The Power of Brevity

Below are two different scripts for beginning the same math lesson.  Read each of the introductions twice – once from a teacher’s perspective and once through the lens of a fourth grade student.


Script I

Yesterday, we learned and practiced drawing models to find equivalent fractions.  We also found that we can solve equivalent fractions by multiplying the numerator and denominator by the same number.  Today, we’re going to learn how to compare fractions when their numerators and denominators are not the same.  But first, let’s review.  (Teacher writes 2/3 = ?/9 ) Who can tell me how many ninths two-thirds is?...Michelle.

Michelle says Six.

Script II

Teacher:  (Write 2/3.)  Say the fraction.

Students (say or write):  Two-thirds.

Teacher:  (Writes 2/3 = ?/9.)  Two-thirds is the same as how many ninths?

Students (say or write):  Six.


Now, ask yourself two questions:

  1. As a teacher, which script would benefit my students the most?

  2. As a fourth grade student, which introduction would I prefer?

Extraneous teacher talk is an instructional epidemic that creates passive learning environments, and in the process bored and/or confused children.  Conversely, brevity in mathematics instruction keeps students engaged, maximizes instructional time, and upholds the subject’s integrity as a thinking/reasoning discipline.

Math educators commonly begin lessons by talking for a minute or longer, while their students sit idly.  Teachers come by this habit honestly.  Many school administrators require their staff to begin every class by stating a lesson objective.  Although academically sensible, this widely accepted philosophy fails to account for human emotion.  During monologues, students often become distracted, forcing teachers to expend energy refocusing them.  In the process, attentive students become frustrated.  When teachers begin class by asking a concise question that all students can discuss or answer correctly, children become active rather than passive participants, and are more likely to learn new content.  Math class is most dynamic when all students never go longer than 30 seconds without answering a question or discussing a topic.  Consistent student participation also helps teachers move efficiently through lessons.

When teachers say everything that’s necessary, but not a single word more, they maximize their instructional time.  Script I’s ratio of teacher words to student words is 61:1 and all the instructor knows is that one student (Michelle) retained part of yesterday’s lesson.  No objective is stated in Script II, but students immediately engage in content, and the teacher performs two informal assessments, helping them adjust their questioning if necessary:

  • Which students can read the fraction correctly as two-thirds?

  • Which students have a mental strategy for finding fractional equivalence?

The teacher also says 49 fewer words and all – or almost all – students answer twice within the first 10-15 seconds of class.  Lastly, and maybe most importantly, Script II is approximately four times more efficient than Script I.  High mathematical engagement involves teachers and students speaking equally.  This reduced talking ratio creates a pace of instruction that allows teachers to navigate far more content than they can in a traditional lecture format.  It also helps them teach the subject with more integrity.

Elementary mathematics education served a utilitarian role in pre-computer society.  Without technology to perform basic calculations, people needed to excel in arithmetic so they could balance checkbooks, count change, and tally large inventories.  Because we now have machines that do these tasks for us, the role of mathematics education has reverted to its genesis.  If we want our children to become excellent thinkers and reasoners, then it’s vital that the subject be taught through thinking and reasoning.  This is impossible when instruction is loquacious and/or procedural.  When teachers elicit student responses with concise questions that require precise answers or stimulate discussions, children see mathematics as a noun and verb.

Excessive teacher talk dulls curious minds and incubates ADHD.  When math teachers speak succinctly, however, they stay connected to their students, cover more content, and honor the subject as a rational, logical branch of learning.  Every unnecessary word in a math lesson is like a small vapor released into the classroom air.  Before long, even the most focused students must sift through fog to understand what the instructor is saying.  Comprehending lessons, therefore, is as hypnotic or clear as their transcripts are to read.