I’ve had two different stories about children and math come through my Facebook feed in the last two days.
In Monday’s online edition of The Atlantic, there is a piece that discusses young children being capable of learning algebra and calculus concepts through play. You can read the article here.
One suggestion that is made in the article is that the normal progression of math instruction that we are accustomed to, is in fact developmentally inappropriate and does not allow for more playful exploration of mathematical manifestations in activities such as nature, art and music.
“Mathematics is fundamentally about patterns and structures, rather than little manipulations of numbers,” says Math educator Maria Droujkova.
In the article, Droujkova goes on to discuss this idea of “complex yet easy” versus “simple yet hard.”
What a great way to think of things.
Complex yet simple – things like origami, building a house from LEGO blocks, snowflake cutouts. Complex concepts but simple (and fun) activities. Children can grasp the more complex concept through these playful activities.
Simple yet hard – doing a worksheet of 100 repetitive math problems or memorizing multiplication tables without recognizing the inherent patterns present.
One of the take-home messages of this piece is that children can learn these complex mathematical concepts in an informal way. They get the concept and can think of it in a more abstract way. From there they can move into a more formal understanding of the subject matter, incorporating words, graphs and equations.
The second article I read was an Op-Ed piece in the LA Times. You can read it here.
The writer, Edward Frenkel, discusses the benefits of incorporating mathematical concepts and ideas, rather than just straight arithmetic, into math instruction. While he stresses that the tried and true method of math instruction, teaching addition and multiplication tables for example, was still essential, demonstrating some of the abstract along with the concrete would go a long way in capturing the attention of children and motivating them to learn math.
Frenkel writes of more abstract mathematic concepts as being “portals into the magic world of modern math, starting points as surely as addition, subtraction and fractions are starting points. The added bonus is that they give us a perfect antidote to the common perception of the subject as stale and boring.”
I think, as with most things, it is important to find a balance that works for your family.
I have written previously about how we have switched over to Saxon Math (starting with Saxon 5/4) this school year. While there is a bit of drill (each lesson starts with a Basic Skills “test” which essentially drills the student on basic mathematical facts), the Saxon lessons incorporate mental math and problem solving, which encourages students to solve a problem without a template, and then prompts the student to note which strategies he/she employed to solve it. The problem sets consist of new concept questions along with problems from previous lessons. While there is a steady build up in skills and difficulty, there is a constant review of previously learned materials.
While we are spending time each week on formal arithmetic instruction, we also incorporate more concept-based learning experiences.
Often these are puzzles and online games that focus on sequences, patterns, or solving. We have spent a lot of time exploring origami and LEGO building projects (if you are using Google Chrome, check out this cool app!) , even Minecraft. Video games, while perhaps not a traditional math experience, does provide ample opportunity to hone arithmetic skills – crafting recipes and working in multiples, tracking points in various skills, etc.
We have also just started using Dragon Box, an app I highly recommend! This app teaches algebraic principles in a simplified way. Starting with simple blocks with creatures, basic concepts are taught, reinforced and built upon. Kyri devoured the lower version (5+, for ages 6-8) in just a couple of days and was quite excited when I installed the higher version (12+, great for ages 8 and up). She is already quite comfortable with the concepts such as positive and negative numbers, reducing fractions, and balancing equations as a result. To her, algebra is a puzzle or game to be solved, not a math subject looming out in the future to stress over.
These activities promote an interest and drive to learn more without the pressure of formal learning. But we are also building a firm foundation in basic skills with the formal instruction. I think we are striking a good balance.
What a beautiful photo with stones! Nice grid work there.
The balance you discuss is dynamic, too. It can shift from year to year and even activity to activity. I’ve seen kids drill themselves on a favorite topic, for example, memorizing 100 digits of Pi for the love of that number. The same kid may only want a cursory familiarity with another topic.
thank you for your comment! you definitely describe my daughter. she goes through phases where she wants to spend all her time on one topic, “neglecting” other parts of her lessons. I have to step back and remind myself that she will return to the other areas in time, and not to stress about it.