Math Activity Design

Students can interact with simulations (sims) at the beginning of an instructional unit to explore which variables influence the mathematical system, and relate what they learn to their prior knowledge. Such interaction supports the construction of mathematical models. Students can also use a sim at the end of a unit to reinforce what they have learned and apply this knowledge to solve problems.

Research shows that students will benefit the most from sims when you give them a high degree of autonomy over their learning, and when you encourage them to explore questions with the sims individually or in small groups. Structured interaction with sims is especially valuable when you have learning goals in mind that target skills and procedures. For example, you can design scenarios that allow students to control system variables. Students can use PhET sims in the following setups:

• Guided-inquiry activities using worksheets during class: Design short activity worksheets focused on sims for student groups to work through in class. You can check in with the whole class and facilitate class discussions periodically during the activity to ensure that students are all mastering key ideas before moving on.

• Homework assignments: Assign homework questions that require the use of a sim as part of pre-class preparation before a topic is covered in class, or as a follow-up in which students dig deeper into a topic you may have demonstrated that day. The design of PhET sims allows students to engage in mathematical thinking, even without the presence of an instructor to guide them.

• Combined physical and digital manipulative activities: PhET sims can complement typical physical manipulative activities (e.g., working with coins, geometric objects, etc.) to help students expand their repertoire of representations and transfer knowledge across different domains within mathematics.

• Guided-inquiry activities in remote learning: Comprehensive mathematics education requires that students engage with mathematical thinking in different contexts, and PhET resources are among your best allies, particularly for remote learning. You can use digital worksheets to engage students in an inquiry activity, and you can easily integrate PhET sims with learning management systems and other tech tools to make the experience more personalized and collaborative while providing quick feedback on students’ understanding.

Note: PhET strongly recommends that teachers avoid using “cook-book” style activities, in which teachers provide lists of detailed, explicit instructions on how to modify the sim, and what to observe, as it can limit student exploration and engagement.

Now, it’s time to step into the role of a student and work through a PhET activity. This will give you an understanding of what it is like to experience a simulation for the first time and how you might progress through it, so you can understand what your students will be going through in your activity.

Imagine you are a 7th grade math student - you know how to identify integers as positive or negative, you can plot integers on a number line, and you understand absolute value as the distance from zero. Today, you’ll use Build an Atom to use this knowledge in the context of atomic charge.

Open Play with Sims

Begin by openly playing around with the simulation for about 5 minutes. Figure out how to use it, find the controls, and take note of what kind of questions you have. We call this “open play time”.

• What can you do with this sim?

• What questions do you have?

Now that you’ve gotten to know the sim, listen to how a discussion following open play time with students may be facilitated.

Student Activity Sheet

Next, you’ll be working on #2-12 of the activity below as a student.

Afterward, review the lesson plan below to get an idea about how this activity can be implemented in a classroom.

• Did you achieve the lesson’s learning goals, and how do you know?

Reflect on the flow of the lesson you just experienced and how it was structured:

• What characteristics and structure do the activities have?

• What skills and attitudes are also fostered by these types of activities?

• What should be your role and that of your students in such an activity?

There are many ways to teach using a PhET sim, but the lesson presented in the previous section follows a simple structure that is easy to replicate:

• Open play: students playing with the sim and learning how to use the sim without guidance

• Share-out: students share how to use the sim and discoveries they made with teacher facilitating

• Activity sheet: students work through open-ended challenge prompts that encourage multiple correct answers

• Discussion and check-in: students pause periodically to discuss with peers or the whole class while the teacher circulates and checks in with individuals and groups

• Summary discussion: teacher facilitates a discussion where students share their thinking and teacher guides students toward the learning goals

• Funky Functions Activity Sheet

  

• Variable Expressions Activity Sheet

  

The sim-centered learning experience should be planned and organized in a worksheet in a way that encourages inquiry. The worksheet should allow students to explore, gather and analyze data, and draw conclusions on the basis of reasoning and analysis, and achieving this can be done with the use of open-ended Challenge Prompts.

Writing an open-ended challenge prompt can be really challenging! The goal is to keep the prompts open enough that you aren’t instructing students on how to use the sim, but specific enough that students are achieving your learning goals.

Use the document below to support you as you try writing Challenge Prompts throughout the following activity. (Avoid looking at the PhET team’s recommended revised prompts until you have tried the activity on your own!)

For each sim activity:

• Review the learning goal and the original prompt. Consider how students will end up using the sim.

• Try modifying the prompt to be more open-ended but still achieve the same learning goal.

• Listen to what some teachers came up with.

Example: Proportion Playground

"In this example, all students will be “answer-makers” because they are following the directions and finding an answer. If every student is doing the same thing with the sim, it is not taking full advantage of the exploratory nature of simulations. If every student is trying to find the same answers, it becomes harder to have a rich discussion."

"In this version of the prompt, students are guided to find structure in their necklaces, and notice patterns in the numbers that produce the same bead pattern. All students get to the same learning goal as above, but by comparing results, students can easily see many iterations and use their own language to generalize their observations."

1. Build an Atom

2. Area Model Multiplication

3. Graphing Lines

4. Function Builder

5. Unit Rates

Remember, there is not a “correct” Challenge Prompt or a “best” activity worksheet. Prompts and worksheets might work differently for each classroom. The modified Challenge Prompts here are only examples that can guide you to take advantage of the characteristics of PhET sims and the activity design tips mentioned in this workshop. However, writing good activities is a process that involves regular adaptation and depends on the nature of your students.

A concluding activity is important for determining if students have achieved the learning goals. Students should be able to communicate their answers and justify conclusions with evidence they have collected during the activity. Additionally, students should be able to answer questions about scenarios other than the exact one used in their activity, thereby demonstrating their ability to apply their understanding to new contexts.

Verifying students’ achievement of learning goals can be accomplished in several ways, such as the following:

• Including final questions on the activity sheet that help students synthesize conclusions.

• Using Concept Questions and facilitating a final oral discussion with the group.

• Preparing a couple of written questions as an “exit ticket” for students to submit.

As you bring everything together, don’t forget to allow time for “teachable moments”, to highly unexpected student discoveries, and to incorporate their learnings into the bigger picture. See one example below of how a skilled teacher does this.

"If you are taking this course independently, we recommend that you complete the following activities and save them to your computer. (Should you later decide to enroll in a facilitated version of this course, you can then submit these assignments to earn a certificate)."