One of the biggest hurdles for parents preparing to homeschool is the subject of Mathematics. Most of us feel a little insecure in our math skills and we have all heard the horror stories about parents and kids weeping over homework because they have both been taught different ways to approach the problems. This doesn’t have to be the paradigm in your homeschool. Learning a thing is always easier when you have a “Why”. In my generation we were always told we had to learn arithmetic because you might not always have a calculator in your pocket. Honestly, nowadays, we do. Kids today will need a different “Why” to learn mathematics, and this difference can be well addressed with a library based approach to learning math.
Math is History
While you could argue over the human calculator efficiency theory, I propose there are other reasons to give educational attention to math. First and foremost, the history of mathematics is part of the history of civilization. Even the elementary seeming ideas of zero and negative numbers have a significant role in the understanding of the cultures and time periods from which they derived. Families with bible based learning can hunt out the instance if Pi appearing in the old testament. The Babylonian mathematics learned by Daniel and his friends still governs the ways we keep time today. On the other hand, the Ancient Greeks mastery of the proof is a great example.
Learning Proofs
In todays landscape mastering arithmetic seems less important to kids than in the past. But mastering the proof is a path to clear thinking and good writing as well as a path to a deeper understanding of the type of math that mathematicians actually do. Studying the Ancient Greeks is a great way to introduce the idea and learn how to write a basic geometric proof. Euclid’s Elements (book I) walks one through the process of building a proof. Many students remember the AHA moment of discovering the Pythagorean Theorem by working through the beginning of that book. In case you are worried about the grade level, while “Geometry” isn’t usually taught until upper middle or high school, Euclid’s Elements has been a part of the one room schoolhouse style of teaching since, well, one room schoolhouses! Continuing through the Ancient Greeks will bring you to Apollonius of Perga, Archimedes, and eventually into the ancient astronomers, which leads to Ptolemy and Kepler and then into Calculous and Isaac Newton! Apples anyone!
Math via biography
One of my favorite ways to sneak in some conceptual math learning is through biographies of famous mathematicians. Their lives are often as fascinating as the concepts they pioneered! The reader usually doesn’t need to know the complicated math involved to grasp the concepts and methods of breakthrough. Checking out titles on people like Katherine Johnson, John Harrison, Alan Turing and Ada Lovelace can inspire kids by showing how math opens doors to amazing discoveries. It is sometimes refreshing to realize that the people involved in such amazing evens like the space race or the discovery of the measurement of longitude, or the cracking of the enigma machine and the advent of modern computers were just people, with lives, who worked with what they had available to innovate solutions! Learning how to approach a problem is something subtle that math at school is not very successful at teaching. Many tomes these biographical stories include the shift in thinking or a new approach to a problem and can make discussion about this important lesson more direct.
Patterns and Language
For the more artistically-inclined, you can’t go wrong with books that merge math with visual creativity. “Mathematical Origami,” books on M.C. Escher’s artwork, or guides to fractals and tessellations let kids play with geometric concepts through hands-on projects. From even very young ages kids can relate to the repeated fractal patterns in nature and begin to understand the underlying geometry in honeycomb and bubbles, or lightening, trees and rivers. pattern recognition is the first step to learning the language of nature.
Mathematics has often been called the universal language – a precisely defined system of symbols, operations and formulas that transcends cultural barriers. Within this lingua franca of numbers, arithmetic and algebraic equations serve as the fundamental grammar and vocabulary for expressing mathematical ideas.
Just as words are built from an alphabet, all mathematical statements can be constructed from the basic symbols of arithmetic. The digits 0 through 9, combined with operations like addition, subtraction, multiplication and division, give us the power to quantify and calculate everything from grocery totals to astronomical distances.
Arithmetic establishes the lexical rules, the conjugations and declensions, that we use to manipulate numeric values. Mastering arithmetic is akin to achieving fluency in the root language of mathematics.
However, arithmetic alone only allows us to speak in concrete statements about specific values. It is algebra, with its symbolic variables and equations, that elevates mathematics from simple quantification to expressing deep conceptual relationships and abstract reasoning.
Algebraic equations are the sentences of mathematical language. They utilize placeholders like x, y, and z to encode general principles and formulas that model the world around us. Just as words arrange into statements to convey complex ideas, terms combine through algebraic operations to describe overarching truths about the patterns underlying nature, science, and theoretical physics.
Finally,
When the subject of mathematics is viewed through a liberal arts lens, it becomes much more conceptual, historical, and language oriented. The library then becomes an obvious place to find resources. There are usually plenty of titles in the kids section as well as the adult side of the public library. Reference titles on the history of science and math, on the Great Books, biographies and popular stories are readily available. Videos from the BBC and PBS, the Great Courses, and others can either anchor or augment any curriculum in math. Don’t be afraid to ask your librarian to point out any other resources they might have. Its the type of subject where any given library might have a more obscure resource like math manipulatives or access to tutoring databases. You may be able to instigate or host math oriented programming, like a math circle, contest team, study group or co-op class.
Innovative approaches welcome in the comments below!
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