I frequently find myself scratching my head trying to convey a crucial topic to students that seems to elude them; this topic, in particular, underpins the intuitions of so much of not just mathematics, but statistics, engineering, science, chemistry, and I could go on. The topic is that of Number Sense, and it is one of the ideas touched upon in the framework of the Common Core State Standards, and for good reason. I have taught students from middle school to college, and a large number of them simply do not understand the idea of “size” and “magnitude” and “quantity” and how this allows sensible statements about numbers.
For instance, in my first year of teaching, I showed my students a jar of jelly beans, not entirely unlike the one here.
The question was a simple one that is a favorite of raffles and carnival games: How many jelly beans are in the jar?
To you and I, at least most of us, this task seems straightforward. We are not likely to guess the number exactly – that probability is quite low indeed, which is what lends the entire viability to a raffle or carnival game. Yet, to many students, this question is a daunting one that cannot be sensibly tackled.
Examples of responses I received:
I’ll note that some percentage of students DID make a sensible guess here, but it’s quite obvious that 40 makes little sense, as you can easily count more than 40 just by glancing at it quickly. And guessing tens of thousands, even a million, is so far out of the realm of possibility as to be laughable. Yet, these students were absolutely serious.
This phenomenon is not unique. I have spoken with many educators and managers of young-adult employers, and the issue is pervasive. Many Gen Z’ers and younger Millennials simply do not have a solid sense of quantity and magnitude. And that deficiency will prove to be a hindrance in life in ways perhaps unexpected. For instance, if you buy 27 pounds of chicken for $2.98 per pound, does it make sense if you are charged $110? Or if your employer asks you to help develop a reasonable budget for your division of the company, how do you know what expenses are expected and which are unnecessary?
Unfortunately, students with Number Sense handicap themselves and lock themselves out of life opportunities (such as jobs) where strategically reasoning with numbers and estimation prove important.
One resource I have come across that has proven interesting and useful is Estimation180.com This innovative website allows users to estimate amounts and give reasoning about numbers every day. I really recommend you check it out due to the vast potential to give practice to students (and even adults!) who lack the traditional practice with estimation. I feel most math teachers have number sense and intuitively understand the idea of Estimation and have a hard time conveying what exactly it is and how to do it to students; indeed, it is a skill that is best learned via practice, and this site gives just that.
If you give the site a look, I’d love to know what you think about it. I’ve used it for a couple of years with my students with some success. Either way, I feel we need to focus on Number Sense, particularly the skill of estimation, in our teaching and curriculum, as it underpins so much of the mathematical reasoning and strategy in higher levels.