Often middle school-aged students arrive at CELC having being taught division but lack solid understanding of division. All too often, students are asked to memorize algorithms without grasping how the steps relate to the concept at hand.
When students work with math manipulatives, such as base ten blocks, Cuisenaire rods, fraction strips, etc., or draw their own models to learn division, for example, they are better able to comprehend, rather than just see numbers on a page without a concept to go along with this written information. A “quotient” becomes a tangible thing when utilizing models and drawing, which can then be translated and understood.
Math anxiety is a real thing – many adults rely on a set of rules that were memorized without fully realizing the math behind those rules.
Recently, a CELC student queried as to how many vegetables she eats per year. She estimated 126 and then figured she’d divide that over 52 weeks to determine how many, on average, vegetables would be eaten per week. As she was new to division, she was asked to take 126 actual objects and literally divide them into 52 groups, rather than computing long division on paper since she was yet without an understanding of that particular set of steps.
Reaching a point in her work where remainders became necessary, her understanding of division became that much more meaningful. She had to find a way to divide the whole numbers into tenths, hundredths, and even into thousandths – another reinforcement of place value and our base-ten number system!
It was quite exciting when she discovered that 126 vegetables per year turned out to be a low estimate, once she determined her answer of 2.423 … and then figured that it meant only about two-and-a half vegetables per week – low consumption in fact, according to this vegetable lover!
Rather than “memorizing” a set of steps with no basis, transferring this concrete understanding onto paper can now be accomplished. Learning by heart requires active involvement – math at CELC is indeed a hands-on and minds-on endeavor!
A math teacher once told me that math is like swimming – you cannot just read it out of a book to learn, you have to get into the pool!
Perhaps this is true for most things, as a way to really retain and remember. Once young people, who are prone to movement as a way to release energy and engage in the world, become truly involved and immersed, their learning gives way to a whole new dimension, which leads to making memories that matter.