A recent tweet from Mr. Hamada led to my thinking about skills and concepts in mathematics. I think both are important. Students need to be able to perform the skills. In addition, students need to understand the concepts behind the skill. Without the concepts, I’m not sure how valuable the skill is. How will they apply the skill, let alone remember it without understanding the concept?
I can’t imagine that many people would say that only one or the other is important1. Yet, how does what we do in the classroom reflect what we value? What do we typically assess? Skills.
Now don’t get me wrong, skills are good. Skills are necessary. But if we never ask them about the concepts, what message are we sending about what we value?
I’m doing my best to try to reinforce both in my daily classroom activities and in assessments. In one of my preps, we’re learning about some basic statistics (mean, median, mode, and range – which they’re mostly done before, mastery level on day one varied greatly though) in addition to standard deviation and normal distributions (which is new to everyone).
I recently gave a quiz2 on standard deviation. I wanted to assess both their ability to calculate standard deviation and their understanding of the meaning. Here are the questions:
- Calculate the standard deviation of the following set of numbers: 20, 23, 32, 34, 16
- Make up a set of data with five numbers that has the same mean but a smaller standard deviation than the set of numbers in problem #1.
- John was calculating the standard deviation of a set of data that ranged from 3 to 18. He determined that the standard deviation was 16. Do you think his answer is reasonable? Why or why not?
I think I did a decent job of writing questions3 that addressed both concepts and skills. The answers to the third question told me that the vast majority of my students have a decent grasp of what standard deviation means. Although we still need to work on how to word these responses. We have time though, they’re only freshmen.
1 I may be totally wrong on this. I often am.
2 I grade by “total points” yet somehow they take something called a “quiz” more seriously than an “assignment”. I still don’t understand this.
3 Writing decent assessments/questions is something I’ve had to learn (am still learning) on my own. I wish it had been emphasized more in my education classes.