I’ve been writing at some length about things that are specifically appropriate for my 7-year-old at this time and place. What if this homeschooling thing continues for some years? What about older students, more advanced subjects? It’s nice that he can do a lot of exploring now, but what happens when the discipline becomes more rigorous?
I’ve been looking into this and here are a number of resources I would look into next.
I might start, in the very near future, with the summer curriculum that Jo Boaler helped develop to improve the numeracy sense of students:
MAP (Mathematics Assessment Project) is an initiative to develop “well-engineered tools for formative and summative assessment that expose students’ mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students’ understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems.” Included on the team are the people from the Shell Centre and may be considered a kind of successor to Harvard’s Balanced Assessment project. It’s meant for middle and high school students, and it could be a good place to look for assessment tools or simply some more math lessons and puzzles.
I mentioned already that I’m looking into iPad games that would help develop fluency in basic calculation skills, but there’s a whole other group of educational games that are more interesting — games that encourage and facilitate virtual experimentation and manipulation of mathematical models.
Calculation Nation is a web site hosted by the National Council of Teachers of Mathematics that has a number of online games and simulations on a variety of subjects appropriate for upper elementary to middle school students (fractions, multiples, symmetry, area, etc.)
Math Breakers is a downloadable (free trial) virtual math game environment designed for all elementary grades (1-6). Heck, if Biggie is going to be into Minecraft; I might as well throw him into this also.
Geogebra is a free software program that “brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package.” It seems to particularly excel in showing visually and geometrically algebraic ideas. It has a very active educational community around it, which makes finding relevant lessons and activities easy.
Desmos is also free and available on most computers and devices, including a sandbox version of it as a web app. It’s basically an interactive graphing calculator. It has features like variable sliders that make it extremely useful to visualize how changes in values in equations affect outcomes. It also has a support web site with searchable activities and lesson plans for educators.
There’s two curricular systems that seem especially promising for homeschooling programs with an un-schooling bent.
The Art of Problem Solving is a curriculum designed by people with Math Olympiad backgrounds, so there’s a huge emphasis on creative problem solving and lateral thinking. The main curriculum starts at pre-algebra, but they are also developing Beast Academy, a lower school curriculum for grades 2 to 5 (I believe they’re still working on grades 5 and 2). Course materials include print textbooks and workbooks but also online classes and support.
Mathalicious is an online database of real world math lessons for grades 6 to high school. It has a pay-what-you-can monthly subscription model.
I’m also looking to see how I can try a more interdisciplinary approach with mathematics that includes lots of tie-ins to economics, engineering, computer science, and science. And history. And everything else. ‘Cause… you know.