Fundamentals of Mathematics

In Fundamentals, students begin a gradual trek toward algebra. At Schole, this trek occurs over a two-year period: Fundamentals and Pre-Algebra. Fundamentals can be thought of as beginning Pre-Algebra. It is a bridge between Arithmetic and Algebra. Students learn to add, subtract, multiply, and divide with negative numbers; including negative fractions. They extend their understanding of ratios to proportions and learn to identify proportional relationships. They then begin their transition from concrete thinking to abstract thinking by learning how to handle variables in algebraic expressions (combining like terms). Their ability to solve equations grows to include 2- and 3-step equations and 2-step inequalities. 

Their understanding of percentages and ratios is expanded to include the probability of simple and compound events. Geometry plays a larger role in Fundamentals than in prior courses. Students learn to classify angles, identify and solve similar figures, and calculate the area and circumference of circles. They will also calculate the volume and surface area of composite 3d figures.

They will complete portfolio projects that deepen their understanding of the concepts, appreciate the role of mathematics in God’s creation, and lead them to explore real-world applications of mathematics. Throughout the course, students will be led to see mathematics as a tool to solve problems. They will practice different problem-solving strategies: Eliminate Possibilities, Work Backwards, and Unit Analysis.

Experience
The teaching of a new concept opens with a brief review of previously covered content. This review connects the previous lesson to the current lesson. The premise of the current lesson is presented via a question or idea. The students now have a puzzle or idea that they want to explore. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We use our prior knowledge and intuition to uncover a new truth about mathematics. Once this truth has been uncovered, we begin to work examples; first as a class and then as individuals or in groups. As our understanding of the concept deepens, we extend our knowledge base to include specific cases or situations that lead to minor adjustments in the truth that we have uncovered – thus expanding the truth. We use a variety of methods to uncover new truths. The most frequent method is a Socratic-style discussion that the entire class participates in. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application). 

Watch a Math Classroom Experience with Joelle Riethmiller.

Delivery
Each teacher has a unique presentation style in delivering the aforementioned experience. Sometimes the teacher leads the discussion using questions; following the example set by Socrates.. Sometimes a problem is presented and the students take the lead in finding a solution based on extending previous knowledge. Sometimes students participate in a hands-on activity to discover new truths. Sometimes a short lecture or presentation is required, however, we aim to minimize lecturing, especially before high school. 

Methodology
Students continue to study the new truth and deepen their understanding of it via homework, classwork, projects, and assessments. Since our classes do not meet 5 days per week, students must spend time studying the concepts outside of class. This also helps students grow in their ability to think and work math concepts independently which is required for future math classes. For this reason, we ask that parents minimize the assistance that students are given on assignments. If a student receives an A on an assignment, it should be a true indication of their independent ability as the teacher interprets this A as independent mastery. 

Review assignments or classroom review activities are utilized to assist students with opportunities to retain or improve their mastery. Assessments are directly or indirectly cumulative and serve as an opportunity to deepen their learning. Assessments are not meant to be a regurgitation of previous homework assignments.

Preparedness
Students who are adequately prepared to take this course will have mastered (can work independently without prompting):

• Absolute Value
• Multiply and Divide MultiDigit Whole Number Divisors
• Divide Fractions and Mixed Numbers
• Convert between Percent, Fraction, and Decimal
• Find the percent of a number and unit rates
• Graph on the Coordinate Plane
• Solve one-step equations, 
• Calculate mean, median, and mode
• Calculate Surface Area and Volume of Composite Figures