Learn about TransMath

When we talk about resources in education, money usually comes to mind first. It’s true: Having money or not can expand or limit options in schools. Still, classroom teachers typically are not involved at that level of decision making. For us, time becomes the most precious resource. Indeed, every choice we make as classroom teachers is an opportunity cost. For example, if we spend five minutes reviewing homework, then we didn’t spend five minutes teaching new content.

In this blog, I review strategies to help maximize instructional time. Although these ideas could be used across subjects, I’m specifically using math examples.

Beyond Cold Calling

Dylan Wiliam, a researcher best known for his work on formative assessment, says that making sound instructional decisions in the moment requires good data. Good data, in this case, means a number representative of most students in the class (and a relevant question or prompt). In a class of 25, if we “cold call” one student, we’ve surveyed less than 5 percent of the class.

To collect better data, consider these strategies:

1. Unison Response: For questions that have a short, definite answer, train students to respond together. The responses could be given orally (choral response) or in writing (such as using mini whiteboards).
   
   

   What it looks like in practice: If we’re teaching a lesson on the Pythagorean Theorem and we want to know if students remember where the hypotenuse is, we might ask: “Which line segment is the hypotenuse of the triangle on the board?” When you give the signal, all students would say the answer or show you their whiteboards.

   For your consideration: How do unison responses support historically struggling students, such as English language learners?

2. Structured Turn and Talk: For questions with multiple correct answers or that require longer explanations, train students to work in pairs. Specifically, we want to allow wait time for everyone to think independently. Remember to make clear who will work together and who will answer first, along with when the second person starts. This structure holds everyone accountable.

What it looks like in practice: After being introduced to a second method of solving quadratic equations, students are asked which method they would use to solve a given equation. Since this question requires a long answer, it wouldn’t be appropriate to do a unison response. Instead, I do a structured turn and talk. As I’m circulating the room, I’m listening for student reasoning.

For your consideration: What additional supports might ELLs need to fully participate in this activity?

Desirable Difficulties

Robert and Elizabeth Bjork, researchers at the University of California, Los Angeles, have uncovered a paradox of memory: The more effortless that learning is, the less students remember in the long term. For teachers, this has huge implications for our day-to-day practice. After all, we don’t want students to remember how to convert mixed numbers just today. We want them to remember on the end-of-year test as well (and after that, of course).

Here are two desirable difficulties—as the Bjorks call them—we can start implementing:

1. Spacing (or Retrieval Practice): After you know students understand a concept during a lesson, don’t ask them about it until much later—days, weeks, and even months later. Retrieving this information after a delay will help them retain that information in the long term.
   

   What it looks like in practice: Instead of giving an Exit Ticket on today’s topic, give an Exit Ticket on what you taught the week before. Or, instead of giving a weekly quiz that covers material from the preceding five days, give a quiz that includes material from the previous month. 

2. Interleaving: Practice should intersperse both new and old content. This forces students to retrieve old information and discriminate (both of which strengthen long-term memory).

What it looks like in practice: If students were just taught how to divide fractions, their practice might include all four operations with fractions rather than just division of fractions (assuming the other three operations have been taught). This could happen as classwork or homework.

Note: The goal of desirable difficulties is to make learning effortful so students have to think. The purpose is not to give students previously unseen content so they can “wrestle with it.”

Beware of Overloading

John Sweller, an Australian psychologist, has researched the limitations of human working memory and the implications for new learning. His findings culminated in Cognitive Load Theory, the idea that instruction needs to respect the limits of our short-term memory—i.e., we cannot think about too many new things at the same time.

The ramifications for our classrooms are numerous. Here are two:

1. Identify prerequisite knowledge: Before teaching a new skill, identify and teach those precursor skills needed to execute the target skill.

   What it looks like in practice: If I want students to compare fractions using benchmarks, I need to build knowledge of the benchmarks. “When is a fraction equal to 1?” “When is a fraction equal to ½?” Once a student can identify these equivalent fractions, reasonably ask them to use those benchmarks to evaluate new fractions.

2. Worked Examples: Work through an example of the desired concept in front of students before asking them to do it.

What it looks like in practice: If the question is: “A jar has three red marbles and two white ones. What is the probability of picking a red marble at random?” As you work through the example, you might say: “There are a total of five marbles because three plus two is five. There are three red marbles. That means there’s a three out of five chance the marble I pick at random is blue. As a fraction, I would write it like this: ⅗.”

There is much classroom teachers cannot control: School budgets, a student’s home life, our colleagues, and so forth. Although we cannot bend time to our will, we can make choices that maximize the time we do have. As teachers, we’re always going to ask questions. Why not ask a question of all students, instead of calling on a few? Similarly, we’re always going to assign classwork. Why not assign practice that will help students solidify old content and retain new skills?

Himilcon Inciarte is an implementation services specialist for Voyager Sopris Learning^®. He worked as a teacher in Boston Public Schools before moving to Southern California. Since then, he has supported the implementation of intervention programs and assessments in the western United States. He believes that, with the right kind of support, all teachers can improve their craft to maximize learning for students.