Instructional Models for Math

Instructional models refer to the structure and delivery method of a lesson. Lecture and "I do, we do, you do" are traditional instructional models that still have their place in education, but should probably be used sparingly if the goal is to actively engage students in standards-based lessons. Instructional models and lesson planning guides should compliment each other, even to the point of redundancy. For example, the "Launch, Explore, Summarize" model below and the Thinking Through a Lesson Protocol share many features and guiding questions. Whether you eventually use one or both of those resources, the key is to focus on creating a focused, engaging, and cohesive experience for students.

These and other tools are part of the District Sample Curriculum Project's (DSCP) Phase IV focus on instructional strategies.

Launch, Explore, Summarize

Source: Connected Mathematics Project (CMP), Michigan State University

The "Launch, Explore, Summarize" instructional model supports an inquiry-based, problem-centered type of teaching. Teachers are expected to shift the doing of mathematics to the students, while they guide, interrogate student thinking, and facilitate sensemaking. The model is structured around three phases of a lesson:

• Launch: The launch of the lesson should connect to prior knowledge and present students with a challenge.
• Explore: The explore phase of the lesson gives the teacher time to focus on individual student needs and plan for the summary.
• Summarize: In the summarize phase of a lesson, teachers orchestrate a discussion and reflect on student learning.

CMP's planning guide has suggestions and guiding questions for lessons using the Launch, Explore, Summarize instructional model. There are strong similarities between this planning guide and other lesson planning guides common in mathematics education.

3-Act Tasks

Source: Dan Meyer

Dan Meyer's "Three Acts of a Mathematical Story" presents a lesson in three parts:

• Act One: Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
• Act Two: The protagonist/student overcomes obstacles, looks for resources, and develops new tools.
• Act Three: Resolve the conflict and set up a sequel/extension.

The basic structure of a 3-Act Task has some similarities to Launch, Explore, Summarize, but usually distinguishes itself through the use of media and emphasis on student mathematization in Act One. Instead of presenting students with the question to be answered, students should be confronted with some phenomenon about which they can ask mathematical questions. Dan maintains a repository of 3-Act Task examples on his website.

5E Instructional Model

Source: BSCS

The 5E Instructional Model was developed in 1987 for use in science instruction, but it has proven adaptable for mathematics as well. The name "5E" comes from the five phases of a lesson:

• Engagement: students' prior knowledge accessed and interest engaged in the phenomenon
• Exploration: students participate in an activity that facilitates conceptual change
• Explanation: students generate an explanation of the phenomenon
• Elaboration: students' understanding of the phenomenon challenged and deepened through new experiences
• Evaluation: students assess their understanding of the phenomenon