Talisker Math Tutorials


MATH TUTORIALS
Algebra - Geometry - Advanced Algebra

Algebra - Algebra UCSMP ("Chicago Math") Series

This course has a wider scope than other beginning algebra courses in that it covers basic algebra as far as quadratic equations while integrating statistics, probability, and geometry. The course's strength is in synergistic emphasis on three major areas: visual representation of algebraic concepts, manipulation of algebraic equations, and application of algebraic principles to real-world problems. Topics include square roots, systems, polynomials, exponents, algebra of linear equations and inequalities, and use of algebraic fractions in probability concepts.

The text is published by ScottForesman. The book's organization maximizes understanding and retention, as concepts and skills introduced in each lesson are reinforced through further application in successive lessons. This reinforcement, combined with text's daily review questions and self-tests, allows students several opportunities to master course material.

Requirements

• Successful completion of a pre-algebra course such as Saxon's Algebra 1/2 or Chicago Math's Transition Mathematics. A placement test may be taken in lieu of this requirement. Contact Talisker Tutorials for placement options.

• UCSMP Algebra text.

• Scientific calculator. A graphing calculator with statistical capabilities, such as the TI-83 Plus which we use in our Advanced Algebra tutorial, can optionally be used to enhance Algebra and will fulfill the requirement for a scientific calculator.

• Free Acrobat Reader version 4 or greater. For viewing exams sent by e-mail.

Register for Algebra

Geometry - Geometry UCSMP ("Chicago Math") Series

This course examines coordinates, transformations, area and volume formulas, and three-dimensional figures early in the year, usually a visually-oriented "hands-on" approach which lays a foundation for intuitive understanding of geometric concepts. Starting mid-year, the course then builds on this foundation by developing proofs and mathematical arguments.

Requirements

• Successful completion of our Algebra tutorial or the equivalent is required for registration in Geometry. A placement test may be taken in lieu of this requirement.

• UCSMP Geometry text

• Geometer's Sketchpad software (optional ... looking into a discount)

• Scientific calculator. A graphing calculator with statistical capabilities, such as the TI-83 Plus which is used the the Advanced Algebra tutorial, can optionally be used in this tutorial also.

• Free Acrobat Reader version 4 or greater. For viewing exams sent by e-mail.

Register for Geometry

Advanced Algebra - Advanced Algebra UCSMP ("Chicago Math") Series

This course integrates all the mathematics the students should have had previously, including a substantial amount of geometry. It develops proficiency in working with linear and quadratic equations, powers and roots, and logarithmic, trigonometric, and polynomial functions. The course's strength is in its synergistic emphasis on three major areas: visual representation of algebraic concepts, manipulation of algebraic equations, and application of algebraic principles to real-world problems.Requirements

• Successful completion of our Geometry tutorial or the equivalent is required for registration in Advanced Algebra. A placement test may be taken in lieu of this requirement.

• UCSMP Advanced Algebra text

• Graphing and Statistical calculator TI-83 Plus

• Free Acrobat Reader version 4 or greater. For viewing exams sent by e-mail.

Register for Advanced Algebra

"Chicago Math" vs. Saxon Math

In reference to a "classical" education, both approaches fail to use the Trivium model. The UCSMP ("Chicago Math") program is logic-oriented in the grammar years, and thus fails to automate the mathematical ability in students. The Saxon program is grammar-oriented in the logic and rhetoric years, and thus fails to teach students how to apply math, how to think about math, how to approach unusual problems in math, and it especially fails at teaching geometry. Saxon purposefully avoids application, concentrating instead on automation of problem solving with the ultimate goal being high standardized test scores.

Saxon is a fine program for the grammar (elementary) years where math facts and drills are most helpful. However, in our opinion, the "brute force" drill-centered approach which makes it a strong choice for elementary application makes it less desirable in the dialectic and rhetoric (secondary) years where concepts and abstractions become prevalent. To be more specific, here are the weaknesses perceived in Saxon that have lead us to adopt the UCSMP ("Chicago Math") series for our secondary math tutorials (we would like to thank Janna Gilbert of The Potter's School for the following 4 point evaluation):

1 Saxon uses a formulaic approach with little emphasis on teaching the students to think their way through a problem. Saxon gives students a rote method of solution, then drills them until they know that method. But experience shows Saxon students often stumble when a similar problem is posed in an unfamiliar form because they don't really understand the reasons behind the method they've been taught. The UCSMP approach, in contrast, stresses first understanding a class of problems and then examines various methods of solution. In short, it encourages the students to think and understand what they're doing.
2 Saxon offers little real-life application of concepts. The "So what?" question is never asked and the student is given no reason to learn the material. Failing to make math relevant is like teaching a student to read words without introducing them to books. The UCSMP series, on the other hand, does a commendable job of applying math to situations which are of interest to the student.
3 For many students the brute force "drill and kill" approach is demotivating. It is also time-consuming, considering the length of the average Saxon problem set. In the UCSMP approach, though a student must initially exert more effort to understand a particular concept, the rewards are tangible: similar-but-not-identical problems are easy vice bewildering, less effort is required master new related concepts , and less subsequent review is required because memorization was not the primary learning tool.
4 We find the organization of Saxon's material to be suboptimal. Conceptual math, like most subjects, is a series of interrelated topics. Learning is enhanced when students understand the relationships between the various parts. Saxon presents each topic essentially in isolation from previous ones with little regard for the order of presentation. UCSMP endeavors to build new concepts from past ones, enhancing understanding acquired in earlier chapters.

To summarize, we believe the Saxon approach is not ideal for secondary math courses. It builds few critical thinking skills and provides little foundation for future application; for some it is confusing and demotivating. In our view it does not optimize preparation for college entrance exams such as the SATs, which is probably its primary goal. Even for a liberal arts student we consider a more conceptual approach to basic secondary mathematics to be the superior alternative. In fact, the traditional classical education included Algebra and Geometry among the core subjects.

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