Every day, scientists, mathematicians, engineers, and technology designers identify problems, explore solutions, make models, test and collect data on these models, and evaluate and revise them—all inquiry practices. However, traditional STEM classes often rely on direct instruction rather than involving students in inquiry practices that are at the core of STEM fields.
The Common Core State Standards, the Next Generation Science Standards, and increased attention to STEM education in K–12 have led to increased funding and the development of new, inquiry-based resources to change classroom instruction. This is all to the good, but it's equally important that teachers use these materials and implement related tasks in ways that preserve the inquiry in lessons.
Implementing inquiry-based STEM lessons requires a different way of planning lessons. We focus here on one key part of a framework we've developed to help teachers plan such lessons: launching a lesson in a way that protects the inquiry (Stephan, Pugalee, Cline, & Cline, in press).
Our Lesson Imaging Framework
Our work draws on a process called lesson imaging (Schoenfeld, 1998) that ideally occurs as a teacher plans a lesson. Lesson imaging involves anticipating the ways in which planned activities will unfold in a real classroom and predicting how interactions with students will likely occur. It includes a number of components that go beyond traditional lesson planning.
Lappan, Phillips, Fey, and Friel (2013) describe the launch-explore-summarize format of a typical inquiry lesson. A teacher launches the activity, students explore and create innovative solution methods, and, finally, teacher and students together summarize the strategies created to solve the problem. When the lesson focuses on an open-ended problem, students might identify many different solution methods and alternative correct answers. They might create solutions the teacher hasn't thought about. Our lesson imaging framework, shown in Figure 1, helps teachers anticipate and prepare for different ways students might think about the problem and the possible correct (or incorrect solutions) they might choose.
Figure 1. The Lesson Imaging Framework
Off to the Duck Races: Planning for Inquiry in STEM - table
STEM Goal(s): |
|---|
| State Standard(s): |
| Cycle 1 |
| Launch (Task presentation) |
| Exploration (Anticipated student thinking, class structure I will use—in small groups, with partners, individually–and potential correct and incorrect strategies or solutions) |
| Whole-Class Discussion (Include tools, symbolizing, technologies, and questions you might pose) |
| Cycle 2 |
| Launch (Task presentation) |
| Exploration (Anticipated student thinking, class structure I will use—in small groups, with partners, individually–and potential correct and incorrect strategies or solutions) |
| Whole-Class Discussion (Include tools, symbolizing, technologies, and questions you might pose) |
| Assessment (Evidence of student learning) |
Effective and Ineffective Launches
So what does an effective launch of an inquiry lesson look like? A good launch preserves a fundamental feature of inquiry-based STEM instruction, the notion of teaching for intellectual autonomy (Piaget, 1948/1973). Too often, STEM instruction focuses on the teacher as authority, even when it uses such "inquiry" techniques as manipulatives and small-group work.
According to Jackson, Shahan, Gibbons, and Cobb (2012), if teachers want to engage students in autonomous problem solving, they should consider four components when imaging the launch of a lesson. They should prepare to discuss important contextual features, key discipline ideas, and common language for key features (terms to define before students explore independently)—and they should be sure their launch doesn't compromise the cognitive demand of the task. This last criteria means that the launch shouldn't compromise students' opportunities for intellectual autonomy.
Let's look at two launches—one more effective than the other—of a problem and student activity called Duck Racing designed to help 7th graders explore the relationship between the diameter of a circle and its circumference.
Launch One: Stealing the Chance for Inquiry
Here's how Ms. Apple introduced this activity to her students:
MS. APPLE: Class, we're going to learn about circles today. Let's go over the parts of a circle again. Does anyone know what to call this part? [She points to the diameter.]STUDENTS: Diameter!MS. APPLE: Correct, this is called the diameter, and the length around the outside is called the circumference. Now I have a story for you. Please follow along as I read.When I was young, my mother bought us a small kiddie pool for our backyard, and my sister and I would play all morning in the pool. Sometimes when we got bored, we would get those yellow, plastic, wind-up ducks that swim across water if you wind them up and release them. One day, my sister (who was three years younger than me) and I got bored with the pool. I had a great idea! I challenged my sister to a duck race! We would each wind up our favorite duck and let them go at the same time. However, I told her my duck's lane would be straight across the center of the pool and hers would be around the edge of the pool.Our neighbor, Tommy, saw this and ratted me out! He told my sister that this was not a fair race. Do you agree? How many laps would my duck have to travel across the pool to make it a fair race with my sister's duck?So which way is longer, class—across the pool or around the outside?STUDENTS: Around the outside.MS. APPLE: OK. Now I want you to find out how many times the diameter will fit around the outside. I'm going to give you each some string and a picture of four different pools. I want you to use the ruler to measure the diameter of each pool and record your measurement in inches. Then, put your string around the outside, like this [modeling it], and measure the length with your ruler. Record that circumference. Do that for all four pools and see if you can figure out a rule about how many times bigger a circumference is than a diameter.
Ms. Apple chose a nice, open-ended inquiry lesson to help students create meaning for the relationship between the circumference and diameter of a circle. However, her launch of the lesson is so prescriptive and direct that it robs students of their chance to do autonomous problem solving.
In Ms. Apple's school, administrators require teachers to write each lesson's objective on the board, making students aware of the goal before problem solving happens. So Ms. Apple states the goal of the lesson and reminds students about the characteristics of a circle. In addition, the introduction loses excitement as Ms. Apple merely reads through the context, with students following along. When she asks students which way is longer, she presumes that everyone views the two lengths as different. Some students may think it's a fair race featuring equal lengths, but her question delegitimizes such thinking so the idea never gets discussed.
Finally, Ms. Apple tells students the strategy to use, including the tools, measurement unit, and step-by-step method. Such direct instruction compromises both the cognitive demand of the task and the students' autonomy in choosing their strategy and tools. The teacher becomes the recognized authority and source of the reasoning, rather than the students.
Launch Two: Inviting Students to Explore
Now let's look at how Mr. Peppers introduced the same task.
MR. PEPPERS: Class, summer vacation is coming up soon. Thinking about my vacation, I remembered some of the cool things my sister and I did when we were kids. My mom bought us one of those kiddie pools. Do you know what I'm talking about? Anybody ever have one of those?ZACH: I had one of those! [Other students offer comments as well.]MR. PEPPERS: What do they look like?CARRIE: Mine was round, like a circle, but it wasn't so deep.MR. PEPPERS: Yeah! Like a circle! Well, we played and played all day in the pool, but eventually we got bored. So, one day I thought up a new game. My sister was annoying me, and I challenged her to a duck race. You know those little plastic ducks that have the wind-up stick on them? When you wind them up, they swim across water. I said, I'll make my duck go across the pool and you make yours go around.JULIENNE: That's not fair! [Other students agree.]MR. PEPPERS: Why not?DARIUS: Because it's longer around the outside of the pool!MR. PEPPERS: Oh, OK! You're on to me. So, how would I make it a fair race? About how many laps do you think my duck should swim across the middle to make it fair? [Students conjecture 2, 3, and 4; Mr. Peppers records those on the board.] I want you all to do a little exploring to figure it out. I have some pictures of pools.GAVAN: Does it matter how big the pool is?MR. PEPPERS: What a great question! Do you think it's going to matter? Well, you read my mind. I have different sized pools, and I'll let you explore that question. You have rulers; I'll give you a string and some pools, and you figure it out. If you need a different tool, please let me know.SARA: Do we use inches or centimeters?MR. PEPPERS: Another good question. Do you think it's going to matter? Why don't you experiment with that, too?
Notice the more motivating introduction. Instead of reading the problem, Mr. Peppers tells a story. He personalizes the launch to engage students in the problem's context. The students provide the information that the relevant features of the problem are the circular shape of the pool and the different distances the ducks travel. Fairness is the issue at play, and Mr. Peppers capitalizes on his students' desires for fairness by asking them to identify the number of laps a duck would need to swim across the middle to make the race fair.
Mr. Peppers also leaves certain key discipline ideas invisible and highlights others. He doesn't inform the students what relationship they are going to explore before they start. He will formally explain the relationship they have discovered (C = πd) later, during the whole-group summary of students' explorations. For now, students only need to understand that they'll be measuring two distances. It's fine for the students to wonder whether the measurement unit and the size of the pools might make a difference in their exploration.
Mr. Peppers leaves the introduction of some key vocabulary for the summary of students' explorations, but he develops common language by noting that the pool is a circle and naming the various tools students can use. Students bring in the measurement vocabulary of centimeters and inches.
Finally, the teacher maintains the cognitive demand of the task. Students have intellectual autonomy because Mr. Peppers doesn't give direct steps for solving the problem. He doesn't tell students how to use the ruler and string, what units to use, which pools to explore, or how to record their results. So students use a variety of strategies to determine that the circumference is a little more than three times longer than the diameter. Some don't use the ruler at all; they merely cut the string to the length of the diameter, iterate the string around the outside of the circle, and mark it each time. Others measure the diameter (in inches or centimeters) with the ruler, then place the string around the outside of the circle and measure the straightened string. Still others cut the string to the length of the circumference and run it back and forth across the diameter, noting that it overlaps three times and a little extra.
Genuine Opportunities
Launches like Mr. Peppers's motivate students to ask mathematical questions about the context of the problem, allow them to decide which tools and recording devices to use, and maintain high cognitive demand as students create mathematical relationships with little interference by an adult. As a consequence, student engagement is higher. The whole-class discussions that occur after students' explorations are more mathematically rich. And students have the opportunity to participate more genuinely in the inquiry practices of the STEM disciplines.
