I wonder how many times we teach for short-term performance but believe that we are teaching for understanding. I ask this question because I have had numerous conversations with teachers about their frustration when students are not able to recall previous learning. The teacher(s) will often share how they spent considerable time on a concept and have documented evidence that students understood not only the concept but how to apply it. However, only a little time after, students are left asking the teacher for support and saying that they don’t remember working on it earlier in the school year. Regardless of the grade level, I believe that many teachers have experienced this with numerous students. If it is only with a few students, we may consider it a student issue. However, if it happens with numerous students and year-after-year, it is likely an instructional issue.

What I want to suggest is that we pause and reflect on what we may be doing to contribute to this frustrating circumstance. Math concepts are typically segmented during the year on the year plan as a way to ensure that coverage happens. Within this approach, it is instruction that is the focus not learning. When the focus is on coverage, we take our eyes off student learning. Think about it, what does a typical year plan look like?

Within this approach to year plans, the teacher provides opportunities for the student to engage with individual concepts (exploratory tasks, explicit instruction, guided math, etc.). Within each topic, students will then be assigned questions to work on as practice that relate to the specific topic. Therefore, students are not required to consider what concept is embedded within the task. When not having to consider the concept, students don’t have to select from various concepts and identify the appropriate one to apply to solve the task. Through structuring the year as such, the teacher has removed the necessity for students to examine their thinking to sift through their previous learning to identify an appropriate plan of action.

Therefore, when provided with a concept later in the year, after not seeing it for a while, students are left at a loss. They now have to search their previous learning and identify a concept that is effective in arriving at a solution. However, when they worked with the concept earlier in the year, they were explicitly (or implicitly from the teacher’s perspective) told what to apply to solve the problem. When engaged within this model of instruction, students were not demonstrating understanding of the concept, instead they were demonstrating that they knew the focus topic of instruction and just applied it. Students were missing an important part of learning: knowing which concept to apply to a given situation.

I want you to consider how many times in the year you assess and evaluate your students as understanding a concept based on their score or performance on a task. In such situations, is success on the task indicative of understanding or is it indicative that students have identified the game of schooling and can regurgitate the concept that has been explicitly explored the past few weeks.

I had the opportunity to chat with a student who just received a grade of 112 % on a fractions test. When asked how she did so well on the test, the intermediate-aged student responded:

Well, below my name it said ‘multiplication of fractions.’ The first 20 problems were multiplying two fractions. Then, when I got to the word problem, I just multiplied the two fractions. I knew it had to be multiplication because all the questions were about multiplying. If it was a subtraction problem, I would have got it wrong. I didn’t even read the bonus question, I just multiplied the two fractions.

Within this situation, the student demonstrated success on the test, but this wasn’t necessarily based on her understanding of multiplying fractions. Sure the student could multiply fractions, but she did not demonstrate the understanding of when a situation would call for multiplication instead of the other operations. We have to be careful, as teachers, that we are measuring understanding as opposed to short-term performance.

My goal of this blog entry is to highlight the stumbling blocks associated when we focus on coverage of concepts instead of student learning. When our attention is on covering a concept, we may be removing an important aspect of learning: students having to understand a problem and deciding on the concept to apply to reach the solution. My fear is that our instructional focus may be on short-term performance instead of understanding. When we focus on short-term performance, whether consciously or subconsciously, we may have a misleading assessment of student learning and this may result in the all-to-common phrase of ‘I don’t remember doing that’ from students. While there is a time and place for students to practice applying a concept, something referred to as blocked practice, it is important that we also provide students opportunities that they have to consider which concept to apply to solve a problem. Learning is about more than applying a concept. Learning encompasses students understanding a problem, having to decide which concept to apply and then applying that concept to reach the solution.