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Five Questions about Tutoring The Art and Science of Tutoring Tem Fuller
Question One How does one assess a student's current mathematical knowledge at the start of tutoring? Jay Lavine
Assessment versus Evaluation I define assessment as the obtaining information about the skills and potentials of individuals, with a dual goals of providing useful feedback to the individual and useful data to the surrounding environment … Assessment ought to become part of natural learning environment. As much as possible it should occur “on the fly” as part of individual natural engagement in a learning situation. Gardner, H. (1993). Multiple Intelligences: The Theory in Practice. Library of Congress Cataloging-in-Publication Data: Basic Books. ISBN 10: 0-465-01822-X ISBN 13: 9 780465 018222
How do we obtain information about skills and potentials of individuals - V-Levels • In tutoring we need to find the Green Zone Tutor’s competence in the subject The student levels
Qualitative Data • Code the data about the parts of the assignment on the V-levels. • Think in terms of the three V-levels – current knowledge (V1), proximal knowledge (V2), and distal knowledge . • Tutors work in V2 - zone
Example of Complexity 1/2 in Why? 1/5 in 3/4 in • Geometry • operational definition versus • conceptual definition • Algebra • Common Denominator • Factoring • Common Denominator • Adding Fractions
Operational versus Transferable Knowledge • The student: “You add the numbers ” • The tutor: _____________________ • Ask for meaning first • Students tend to learn math and science to answer the questions. • The student: “So, what is the answer?” Advantages of concrete knowledge (old low skill jobs ) Advantages of abstract knowledge (modern jobs)
Q2 How does one deal with "math anxiety" in a student? Jay Lavine
Website about Math Anxiety http://mtsu32.mtsu.edu:11064/skill.html Study Skills Inventory
Csikszentmihalyi, Mihaly (1990). Flow: The Psychology of Optimal Experience. New York: Harper and Row. ISBN 0-06-092043-2
Q3 We have a society in which people often listen only to what they want to hear and engage in erroneous thinking, especially with regard to scientific matters. How does one counter erroneous thinking and teach people to think in a discriminating and scientific manner?
Tutors Teach Excitement You need to find the V2 - zone Students Skills
Some students … • I do not worry that tutees are asking questions outside of the area of tutoring. • I do not teach content directly; I teach learning. • If my tutee is getting out, I “run faster” with something like connector back to the point of escape.
Q4 I am working with 7th, 8th, and high school math students in San Manuel. The students represent the full spectrum of capabilities. They have a very structured program with student mastery of objectives which drives their individual progress. I have noticed that some students lack multiplication skills, i.e., they do not know their basic "times tables." They get all caught up in that, become discouraged, and then are unable to learn some of the other concepts. Do you have any thoughts on how we might help them learn this? I understand the school district has been addressing this in the lower grades. Are there any methods you know of which might make this easier for them?
Multiplication • Most students are excited by the magic of prime factorization. • Multiplication with all prime factors may look like a new skill: • Learn Multiplication with the first five primes 2, 5, 7, 11, 13 • Then ask them to present the whole multiplication table as prime factorization … Never look back – only ahead …
Q5 Sometimes I find myself wanting to justify to a child why math really is important for him/her in life. I look at math as being a language which allows a person to discuss and figure out things which would otherwise be too complex. Do you have any thoughts on this subject with particular consideration of the child's cognitive developmental level, or must we wait until the hormones are all burned out?? Marge Osborn-O'Dom
Q5 • Math is a model based on a small amount of data. • Math is a symbolic, tabular, and verbal language which allows a person to discuss and figure out things which would otherwise be too complex. • Math is a simplification that model specific phenomena. • The illusion that math is difficult is due to the fact that we do not “do” reality.
References • Gardner, H. (1993). Multiple Intelligences: The Theory in Practice. Library of Congress Cataloging-in-Publication Data: Basic Books. • Study Skills Inventory (n.a.) Retrieved from Internet http://mtsu32.mtsu.edu:11064/skill.html