Many math instructors use pre-assessments as a lead in to units and chapters throughout the school year. Pre-assessing, they rationalize, helps them know what skills and concepts to review before teaching curricular lessons. Although the philosophy is sensible, the practice is inefficient and often ineffective. Regular pre-assessments tend to waste instructional days, frustrate students, and lead to worse academic results.
During assessments, children neither learn new topics, nor advance their mathematical understanding. Review days aside, students who take 15 pre-assessments and 15 chapter tests during the school year, spend 30 schools days not learning math. Unlike other subjects, mathematics is a discipline that students rarely practice outside of their class time, which – at most – is 175-180 hours/year. Therefore, teachers should aim to optimize their students’ learning by delivering as many dynamic instructional math periods as possible.
Reviewing topics from previous lessons, chapters, units, and grades is usually laborious for strong and weak students, alike. The former becomes bored and frustrated, while the latter can feel stigmatized knowing that their lack of understanding is slowing the pace of their classmates. The resulting chemistry is a lethargic malaise in which few - if any - students are enthused or progressing.
In addition to reducing instructional time, frontloaded reviews are not optimal for committing concepts, skills, etc. into long-term memory. Solidifying shaky mathematical foundations that were supposed to be mastered in previous grade levels requires instructional time that teachers rarely have. Addressing them through massed review practice is inefficient and unproductive (1).
Math teaching and learning flows best when instructors teach grade level content and address misunderstandings as they arise.
The most effective method for plugging these skill and/or conceptual gaps is short fluency reviews spread out over several days (2).
The most skilled teachers anticipate challenges and prepare their students for upcoming topics in the days and weeks before they teach it. (See examples above.)
Although well intentioned, copious pre-assessments consume precious class time and bore students, hampering their mathematical progress. Conversely, brief interspersed practice maximizes instructional time and student interest, while optimizing learning.
1: “By massed practice we mean the single-minded, rapid-fire repetition of something you’re trying to burn into memory. Rereading and massed practice give rise to feelings of fluency that are taken to be signs of mastery, but for true mastery or durability these strategies are largely a waste of time.” Make it Stick by Peter Brown, page 11.
2: “Retrieval strengthens the memory and interrupts forgetting. While the brain is not a muscle that gets stronger with exercise, the neural pathways that make up a body of learning do get stronger, when the memory is retrieved and the learning is practiced. Periodic practice arrests forgetting, strengthens retrieval routes and is essential for hanging onto the knowledge you want to gain. When you space out practice at a task and get a little rusty between sessions, or you interleave the practice of two or more subjects, retrieval is harder and feels less productive, but the effort produces longer lasting learning and enables more versatile application of it in later settings.” Make it Stick by Peter Brown, page 12.