Teaching homeschool math

The Art of Problem Solving curriculum

While many subjects can be taught without formal textbooks and workbooks, we feel that math is best learned using a formal grade-by-grade curriculum. Math requires more systematic teaching than other subjects, as presentation of new material assumes mastery of concepts taught previously. Math also requires substantial and consistent practice, something best provided by workbooks or problem sets matched to the textbooks being used.

Nautilus Homeschool uses the math curriculum produced by Art of Problem Solving for elementary through high school math. We chose Art of Problem Solving because of its thoroughness and rigour, and also because of its fun teaching approach.

Art of Problem Solving's elementary curriculum is presented in a comic storybook format called Beast Academy (about a school for monsters). The textbooks are so enjoyable that our kids read them for fun, but they also effectively introduce challenging math concepts. In addition to the textbooks and workbooks, each level also contains a puzzle and game book which provides additional practice.

Starting in middle school, the Art of Problem Solving curriculum switches to a more traditional textbook format. Each textbook section is accompanied by one or more short videos, which present new concepts in a concise and entertaining way. The core middle and high school sequence is Prealgebra, followed by introductory Algebra, Geometry and Algebra 2. Optional high school courses include Number Theory, Statistics, Precalculus and Calculus.

Despite its playful elementary grade format, the Art of Problem Solving curriculum presents material in much greater depth than is typical in American schools, and prioritizes understanding why concepts are true over rote memorization of mechanics.

Recommended pace

During the first grade year, aim to spend fifteen to thirty minutes per day on math, depending on your child's attention span. Thereafter math should occupy thirty minutes to an hour per day, four or five days per week.

Each session, go over any new material together with your child by reading the textbook (and watching the explanatory videos starting with the Prealgebra course), then have your child complete a set of practice problems from the workbook (or textbook starting with Prealgebra). The number of problems depends on their difficulty and how quickly your child tends to work. Aim to assign about half an hour's worth of problems per day. At first you may help your child with the practice problems, but try to transition to independent work by the end of second grade.

Aim to make steady progress without rushing. The time it takes to complete each Beast Academy level will vary and does not necessarily need to correspond to the student's grade level. Our curriculum assumes a twelve-month homeschooling year and schedules one Beast Academy level per year from first through fifth grade, but this can be adjusted as needed. The next course, Prealgebra, can be started in sixth, seventh or eighth grade and still leave the student well prepared for high school math.

Calculators and memorization

We don't feel it is helpful to drill addition and subtraction facts before your child has had the chance to understand addition and subtraction conceptually. The Beast Academy curriculum provides enough practice that most students will absorb single-digit addition and subtraction facts naturally over the first year or two.

That said, we do recommend systematic memorization of times tables once multiplication is taught. The simplest way is to make or purchase flash cards, and practice them daily until they are mastered.

We recommend waiting to introduce calculators until after completion of the middle school Prealgebra course. None of the material prior to this requires a calculator, and solving problems without one will provide the practice that is necessary for developing an intuitive sense of numbers.

Supplementary books and activities

The curriculum includes optional books, such as The Adventures of Penrose, the Mathematical Cat and Math Without Numbers, as engaging presentations of interesting mathematical concepts not usually taught before the university level. We also recommend the Mathematicians Are People Too short biography collections about great historical mathematicians.

Finally, don't overlook games as a fun way to practice math. The Math You Can Play series includes dozens of ways to practice arithmetic and even more advanced math using card games. Board games like Monopoly and Scrabble (have your child add up the points) also provide opportunities to practice math skills.