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Graphing the rational functions

posted by WyzAnt tutor: Alexander C.

Course Description:

Examines polynomial and rational functions as well their graphing with analysis of critical properties in the context of real life situations and will include student investigations and hands on activities. 3 credits

Prerequisites:

2 years of high school Algebra
(Students are responsible to review material prerequisite for this course on their own.)
Note: It is highly recommended that "Polynomial Functions" and “Graphing Quadratic Functions” be completed prior to this course with a grade of C or better.

Course Objectives:

a. Polynomial Functions
Use the Fundamental Theorem of Algebra and the Linear Factorization Theorem to write a polynomial as the product of linear factors
Find all real and complex zeros of a polynomial function
Find a polynomial with integer coefficients whose zeros are given
Use the Leading Coefficient Test and the zeros of a polynomial to sketch the graph of a polynomial
Apply techniques for approximating real zeros to solve an application problem

b. Rational Functions
Find the domain of a rational function
Find the vertical and horizontal asymptotes of the graph of a rational function
Sketch the graph of a rational function
Use a rational function model to solve an application problem

The purpose of this course is to increase students' understanding of mathematics, which contributes to a foundation for teaching in K-12. This course emphasizes the concepts and applications of functions, graphical analysis and pre-calculus.

Students should become better problem solvers using the concepts in this course both individually and in working positively with others in solving problems and in the learning process. It is hoped that this course will not only increase the students' knowledge, but also their confidence and enthusiasm to teach K-12 school mathematics.

Required Materials:

Please bring to each class: a copy of the text, the Lab Manual, a graphics calculator, computer 3.5" disk, colored pencils (optional), graph paper 1/4" x 1/4", and a loose leaf notebook. (There is a 5-point penalty for not having materials).

Quizzes and Exams:

There will be 2 exams and a cumulative final exam. Exams are based on the text, supplementary material discussed in class, and on assigned work. Exams will have many problems similar to previous work, but will also contain some novel examples. A request to miss a regularly scheduled exam must be made in advance and must be documented. For a documented excused absence, students may request to have an adjusted average computed instead of taking a make-up exam. Make-up exams will always be more difficult than the regularly scheduled exam. There will be frequent short quizzes on previously discussed material and the quiz average will be equivalent to a third exam.

Homework and Student Presentations:

Students are expected to attempt all of the assigned homework problems in a neat manner, showing all necessary solution steps. Students should seek help prior to class on any homework problems they cannot complete, as they are asked to present homework solutions to the class.

Homework will be spot checked and recorded as "completed assignment or not" during class. Problems with just answers and insufficient solutions steps are considered incomplete. Student presentations and class discussions will center on a few of the homework problems. If additional help is needed, students are advised to come to office hours. Homework should be organized in a loose-leaf notebook and is evaluated again at the end of each unit.

Attendance:

Students are expected to attend all classes. Absences should be only for illness, and documented or recognizable emergencies. The final grade will be lowered one letter grade if a student has missed 10% of classes due to unexcused absences, and students receive an F if they miss more than 25% of the classes for any reason. Students are responsible for all course information during an absence, i.e. securing class notes or handouts, getting extra help, etc. Some of the course materials and labs are not in the text, and some labs require completion at the computer lab outside of class-time.

Journal, Projects, Portfolio & Class Participation:

Students will be asked to write some journals about mathematics. A Portfolio of some of the student's interesting work will be collected near the end of the course. Several special problems and projects will be due as assigned. Much of this course is class discussion of homework or new concepts and working with cooperative partners or groups. Consequently, the "Journal, Homework, Projects, Portfolio & Class Participation" grade is greatly dependent on lively participation with a cooperative and positive attitude. Participation and attitudes, which help the whole class succeed and enjoy mathematics, is highly valued in this course.

Grading:

The grade in this course will be determined using 90%-100% = A, 80%-89% = B, etc. If excused absences would affect a student’s grade, it is the student’s responsibility to present verification of excused absences during office hours near the end of the course. Late work receives half credit if it is received before the next class. The grading scheme and tentative exam schedule are as follows:

Honor Code:

The students in this course should respect and appreciate the Common Honor Code of Learning. They all agreed to assume full responsibility for our actions and will refrain from lying, cheating, stealing and plagiarism and will endeavor to see that others do likewise. While some of the work in this course is cooperative group work, most is individual work. Tutoring and assistance on homework is allowed to help gain understanding; however, the students must actually do the work themselves and be able to explain their process.

Course Information:

Hopefully the students will enjoy this course as much as this instructor does. I think you will find it has a little different format for learning mathematics compared to a traditional math class. Class time will be used for group work and discussions and presentations by myself and by students. Students are expected to be quite active in discussions and in sharing ideas. Students should expect to spend several hours preparing for each class. I welcome you to seek extra help during my office hours; however, I will expect to see serious efforts made by you prior to coming for help. Feel free to stop by. Keeping up to date in this course is extremely important. It has been my experience that students who fail the first exam and who do not have a passing quiz grade will not do well in this course and should seriously consider dropping before the drop date to receive a W grade. Exceptions to the drop date may be made for a major medical emergency and require the deans signature. The syllabus is subject to changes as announced in class. A daily class schedule is available upon request.

“Polynomial and Rational Functions” content delivery

Polynomial Functions

Motivation: [5 minutes] Solving equations is at the heart of any math course. For example, in calculus, to find the critical values students will need to solve equations. Polynomial equations are one example of such equations. Historically, students learned how to find the roots from the given polynomial. Now this can often be done much more easily with the graphing calculator. But the reverse process is also interesting; that is, from the given graph of a polynomial, recover a formula for it. In addition, polynomials are used frequently to model real-life scenarios and make predictions. Polynomial models are often simpler than other models. Solving polynomial equations often leads to simple solutions for real-life applications.

Warm Up Discussion: [5 minute] Provide an example of a polynomial function (in completely factored form) with only real roots. Ask students how many roots it has. Then provide an example of another polynomial function (in completely factored form) with mixed real and complex roots. Ask students how many real roots and how many complex roots it has. Then help students generalize that an nth degree polynomial has n roots.

Find all real and complex zeros of a polynomial function

Warm Up Example or Activity: [20 minutes] Give a polynomial of degree 3 with integer coefficients and one rational root. Use the rational root theorem and synthetic division to find that root. Then use the quadratic formula to find the other complex roots. Point out that complex roots occur in complex conjugate pairs. Point out that this polynomial can be completely factored as a product of three factors. (Then use the graphing calculator to demonstrate that the graph has just one real root; the complex roots do not show as x intercepts.)

Formal Concept: [5 minutes] The Fundamental Theorem of Algebra and the Linear Factorization Theorem can be used to write a polynomial as the product of linear factors. Find a polynomial with integer coefficients whose zeros are given

Warm Up Example or Activity: [20 minutes] Ask students to find a formula for a degree four polynomial with integer coefficients that has two real zeros and one complex zero (a + bi, with b =/ 0). Demonstrate that this polynomial also has the other complex conjugate as a root. Explore different possible solutions, based on the leading coefficient. Have the students graph the functions and observe how changing the sign of the leading coefficient from positive to negative changes the global behavior. (In the previous example, with n = 3, an odd degree, explore how changing the sign of the leading coefficient would change the global behavior of the 3rd degree polynomial.)

Formal Concept: [5 minutes] Have students generalize the Leading Coefficient Test in their own words.

Apply techniques for approximating real zeros to solve an application problem

Example and In-Class Activity: [10 minutes] Have students solve a problem involving a 2nd degree or higher polynomial model for revenue, cost, or profit.

Suggested Follow Up Assessment: the assigned homework problems, and a quiz or warm-up review example at the beginning of the next class.

Rational Functions

Motivation: [5 minutes] Some things grow with limited capacity because of limited space or resources, such as a fish population in a pond. Other things cannot realistically reach 100% optimization, such as pollution removal. Other things decrease over time, such as the concentration of medicine or alcohol in the bloodstream. Rational functions can be used to model these situations and also are used with limits and applications in calculus.

Warm Up Discussion: [5 minutes] One of the most important aspects of rational functions is the concept of vertical and horizontal asymptotes. The graphs of rational functions often are in pieces, with vertical asymptotes (local behavior) at places where the input is not defined and horizontal asymptotes (global behavior). Horizontal asymptotes demonstrate the limiting capacity in applications of rational functions.
Find the domain of a rational function.
Find the vertical and horizontal asymptotes of the graph of a rational function

Warm Up Example or Activity: [20 minutes] Choose a rational function of degree one over degree one in completely simplified form. Ask students for the domain. Remind them that the domain of the function is those real values of x that make the function have meaning. Pick some x values in the domain and the number that is not in the domain. Then talk about the presence of a vertical asymptote on the graph at that x value. Ask students to graph the function to verify this. Demonstrate for them the behavior to the left and right of this value.

Also, ask the students to zoom out to demonstrate the global behavior of the function. Discuss the equation of the horizontal asymptote. Give other quick examples of other cases for horizontal asymptotes, i.e., when the horizontal asymptote is zero or when there is no horizontal asymptote.

Formal Concept: [5 minutes] Have students explain in their own words how to find the domain and the vertical asymptote of a rational function algebraically. Also, lead them to examine and state in their own words how the ratio of the leading terms of the polynomials in the numerator and denominator is related to the equation for the horizontal asymptote.
Sketch the graph of a rational function

Warm Up Examples or Activities: [20 minutes] Give students more examples of higher degree polynomials in the numerator and the denominator to help the students learn to
1. find the y and x intercepts and the domain
2. find the equations of the vertical and horizontal asymptotes
3. select some extra x values to aid in graphing (choose values between vertical asymptotes and the x intercept)
4. graph the function by hand and confirm using your calculator

You may choose an example where the graph intersects the horizontal asymptote locally. (Many students think that the graph cannot intersect the horizontal asymptote.) You may also choose to give an example of a denominator with no real roots and examine the effect this has on the graph.
Use a rational function model to solve an application problem

Warm Up Examples or Activities: [15 minutes] Choose any real applications from the book, e.g., population of animals, pollution removal, drug concentration, average cost, etc. Help students discover that the horizontal asymptote of the function is the limiting capacity (maximum population) or minimum concentration for these kinds of problems.

Suggested Follow Up Assessment: the assigned homework problems, and a quiz or warm-up review example at the beginning of the next class.

Definition of a Rational Function (RF)
A rational function is basically a division (quotient) of two polynomial functions. That is, it is a polynomial divided by another polynomial. In formal notation, a rational function would be symbolized like this:
y = R(x) = g(x) / h(x)
Where g(x) and h(x) are polynomial functions, and h(x) cannot be equal zero.
RFs can have two types of discontinuities: asymptotic discontinuities and hole discontinuities.
Asymptotic discontinuities occur when a denominator h(x) of RF is 0, i.e. h (x a ) = 0.
Hole discontinuities occur when both a numerator g(x) and denominator h(x) are equal to 0,
i.e. g (x h ) = h (x h ) = 0.

The steps of RF analysis:
I. Factorizing and simplifying an original RF.
II. Finding a domain of RF.
III. Finding discontinuities of RF:

1. asymptotic discontinuities
2. hole discontinuities
IV. Intercepts of RF
1. X- Intercepts
2. Y- Intercepts
V. Turning (stationary) points of RF
VI. Sketching the graph of RF
VII. Sign analysis of the graph

Along with polynomial representation the rational functions can be represented in factored form.
Here is an example of a rational function:
y = R(x) = x2-3x / x2-9
Because the graphical examples in the classroom communicate far better than abstractions and generalities, let's address some illustrative rational function f(x) = x2-3x / x2-9 and consider further all the attributes, properties and methods of graphing rational functions following this example.

I. Factorizing and simplifying an original RF.
The very first step is trying to factorize and simplify a given function.
To understand the behavior of a rational function it is very useful to see its polynomials in factored form. Obviously, factorizing f(x)=x(x-3)/(x-3)(x+3) which simplifies to x/x+3. The polynomials in the numerator and the denominator of the above function would factor like this:
R(x) = x(x-3) / (x-3)(x+3) = x / x +3
Take a notice that x=3 gives R(x) = 0 / 0. So, value x=3 provides a pointed, steep type of discontinuity called “hole”. Another type of discontinuity is smooth, non-steep approaching to infinite values called “asymptotes”.

II. Domain
The Domain of RF is the set of all real numbers for which f(x) g(x)/ 0 or f(x) 0/0. In other words, the domain of RF is the intersection of the domains of g(x) and h(x). Now the roots of the denominator are obviously x = -3 and x +3. That is, if x take on either of these two values, the denominator becomes equal to zero. Since one cannot be divided by zero, the function is not defined for these two values of x. We say that the function is discontinuous at x= +3 and x= -3. The domain for the given RF, as expressed in interval notation, is:
D = (- , -3) U (-3, +3) U (+3, + ), where x=-3 and x=+3 are discontinuities.

III. Discontinuities.
Other values for x do not cause the function to become undefined, so, we say that the function is continuous at all other values for x. In other words, all real numbers except -3 and +3 are allowed as inputs to this function. As mentioned above, there are two types of discontinuities: asymptotes and holes.

1. Hole discontinuities
We determined already that hole (steep) discontinuity for the given RF is x=+3 because both g(x) and h(x) have a common factor (x-3) and become equal 0 at x h = 3. If RF is then reduced to lowest terms, the graph of RF has a hole in it where x h = 3. To find the y value, plug x=3 into the simplified function and get 3/6=1/2. The hole is at (3, 1/2). If you have a common zero of g(x) and h(x), this represents a hole in the graph!

2. Asymptotic discontinuities
Asymptotes of a function are lines that the graph of the function gets closer and closer to (but does not actually touch), as one travels out along that line in either direction. Generally, there are three types of asymptotes: vertical, horizontal and oblique (slant).

a. Vertical asymptotes
The vertical asymptotes for a RF are determined by the zeros of the denominator (i.e. the values for which the denominator equals 0). Find the zeros of the denominator after you simplified. You can find the vertical asymptotes by equating the denominator to 0 and solving, and then see if y approaches infinity or negative infinity on each side of the potential asymptote.
Find the zeros of h (x). These will be the vertical asymptotes unless it's also a zero of g (x)!
Set h (x) = 0 and solve for x.
A vertical asymptote for RF is a vertical line x=k; k. is a constant, that the graph of RF approaches but does not touch. For the given RF the vertical asymptote is x v a = - 3.

b. Horizontal asymptotes
A RF has a horizontal asymptote y = a, if; as |x| increases without limit y approaches a. RF y = f(x) has at most one horizontal asymptote. The horizontal asymptote may be found from a comparison of the degree of g(x) and the degree of h(x).
Find the horizontal asymptotes of the function after you simplify.
a. if degree(h(x)) > degree(g(x)) then horizontal asymptote y =0;
b. if degree(h(x)) = degree(g(x)) then horizontal asymptote y = a/b (leading coefficient of g(x))/ (leading coefficient of h(x));
c. if degree(h(x)) < degree(g(x)) then no horizontal asymptote

The graph of y=f(x) may cross a horizontal asymptote in the interior of its domain. This is possible since we are only concerned with how RF behaves as |x| increases without limit in determining the horizontal asymptote.

Lim x/x+3 = Lim (x / x) / (1+1/x) = 1/1=1
x x
The horizontal asymptote is y h a = 1.
The horizontal asymptotes of a function can be found by dividing both the numerator and denominator of the rational function by the highest power of x that appears in the denominator. You will then likely produce at least one term of the form c/x n. As x approaches infinity (positive or negative), this term approaches zero, thus it can be eliminated from the expression, and you can solve for y to find the horizontal asymptotes.

C. Slant (oblique) asymptotes
Utilize polynomial algebraic division. In this case: R (x) = x / x + 3.
Linear oblique asymptote like R(x) = kx + a will occur if degree (h(x)) = degree (g(x)) – 1.
Because this condition fails there is no oblique asymptotes for the given rational function.

IV. Intercepts
1. X-Intercepts
The x-intercepts (if any) of y are the zeros of the numerator, p(x), since the function is zero only when its numerator is 0. R(x) = g(x) / h(x); if R(x) = 0 then g(x) = 0
Find the zeros of g(x). These will be the x-intercepts unless it's also a zero of h(x)!
Find the x-intercept by finding the zeros of the numerator: x int = 0.

2. Y=Intercepts
Find the y-intercept by replacing the x value with 0. R(x=0) = g(x=0) / h(x=0) = 0 / 3 = 0.
If the denominator is not zero, you have found the y-intercept - y int = 0!

V. Turning (stationary) points
Turning (stationary) points - extremes (local relative minimum or maximum)
To find extrema you have to equal a function derivative to 0 and determine X-coordinate of a function extreme. With usage of a known formula for a derivative (division of two polynomials Y=U/V):
Y’ = (VU’ - UV') / V2
For the referred example:
Y = (x2 - 3x) / (x2 - 9)
Y' = 1 / 3(x+3)2
There are no extrema because Y’ 0 (never equal to 0)

VI. Sketching the graph
Graph sketch: Use the vertical and horizontal asymptotes to help sketch the graph. If x = c is a vertical asymptote, then the graph approaches infinity as it nears the asymptote in a region where the function is positive, and it approaches negative infinity as it nears the asymptote in a region where the function is negative. (Note: vertical asymptotes cannot be crossed because they describe where the graph is undefined. Horizontal asymptotes may be crossed as they describe only what happens to the graph as x gets very large or very small!)
a) Find the zeros of the denominator after you simplified. The vertical asymptote is x = -3.
b) Find the limits on infinity of the function after you simplify.

The horizontal asymptote is y = 1.
c) Find the x-intercept by finding the zeros of the numerator. x =0
d) Find the y-intercept by replacing the x value with 0. y-int is 0.
e) Find the holes in the graph. The hole appears at the factor that was canceled. In this case, at x =3.
To find the y value, plug x=3 into the simplified function and get 3/6 = 1/2. The hole is at (3, 1/2).

VII. Sign analysis
Do a sign analysis in each interval separated by asymptotes and intercepts. Sign analysis for each area of the graph. In the upper left corner, the y values are + which means the graph is above the x-axis approaching the vertical and horizontal asymptote. The area to the left of the zero is negative and approaches the vertical axis downward. The area to the right of the zero reverts back to positive and approaches the horizontal asymptote. It will not cross the horizontal asymptote because setting 1 = x/(x+3) yields no solutions! The hole y h = 0/0 not allowed to divide 0 by 0 (infinity).

Generating identity expressions

posted by WyzAnt tutor: Alexander C.

“Generating purposefully specific algebraic and arithmetic identity expressions”

Setting up the Problem:

Using any mathematical signs (including parentheses), provide nine arithmetic expressions each with the same three digits (1<=n<=9) as inputs, which produce the same result for all nine expressions (1<=R<=9). Then deduce algebraic formulas (there can be multiple possible solutions), those produce the same result and valid for any input digit from 1 to 9, as a function for an independent variable N ( 1 N - 9). The signs of square and cube roots as well any exponents are admissible. For inferring an universal algebraic identity expression a single extra digit is admissible.

I. Goal

Inquiry and problem-based learning increases students’ engagement, learning gains and retention of what they learned. There are three points that is supposed to be taken away from this lesson.
1. First, viewing mathematics as a "science and process of making sense of things" and "to understand what it means to do mathematics." Math is not just a collection of rules and procedures but it can and needs to be done with understanding. Students should never be allowed to use a strategy without understanding it.
2. Maximize students' learning gains, embracing problem-based, student-centered approaches in mathematics instruction. These approaches are based on students thinking about mathematics and making sense of ideas, not just copying the teacher or text's rules into a notebook and plugging in the numbers to find answers.
3. Finally, math can be intrinsically rewarding - fun to learn and fun to teach. Students’ past experiences with mathematics may not have been positive, but an effective teacher needs to see how math can be fun and be prepared to make math enjoyable for the students.
This problem-based lesson illustrates designing and conducting inquiry sessions that lead students to construct mathematical concepts and discover mathematical relationships. It employs strategy for conducting minor experiments to monitor students' progress during these types of lessons and assess how well the objectives were achieved.

II. Objectives

Students should become better problem solvers using the concepts in this lesson both individually and in working positively with others in solving problems and in the learning process. It is hoped that this lesson will not only increase the students' knowledge, but also their confidence and enthusiasm in creative math thinking and applying mathematics knowledge in their future careers and everyday life.

Mathematics is an everyday human endeavor by which students and other ordinary people construct concepts, discover relationships, invent algorithms and models, organize and communicate their thoughts in the language of mathematics, execute algorithms, and address their real-world problems. Problem-based and inquiry lessons can help students learn and creatively apply mathematics to their everyday lives. But most students do not have these prior experiences of applying mathematics in real life. Rather, they acquire a considerably different view of mathematics, perceiving it as a boring string of things truly understood only by rare folks. Often the students are asked only to memorize mathematical content without ever discovering on substance or creatively applying it.

As a result of this lesson, the students will:
1. Understand and use the relevant NYS Mathematics Learning Standards as well the National Council of Teachers of Mathematics (NCTM) content and process standards for secondary school math education and their role in designing learning experiences.
2. Describe how elementary and middle school aged children construct and develop mathematical knowledge and competencies at different levels of complexity including number concepts, operations, place value, computation, arithmetic and algebraic reasoning.
3. Take an active participation in problem-based mathematics instruction and sharpening critical thinking skills those meet the diverse needs of all students.
4. Be continuously monitored of their mathematics progress through a variety of formal and informal assessment strategies.
5. Reflect upon their own readiness to learn mathematics in settings requiring intensive ingenious mathematical and logical reasoning and establishing their personal goals for mastering critical thinking in math learning process.

Creative thinking and problem-solving assignment

posted by WyzAnt tutor: Alexander C.

“Proving a special relationship between geometric representations”

Setting up the Problem:

Construct semicircles on the three sides of an isosceles right-angled triangle ABC that will form two lunes on the triangle legs. Prove that each lune area equals half the area of the triangle.

Definition: Lune is a crescent-shaped figure formed on a plane surface by intersection of the arcs of two circles.

I. Goal

The goal of the Lesson Plan is implementation of problem-based teaching / learning as an instructional method that develops the problem-solving skills needed to accomplish tasks both in the professions as well as in everyday life. In problem-based learning, students encounter a problem or issue and perform research in an attempt to reach a solution. As in everyday experiences, the process may begin with insufficient information. Students develop hypotheses in response to the problem. They gather and evaluate data from a variety of sources, and then revise their hypotheses in response to the data they encounter. A problem may have one or more solutions, and students' perception of the problem may change through synthesis, evaluation and communication with others.

Benefits of problem-based learning include skill development in areas such as problem-solving, critical thinking, creative insight, decision-making, conflict-resolution, and higher reasoning, as well as in written and oral communication. Students, by working through various challenges, acquire knowledge of problems and concepts through their own initiative, and gain greater respect for themselves and their fellow students. Students can also engage in problem-based learning through a cooperative-learning approach, in which students work in groups that determine different solutions to the same problem. This adds the further benefits arising from cooperative effort, including interpersonal and communication skills. And students come to recognize that a problem may inspire more than one reasonable solution.

II. Objectives

The purpose of this lesson is to increase students' understanding of mathematics, which contributes to a foundation for teaching school mathematics. This lesson emphasizes the concepts and applications of functions, graphical analysis and pre-calculus to perform research to reach a solution.

III. Prior Knowledge and skills (Prerequisites)

3 years of middle and high school Geometry
(Students are responsible to review material prerequisite for this course on their own.)
Note: It is highly recommended that school geometry course be completed prior to this course with a grade of C or better.

Required Materials:

A copy of the Lesson Plan, the Lab Manual, a graphics calculator, computer 3.5" disk, colored pencils (optional), graph paper 1/4" x 1/4", and a loose leaf notebook. (There is a 5-point penalty for not having materials).

IV. Action Plan

Procedural plan of actions:

Students will work in groups (of about four members) to address the problem. Within these groups, they (preferably, each of them) propose hypotheses and choose one for further inquiry. They then perform research directed by the hypothesis until they reach a reasonable solution in the time allotted by the teacher.

Summary of the steps in the procedural plan of actions and the rules those students should follow through the problem-solving process:
Step 1: Define the problem. The teacher confronts the students with a plausible hypothetical problem. The teacher does prior research to verify that material is available and suitable for students to research the problem.
Step2: Propose hypotheses. Hypotheses are intuitive hunches (gut feelings) or educated guesses about possible solutions. In problem-based learning, students form hypotheses based on group discussion, previous knowledge, and any information acquired up to that point. Through the course of the problem-based exercise, hypotheses will be continually evaluated and may be rejected, corroborated, synthesized, or modified. New ones may also be proposed as incoming data is evaluated. The teacher organizes and supervises discussions on hypothetical solutions.
Step 3: Gather and evaluate information. With their hypotheses providing direction, students may explore a variety of sources to acquire data. The teacher provides help in organizing the information that students gather. An important aspect of gathering information is evaluation (Is the material relevant? Is it current? Are the sources unbiased and is the information they provide accurate?).
Step 4: Synthesis and solutions. Students develop their solutions. Discussion of the various solutions may follow, and synthesis and consensus may be used to come up with a solution that effectively incorporates important points from more than one point of view. The teacher provides help in facilitating this process. The groups can then present their solutions. They may include both written and oral components. Students may then be invited to write papers on their own positions, and how they may have changed from when the problem was first proposed.

There's Nothing Like Proper Preparation

posted by WyzAnt tutor: Richard S.

If you're like many college graduates, you may be scratching your head wondering what to do with your life. You might be asking yourself, "so I have a college degree, now what?" The job market is tougher than ever and getting an interview is like playing the lottery, unless you know someone on the inside who will recommend you to a hiring manager. The thought of going back to school might be the furthest thing from your mind but if you've ever considered graduate school, now might be the right time.

The deadline for applying to next Fall's Master's, JD, and PhD programs is quickly approaching. However, it's never too late to explore the possibilities. One of the requirements is taking entrance exams like the General Record Examination, or "GRE" for short. According to research by leading GRE preparation groups, it takes a minimum of four to twelve weeks to properly prepare for the exam.

The key is to start as soon as possible and go online to www.ets.org/gre to check for available test dates in your area. If you have not successfully taken or "passed" the GRE within the last four years, you will need to complete it before applying to graduate schools. Good luck!

Deep Fry I Leadership Charges in Proverbs 21-22

posted by WyzAnt tutor: Cameron F.

Proverbs is abundant with divine guidance and discerning counsel. Among the books' moral, ethical, and spiritual precepts, Proverbs succeeds in providing principal leadership pointers in addition to its axioms.

While many themes extend from Proverbs 21 and 22, the broader scope delves into how a righteous man should be aware of his ways and act cautiously in training and dealing with principalities of darkness. The following verses additionally highlight key leadership traits discussed in these chapters as to how they apply to the heart of an aspiring commander in Christ.

Proverbs 21:2 - "Every way of a man is right in his own eyes, but the Lord pondereth the hearts." (KJV)

In Hebrew, pondereth (tákan) possesses several definitions, perhaps most prominently as to measure out, arrange, and direct. Naturally, when one thinks of "pondering", intense contemplation comes to mind; however, if one stops there, the magnitude of the verse diminishes.

If we push the 'pause button' prematurely, the verse stalls as God thinking intently about a man's heart. But God does not accomplish anything half-heartedly. He not only focuses His attention, but He carefully calculates and appraises every internal nook and cranny. If something is out of line, He is faithful to direct and lead us onto a better pathway to holy fulfillment.

Proverbs 21:12 - "The righteous man wisely considereth the house of the wicked, but God overthoweth the wicked for their wickedness." (KJV)

Considereth, from the Hebrew word, sákal, needs to be examined as well, given its superficiality evident by the English translation. In today's world, "consider" has a painfully neutral connotation. When ones "considers", we tend to imagine an authority figure pitching the phrase, "I'll get back to you on that..." as a lethargic copout for dismissal.

But the Hebrew meaning digs much deeper. To "consider", implies both instruction and prosperity - to not only teach, but bear good success. How much richer does v. 12 become then? The righteous leader does not merely settle for indifference or objectivity as compared to actively apprising and educating the church of her sin. God will take care of those stuck in rebellion, but part of a leader's charge is to make known the ways of the righteous not only so he may prosper, but that those under him may succeed as well. A righteous leader is proactive in bestowing knowledge to others; such is the core of this verse.

Proverbs 21:22 - "A wise man scaleth the city of the mighty, and casteth down the strength of the confidence thereof." (KJV)

In v. 22, the word scaleth (álåh) is a wild card - multiple meanings cast various versions on how this verse can be interpreted. People often associate the world "scale" to measuring or clambering. But alas, the Hebrew significance offers a better inside scoop. To "scale" means more than ascending or climbing. In the Hebrew, we find it also represents restoration and perfection, even arousal.

A leader should not take pride in surmounting obstacles, but should focus on how God can use him to restore and perfect situations and outcomes. Whatever pride or self-centeredness exists should be cast away, so that completeness and excellence may become reality.

Proverbs 22:6 - "Train up a child in the way he should go, and when he is old, he will not depart from it." (KJV)

On a basic level, to train (chånak) is to instruct; however, in the Hebrew, to train is to teach emphatically in a way that encompasses discipline.

A secondary definition involves "initiative." As a leader, one must treat training as a pursuit, not merely a privilege. Like evangelism, training must be perceived as a command as compared to a prerogative.

Chånak owns a similarity to sákal in the sense it also stresses fruition by way of faithful dedication to raise up new leaders. Thus, leadership must be viewed as the summation of what is amassed and how the baton is passed to future generations.

Proverbs 22:29 - "Seest thou a man diligent in his business? He shall stand before kings; he shall not stand before mean men." (KJV)

A final examination features the term "seest" (chåzåh). The obvious visual in "seest" is "see", which offers several dimensions of the word. A few chief alternatives include: perceive, vision, behold, prophecy, and provide - all which provide various spins if applied directly to the verse.

One necessity of a leader is diligence, as the verse suggests. But a spiritual leader must acquire a certain boldness that comes only by seeking the Lord in a Daniel-like way. Disciplined dedication to know God more opens the door to perceive with new lens. In Daniel's case, perception paved the way for his prophetic ministry to catch divine vision. Even at a young age, Daniel provided strong living examples of how to be diligent in both personal and business life. Since Daniel displayed consistent faithfulness in aligning his ways with God, he indeed was able to stand before kings and alter the course nations' futures.

Ken In Houston Reaches 400 Hours of Tutoring

posted by WyzAnt tutor: Ken B.

Ken B., known as "The Best Little Tutor In Texas", has just surpassed the 400 hour tutoring mark in Houston, Texas! What makes Ken so good and popular in Houston? It is because of his diverse background and of being able to do the following: mathematics, statistics, chemistry, physics, computers, and computer programming. He can help a student in many many different areas. Ken does both high school and college and does regular, honors, IB, PAP, AP, etc... All that is quite a talent. Ken says that the subject most tutored in the past several months is statistics, and the reason for that is that most teachers use the 'dump' method...they 'dump' a copious quantity of power point files onto the student but the teachers do not really teach how to 'do' the problems...he has seen the same trend with other subject areas, and this is most unfortunate for students taking the classes...so, if you need to get on top of your mathematics and science courses (except of biology), then Ken in Houston is the person to contact.

The Japanese connection

posted by WyzAnt tutor: Gennifer H.

Yesterday I worked with a student on his sick make up work in Japanese and English, two of my favorite subjects in high school. I speak conversational Japanese and I took Japanese language in high school and college. As a kid I also went to Japanese school on Saturdays for a short period. I still don't speak the language fluently, however, and haven't really studied it since my undergraduate college days but I am definitely competent in most high school level Japanese 1 and 2 courses. Tutoring basic Japanese for me is like teaching someone to ride a bike. It is something that is ingrained in my ethnic culture. My desire to learn as much as I could about my people’s culture and language never really manifested itself in perfect fluency but was always a goal throughout my schooling years. I was "eliminated" in the college round because UC Berkeley’s Japanese program was very challenging and bad grades outside of my major were going to be too detrimental, so I had to drop the course.

It is something that I still love and enjoy teaching to others. Yesterday was a great lesson because it helped ME to revisit one of my passions. When you become a high school teacher you have to choose a SINGLE subject to specialize in and English was the subject that I chose. Once you pass your single subject credential tests, you are not really allowed to teach other subjects outside of your specialization unless you substitute teach them. Japanese is also not the most common language taught in high schools either, especially in Latino/a saturated California schools. Tutoring has allowed me to access many many subjects that I never formally studied how to teach. I believe that I have done them well and that my students have been satisfied. I have been pleasantly surprised at my ability to use my mastery of instruction and curriculum to be a great tutor in all of the subjects that I have taken assignments in to date as it is something that I was not able to to do when I was a high school teacher.

Tame the Math Monster

posted by WyzAnt tutor: Kate K.

As I said in my previous post, math has become a problem for so many students. Parents are frequently at a loss as to how to help their child in math (or pre-algebra, algebra, or ASVAB) as well. Why is math so difficult and scary for so many students? Is it because math is inherently more difficult than English and History? Is it because you "just can't understand or learn math"? Are pre-algebra and algebra too hard to learn? Is it the teacher's fault you haven't been able to comprehend math? If you are trying to get ready for your ASVAB is it too late to learn math? The answer to all of these, of course, is a resounding "no"!

You just need to find the right tool for the job. After all, a master carpenter would never succeed if he tried to cut a board with a hammer instead of a saw. The right study skills and right tutoring session can help you succeed. You really can become successful in math, pre-algebra, algebra, study skills and test taking! Would you like me to help you develop into a high achiever? You do not need to feel like a failure; you actually were built for success!

Math can actually be fun. As I said yesterday, understanding each concept gets you to the next level, like levels in a video game; it is all related. If you are struggling, I would love to tutor you so that you can reach the top level! Don't live in fear of the Math Monster. You can tame that monster--make math your friend! I do not believe math is beyond your abilities. Look at all that you learned in your first few years of life! You learned to communicate by learning an entire language, you learned to walk, feed yourself, and learned your role in life. So if you learned all of that, I can teach you how to learn math.

Let's get started!

Feliz Dia de los Veteranos - Happy Veterans Day

posted by WyzAnt tutor: Dagny N.

Gracias a los hombres y mujeres que han peleado y muerto en la guerra para que nosotros pudiramos vivir en un pais libre.

Thanks to all the men and women who have fought and died in the war, so we can live in a free nation.

Why English as a Second Language Tutoring is Important to Me

posted by WyzAnt tutor: Debra B.

Throughout my life, from the time I was in Kindergarten until the present time, I have been involved in learning different languages. Every school day from K-6th grade, our classes learned French from the TV. That's a lot of French lessons for a child. Sometimes I dream in French.

In Middle School I took Spanish for three years and it was quite easy since I had that French background. Three years ago I decided to take Chinese, just to satisfy my own curiosity to see if I could. Using Rosetta Stone, I found I was quite good at recognizing characters and their meanings. I could never speak a word of it, but my focus was on understanding the written word. This year I corresponded with a Danish man and went back to Rosetta stone to learn Danish. It was quite fun for me. Rosetta Stone is a no-pressure, fun way to learn a language.

However, a personal tutor is much faster and gives immediate feedback for correct pronunciation and grammar. No software can do that. Your tutor can show you how their mouth looks and the position of the tongue for exact pronunciation. Your personal tutor assesses your needs and progress during every lesson and tailors them to your exact need. Need to fill out an application? No problem. It becomes part of the lesson. Need to be able to read a restaurant menu and know what you are ordering? No problem. Whatever your language needs are, we can succeed together!

I can help your child get math

posted by WyzAnt tutor: Kate K.

Math has become a problem for so many students. Parents are frequently at a loss as to how to help their child in math, as well. Why is math so difficult and scary for so many students?

Is it because math is inherently more difficult than English and History? Is it because some people "just can't understand math"? Is it the teacher's fault? No to all of these, of course.

As my mom has always told me when I had difficulty with a subject and told her I couldn't learn that subject; "It's the same muscle, the same brain. If you can succeed in one area, you can learn to succeed in another." You need to find the right tool for the job, just as a carpenter would do!

So, let's look at where your struggle is. If you are struggling with solving for an unknown in an equation, and it looks like weird mystical magic, you must look at the concept behind it. Where does it begin? Do you remember memorizing your addition and subtraction facts? Your multiplication and division facts? Yes, that is what is behind solving for unknowns. In math it is important when problem solving to figure out what you DO know in the problem. Lay those out on your sketch or in your formula. Sometimes this helps you make that leap and see what to do next.

Before you leap, though, be sure to carefully look at what you are trying to determine. Don't panic, you can figure it out! If you do not know which method to use to solve the problem at this point, review the concepts. Can you see it now?

Math can actually be fun! Getting each concept gets you to the next level, like in a video game. It all builds and is all related. I would love to tutor you so you can reach each level. As one of my students says "Wow, I am a smarticus after all!". Yes you are!

It isn't too late. You can learn how to be superb at math! What are your thoughts about building your math levels concept by concept?

November 11th Writing Challenge

posted by WyzAnt tutor: Ramona D.

Circle Game (from The Write Brain Workbook)

1. Select the word that most appeals to you: Carousel, Banister, Alabama, Diesel, Exorcist

2. Select another word that appeals to you: Flatulence, Garage, Harried, Insensitive, Jambalaya

3. Select yet another word that you find appealing: Keepsake, Lamb, Nonsense, Massage, Oriole

4. Use these three words in a story. Start with: Sometimes I feel just like a gerbil, running around and around on his wheel!

Parent comment

posted by WyzAnt tutor: David F.

"Dear [David F.],

[My] family would like to express our gratitude to you for working with [our son] this summer.

Excellent job!

If there is anything I can do for you, please feel free to call . . .

Sincerely,
DK"

Seeing student progress

posted by WyzAnt tutor: Emily S.

Both tutors and students (and maybe their parents) may wonder how to actually see student progress. In the case of English or ESL, there are subtle and indirect signs, but seldom anything stark or quantifiable. Therefore, I have to pay careful attention to notice when a student has actually "learned" something, such as new vocabulary, sentence structure, or how to read a complex article. Yet the signs are there.

Here are a few examples. One student who I helped with writing first showed me some essays written for various classes, which were frankly failing papers in my estimation. They were full of sentence errors, mechanical errors (spelling and punctuation), and generally failed to make a strong point. I helped her by showing her the types of errors, and having her make corrections and do other practice exercises in her weak points. At the end, I asked her to produce a new paper from scratch, and with essentially no help from me, she produced a decently-written three-page essay on her university experience. This was progress.

In another case, a student also working on writing had serious errors with her sentence structure, as a non-native speaker. I've worked with her to show and explain the basic rules, and give her practice. Now she is making far fewer errors, and is able to analyze and catch some of her own mistakes. This is another kind of progress.

Sometimes, a student may feel frustrated and not see any obvious improvement, any leaps of skills. But ask your tutor, who should be paying careful attention, and hopefully he/she can show you some clear examples of where your work has improved. Tutors, do the same: show your students examples of progress you observe whenever possible. Help them see how they have learned a particular skill or concept. Your students will appreciate you for it.

Are you chasing after scholarships? I can tutor you in another way!

posted by WyzAnt tutor: Kate K.

This is the time of year that high school upperclassmen and college freshmen are often in a panic. So are their parents. In today's economy, this is understandable. What is often surprising news to students and parents alike is how much the face of college education has changed!

In addition to tutoring at WyzAnt, I also have experience in showing students how to study, and how to maximize their college credits in a cheaper way---and often faster. The sooner you get your degree, the sooner you (in theory) can start earning a salary as a college graduate. If you earn your credits cheaply enough, you might not need scholarships or loans. You may be able to afford college without it. Or, at least you can minimize how many loans you need.

When I teach study skills, if the student and parent wish, I can provide this advisory service as well. Many people do not know the techniques for maximizing credits for as cheap as possible. No, you do NOT have to be a genius, a super-brilliant all AP student. That is a fallacy. You can learn, you can earn your degree--FAST!

If you are interested in learning how to do this, feel free to contact me through my blog; or you can hire me as your tutor.

Tutoring Takes Patience!

posted by WyzAnt tutor: Jillian B.

As a tutor with 4+ years experience at a college writing center, I have had my fair share of tutoring sessions. Tutoring is probably one of the most challenging, yet most rewarding jobs a person can have. Nothing is more rewarding than to see the light bulb go off in a student's head when he or she finally understands something new about the subject!

Tutoring has taught me some valuable lessons about myself and who I am. I wouldn't trade my time tutoring in college for anything, and I can't wait to help someone else become a better writer!

First Meeting!

posted by WyzAnt tutor: Adrienne C.

This week I will be meeting with two potential students for the first time. In my opinion, the first meeting is the most important because it allows the tutor and student to get to know one another and set the standard for their future sessions. Here are a few tips for tutors and students who are meeting for the first time:

Tutor:
- Get to know your student
- Ask the student and/or parents to help identify the student's strengths and weaknesses
- Build trust with student and parents
- Identify student's and parents' expectations and goals for tutoring sessions
- Meet in a location that is comfortable for your student and not a distraction
- Encourage, encourage, encourage!

Student:
- Come prepared with questions for your tutor about their style of teaching and their tutoring plan
- Bring any books or materials that you have been using in school or on your own to demonstrate your current level of understanding
- Tell your tutor what you hope to achieve through your sessions
- Make sure you feel comfortable with your tutor and the space where your sessions take place
- Learn, learn, learn!

I hope these tips will help you prepare for your first meeting! Good luck!

November 4th Writing Challenge

posted by WyzAnt tutor: Ramona D.

Write a 250 word piece about the best birthday you've ever had and include the words: worst, lousy, bad, irritating.

Using Pen Pals to Enhance Tutoring

posted by WyzAnt tutor: Chrissanne L.

Sometimes, it is essential to provide students with additional perspectives, besides the tutor's. As I tutor more and more, I realize that even with the one-on-one benefits of tutoring, there is a need for interaction with other students. However, the problem is, there are no other students to provide this feedback when you are tutoring a student. I have found that creating relationships with other students is a remarkable enhancement to the tutoring experience.

I have used Pen Pals to meet this need. There are a variety of websites that offer pen pals for different purposes. If I am tutoring a student in Social Studies, Geography or History, a Pen Pal is an amazing resource for FREE and REAL information about the study topics. This is usually an exciting concept that is well-received by the student because they thrive with interactions with others and they think it's amazing to connect with people like them all around the world! Using the right resources for this is essential, so I suggest that tutors spend some time locating the right program for their needs. Usually, those that are dedicated to teachers offer the most security and less potential for spam and unwanted leaks of information to the Web. Additionally, these sites allow the tutor more access to hand-picking the pen pals for their needs. The greatest benefit for this type of tutoring lesson is the ability to focus on the writing skills of the student while not needing to create writing assignments for the sake of writing! This makes the students more likely to give their effort to their tasks AND it allows the tutor to challenge the student to become eloquent in their writing efforts because it is directed at a "friend". I encourage tutors to give this a try in Foreign Languages, Writing, History and Social Studies, ESOL... actually, the possibilities are endless! I'd love to know how YOU are using Pen Pals in your tutoring!

Greetings and Salutations

posted by WyzAnt tutor: Eric B.

I am excited about working with people and helping with learning. Mathematics is my best subject and I am willing and able to help.

I have been out of school for some time, but I use the concepts of algebra on a daily basis to perform my job so I know I would be able to help with this subject.

Please keep me in mind if you need help!

Do you find yourself procrastinating? Don't give up now!

posted by WyzAnt tutor: Kate K.

Do you find yourself giving up or procrastinating on your reading and studying? Does it seem like there is an endless amount of work to finish between now and Christmas? I know you have heard a million times, "break it into smaller pieces". Maybe you need another way to do that.

Here is a way that has worked for some of my students. Let's say you have 9 chapters in your history textbook to read and understand by the end of the semester (and 3 exams---3 chapters per exam). Rather than be overwhelmed by that concept, what you can do is make up 3 separate index cards (one per exam--and write which chapters must be covered for that exam). For now, just refer to the card for the first exam. Take 3 post-its (and write 1 chapter on each). Stick the post-its on the exam card. Pick a deadline for each chapter. As soon as you finish a chapter--throw the post-it for that chapter away. There is something very satisfying and empowering to be able to pitch that post-it.

As soon as you feel like procrastinating, odds are you are focused on the 9 chapters. Re-focus! Grab your chapter cards. Tell yourself---I will finish 1 card; I will throw away post-its.

This may sound like an idea that cannot work. But it gets around the mental blocks that we tend to create and then use to procrastinate. This concept worked great for one of my students. He just couldn't get started on his reading assignments. As a matter of fact, we took a step backward from this strategy. I made a card for just 1 chapter. If the chapter was 21 pages long and he had a week to cover it, I would direct him to read only 3 pages a day. I added that if he knew he needed to take a day off during that week, he needed to have his page count for the week taken care of anyway. We would make a game of it, and try to estimate how many minutes it would take to thoroughly read those 3 pages. He began to see that no matter how huge the reading assignments, he could break it down into manageable sizes. If he had to read 140 pages during the week, but he could only bear to read 5 pages at a time, he needed to read 5 pages 4 times a day. Guess what? He quickly decided that he would rather read 20 pages at a time and be done for that day. But even if he needed to read only 5 pages at a time, he could get it done. Get the challenge or mountain down to the size where you almost laugh and say---of course I can do that much!

Success breeds success. Baby steps to the end of the course.....as one of my favorite students says, "slow and steady wins the race"!

You can succeed! Let me know if you try my techniques! I would love to tutor you and get you on your wonderful road to success!

The True Value of Education

posted by WyzAnt tutor: Emily S.

A student told me recently that she was only the third person in her family who ever went to college. She has recently finished her B.A. and will soon start an M.A. program, at the age of 50. I told her how proud I was of her achievement and perseverance. But what most impressed me was her answer when I asked, so what do you feel has changed about you now that you have been to college. She answered, now I know I shouldn't waste my time on meaningless activities, like watching silly TV shows. I know that reading is much more interesting and stimulating, and I even enjoy doing the research required to prepare my school writing assignments. If there was ever a reason to be educated, this is it. Education means you know better than to waste your mind and your life on empty pursuits, and you might even decide that tutoring to improve your skills or knowledge, to have better career options, is something worthwhile. This kind of new awareness in a student is what makes me want to be a tutor.

How to get great grades without really trying (too hard)

posted by WyzAnt tutor: Jana P.

Do you study for endless hours and still get average grades, or just pass by the skin of your teeth? Or, do you just plain hate to study and can't get motivated no matter how hard you (or your parents) try?

Let me tell you, I've been there and I know how disheartening it can be. I routinely received C's, D's, even some F's in my bachelor's program; I hardly dared to plan or even hope for a bountiful future when my grades reflected less than my actual abilities.

Now it's so different. I graduated with a 3.9 GPA in my master's program and I just plain love to learn and love school ... now more than ever! I finally learned how to be successful in school, and the steps are really very simple.

You too can be on your way to TOP GRADES, so if that's what you're after, just follow these straightforward steps:

1. Diligently record all upcoming assignments, tests, and projects in your planner -- you should have your planner sitting on your desk along with other relevant materials for the class.

2. If you were not given a calendar by each teacher for the entire term's assignments, ask each teacher for one, or see if calendars are posted online, so you can record and prepare for assignments well in advance. You can also track your grades, online or in your notebook, to monitor your own performance.

3. For classes in which you use a textbook, read pages as soon as they are assigned, then bring your text and handouts to each class -- very likely the teacher's lecture will closely follow the student materials.

4. Read along in the text or handouts as the teacher lectures, highlighting points that are mentioned, and recording notes (as needed) directly on the handouts and in the text (if allowed). The teacher will lecture on points s/he wants to emphasize. Since you will have read the assigned material beforehand, the lecture will serve as a review. Depending solely on notes taken from the teacher's lecture is unwise, since even a minor distraction or a little daydreaming may result in a loss of important information. Taking this proactive approach to studying will help you become a self-sufficient learner. Your grades then will not suffer if your teacher's teaching style is less than adequate, or if you are out sick.

5. Every couple days, look over your text/handouts, paying close attention to the highlighted sections. You should have little need to put in more than your average study time before tests, as you will already have learned what you need to know with regular review of the material. If you're lucky enough to get extra credit assignments, do them! That one or two point bonus just might be the difference between a B and an A.

Before long, you will start expecting and receiving top scores since you will have studied all you need to achieve them. And experiencing success in school is a great motivator for excelling in all areas of life.

So, in summary ...

* Record all assignments in your planner, as far in advance as possible.
* Read assigned pages in text and materials before class, ideally as soon as they are assigned.
* Bring text and materials to each class, and highlight lecture points.
* Review highlighted areas and any notes every couple days.
* Be consistent -- study at the same time each day in a distraction-free study zone; take a short break each hour to check in with family or have a snack.
* Take a day off from studying every now and then as a reward, when no deadlines loom.
* And, an important lesson I learned ... if you truly want top grades, you need to prioritize your homework. Balance your social/sports activities with your schoolwork to keep your stress level to a minimum.

You will be amazed to find you can actually trim study time using this plan. Good luck ... but you won't need it, because now you've got the skills to succeed!

Explaining algebra

posted by WyzAnt tutor: Janet W.

Sometimes a student must take algebra in order to complete requirements for a degree other than in a mathematics field. Algebra seems strange and incomprehensible to the non-math mind.

Algebra concepts and methods can be explained clearly and simply enough for most students to be able to successfully solve problems. A recent student of mine faked his way through Algebra I and found himself in an Algebra II course without the necessary preparation. He was failing. The student was dedicated to listening, being well organized and trying his best. With the combination of an understanding college professor, a sincere student and my supportive, clear and helpful tutoring, the student was able to achieve in the 90 percentile for a final grade.

Family and teachers are all very proud of this student. But all believe that, without the tutoring, the student would have continued on a failing track. This real-life example illustrates the importance of tutoring. Sometimes a good tutor is needed to make the impossible seem understandable and, suddenly, possible!

Educating Austin One Student at a Time

posted by WyzAnt tutor: Corey D.

As part of the WyzAnt community, I am honored to serve Austin's students. The students take their education rather seriously and want to receive maximum benefits from it. Their dedication to success, tenacity in their studies, and willingness to work hard greatly pleases me and drives me to provide the best possible instruction to aid in their endeavors. I always attempt to demystify the complexities of students' lesson materials but simultaneously keep them challenging and interesting. Furthermore, I push them to put forth the best possible effort, to think outside of the box, and discover their true capabilities by asking questions along the way; by the same token, I encourage them to ask me questions. This enables me to determine how to tailor my teaching styles to best suit their learning styles; moreover, it enables them to learn from and about me; I also learn from and about them. Most importantly, my detailed explanations and reviews during subsequent lessons make a difference in how much and how well students learn; what they learn, or fail to learn, could very well matter for the remainder of their academic careers. Helping students realize their full potential is part of my job as an educator; seeing them reach it confirms that I do it well and gives me a tremendous sensation. I have been given so much academically over the years; I now share my knowledge with others and grant them usable skills both inside the classroom and in their daily lives. After all, education is both a continuous process and a ceaselessly giving gift. To paraphrase a quote from former Harvard president Derek Bok: "Education carries great costs, but ignorance carries far greater costs."

October 28th Writing Challenge

posted by WyzAnt tutor: Ramona D.

Just 3 more days til Halloween! I'd like to share that this is my favorite holiday of the year because it's the only day that you can be whomever you want, and no one faults you for it *smiles*

Today's challenge:

Write a 3 paragraph story, set in the fall during a hayride, using each of the letters of HALLOWEEN, in sets of 3, as the beginning letter of the first 3 words in each of your paragraphs.

Example:

Paragraph one: He Always Loses...

Paragraph two: Lucy Owes Warren...

Paragraph three: Eventually Everyone Nodded...

The Utility Tutor

posted by WyzAnt tutor: Marc R.

In sports, there are utility players who are not restricted to playing one position, but can be put in at any position as the situation warrants. In tutoring, there are specialists who concentrate only in specific areas and there are the utility tutors who can handle many different areas.

I have just returned from a Physics tutoring session which became a Calculus tutoring session when the student realized that he did not have a list of the Physics topics for his next exam, but did have his Calculus text. When he asked if I could do Calculus with him, I said ok. Had I been only a Physics tutor, the evening would have been wasted.

Anyone who has gone through Classical Physics (Mechanics, Heat, Sound, Electricity, Magnetism and Optics) could not have done so without being proficient at Calculus. Why should a tutor limit himself or herself to their favorite subject by not taking the proficiency exams in the various mathematics levels offered by WyzAnt?

I am not sure if a rhetorical question is followed by a period or a question mark. But then again, I have not qualified myself in English, Grammar, or Writing.

By qualifying in a range of topics, the tutor not only has a bigger selection of students, but he or she can illustrate the relationships between one subject and the other, between Calculus and Physics, between Chemistry and Physics, and most essentially between what is being taught in the text, in the lesson, and in everyday life.

Being a utility tutor may not be as glamorous as being a tutor teaching only about the Special Theory of Relativity, but it is infinitely more rewarding to the tutor and to the student.

Super Teaching - The Light of Understanding

posted by WyzAnt tutor: Marc R.

I have been teaching for over 50 years as a university faculty member and as a tutor. I also testify as an expert witness in both civil and criminal trials. Testifying on the witness stand counts as super teaching because you have only five or ten minutes in which to explain a complex topic to a jury, a judge, and attorneys who may not have the faintest idea of what you are saying. You must keep it simple, use common language and everyday examples, and watch the faces of the jurors to see if they are following and understanding your testimony.

Jargon is a way to keep people outside of your narrow professional field from understanding what you are saying. Never use jargon. Use simple words and simple examples.

Watch the face of the student you are tutoring. Watch for the moment when he or she first understands what you are saying, even though their teacher or professor as well as their textbook had made the subject unintelligible. When you see that light of understanding, you have succeeded!

Microsoft Excel at home and at work

posted by WyzAnt tutor: Sharon D.

I have been teaching and training for over 20 years and seeing a student learn is always a joy. I use many techniques to help students learn and understand the subject. One of the most effective methods is drawing on the student's own knowledge even though it may not relate to the subject. With Microsoft Excel one of the methods I use is to ask the student to picture paying the bills for his/her home. We go through the process on paper then we take that process and put it in Microsoft Excel.

I used this technique with a group of adults I was training and one lady used the spreadsheet we created to keep track of her bills and household expenses. Her husband was very proud of her, because not only could she show him were they were spending money for household expenses but she could also graph it for him. The found it valuable and started doing it for all their finances and at tax time they were surprised at some of the deductions they received because they had kept tract of thing they had forgotten to do before.

As a teacher helping other teachers always make you feel good about what you teach. I created a Microsoft Excel spreadsheet to help with doing grades for my students. I showed it to a few other teachers and soon I was helping them set up customized grade books on Excel for their classes. The teachers were very happy because before not only did they have to grade the papers and enter them into the grade book but then they had to calculate the grade. If a student needed a progress report before grades they had to spend time to calculate the grades or just guess. Now once they had graded the papers they could enter the grade for that paper and it would carry a running calculation of that’s students grade. Also if the teacher was concerned about a student passing they could use the spread sheet and tell a student if you get a 75 on the next three tests you will pass. Many teachers tell me how much they love their grade book and how much time it saves them.

Using Microsoft Excel can also enrich you life and I look forward to helping you understand the various elements of the program. Thanks you for taking the time to read my article and hopefully you will enjoy working with Microsoft Excel too.

October 21st Writing Challenge

posted by WyzAnt tutor: Ramona D.

For 5 minutes, list all the questions you had when you were a child.