## System of Two Masses – Reflections

### Why is this science?

In this episode, we see the students doing theoretical science, seeking coherence across their understandings of multiple physical situations, including a previous problem that involved equal and opposite forces and this problem, with unequal forces but equal accelerations, as well as additional situations they raise along the way. They do not simply settle on what’s been signalled to be the correct answer, but rather they work to reconcile a conflicting line of reasoning.

### What contributed?

#### 1. The students and instructor show care for each other.

Throughout the episode, the students and instructor show how they care for each other, their ideas, feelings, and well-being. They express encouragement and empathy for each others’ participation, and the instructor makes space for hesitant voices. Examples include Jared’s checking with his peers about the premise of his argument, Korri’s summarizing both Mischael and Jared’s arguments, students encouraging Alejandro at the board, shouting “Keep going, keep going” when he starts to doubt his math.

#### 2. The problem raises multiple ways of thinking.

There are multiple ideas to be heard. In part because this problem is similar to another the students worked on recently that involved equal and opposite forces, this problem cues multiple connections and patterns of reasoning for the students. These include an sense of equivalence that’s maintained as objects move away from each other at equal rates, considering the two objects as a single system or as separate, different possible references points for defining “movement”—the midpoint or the center of mass—and different mathematical strategies for considering proportionality. They also connect to various physical analogies, including the image of an expanding pen, and pairing a water bottle and phone as a system of unequal masses.

#### 3. The students engage with each others’ thinking.

With multiple ideas in play, the students work to address and convince each other, trying to account for their differences. Mischael’s role is key, in his persistence in expressing ideas that are contrary to others’, including the instructor’s. For Mischael and for others, the discussion needed to continue to resolve the question to mutual satisfaction.

#### 4. The students are willing to be wrong.

Students seem to see changing one’s mind as OK or even good. On at least three occasions, students communicate that their thinking changed or describe how it changed. For example, at the beginning of the episode, Jared narrates the evolution of his own reasoning from before to after some class discussion.

#### 5. The students engage playfully.

The students show excited interest, as in a friendly competition, raising their voices, at multiple points clamoring to speak or interjecting, responding to what they’re hearing and thinking with exclamations (“Yes!” “No!”) or laughter or groans. The discussion gets intense and focused at times, but the students keep breaking the tension with smiles and jokes, signals of camaraderie.

#### 6. The class sits in an open circle.

The seating arrangement gives students ready access to the board and allows students to see and converse with one another. Much of the episode consists of students at the board and students looking intently at each other while talking and listening.