A fifth-grade teacher at Highland Elementary was teaching his students to understand linear equations. In a prior lesson, students had learned about variables. In this lesson, the focus was on mathematic expressions. The teacher succinctly explained to students that an algebraic expression combined a variable and a value. He provided a variety of practical examples and then engaged the students in brainstorming many additional examples.
One student offered, “Like the number of points your team gets for a score could be a variable and the number of scores could be the value.”
“Yes,” the teacher responded. “So, what might an expression be for three scores?”
“Three S,” the student answered proudly.
“Exactly! So, what does the expression ‘Three S’ mean?” the teacher asked a different student. “It means three times an unknown number,” the student answered.
“An unknown number of what?” the teacher probed?
“An unknown number of scores,” stated another child.
Students were then directed to list expressions on sentence strips and then, on separate sentence strips, write out words that would indicate what the expressions meant. Later students played a matching game in which they matched the sentence strips by pairing the algebraic expressions with the matching word sentences.
Highland Elementary is in the Montgomery County Public School District in Silver Spring, Maryland. The school serves approximately 550 students in grades pre-kindergarten through five. The school won the America’s Best Urban Schools Award in 2009.
Mastery is not achieved by accident. The manner in which teachers introduce content accelerates or decelerates student understanding. Students master more when teachers introduce content logically, clearly, and concisely. In high-performing urban schools, teachers introduce information in ways that make it easier for students to understand. They plan instruction so that mastery is likely. This starts with clarity about what students are expected to learn. Effective teachers know specifically what they want students to master, and they know what they will accept as evidence of mastery. Unlike teachers who might just “cover” the chapter, follow the teacher’s guide, or read the script, effective teachers know what they want students to be able to explain, analyze, discuss, solve, perform, or otherwise demonstrate, and they know how well they want students to be able to perform. While these teachers start with the “end in mind,” they plan instruction that students are likely to perceive as clear, logical, and understandable.
What It Is
Breaking down complex tasks into logical step-by-step sequences and teaching one step at a time
Example: The teacher wants students to be able to describe and discuss the factors that led the German people to follow Hitler, but first she devotes a lesson to helping students understand the sanctions imposed upon Germany at the end of World War I. Then she helps students understand the economic strife experienced by Germany and other nations during the 1930s.
What It Isn’t
Teaching complex tasks without identifying, distinguishing, or sequencing the steps involved
Example: The teacher presents the chapter on the causes of World War II as one lesson with a huge mix of facts, dates, personalities, and contexts.