What is proof?
Proof is really nothing more than providing a reason for statements made or steps taken. In the standard American government school 3-year “layer cake” approach to high school math, the concept of proof is normally limited to some sections in the geometry layer. But proof is not a concept that is the exclusive domain of geometry. Shormann Math teaches proof in 3 main ways, by 1) studying Euclid’s foundational work on proof, 2) showing that proof is for all of math, not just a few weeks in geometry class, and 3) showing how proof applies in the real world.
Euclid and proof
Around 300 B.C., Euclid (330 – 275 B.C.) organized the previous 3 centuries of Greek mathematical work into a 13-volume thesis known today as The Elements or Euclid’s Elements. Scholars believe that only the Holy Bible has been more universally distributed, studied and translated. Starting with a foundation of 5 postulates, 5 axioms, and 23 definitions, Euclid proved 465 theorems, or propositions.While postulates are basically rules that are assumed to be true without proof, theorems are true statements requiring proof. Postulates are also referred to as self-evident truths.
Surprisingly, even though Euclid is considered the “Father of proof,” most American high school geometry textbooks mention little to nothing about Euclid. In Shormann Math though, students will learn who Euclid was, and the importance of his contribution to Western Civilization. Shormann Algebra 1 and 2 students will become very familiar with Euclid’s first 5 propositions, giving them a good understanding of proof technique. They will gain an appreciation for the deductive nature of geometry and geometric constructions, seeing how one proposition often requires the previous one. And they will also see the simple beauty and elegance of Euclid’s propositions.
Proof and mathematics
Perhaps one of the greatest flaws in the “layer cake” approach to high school math is that the concept of proof is almost always limited to a few weeks during the geometry year. In Shormann Math, we’ll do the standard triangle proofs and circle proofs, but we will also apply proof technique in other topics like algebra, trigonometry and calculus.
But how can proof be for more than just geometry? Well, proof is based on a type of reasoning called deductive reasoning (applying rules). Every single math concept begins with rules. And every single math problem can be solved by applying those rules. All of mathematics is deductive in nature, which means at any time, a student should be able to explain the rules (provide reasons for) they used to solve a problem.
Because Shormann Math is integrated, we’re able to help students make connections between the major concepts like algebra and geometry. This results in students getting a better feel for what mathematics is about, which will make it easier to learn. Instead of thinking that they are always learning something new and different, they will see how one lesson builds on previous ones, which makes it less intimidating.
Proof and the the real world
Sure, proof is important to mathematicians, but it’s also important in the real world. As we explain in Lesson 68 of Shormann Algebra 1,
“Supporting statements with reasons is a technique used by, and expected of, people that society refers to with words like professional, leader, wise, helpful, and trustworthy. People like Abraham Lincoln, the 16th President of the United States of America, known for his study of Euclid’s Elements and his application of the idea of proof to solving societal problems.”
We also helps students see the application of proof technique in the real world, as this table from Shormann Algebra 2 explains:
Most importantly, proof is profoundly important in sharing the Gospel with unbelievers. God wants us to be ready to give reasons for the hope of salvation (I Peter 3:15). Our reasons should primarily be Scriptures we have memorized, or at least remember where to find them.
As you can see, proof is about a lot more than geometry! Shormann Math gives students a basic understanding of proof technique and it’s application to the real world. It’s a great tool to help them in their thinking, planning, designing and serving. If you think you would like your child to learn math in a more natural way that connects them to their world and their Creator, click here to learn more!