Ida Tarbell's autobiography), N. does a short 5-problem set in a workbook I bought called Daily Math. Then Tim makes up a series of problems for N. to work, sometimes building on any mistakes he may have made in the Daily Math book. Earlier this fall, as you can see at right, they were working on sequences, adding, and subtraction. They also worked a lot on money recognition and money-related arithmetic. Lately N. has been doing a variety of types of problems: big addition and subtraction problems, word problems, simple algebra (solving for x).
The workbook made it easy to incorporate some formal math into the daily routine and gives a nice platform for further work. In addition it is giving N. some good practice in the conventions of typical math problems such as he will encounter when he takes the state-required annual standardized test. Test-taking is not a focus for us, but it seems good for N. to be exposed to and have the opportunity to practice reading and working problems. N. enjoys doing his math problems, and I like that Tim can tailor his additional daily problems to whatever N. is less confident in; earlier this fall, for example, that was coins/money. When he makes up word problems, Tim always uses people and places and objects from our life, to highlight the relevance of math in the real world. The variety of the problems also keeps N.'s interest. As you can see in the picture, Tim and N. correct the problems together. N. likes to report to me what his daily "score" in math is, and I remind him every day that making mistakes is how you learn! Our assessment so far is that while N. is academically unusual in some subjects, in math he is quite typical for his age. The second-grade Daily Math workbook is right at his current level.
The first two years of N's homeschooling our approach to math was very intuitive and organic. We did a bit of formal written practice of math but mostly talked math a lot and provided many opportunities for the play and creative problem-solving that encourages strong numeracy. We're building on that foundation this year with more formal problems, but we are still always on the look-out for ways to develop N.'s math facility beyond his daily math practice. I'm feeling good that we're helping N. build his math skills in a gently rigorous way while maintaining a positive attitude about math in general and especially about making mistakes and getting things wrong in order to learn. When you do a little math every day, it's easy to keep mistakes in their proper perspective.