We recently had a great question from a teacher. She asked if anyone else hated teaching non-standard units of measurement in math.
That reminded those of us who teach math of many years of the same frustration and struggle.
However, when we sat down and talked about it as a vertically-aligned group, we did find some interesting things that helped us hate the non-standard measurement lessons a little bit less.
In Kindergarten terms, measurement is defining something you don’t know by comparing it to something you do know. Later, we are able to use standard units like inches, feet, and yards in the U.S., and centimeters, meters, and kilometers in the rest of the world.
As we age, these vague concepts become concrete because our reservoir of stored information provides us with many things to mentally compare them to.
As a young child, though, most children have very little to use as a basis of comparison.
Thus, the “non-standard units” of measurement are used.
Neurons and Dendrites
One of our most important jobs as educators is to meet children where they are in learning and escort them forward. In order to do that, we have to start with what they already know. This is a scientific truth, and we can see evidence of it in neuroscience.
Our brains have thousands of neurons, tiny informational subway systems in our brains. Dendrites are the actual subway tracks that connect one station to another. In order to move information from one neuron to the next, you have to have a connection point, or in this metaphor, a station. Old information has to be established before new information can be understood.
In measurement, that means we use items our students are likely already familiar with: paper clips, Unifix cubes, pennies, crayons, erasers, and pencils.
These objects build a basis for future comparison with abstract concepts used in standard units. At some point, students will begin to replace 300+ Unifix cubes with a pound, standard paperclips with an inch, and twelve Pink Pearl erasers lined up sideways with a foot.
It’s vital to give students the time they need exploring with these basic tools as non-standard measurement units so they can begin to create their deeper future database for connection with standard units. The“space” measured by the concrete unit of an eraser has to be solidified in a young child’s mind before the abstract “inch” can ever be fully approached.
We know from numeracy that without those concrete concepts to attach to, students will never be able to jump to the abstract. The concrete is the pathway to the abstract. It’s not an option.
In neurotypical child development, we know that it takes several years for children to be able to move from concrete to abstract. Unfortunately, not all of education is adequately informed about neurotypical development, and many of our standards and practices push students to engage with material that is inappropriate for their brains’ ages.
That means, in terms of measurement, students may be expected to transfer to the abstract before they are developmentally able to do so.
It’s okay to continue offering non-standard units of measurement until they grasp the concept, though.
And some of our non-neurotypical kids are far more advanced in their understanding of the abstract. Those students may balk at using concrete units when they find it quicker and more efficient to use abstract methods.
It’s okay to mention formal units and make comparisons before it’s considered developmentally appropriate. Just remember that on the whole, your general ed. class will need that concrete support for much longer.
Think of offering the abstract as a preview for a movie and the concrete as the main movie event. There will always be one or two students who are ready for that preview to be their personal main event, and you can pull them into a small group and teach ahead or teach abstract along with concrete to be sure they are as ready as they appear.
Most of your students will be best served by the concrete ideas presented in the “movie” or “feature presentation” itself.
And some are still a year behind, doing things developmentally appropriate for a younger child, like trying to eat the Unifix cubes or crayons. Offer the concrete units, celebrate when they seem to understand, and watch them closely so they don’t choke on anything. Try again next year.