use a similar scheme to aid the student. Help the student identify the scheme in his/her specific Text and learn to use it. Make certain that the student carefully reads the introduction of each section, carefully studies the example problems present, works the practice exercises contained in the section, and understands the concepts that are presented. Reading along with the student can often be helpful, especially if the tutor asks pertinent questions throughout the reading. Have the student read the next day‟s material the night before. This way, the student will have a better understanding of the material covered in the lecture and the material will not be completely new to them. Some students have a better understanding of new concepts if they get a “Birdseye view” of the material before they begin. Encourage these students to read the chapter summary, present at the end of each chapter, before starting a new chapter. This will allow them to get the big picture by observing the structure of the chapter before entering it in greater detail. Encourage students to try to work the margin exercises as they read the chapter. Each solution for the margin exercises is given in the back of the book. Margin exercises are similar to the examples that are worked out step by step in the chapter. This enables the students to have a more active involvement while they read. 7 Word Problems Word problems are one of the biggest causes of distress for most students. Here are some tips to pass along to the tutee for working word problems. Use a highlighter to highlight keywords in the problem itself. Write out the equations in words then fill in the numbers. Make certain the student identifies the variable in the problem. Put the solution to the problem in the form of a sentence. Help the student develop a word problem solving routine. Organizational Skills The tutor should convey the importance of organizational skills to the tutee. Here are some skills that can be passed along. Line up the equal signs in the work and use one equal sign per line. Use a #2 pencil or dark pencil and always have a good eraser. Straight edges should be used to draw lines (if a straight edge isn‟t present, use your driver‟s license or student I.D. card). Flash cards can be stored in small sandwich bags for safe keeping. The tutor should look at a student‟s notes to give suggestions for better organization. Encourage the student to actively take organized notes during the lecture. Remind the tutee to date his/her notes. Encourage the student to use a binder with separators to keep notes and work. Use separate sections for class notes, homework, extra practice and test/quizzes. Discourage the use of spiral notebooks. Encourage the use of a scientific calculator, especially a graphing calculator (when the professor allows it) if he/she can afford it. A graphing calculator can be checked out from the Learning Resource Center. Tests The one subject that causes the most anxiety of almost any math student is tests. Share the following ideas to help students fight test-taking anxiety. Before the test: Know the difference between a „test‟ and a „quiz‟. Go to class--Do NOT skip the class right before the test. Eat breakfast, but avoid acidic foods such as orange juice. Close the book and put away the notes about 30 minutes before bed and do something enjoyable. Use breathing exercises to calm down before the test. Review old tests and quizzes. Have the student choose problems from the text to make up their own test. Notecards work nicely for this, see “proven study method.” Have the tutees say, “I‟m going to do my best”, discourage them from saying, “I‟m going to fail”. 8 During the Test: (Instruct the tutee to) Read through the whole test. Pay close attention to the directions. Do the easy problems first. Don‟t spend any enormous amount of time on any one problem. Don‟t leave anything blank. Sit back for a moment and take a deep breath should you find yourself tensing up. Go back and check their work, if there is time. After the Test: (Instruct the tutee to) Don‟t be discouraged if you didn‟t get the grade you wanted. Work all problems you got wrong. Save the tests and quizzes to study from later. Use your text to review concepts missed on the test. Resources The tutor should let the tutee know of the resources on campus. Math videotapes are available from the Steely library or are available to be viewed in the Math Center; however, they should be actively and not passively viewed. The student should take notes and carefully follow through the examples presented not simply watch, as one would watch a movie. They should think of it as a lecture that they can control the pace of. Computer aided assistance is available through software (MathMax is the software that comes with the MAH 095,099 book) and a list of helpful websites is available on the Math Center‟s Webpage (www.nku.edu/~mathcenter). 9 Math Center Policies Cell phone ringers should be turned off as to not disturb other students. Cell phones should not be answered in the Math Center. If a call must be taken, please take it outside the center. (This policy is for both students and tutors, if a student is not abiding by this policy let me know.) The computer directly next to the door should only be used for TutorTrac purposes such as logging students in or out and making appointments. If the lab is not busy, you may work on your own homework. However, students using the lab must not get the impression that you are “busy” and not available to assist them if they need you. Students must always be helped first. The two computers on the wall with the printer may be used by tutors for personal business if and only if there is not a student who needs help or who needs to use Minitab (computer to the right of the printer). Tutors who are not working with a student should always be aware of students coming into the center. The tutor should welcome the student and then assist them (log them in, help them make an appointment, tutor them). If all tutors are working with students, greet the student and either get me or ask them to wait for a moment and help them when you come to a stopping point in the tutoring session. If a student comes in looking for help but does not have an appointment and a tutor is available, a tutor should help them until the tutor’s next appointment shows up or the tutor is scheduled to leave. Please let me know of an absence as soon as possible. When a tutor calls off, it is possible that I will need to cancel a student’s appointment, so please make every attempt to come in. Please check your email at least every 48 hours. 10 How to Register For NKU TutorTrac NKU TutorTrac is a web-based program that allows NKU students to make Writing Center consultations and/or Math Center tutoring appointments on-line, or to access contact information of Academic tutors. First, however, you must register. Follow the directions below to register for NKU TutorTrac. 1. Access NKU TutorTrac via Norse Express. 2. In User Name box, type “new”; click “Login.” 3. NKU TutorTrac invites you to register. Your ID is your Social Security #. Your Account (or User) Name is your NKU email prefix—what comes before the @. Your Password should be your SS#—the same as your ID, easily remembered. Please complete the form: ID: SS# First Name: Jane Last Name: Doe Account Name: doej1 (NKU email prefix) Password: same as NKU email password Confirm Password: same as NKU email passwor Click on “Confirm” 4. The next screen requests information about you. We need this information so we know what NKU student population groups we are serving and how well we are serving them. Complete the form, using drop down boxes when available. Be sure to click on Save! ID: SS# Last Name: First, Middle Name: Referred by: Gender: Age: Phone: (optional) Permanent Residence: Cell: (optional) Live on campus? Major: (optional) Currently member of Student Email: Support Services (SSS)? Ethnic Background: Admitted to NKU with College: conditions? Class: Tutoring selected for …? Click on “Save” 5. The next screen should be the Student Main Menu, with your name on it. You are now ready to make tutoring appointments on-line or to access tutor contact information on-line! 11 Entering the Realm of NKU TutorTrac: https://tutortrac.nku.edu Student Instructions [If you have any questions please contact the Math Center (FH 201; 859-572-5779).] 1. Once you are registered, you can access Tutortrac remotely by using any browser (Explorer, Netscape); type in the web address http://tutortrac.nku.edu. Bookmark or mark it as a favorite! 2. Enter your login user name and password and click the Login button. [Your user name is your NKU email name. (Ex: paule – Do Not include @nku.edu.) Your password will be the same as your NKU email password. 3. On the Student Main Menu page, you will see your name and all upcoming appointments you have scheduled, as well as other messages, including reminders of tomorrow‟s appointments, if any. You may cancel an appointment by clicking on its Date, then clicking Delete. 4. Near the top of the Main Menu page are the buttons: More Info | Make Appointment | Find Resources | Edit Information | Exit. Click on Edit Information if you need to update biographical information, like a change in your email address, class status, etc. 5. Click on Make Appointment if you wish to book an appointment. 6. At the Availability Search screen, you may search for an appointment during the upcoming week in one of two ways: You may select a specific center and a specialty area (course), OR you may select specific Tutor. NOTE: Not every tutor can help with every course. It is best that you only specify a tutor if you have already worked with him or her. Verify that the date range is okay (you can change the dates if it is not); click the Search button. 7. You will need to scroll down to see all the Search Results. Click on an Availability’s time that you want. 8. Select a time, type in location [FH 209 for Writing], verify duration (.5 hour default, 1 hour maximum), identify “Request Help In” (Prewriting, Revising, Editing for Writing); Click on Save Appointment. Your new appointment will appear on your Main Menu page. 9. You can cancel an appointment by clicking on its Date, then clicking Delete. 10. Click Exit to quit. To Login a student: 1. Make sure the computer is on the login screen by going to tutortrac.nku.edu and typing in the login username and password (found on the black binder in the cabinet. 2. On the login screen, have the student type in either their username or social security number. 3. Have the student select their course, reason for visit and type in their instructor’s last name. 4. Click Continue. To Logout a student: 1. Click the logout button next to the student’s name. 2. Select the reason for the visit and the place. Also select the tutor the student was working with. To Login as a tutor: Your username is your first name, last initial. (ex. My tutor username is bethw) 12 QUESTIONING as an EFFECTIVE TUTORING TECHNIQUE ********************************************* Beth Kupper-Herr <email@example.com> Writing Specialist / Tutor Supervisor Learning Resource Center Leeward Community College Pearly City, Hawaii ********************************************* Asking questions is one of the best and most important ways to help others learn. Socrates, the ancient Greek philosopher, was perhaps the first teach to sue this method. He didn’t TELL his students what to think; by skillful questioning, he guided them along their own path to the truth. This means of teaching is known as the Socratic Method. QUESTIONING AT THE BEGINNING OF A TUTORING SESSIONS: Use questions for the diagnosis and focus – to find out what your tutee needs to work on and to determine what to cover during the session. QUESTIONING DURING THE SESSION: Questions can be used in many ways during a tutoring session. Below are three question types. Discuss the effectiveness of these types. Is one type more useful than another? When should each type be used? Give reasons for your conclusions. Closed questions – including yes/no and short answer questions: Do you understand? In what state is the Yukon River? Who was the first Prime Minister of India? Rhetorical questions (no response needed): Didn’t the Chinese reject Western culture for a long time? Should your introductions include a thesis statement? Open questions – asking for broadly inclusive statements, assertions, explanations, or opinions: What’s the most important thing you want to tell your reader? What’s the difference between moncotyledons and dicotyledons? What do historians mean by the Colombian Exchange? Why do you think that labor issues have been omitted from most history textbooks? QUESTIONING AT THE END OF A TUTORING SESSION: Use questions for summary, review and to establish directions for further study. 13 What to do when you get stuck! Math Lab & Tutor Training Bethel University 3/16/07 It’s bound to happen – you are working with students and you get stuck on a problem… Two Important Ideas: 1. Use the opportunity to model good problem solving skills (do what you do when you get stuck!). 2. Be honest and don’t give incorrect answers: giving incorrect answers leads students astray and often spreads like a disease (they tell someone else, the incorrect material ends up on an exam, etc.). It is much better to say “I don’t know the answer, but let’s work to find a solution” than to lead someone down the wrong path. Some Strategies: 1. Have the student state the problem in their own words. - Define any unknown terms (use index or current section in book if necessary) - Write the problem in the form: Given: Find: 2. Use the student's resources, ask lots of leading questions. - Find out which pieces of the problem the student understands - Write out any formulas or theorems that may apply - See if there is a similar example in the book - Use their class notes - Ask them if they have done a similar problem before 3. Other Strategies - Draw a picture or graph, make a model, or act it out - Break the problem into smaller parts, solve an easier problem - Make a numerical example that fits the problem, and solve it first (this is especially helpful if the problem is full of parameters) - If possible, estimate a solution, then check with this estimate - Look for patterns - Brainstorm - throw out all kinds of ideas - Incubate! (let it sit for awhile) 4. If you still have not found a solution... - Ask another student from the same class or another tutor to help. - Check the answer key (if available) - Refer the student to their instructor and follow up when you see them again! 14 TIPS FOR TUTORS 1. Use simple language. Remember, there is a difference between understanding a topic and teaching it. 2. Paraphrase what the student says. 3. Provide information that the student needs, rather than what you know. 4. Ask one question at a time. 5. Use "wait time". 6. Avoid asking "yes" and "no" questions. 7. Check to see if you have been understood. 8.Ask a student to explain back to you the steps that were needed to solve a problem. 9.Admit when you don't know the answer. 10. Avoid being condescending. 11. Refrain from commenting on how easy a problem or concept is to understand. 12. Provide realistic feedback about learning from high school vs. university perspective. 13. Listen actively. 14. Keep a positive attitude about the person you are assisting. 15. Be conscious of your body language. 16. Show enthusiasm for learning. 17. Look for opportunities to encourage and affirm the student’s work 18. Actively teach study skills. From Cornell University’s Learning Strategies Center 15 How to Promote Active Learning * The goal of the tutor is NOT to solve problems, provide answers, or write papers for students. The primary goal is to show students how to solve problems, how to think through questions, how to work through the writing process. Tutors should get the students to do the thinking and talking as much as possible. Sometimes it is important to slow things down so that students can become more aware of what they are doing – more aware of their thinking processes. This awareness can lead to intellectual change, development, and growth. Some ways to get students to slow down and reflect on their thinking processes: Have students read the problem/question/assignment aloud and tell you what is needed before they start work. Get students to “think out-loud” as they respond to a problem/question/assignment. Encourage students to constantly talk about what they are doing and why. This will slow down the thinking process and make it more explicit – and perhaps more accurate. It will at least allow you to help students check their own reasoning and find their own mistakes by having them express exactly what they know about the problem/question/assignment. Ask questions or make comments that can help students clarify their thinking: o What are some possible ways you might go about solving this problem/question/assignment? o Tell me what you know about the problem/question/assignment. o How might you break the problem/question/assignment into small steps? o What are you thinking right now? o I don’t understand. Will you please explain? Sometimes you may find it appropriate to model good problem solving techniques. You may need to demonstrate how you would go about reading and understanding a question before responding to it. Make sure that your model or demonstrations is clear (e.g., work step-by-step, back up if necessary when things don’t work out, break a complex task into parts, move from simpler to more complex, construct visual representations on paper, etc.). After modeling or demonstrating, require that students work through a similar task to make sure they understand the process. *Adapted from Beverly Black and Elizabeth Axelson, University of Michigan. 16 Learning Styles When you.. Visual Auditory Kinesthetic & Tactile Do you sound out the word or Do you write the word down to Spell Do you try to see the word? use a phonetic approach? find if it feels right? Do you sparingly but dislike Do you enjoy listening but are Do you gesture and use listening for too long? Do you favor impatient to talk? Do you use expressive movements? Do Talk words such as see, picture, and words such as hear, tune, and you use words such as feel, imagine? think? touch, and hold? Do you become distracted by Do you become distracted by Do you become distracted by Concentrate untidiness or movement? sounds or noises? activity around you? Do you forget faces but Meet someone Do you forget names but remember Do you remember best what remember names or remember again faces or remember where you met? you did together? what you talked about? Do you talk with them while Contact people Do you prefer direct, face-to-face, Do you prefer the telephone? walking or participating in an on business personal meetings? activity? Do you enjoy dialog and Do you like descriptive scenes or Do you prefer action stories or Read conversation or hear the pause to imagine the actions? are not a keen reader? characters talk? Do you prefer verbal Do something Do you like to see demonstrations, Do you prefer to jump right in instructions or talking about it new at work diagrams, slides, or posters? and try it? with someone else? Do you ignore the directions Put something Do you look at the directions and and figure it out as you go together the picture? along? Need help with a Do you call the help desk, ask Do you seek out pictures or Do you keep trying to do it or computer a neighbor, or growl at the diagrams? try it on another computer? application computer? Adapted from Colin Rose(1987). Accelerated Learning. 17 Tutoring Tips based on Learning Style AUDITORY LEARNERS TACTILE/KINESTHETIC LEARNERS VISUAL LEARNERS Encourage them to explain the Encourage them to pick up the book as Let them take notes during the material to you. they are reading or talking. tutoring session. Ask them to read Have them write while they are reading or Use a blackboard or notepaper explanations out loud. talking. for both of you to write questions and answers. Ask the student to make up a song Encourage them to walk around the room Encourage the use of color- using the subject material. The for appropriate books and other resources. coded highlighting. 'crazier' the better. Tell the students they can review Advise them to sit near the front of their Use graph paper to help them audio tapes while they drive. classroom and to take notes. This will create charts and diagrams keep the student focused. that demonstrate key points. Advise them that when they are Advise them to spend extra time in any Have them use mnemonics, learning new information, state the labs offered. acronyms, visual chains, and problem out loud. Reason through mind maps. solutions out loud. Ask the student to say words in Encourage them to use the computer to Advise them to use the computer syllables. reinforce learning using their sense of to organize materials and touch. to create graphs, tables, charts, and spreadsheets. Encourage them to make up and Advise them to write with their fingers in Ask the student to organize the repeat rhymes to remember facts, sand. material. dates, names, etc. Advise the student to join or create Have them write lists repeatedly. Use visual analogies. Use a study group, or to get a study photographs. partner. To learn a sequence of steps, write Advise them to exaggerate lip movements Use visual metaphors. them out in sentence form, then in front of a mirror. read them out loud. Ask the student to use mnemonics Ask them to stand while they explain When you ask them to explain and word links. something to you. something, suggest they do so by writing the explanation down. Involve the student in a discussion Ask them to use rhythm (beats) to Ask them to make flashcards, of the material. memorize or explain something. then use them during the session/s. Make sure they go over all As the student is explaining something, The act of writing (the cards) and important facts aloud. have the student point to the subject viewing them doubles their matter in the book, on the board, etc., comprehension. while reading it out loud. Ask them to use gestures when giving Encourage them to visualize the explanations. scene, formula, words, charts, etc. Advise them to make models that Refer them to the Book’s or other demonstrate the key concept. (The computer software. purpose here is the act of making the model.) Advise students to use hands-on Use illustrations. experience when possible. Make flashcards for each step in the procedure. Put the cards in order until the sequence becomes automatic. Use audio tapes from classes. Play them while they walk or exercise. Ask them to stretch and move in the chairs. Adapted from Three Rivers Community College’s Tutoring and Academic Success Centers’ Website http://www.trcc.commnet.edu/ed_resources/tasc/Training/Learning_Styles.htm 18 Some Causes of Math Anxiety 1.Inability to handle frustration 2.Poor self-concept 3.Excessive school absence 4.Parental attitudes toward mathematics 5.Teacher attitudes toward mathematics 6.Emphasis on learning mathematics through drill without understanding 7.Lack of mathematical experiences 8.Negative Math Experiences: Singled out/embarrassed Overwhelming pressure Forced to stay at board Physical punishment Verbal messages Competition with siblings/friends Moved to new school/teacher 19 Mathematics Anxiety Bill of Rights By Sandra L. Davis I HAVE THE RIGHT: 1. to learn at my own pace and not feel put down or stupid if I’m slower than someone else. 2. to ask whatever questions I have. 3. to need extra help. 4. to ask a teacher or a tutor for help. 5. to say “I don’t know” or “I don’t understand.” 6. to not understand. 7. to feel good about myself regardless of my abilities in math. 8. not to base my self-worth on my math skills 9. to view myself as capable of learning mathematics. 10. to seek help in learning math. 11. to be listened to and taken seriously when I ask for math help. 12. to assess my math instructors and how they teach. 13. to seek out the best math instruction possible. 14. to relax. 15. to be treated as a competent adult. 16. to dislike math. 17. to like math. 18. to define success in my own terms. 19. to demand explanations I can understand. 20. to explain what I’m thinking and receive clarification. 21. to ask “Why?” 22. to make mistakes in math and to learn from those mistakes. 23. to protest unfair treatment or criticism when I’m doing math. 24. to remain calm and confident when doing math. 25. to work hard toward achieving success in math. 20 Overcoming Anxiety Acknowledge your feelings. Admit that you are anxious. Stop yourself from thinking irrelevant thoughts or putting yourself down. Rework your negative statements into neutral statements and think in positive terms. Learn that even failure has a bright side: you can learn from your mistakes. Remember, if you do not take risks, you are not growing. And taking risks means allowing yourself the freedom to fail. Don’t worry about what others may be doing or thinking. It’s what we say to ourselves that counts the most. Think, “I can” or “I want” instead of “ what if.” Don’t worry about everything at once. Set goals that you can accomplish one step at a time. If you occasionally stray from your goal, don’t give up on your self. It’s okay to feel guilty for a little while, but resolve to get back on track. Practice the situation that makes you anxious. Set up a “dress rehearsal” as closely to the real life situation as you can. Practice the situation over and over in your mind picturing how you will succeed. Picture a time when you felt confident about an accomplishment. Focus on all the details of how you felt. Now picture the situation that causes you anxiety. Replay the picture with you feeling confident and succeeding. And finally, focus your attention away from yourself and toward the task. 21 MATH TEST ANXIETY REDUCTION CHECKLIST 1. ___ I’ve reviewed and worked out lots of problems so I know my material out of context. 2. ___ I know the format and content of my upcoming math test. 3. ___ I know how many questions will be on my exam and its duration. 4. ___ I’ve given myself several practice exams. 5. ___ On practice exams, I’ve noted areas of difficulty so I can strengthen them. 6. ___ I’ve analyzed my past pattern of typical errors so I can be alert to them on my exam. 7. ___ I’ve gotten seven to eight hours of sleep in the days prior to the exam. 8. ___ I’ve kept a regular program of moderate exercise. 9. ___ I’ve eaten a small meal of low-fat protein one to two hours before the exam and avoided too much caffeine. 10. ___ I’ll arrive at the exam on time and avoid talking with others. 11. ___ Throughout the exam I’ll remain calm, relaxed and positive. 12. ___ I will say positive self-statements to myself and push away all disturbing or distracting thoughts. 13. ___ I will write out all my formulae and key ideas on the top corner of my exam sheet before beginning the test. 14. ___ I’ll quickly read through the exam, note point values, and schedule my time accordingly. 15. ___ I’ll proceed comfortably throughout the exam, working first on the problems that come most easily to me. 16. ___ I’ll carefully read the directions to all problems and circle significant words to avoid misinterpretation. 17. ___ After finishing the exam, I’ll check my answers, proofread for omissions and check for my typical errors. 18. ___ I’ll leave and reward myself for a job well done! Adopted from “Conquering Math Anxiety” by Cynthia Arem 22 21 WAYS TO GET MORE DONE IN LESS TIME 1. Monitor your time for a week to see how you actually spend your time. The results are always surprising. 2. Create a schedule for yourself as a guide - but be willing to be flexible when necessary. 3. Each night prepare a list of things you hope to accomplish the next day. 4. Every morning look at your to-do list. Determine which task you dislike the most, and do it first. Completing unpleasant task decreases anxiety and gives you a sense of accomplishment. 5. Write things down to eliminate confusion and forgetting. 6. Keep a record of all test dates, assignment deadlines, appointments etc. on a calendar. 7. Improve efficiency by “bunching” activities. For example, plan one afternoon a week for running errands such as shopping, banking, picking up cleaning, etc. 8. Do specific tasks on specific days. 9. Focus your efforts on items that will have the best long-term benefits. 10. Start off with the most profitable parts of large project. You may often find that it is not necessary to do the rest. 11. If a project seems overwhelming, divide it into smaller tasks and complete one immediately. Doing the first task will help dissipate negative feelings and encourage you to go on. 12. Cut off nonproductive activities as quickly as possible. 13. Learn to delegate tasks to others when you can. 14. Use your personal time clock; know you own best working style. 15. Set time limits for projects and activities. 16. Concentrate on one thing at a time. 17. Give yourself time off and special rewards when you’ve done important things. 18. Make maximum use of short time periods. 19. Keep you study area/desk cleared to prevent distractions while working. 20. Don’t waste time regretting your failures. 21. Remember, the less time you feel you have to spare; the more important it is for you to plan your time carefully. 23 Math Study Skills Inventory (Taken from Conquering Math Anxiety by Cynthia Arem) This inventory will help you assess the effectiveness of your math study skills. Read each of the statements carefully and determine how frequently each applies to you. Enter the correct point score for that item on the line. (Usually=3, Sometimes=2, and Rarely=1) 1. ____I attend all my math classes. 2. ____I read my math assignments before attending class. 3. ____In class, I mentally follow all explanations, trying to understand concepts and principles. 4. ____In class, I write down main points, steps in explanations, definitions, examples, solutions, and proofs. 5. ____I review my class notes as soon after class as possible. 6. ____I review my notes again six to eight hours later, or definitely the same day. 7. ____I do weekly and monthly reviews of all my class and textbook notes. 8. ____In reviewing, I use all methods, such as reciting aloud, writing, picturing the material, etc. 9. ____I study math before other subjects, and when I am most alert. 10. ____I take small breaks every 20 to 40 minutes when I study math. 11. ____I work to complete my difficult math assignments in several small blocks of time 12. ____I reward myself for having studied and concentrated. 13. ____I survey my assigned math readings before I tackle them in depth. 14. ____When I read, I say aloud and write out important points. 15. ____I underline, outline, or label the key procedures, concepts, and formulas in my text. 16. ____I take notes on my text and review them often. 17. ____I complete all assignments and keep up with my math class. 18. ____I study math two hours per day, at least five days a week. 19. ____I work on at least ten new problems and five review problems during each study session. 20. ____I work to “overlearn” and thoroughly master my material. 21. ____I retest myself often to fix ideas in memory. 22. ____I work to understand all formulas, terms, rules, and principles before I memorize them. 23. ____I use a variety of checking procedures when solving math problems. 24. ____I study with two or more different math books. MY GRAND TOTAL IS:_______. If your score is above 68 points, you have excellent math study skills. If your score is between 54 and 68 points, you have fair study skills, but you need to improve. If you score is below 54 points, you have poor math study skills and you need help fast! 24 20 Tips for Academic Success 1. Each night prepare a course of study that you hope to accomplish the next day. 2. Create a schedule for yourself that is flexible but informs you of your weekly time commitments. 3. Plan and schedule some time each day to accomplish your goals. 4. Schedule leisure time the same way you schedule work commitments. 5. Keep a record of all test dates, assignments, deadlines, appointments, etc., on a calendar. 6. Make sure your desk faces a blank wall – not another desk or window. 7. If you are studying at home, find a place that you use only for studying. Keep noise distractions to a minimum. Keep your door closed; avoid all conversations including unnecessary phone calls. 8. Keep the surface of your desk and the space immediately surrounding your study area free of visual distractions such as photographs, mementos, etc. 9. Keep your desk uncluttered and have all the necessary materials readily available. 10. Have decent lighting and a good straight-back comfortable chair. Avoid studying in bed or stretched out on a couch. 11. Remember the importance of consistency: the most effective studying is done in the same place at a regular time. 12. Begin with your hardest subject, while your concentration is at its peak. Remember to take a 15-minute break every hour. Do not study in segments longer than 3 hours. 13. Begin studying your first subject by briefly surveying the material to be learned. 14. Make sure you understand the material you are studying; otherwise it becomes more difficult to learn. 15. Be a questioning reader. Ask yourself, “What re the main points the author is trying to tell me?” Read to find the answers to your questions. (Yes, you do need to read a math book!) 16. Become actively involved in your studying. Underline or highlight key words and phrases. Write down important points and definitions. If you are having a hard time concentrating, begin outlining the chapter. Remember that you are learning by writing. 17. Don’t be afraid to ask your professors for help. NO question is too “dumb.” 18. When preparing for a test, make sure you have a clear idea of what is to be covered on your test. Review copies of old tests if possible. 19. Remember to eat well and get enough sleep and exercise around exam time. An unrested and poorly fed body has to work harder to do regular things. 20. Arrive for tests early so as to be organized and ready instead of in a panic. Try to go into the test alert and calm. 25 Differences between English Language and Math Language SPOKEN AND WRITTEN ENGLISH USES ACTIVE AND PASSIVE VOICE, which means that it… 1. …has a sense of action or time depending on the context, i.e. narratives require active voice, but a psychological study would require a passive voice. 2. …sometimes uses emotion but often requires an objective tone, i.e. persuasive papers might rely on emotional language but summaries need to be neutral. 3. …first-person “I” is used to convey personal experience but when summarizing, informing or reporting stay unbiased. 4. …follows grammatical conventions depending on the context, discipline, and format. 5. …prepositions allow us to express relationships betweens ideas particularly time and space. 6. …is a highly flexible language which varies on purpose and context, which articulate different language standards depending on the academic discipline. 7. …is a language full of coordinating conjunctions and subordinating conjunctions which allow us to express complex thoughts. MATHEMATICAL LANGUAGE USES PASSIVE VOICE, which means that it … 1. …has no sense of action or time. 2. …uses no emotional words. 3. …does not use the first-person “I”. 4. …has a different grammar. For example, find the verb in: “If x = 5, then x + 3 = 8.” 5. …puts great emphasis on prepositions. For example, compare: “3 divided by 6” and “3 divided into 6.” 6. …is a high-density language to be read for detail, in which even a two letter word cannot be missed. 7. …is a propositional language because of its logical structure like the “if-then” construct. By Carrie Ann James (English, Urbana U.) and Rose Kleski Hart (Math, OSU-Newark) 26 Steps for Solving a Word Problem 1. Read the problem through quickly. 2. Pick out the question. 3. Read the problem until you have a complete understanding. 4. Write out the important information 5. Organize the information. Draw a picture if relevant. 6. Collect any formulas that may be useful. 7. Define variables. Don’t be afraid to stray from the popular “x”. 8. Write out the relationship in English. 9. Write out the equation in Algebra. 10. Solve the equation. 11. Check your solution. Is it realistic? 27 The Natural Human Learning Process Information from presentation and book by Rita Smilkstein, PH.D We’re Born to Learn: Using the Brain’s Natural Learning Process Summary of Natural-Learning Stages Based on NHLP Research with Approximately 6,000 Children and Adults STAGE 1: MOTIVATION/Responding to stimulus in the environment: watched, observed, had to, interest, desire, curiosity STAGE 2: BEGINNING PRACTICE/Doing it: practice, practice, practice, trial and error, ask questions, consult others, basics, make mistakes, lessons, some success STAGE 3: ADVANCED PRACTICE/Increase of skill and confidence: practice, practice, practice, trial and error, some control, reading, encouragement, experiment, tried new ways, positive attitude, enjoyment, lessons, feedback, confidence, having some success, start sharing STAGE 4: SKILLFULNESS/Creativity: practice, doing it one's own way, feeling good about yourself, positive reinforcement, sharing knowledge, success, confidence STAGE 5: REFINEMENT/Further improvement: learning new methods, becoming second nature, continuing to develop, different from anyone else, creativity, independence, validation by others, ownership, habit, teaching STAGE 6: MASTERY/Broader application: greater challenges, teaching it, continuing improvement or dropping it, feeds into other interests, getting good and better and better, going to higher levels 28 Major Points about Learning FOR STUDENTS We’re Born to Learn, page 103 1. Your brain was born to learn, loves to learn, and knows how to learn. 2. You learn what you practice. and again. 3. You learn what you practice because, when you are practicing, your brain is growing new fibers (dendrites) and connecting them (at synapses). This is what learning is. 4. Learning takes time because you need time to grow and connect dendrites. 5. If you don’t use it, you can lose it. Dendrites and synapses can begin to disappear if you don’t use them (if you don’t practice or use what you have learned). 6. Your emotions affect your brain’s ability to learn, think, and remember. -doubt, fear, etc., prevent your brain from learning, thinking, and remembering. Remember, you are a natural-born learner. 29
"Tutor Training Workshop"