"You may think that your child will never grasp a math concept, but I challenge you to step back and give him/her time."
Before homeschooling my daughters, I taught middle school math in the Upstate of SC. My first year teaching, I taught 7th grade math. As we covered topics throughout the year, my inexperienced self assumed it was the first time the students had encountered most of the math concepts because the students acted like they had never seen the information before.
Imagine my surprise when I taught 6th-grade math the following year and discovered that a majority of the topics were EXACTLY the same! Yet, many of the students had not grasped the concepts, and they did not even remember learning the concepts the previous year nor could they apply those concepts beyond drill and practice during the current school year.
Math curriculums can be very repetitive throughout the years, especially in 4th - 7th grade. Math will often slowly build on each skill, but each year the skills are often taught as if the student has never seen them before and each concept is only taken a little farther. This repetitiveness can help math-inclined students build a strong foundation in math, but for students who struggle in math, this can cause math anxiety and a hatred for the subject. A student gifted in math can easily become bored because they are not learning new topics or challenged.
However, imagine if you covered math at your child's individual pace? A student with strong math skills can move ahead as needed, and a student with weaker math skills can take it slow or take a break from a formal curriculum until they are ready.
Many students need time for their brains to mature and the need to be realized to learn math. As homeschoolers, we have the awesome privilege to teach math at our children's individual pace. Maybe your child does not understand fractions until middle school. As a Third Option homeschooler, that's OK!
Maybe your child needs to spend time "playing" with numbers and building a foundation that they can later base more technical math concepts on. Don't underestimate the power of board games, real life, living books, and pretend play to build math skills.
"...a child could learn math - all of it grades K through 12 - in eight weeks. "
I recently read an interesting book excerpt that commented that "the Sudbury Valley School- a democratically managed, child-directed learning environment that has been around for almost 40 years - has demonstrated repeatedly that a child could learn math - all of it grades K through 12 - in eight weeks. Average (if there is such a thing), normal (never met one), healthy children, hundreds of them, learned it all, leading to admissions to some of the leading colleges and universities in the nation." (Have Fun, Learn Stuff, Grow by David Albert)
I am by no means suggesting that you wait until high school and teach your child math in 8 weeks. As a Third Option homeschooler, you are required to teach math each year. However, how you teach math concepts and what concepts you teach each year are up to you. Perhaps your child would benefit from hands-on, playful learning in elementary school, and then in high school or middle school dive more into the nuts and bolts of math.
Perhaps struggling through fractions year after year is not the answer. What if you gave your child's mathematical mind time to mature? Then, you can cover fractions without any struggle at all.
"Many students completed as many as 4 math courses in one semester!"
Columbus State Community College discovered that they could offer math courses that allowed the students to learn math at their own pace. Many students completed as many as 4 math courses in one semester! Many of these students who had struggled in math in high school were finally getting it and moving quickly through math concepts. (Learning math at one's own pace)
Harvey Bluedorn from The Trivium Pursuit suggests waiting until age 10 before beginning formal textbook or workbook instruction because "it is about age 10 that the developmental light bulb comes on, and the child becomes capable of a great deal more mental and physical skill...Once all the developmental parts are there, most children can learn - in a few weeks - everything which they might have spent six years learning." (Research on Teaching Math)
"...most children can learn - in a few weeks - everything which they might have spent six years learning."
Our goal as homeschoolers should be to build a love of learning in our children. Because we are not tied to a specific timetable, we can allow our children to discover and learn math in their own time. If we are drilling students year after year in a concept that they aren't ready to comprehend, we are creating students that not only hate learning but also ones that are unable to apply anything they learn.
You may think that your child will never grasp a math concept, but I challenge you to step back and give him/her time. Provide real-world opportunities that build skills, and one day, you will look back and be amazed at how far your child has come!
