Why do middle school students seem to bring very little fraction knowledge to the classroom? We start fractions at such a young age, intuitively then materially then abstractly. According to the CCSS, abstraction begins as early as third grade. Many early childhood classrooms have shapes that are divided into fractional quantities so students get a physical “feel” for fractions long before they’re representing them as symbols.
So why…when students are inundated with fractions their entire school career…do they forget they know anything about them when they hit middle school!?!
This phenomenon is as frustrating to middle school teachers as it is to their last year elementary teachers. Of COURSE students have seen fractions before they hit 6th and 7th grade. But something about either the way we’re teaching it, or simply their own brain development, is preventing them from truly integrating and understand what a fraction is.
Yes, they can repeat that is a pizza dividing into parts. Or, they can talk about fraction insets and do complicated equivalencies with physical materials.
But they do not, and likely will rarely, remember the different between “cross multiplication”, multiplying fractions, and adding fractions. They come to me with a list of memorized algorithms—even the Montessori students—that are confusing and irritating to say the least.
I want to be clear here—this is not a failing of the elementary teachers. And further, who knows if the way I’m “clearing it up” in middle school has any lasting effect on students in high school—I’d have to hear from high school teachers, but do I really want that sort of frustration in my life?
What I do know, is that when I teach students the definition of a fraction on a number line, they are able to take all those fabulous lessons from earlier years and integrate them into a concrete understanding. They are able to “see” fractions in a different way than before. Rather than memorizing cross multiplication, they are able to think seemlessly between the whole number value contained in the numerator.
This is why, no matter how many fraction lessons students have had in the past, I always start my 7th grade PreAlgebra year off with a good long number line lesson. Students play movement games and card games designed to teach them how to count, order, and compare fractions.
More importantly, this is when I introduce negative fractions to them as well. NOT after I teach them adding and subtracting whole integers, but now…when we’re learning symmetry of the number line and working with comparing values, absolute value, and the goodies that come with the rudimentary x-axis.