When we first started homeschool, a friend of mine was concerned about how we would approach math. (That is at least one friend decided her concern was so great that she had to breach the bounds of propriety and actually tell me this — 😉 and you know I love you, sister, if you’re reading)
“Math follows a specific sequence,” she told me, using a phrase I would hear echoed again and again. “Things have to be taught in a specific order. You can’t jump ahead, or you could end up creating a math-phobic child.”
There was not a lot to do, however, to prevent a child who was solving simple algebra problems in her head before memorizing the 7s on the times table from jumping ahead. What was I to do? Sedate her? I did a lot of reading on asynchrony and mostly trusted my gut. We interspersed geometry and algebra with multiplication facts and fractions. This has worked fairly well, so far. Now Violet is zipping through a pre-algebra text to review and prepare for starting what I would call real algebra — you know, quadratic equations, graphing, etc. Math is not her favorite, but she often finds it interesting (though she would likely never confess that to her friends!).
I remembered this when I read two other pieces of “sequencing” advice recently. The first was in a Catholic homeschool piece, by an author I admire, though I have not adopted the classical model she advocates. She was writing about moving slowly through a learn-to-read curriculum (Thank you, God, for giving me girls who taught themselves!), and added this analogy:
A child who sees things at a glance may well have a strong imagination, which is good, but in addition to this strength he needs to have a disciplined imagination. A student should be able to lead his imagination, not to be lead by it. An undisciplined imagination is a severe cross, and encouraging our children to review, retell, “do it one more time,” and do one lesson at a time, will help them discipline their imaginations by habituating them to a slower, more careful pace. [emphasis mine]
OK, there is a certain logic to this, but — gahh! I’m in pain just imagining us crawling along that way. We jump forwards and dip back, we skip, we combine multiple lessons into one. Naturally, I am also a little dubious about the thought that we don’t want to be led by our imaginations. I am quite sure that from time to time that is the only way to go forward — and I also believe quite firmly, since we’re talking Catholic homeschooling here, that sometimes being led by the imagination is *at the same time* being led by the Spirit.
Anyway, I’m not trying to pick on a nice article by a nice lady. Those of us who have galloping imaginations and rush through easy stuff and consequently make silly mistakes should take her general point. I just had cause once again to reflect on the idea of doing things in order, and how that often does not work for us.
The second example was in a curriculum catalog, in a section explaining why the company did not have a heavy “Great Books” curriculum for younger students, compared to many “classical” homeschool programs:
The Great Books will be drudgery to anyone not yet taken captive by the Great Questions, the Big Ideas. If you are not yet given to pondering the meaning of life, it is doubtful you are ready to read the ponderings of others [on these subjects].
This resonates with my instincts thus far. I have held back a lot of books for my kids that they could read, that gifted kids “at their level” have read, because I do not think they will connect with them. It’s not that they don’t think about big ideas — I just think they need a little more time with their own thoughts and collecting more of their own experiences.
I’ve been reading (and reading about) the humanist education reformer Juan Luis Vives, who was among the first of the Renaissance education philosophers to re-emphasize the importance of getting students out of doors, into nature, into the artisan’s workshop, into life, as an essential balance to contemplation and the acquisition of abstract knowledge.
I think there is a dance that happens here, as we encourage children to enter into the “Great Conversations.” They ponder ideas, they are encouraged by what they read to ponder more, and on and on. Does it matter where in this “sequence” you start? Maybe not, but in our case, I’m confirmed in letting life and the child herself take the lead — though probably because I am totally confident that the love of pondering big ideas and questions through books is there and will only grow with time!