How STEMscopes Works: A Teacher’s Introduction to STEMscopes Math Lessons

STEMscopes is built around an instructional concept pioneered by Rodger Bybee in the 1980s and further refined over the subsequent decades. In this model, called the 5E model, each scope (lesson) follows a sequence of 5 phases:

1.     Engage
2.     Explore
3.     Explain
4.     Elaborate
5.     Evaluate

In science subjects, these phases are completed sequentially with little doubling back. In math, though, teachers cycle through the three “middle” phases—Explore, Explain, and Elaborate—in several iterations to make sure students understand the concept fully. So you might think of these three as being the heart of the lesson, “bracketed” by the Engage and Evaluate phases. 

STEMscopes adds two other optional elements that teachers can use, depending on their students’ needs: 

•       Intervention
•       Acceleration

In this guide for teachers about the STEMscopes Math approach, we walk through each of the 5Es and the IA. For each, we’ll describe its purpose, its typical content, its relationship to the other phases, and the elements provided to teachers by the STEMscopes curriculum.

Before diving into the five E’s, though, we should mention the teacher support resources provided in the Home section of each scope. Home helps teachers prepare to use the 5E + IA model to teach the particular scope. It’s the first place to go for lesson planning materials and helpful content background. In STEMscopes Math, the Home section includes:

•       A Scope Overview, summarizing the concepts covered in the scope, refreshing your knowledge of the content, and reviewing the relevant state and other curriculum standards that the scope supports
•       Content Support, including background information about why a concept is being taught a certain way, what students have already learned, and what they will learn next
•       Standards Unwrapped, this verbs, nouns, and key concept breakdown helps teachers dissect the language of the standard

The 5E Components

Engage: An introduction to pique students’ curiosity, uncover student misconceptions, and assess prior knowledge. Each Engage includes several components:

•       A Hook activity that introduces the scope to your students, so they can connect the overarching concept that will be taught in the scope with their personal experience of the world. Engage activities are always interactive and often hands-on, especially in earlier grades. Additional Hook activities are provided for use on subsequent days of the scope, to re-engage your students in the topic.
•       If you choose, you can use an APK (Accessing Prior Knowledge) during the Engage to determine whether your students are ready for the lesson. If not, you can circle back to previous standards to review the foundational knowledge they’ll need to move forward with the scope. Foundation Builders are provided within the Engage teacher materials to review prerequisite knowledge with your students.

Explore: The heart of inquiry-based instruction, where students explore a concept through hands-on experiences and investigations. Each scope contains several Explores. 

•       For each Explore, teams of students collaborate on hands-on Explore activities. 
•       STEMscopes develops understanding by progressing from the concrete to the representational to the abstract (the “CRA model”). For earlier grades, this means that students start with hands-on experiences with concrete objects; as they progress, students transition to pictorial models and eventually symbolic representations of mathematical concepts that use numbers, symbols, and notations. 

Explain: A series of elements that help students develop a more in-depth understanding of the concepts they investigated in the Explore. Explain elements include

•       Picture Vocabulary activities to develop vocabulary and develop student fluency in math-specific terminology, conventions, and language used in discussing math concepts
•       Show What You Know exercises, completed by each student independently to demonstrate their understanding of the concept
•       My Math Thoughts writing practice, to integrate mathematical learning with vocabulary and the process of inquiry
•       An Exit Ticket that a teacher applies as a quick test of student knowledge, to determine whether instruction needs to be adjusted the next day

Elaborate: Opportunities for students to practice and integrate what they have learned about math in the scope with other knowledge and skills. Elaborate elements include:

•       Fluency Builder activities, including gamified practice of math skills
•       Spiraled Review, where students practice through games or independent activities 
•       Problem-Based Tasks, where concepts learned in the scope are applied in a real-world context
•       Math Story, in which students practice finding information they need to solve a problem in a text-based description of a problem
•       Interactive Practice, giving students another hands-on opportunity to see the concept in action
•       Career Connections that profile people using mathematics in real-world work settings 
•       Life Connections is meant to be an avenue that introduces your students to careers and everyday life experiences that highlight the mathematical concepts being learned in the classroom.

The Explore, Explain, and Elaborate phases are designed to complement each other as they support student learning. You will typically weave all three together within a lesson plan, and use multiple Explores in succession. So a typical order might look like this:

1.     Explore I
2.     Exit Ticket
3.     Explain elements
4.     Elaborate elements
5.     Show What You Know
6.     If students demonstrate understanding of Explore I, move on to Explore II, and so on.

Using the wide range of elements provided by the curriculum, the teacher has the flexibility to cycle back and forth through Explore, Explain, and Elaborate elements until students have a solid understanding of the concept and are ready to move on to the next Explore within the scope.  

Evaluate: Alternative approaches to assessing student learning and determining whether Intervention or Acceleration is warranted. The teacher can choose among three assessment tools:

•       Decide and Defend, an assignment where students are prompted to write an argument using mathematical evidence and reasoning
•       Standards-Based Assessment, an exam that simulates the rigor and questions types found on state tests in multiple choice and “gridable” formats
•       Skill Quiz, a traditional multiple-choice or short-answer test assessing knowledge about the topic

The “I & A” of the 5E + IA Model

The STEMscopes model augments Rodger Bybee’s 5E instructional approach by adding two enriching resources for learners: Intervention (I) and Acceleration (A). Based on each student’s Evaluate results, the teacher may decide to move students into either Intervention, if they need more help to master the concept, or Acceleration, if they fully grasp the concept and are ready to be challenged to explore further.

Intervention: Small group intervention and independent activities for students who need additional instruction and practice to gain full understanding of the concept. A Checkup assessment is provided to evaluate student understanding. Students can progress from Intervention to Acceleration if they master the knowledge and skills.

Acceleration: Resources and activities that enable students who have mastered a concept to explore it further, look at it from a different perspective, or reinforce what they have learned. Elements include Math Today and Create Your Own, and students can also be assigned an Elaborate that was not used in class. 

All the components of the STEMscopes Math 5E + IA instructional model provide teachers the flexibility and tools to create a meaningful learning experience for our 21st-century students. In STEMscopes Math, student learning is rooted in real-world scenarios, and the goal is for students to develop a deep understanding of mathematics so they can reason through a situation, collect the information necessary to solve a problem, and use the mechanics of math to develop a reasonable answer. They also learn the vocabulary and discourse skills they need to communicate and defend their reasoning, skills that will be essential for living and working in the world of the future.