An ASCD Study Guide for Lesson Imaging in Math and Science: Anticipating Student Ideas and Questions to Deepen STEM Learning

This ASCD Study Guide is designed to enhance your understanding and application of the information contained in Lesson Imaging in Math and Science, an ASCD book written by Michelle Stephan, David Pugalee, Julie Cline, and Chris Cline and published in October 2016.

You can use the study guide before or after you have read the book, or as you finish each chapter. The study questions provided are not meant to cover all aspects of the book, but, rather, to address specific ideas that might warrant further reflection.

Many of the questions contained in this study guide are ones you can think about on your own, but you might consider pairing with a colleague or forming a study group with others who have read (or are reading) Lesson Imaging in Math and Science.

Chapter 1. STEM Literacy: The Nature of STEM Teaching and Learning

Before reading Chapter 1, define what it means to be literate in your particular content area or STEM. After reading Chapter 1, how would you change your definition? Why?

Look at the Venn diagram in Figure 1.1. Consider the intersection of Math, Science, and English Language Arts. Pick a problem from your content area and discuss what it would look like if a student met the five standards that intersect all three disciplines (E2, E4, E5, M3, and S7). What would a student's argument sound like (or look like, if written) for the problem you picked if she has a strong handle on all five standards?

Consider each of the vignettes from a science class. Which illustrates students 'doing science" as defined in Chapter 1? Each vignette addresses the 7.P.2 "Understand forms of energy, energy transfer, and transformation and conservation in mechanical systems."

Vignette 1. After showing students some of Rube Goldberg's drawings, a teacher presents students with the task of drawing a similar contraption. Students must choose a task for their contraption to complete from six options given: turn on a computer, open a door, turn on/off a light switch, erase the board, close a flip phone, or sharpen a pencil in an electric sharpener.

They are also given a list of nine simple machines and must use six of those in their drawing: fixed pulley, movable pulley, block and tackle pulley, incline plane, 1st class lever, 2nd class lever, 3rd class lever, screw, and wedge.

Once the drawing is complete, it must be colored and given a title. The last part of the task requires students to identify the simple machine in each step and describe what type of energy is being used, transferred, or transformed.

Vignette 2. After showing students some of Rube Goldberg's drawings, a teacher presents students with the task of building such a contraption that would help an elderly person complete a difficult task. Before students begin, the teacher asks them to identify the various machines in Goldberg's drawings and record the function of each one. Students are provided with a variety of materials that allow them to investigate simple machines and their functions. Next, students are asked to brainstorm a task that they want their contraption to complete as well as identify the simple machines needed to complete the task. Students sketch their prototypes and share their ideas with other groups to receive feedback on their plan. Students can make changes and get feedback from other groups several times if needed. Finally, students begin the process of building their contraptions, documenting how each machine works and noting any modifications needed to be made.

Chapter 2. Beginning the Imaging Process: Unpacking the Goals

Chapter 2 suggests that there are two processes that overlap the STEM disciplines: Modeling and Inquiry. Does your current teaching practice genuinely incorporate those two processes? Share an example of an activity you have used that genuinely involved the two processes.

What is the main concern with current popular use of the word "inquiry," and why is it problematic to the authors?

Does teaching for intellectual autonomy mean that students should work alone? Why or why not? Do you think that all students, including those with disabilities or those who are English language learners, can be taught for autonomy?

Choose one of the websites from the list in Figure 2.6 and explore it for resources.

Chapter 3. Imaging the Launch

What is the main difference between launching a unit and launching an activity? Discuss the relationship between language arts teaching techniques and launching. What other techniques can be used?

Consider the stacking cups lesson from Chapter 2 (Figure 2.4). Which of the following launches maintains the cognitive demand of the activity? Why?

Launch 1 Vignette. The teacher begins the launch by showing the students a plastic cup and saying that she has a lot of these cups to store in a cabinet that is 50 centimeters tall. She wants to stack them (demonstrates stacking four of them) and put them in her cabinet, but she needs to know how many cups would fit in one stack.

She tells students that they will need a ruler to do this activity and asks students how they might measure the cup to find out how tall a stack of 6 cups would be. When she gets some ideas from the students, she tells them that the ideas were very helpful hands out the Stacking Cups instructions in Figure 2.4. She reads it out loud and demonstrates what is meant by the rim (on her cup) and the hold.

Launch 2 Vignette. The teacher begins the lesson by telling the students that her teenage son works as a shelf stocker at the local supermarket. He was asked to place stacks of plastic cups on a shelf that is 50 centimeters long. His shift ended before he had time to stack the cups, but he promised his boss that he would figure it out at home tonight and text him how many cups could be stacked and still fit in the 50-centimeter shelf. He brought four cups home with him, but since he was not at work, he could not just stack the cups until they fit and then count the cups for one stack. So, he looked around the house for some tools and set to work with a ruler, pencils, tape, and a calculator.

With partners, students take three minutes to explore a plan to figure out how many cups would be in one stack to fit inside the 50-centimeter shelf.

After planning time is complete, the teacher calls on students for their ideas and asks them to find some similarities (many students would mention using the ruler to measure the height). Acknowledging the pros and cons of the students' methods, the teacher then introduces her son's strategy by showing them a picture of a cup and pointing out the hold and the rim. Her son claimed, "All I need to know his how tall the hold is and how tall the rim is! Then I can figure out how tall six cups are. I don't even need the actual cups!" The teacher asks them to determine the height of one, two, three, and four cups and then use what they have figured out to find the height of six cups, nine cups, and 20 cups.

How would you change either of the launches in the vignette above to preserve the cognitive demand better?

What contextual features of the stacking cups activity should be highlighted in the launch? What key discipline ideas? What common language needs to be shared?

Pick an inquiry-oriented task that you might teach in the future, and write down how you will launch it to preserve the key features listed in Figure 3.2.

Chapter 4. Imaging Student Reasoning

Name at least three reasons it is critical to anticipate student reasoning, both correct and incorrect, before teaching the lesson.

Find a rich task in your textbooks, one of the websites we recommended in Figure 2.6, or one of the journals in Figure 4.5. Work the task alone in as many ways as you can anticipate and then share them with your colleagues. Or pose the task to a group of three to five students who have yet to learn the concept and have them explain their different strategies aloud.

How does unpacking and keeping the STEM goal for a task in the forefront of imaging lead to a productive whole-class discussion?

What is the difference between selecting and sequencing possible solutions in the imaging process, and why is it important?

What is the difference between social and sociomathematical norms? Do you think there are such concepts as socioscientific norms? Socioengineering norms? What would they look like?

How will you develop the social norms necessary for students to engage in whole-class discussions? For additional suggested techniques, read "Establishing Standards for Mathematical Practice" by Michelle Stephan in Mathematics Teaching in the Middle School.

What counts as an acceptable explanation in your STEM classroom? Do your questions and subsequent student explanations focus on just the facts involved in the task or the facts AND reasons for conclusions? For additional reading on types of justifications, read "Calculational and Conceptual Orientations in Teaching Mathematics" in Professional Development for Teachers of Mathematics.

Examine the funneling pattern illustrated in Figure 5.6. Have you found yourself engaging in this type of questioning? How does the funneling pattern rob students of their autonomy?

Chapter 6. Putting It All Together

When you completed your anticipated responses and compared them to those of the teacher in the text, did you have all of the same responses? Did you have additional ideas?

Based on your answers to question 1, why is lesson imaging within a community of learners beneficial?

Brainstorm how the lesson imaging and implementation in this chapter is the same and different as a typical lesson in your classroom.

Why do you think your lesson implementation might differ from your lesson image? Is that OK? How do you proceed with your next lesson image if the implementation of the current lesson is dramatically different than intended?

What role do symbolizing and diagrams play in lesson imaging and lesson implementation?

When is it OK to walk away from a student who does not have a solution method?

What are the goals of the teacher during monitor time? How do you keep yourself from telling or funneling students to correct answers during monitor time?

Examine the four student solutions in Figure 6.13. Would you have made the same decision the teachers did regarding the task for the subsequent class period? Why or why not?

Chapter 7. Getting Started

What resources, including material and human, do you have at your school that can support teaching for autonomy and lesson imaging? What do you need?

If you are working alone on lesson imaging, create a strategy for finding a teacher or two for collaboration. If you are working with another teacher or two, create a strategy for engaging your principal for support.

What role can a STEM coach or facilitator play in supporting your quest to teach for autonomy?

If you are working alone, what anxieties do you have about teaching for autonomy and lesson imaging? If you are working in a community of learners, discuss your anxieties and get your beliefs on the table. Make a commitment to try at least one unit this year.

What can your administrative team do to support you this year? With your team, create a plan of support including working with students, parents, counselors, and other key stakeholders to understand the change they will see.

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