Let's Learn!

Guy is the Director of the Discovery Learning Institute. Graduated from University of Connecticut and attended Graduate School at University of Illinois at Urbana-Champaign. Guy is extremely knowledgeable, patient about teaching, and is commitment to help each student reach their full potential.

The primary benefit of tutoring is the one on one nature inherent to the process. When a student is one on one then the tutor can identify individual problems that the student is having difficulty grasping. The tutor can then directly teach these problem areas.

Math: All levels of math

Test Prep: SAT ACT GED ASVAB

Study Skills

Reading and Writing: 4th Grade to High School.

**Math Facts**

After learning to count the math facts are very important, especially the multiplication tables. Moving forward once the multiplication tables are well understood makes learning other material much more straightforward. If one knows that 5 x 8 = 40 it is much easier to see that 40 ÷ 8 = 5

**Fact Families**

Fact families are our addition/subtraction facts considered in groups:

4 3 7 7

__+3__ __+ 4__ __- 3__ __- 4__

7 7 4 3

There are similar families with multiplication and division.

4 3 12 ÷ 3 = 4

__ x 3__ __ x 4__

12 12 12 ÷ 4 = 3

Learning these facts as a group helps students understand how these math operations are connected without involving a lot of abstract languages. Then when the abstract language is introduced it is more easily understood.

The concepts here are the commutative property and the concept of an inverse. These ideas are also a kind of data that is helpful to the student when they are learning the steps involved in long division.

Geometry is the study of two and three-dimensional figures. It is, like most math, sometimes very practical and at other times very theoretical. Geometry is also the branch of math that teaches proofs. Learning proofs is most students' introduction to formal logic and helps teach us to think logically.

Most courses in Geometry will consider lines and angles, quadrilaterals, and Circles. Classes will also usually touch on Trigonometry and as mentioned proofs. Of course like most math Geometry also teaches problem-solving.

Trig is a study of the relationship between angles and the ratios of the length of sides of triangles. So it is kind of amusing that it would turn out to be so practical*. Of course, most HS trig is not really that practical but it does introduce those ideas. As in all math, it is very important to grasp the core concepts. One of the big topics in Trig is the unit circle. If one understands the idea of the “Unit” in the unit circle then the work is much clear. But if one misses either the meaning of that or why it is important the rest of the math can seem like so many unrelated facts.

Like many of the more advanced math topics, the biggest problem students often have is that there is a weakness in earlier math. Taking the Unit Circle as an example again weakness in the coordinate grid can cause a lot of trouble. If one’s Algebra is weak, the trig seems difficult when in reality the problem the student is having is following the Algebraic operations. If, for example, one is weak at exponents then it can be hard to follow some trig identities. Another common problem with Trig is that when it is taught as part of Pre-Calc the pace of instruction is often very rapid.

In helping students with Trig it is helpful to identify the areas of difficulty. It is at least an even chance that most of the trouble is not with the Trig itself.

*Trig is used in welding and trig functions apply to sound, electricity, and wave motion among other items.

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