## Archive for July 2014

### Should my Child Do Saxon Math 8/7 or Algebra 1/2?

July 31, 2014

For students ready for pre-algebra, we recommend Saxon Math 8/7 for most of them.

A pre-algebra course is a normal and recommended part of a child’s math education as they make the journey from a world of mostly numbers (arithmetic) to a world of mostly letters (algebra). John Saxon, together with Stephen Hake, authored two pre-algebra textbooks: Saxon Math 8/7 and Saxon Algebra 1/2*. Both books prepare a student for either Saxon Algebra 1, or our new Shormann Math Algebra 1. So should a child do Math 8/7, Algebra 1/2, or both?

### Math 8/7 is all most students need for pre-algebra

Both Math 8/7 (2nd and 3rd editions) and Algebra ½ are pre-algebra courses. While Math 8/7 teaches all the prealgebra concepts required to succeed in Algebra 1, it also teaches students to memorize essential arithmetic skills like ratios, reducing fractions, and converting a fraction to a decimal or percent. Lack of skill in these areas can cause students to struggle in Algebra 1. Like memorizing multiplication facts is required to learn long division and fractions, memorizing and developing fluency in these essential skills is required to learn Algebra 1. Math 8/7, 3rd Edition does a much better job of this than any other curriculum I know of, including Saxon Algebra 1/2.

Therefore, Saxon Math 8/7, 3rd Edition (a.k.a. homeschool edition) is recommended instead of Algebra 1/2. Upon successful completion of Saxon 8/7, students should start Shormann Algebra 1.

For most students, Saxon Math 8/7 is all they need to prepare them for Algebra 1. It has more arithmetic review than Algebra 1/2. Prior to Algebra 1, we’ve found that most students need more review of things like addition, subtraction, multiplication, and especially division. And division is related to fractions, and Math 8/7 has more review of things like simplifying fractions and converting between fractions, decimals, and percents. Fluency in these areas will almost guarantee a smooth transition to Algebra 1.

Prior to each lesson of the Math 8/7 homeschool edition pictured above, students complete a Facts Practice that will help them build fluency in the areas mentioned. Algebra 1/2 does not include this daily practice, although it does review arithmetic (including fraction/decimal/percent conversions) in the daily homework sets.

Math 8/7 includes daily Facts Practice that Algebra 1/2 does not. This daily practice provides an opportunity to build fluency in areas many students struggle with, such as fraction/decimal/percent.

Have your child do Saxon Math 8/7, Homeschool Edition, if you feel like they need to work on becoming more fluent in the arithmetic areas mentioned above. This is what we recommend for most students.

Have your child do Saxon Algebra 1/2, 3rd edition, if you feel like they are fluent in arithmetic and are ready for a little more algebra, which Algebra 1/2 provides.

Have your child do both books if they complete Math 8/7, but you don’t feel like they are proficient enough and maybe need to be eased more gently into Algebra 1.

The beginning of each Saxon course contains review from the previous course. Therefore, since Algebra 1/2 covers algebra in more detail than 8/7, there will be more in Algebra 1 that the Algebra 1/2 student has already seen. For students who are extremely fluent with their math, you may want to skip some of the first lessons to avoid unnecessary repetition.

### Shormann Math Core Ideas: Defining Mathematics

July 30, 2014

The following is the second in a series of posts covering Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

Thinking of mathematics as the “ship,” and the definition as the “captain,” the way we define mathematics can greatly influence how we use it.

### Definitions Matter

Thinking of mathematics as the “ship” and the definition as the “captain”, a good captain can use the ship for what it’s designed for. A good captain knows who built the ship. A good captain can help others better understand what the ship is capable of. Here is how mathematics is defined in Shormann Math:

### mathematics: The language of science and a God-given tool for measuring and classifying pattern and shape.

This definition tells us that mathematics, with all of its unique symbols, is best thought of as a language. It is a language we can use to study creation. Next, this definition tells us mathematics is about measuring things. It also tells us mathematics helps us find truth, goodness, beauty, and unity and diversity as we classify pattern and shape.

But most importantly, this definition of mathematics tells us “who built the ship.” Mathematics is not man-made, it is God-given. Created in His image (Genesis 1:26), we are designed by God to use this tool to be creative, too! God designed us to be creative and to engage in fruitful, productive activities (Genesis 1:28). Click here to learn more about the Shormann Math definition of mathematics.

### Shormann Math, Algebra 1 Overview

July 22, 2014

The following is an overview of Shormann Mathematics, Algebra 1, the newest product from DIVE Math and Science! Click here to read the complete document that covers Shormann Math core ideas, course description, and Algebra 1 table of contents.

### A complete math curriculum

Unlike our DIVE Math Lectures that teach the content in textbooks authored by the late John Saxon, Shormann Math is a standalone curriculum.  Shormann Math is designed to connect students to their world and their Creator by using an incremental approach with continual review to teach 10 major math concepts from a Christian foundation. The 10 major concepts are: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, calculus, statistics, and computer math. The first course produced will be Algebra 1, followed by Algebra 2, Precalculus and Calculus.

### Math, the language of science

If you are wondering “Where’s the geometry?” in the 4 courses listed, it’s there! Because scholars consider mathematics to be “the language of science,” Shormann Math teaches math like a language, where you don’t just learn nouns for a year, verbs for another year, etc. You learn a little of each concept, combined with lots of review, and then you combine the different concepts together. So, Shormann Math Algebra 1 and 2 in particular will also contain a rigorous survey of geometry, including lots of proofs, even some straight out of Euclid’s famous book, The Elements. We’ll even cover non-Euclidean geometry, and show students how the concept of proof applies to all of mathematics, not just geometry. All the geometry, and trigonometry, that a student needs to be ready for the SAT or ACT will be covered in Algebra 1 and 2. Scroll down to the Algebra 1 Table of Contents where you can see more detail about geometry coverage.

### Connecting your child to their world and their Creator

While Shormann Math will guide your child through high school algebra and geometry, that is not our primary goal. And it is definitely not our goal to align Shormann Math with the Common Core standards. Our goal is to connect your child to their world and their Creator by teaching them math, the language of science, from a Christian foundation. And because the last 300+ years of technological innovations can be connected to calculus in one way or another, we will present calculus early and often, and not in an intimidating way, but in a way that is based off things students already know.

### Standing on the shoulders of giants

Unlike many new math programs, Shormann Math is not about an entirely different approach. Instead, Shormann Math builds on a foundation of time tested and proven methods. Famous mathematicians and math educators like Euclid, Euler, Saxon, Whitehead, Kline, Sawyer, Nickel, etc. were studied for years before work on Shormann Math began.

For 2014-15, Shormann Math will be offered as a live, online class only. For more details on Shormann Math, including the Algebra 1 Table of Contents, click here. Then, if you are ready to dive into this new adventure in learning math, click here to register!

### Defining Mathematics

July 11, 2014

Thinking of mathematics as the “ship,” and the definition as the “captain,” the way we define mathematics can greatly influence how we use it. (Wikipedia photo of the tall ship “Elissa.”)

#### The Challenge of Defining Mathematics

Throughout history, humans have never settled on one particular definition for mathematics. Part of the reason is the abstract nature of mathematics, and the way general mathematical truths can apply to an infinite number of situations. For example, think of numbers. Numbers are abstract ideas. The number 3 is an idea of “threeness,” and can be used to describe 3 bears, 3 cars, 3 words, etc.

Here are a few of the ways famous mathematicians and mathematics teachers have defined mathematics:

• The science which investigates the means of measuring quantity(L. Euler, Elements of Algebra, 1765).
• The foundation of exact thought as applied to natural phenomena(A.N. Whitehead, An Introduction to Mathematics, 1911).
•  Mathematics is the classification and study of all possible patterns(W. W. Sawyer, Prelude to Mathematics, 1955).
• A study of space and quantity (Kline, Mathematics and the Physical World, 1959).

#### If Math is the Ship, Then its Definition is the Captain

Do you think it matters how mathematics is defined in the math courses you or your children do? I’ve been thinking about this question for many years now, and I think the answer is most definitely “yes!” A good definition can set the foundation for the entire course. And for a mathematics curriculum writer like myself, it can set the foundation for not just one course, but the entire curriculum. Thinking of mathematics as the “ship” and the definition as its “captain,” a good captain can use the ship for what it’s designed for. A good captain knows who built the ship. A good captain can help others better understand what the ship is capable of.

#### How Shormann Mathematics Defines Math

At DIVE, we are getting close to launching our own standalone mathematics curriculum, Shormann Mathematics. Algebra 1 is the first course. For the first year, it will be available as a live, online class (click here to register). In Shormann Mathematics, we will use the following definition for mathematics:

mathematics: the language of science and a God-given tool for measuring and classifying pattern and shape.

This definition tells us that mathematics, with all of its unique symbols, is best thought of as a language. It is a language we can use to study creation. Next, this definition tells us mathematics is about measuring things. It also tells us mathematics helps us find truth, goodness and beauty as we classify pattern and shape.

But most importantly, this definition of mathematics tells us “who built the ship.” Mathematics is not man-made, it is God-given. Created in His image (Genesis 1:26), we are designed by God to use this tool to be creative, too! God designed us to be creative and to engage in fruitful, productive activities (Genesis 1:28).

#### What’s the “Common Core” of Your Math And Science Curriculum?

A lot is being discussed right now about “Common Core” curriculum promoted by the United States government. Unfortunately, man and his ever-changing ideas are at the core of this curriculum. At DIVE, we strive to place Jesus Christ at the core of all our products, and we pray that this will result in students learning math and science for His glory and the service of others. We would appreciate your prayers as we seek to put a new captain at the helm of the ship of mathematics, helping students use the ship for what God intended it for!