15

I have recently been a homeschool parent, as well as a school maths teacher so I hope I have some perspective that can help. I will suggest a textbook that does what you want, hidden somewhere in this post. But I would like you to understand a few things first. It is very likely that your son has never done any mathematics. He has done years of arithmetic. ...


8

What do you mean by "the rote method"? If you mean lots of questions to pass a specific exam then past papers an option. These are usually available from the exam boards. I would ask you to consider other options in addition. Rote learning has a role in memory and retention but will not provide a deeper understanding. The beauty of maths is in the rich and ...


5

Teach your son how to: understand that "x is just a number you don't know yet." do the same thing to both sides of the equation (but don't divide by zero). solve story problems. use Check-By-Substitution to check his work. keep track of his common mistakes. Consider the Saxon math series. My high school math classes were taught using traditional math ...


3

The University of Waterloo (Canada's MIT, roughly speaking) keeps a large catalog of high quality math problems online at http://www.cemc.uwaterloo.ca/contests/past_contests.html. A strategy for a student in the situation you've described could be to download and attempt one contest every week. These aren't as curriculum focused as some other materials might ...


3

Here are some resources: nrich They have a wide range of rich problem solving explorations for students in primary through secondary and some post secondary. They have student pages and teacher pages. NCTM illuminations Explore the interactives for grades 9-12. They have tools to explore fractals, a game to explore vector addition as a boat travels ...


2

Many homeschoolers attend community college while of high school age. She could take whatever math class she wants at a community college. The local math circle sounds like a good idea. Girls' Angle posts interesting math problems. She might like my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers.


2

'Rote math' had what effect on you? Buy these three books, and use them to guide your instruction: "What's math got to do with it?" by Jo Boaler or take her MOOC with your son, "the Joy of X" by Steven Strogatz (preview it), and "Innumeracy" by John Allen Paulos.


2

Check into the courses offered by Art of Problem Solving. They get good reviews from the homeschoolers I am in contact with. Although their description does not mention honors-level or AB, they train students for competitions, and their materials include the rigor you desire.


2

Unfortunately, all too often what is done with bright students (especially middle school and beyond) is that their mathematical clocks are pushed - that is if they are in "grade x" they are shown the mathematics at grade (x+1) because they are already proficient with the mathematics at grade x. There are similar issues for the home schooled. My advice is to ...


2

In addition to the above recommendations, I'd add resources from the Art of Problem Solving. (BTW, the answer to this question depends heavily on the homeschooler. I was homeschooled and found my way to mathematics through physics. I didn't like pure mathematics at all until I needed it for a better understanding of physics. Only much later did I develop a ...


2

This is coming from an educator that isn't fond of common core for various reasons. What I believe is at the heart of common core math tho, is that the "Why?" is important. Math isn't just a series of steps to get to an arbitrary answer that someone says works, but it's a logical method of using order built into numbers to arrive at the correct answer. My ...


2

I rather like The Art of Problem Solving's Beast Academy series. It is a complete curriculum, but in a "graphic novel" format, with problem solving emphasis. This can lead into other resources from AOPS for middle and high school. (I was myself homeschooled, homeschool both of my children ages 5 and 8, and am a mathematics professor. In my experience, the ...


1

After three years of intensive work with the new math standards (as part of the writing team for a new, national common core-based mathematics curriculum), my partner and I began consulting for school districts, training their teachers in the very thing you inquired about....HOW best to teach this new math. Almost without exception the teachers we worked ...


1

There are so many mathematical directions you can go. I have found Living Math Forum (a yahoo group) to be incredibly eye-opening. There are about 5,000 members, and questions usually get a variety of answers from other homeschoolers. How do you want to approach math? There are various curricula available, there are "math readers", there are activities that ...


1

Stacking the numbers, and carrying the tens, works and is understandable to generations of people. You can explain each step as being correct by itself. I recommend teaching your daughter how to count on her fingers using roman numerals. This will let her see how she can "carry the one". Her four fingers on her right hand are Is; her right thumb is a V; ...


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