When I am preparing a task for my classroom, I first create a rubric (pictured above). I consider what the goals of the task are: are students generating ideas about how to solve a new type of problem? Are we solidifying understanding they should already have? Are they creating a new representation or algorithm? I do not always use all 4 pieces of the rubric, but instead use the ones that align most closely with my mathematical goals. I define each of these at a beginning, developing, accomplished, and exemplary level.
Conceptual understandings refer to the actual extent to which students understand the mathematics, as evidenced by their work and explanations. Justification and thinking I separate from this, as it refers more to the level of thinking presented in a students answer and in the discussion phase. When developing a rubric, consider the possibility a student is valiantly defending a wrong answer. While their conceptual knowledge might be low, their justification and thinking may still be high-level. I consider the terms and notations (equations, use of correct vocabulary) and the use of tools when applicable (ten frames, hundreds charts, fingers, etc.).
Once I have aligned the task to the mathematical goal, I am ready to think about how I will formatively assess to determine student progress. This is where the "formative five" come into play:
1. Observation: Usually a simple check list, this type of formative assessment allows teachers to quickly assess an entire class or large group. Using the rubric, pick a few things you can check off as you circle the room asking assessing and advancing questions. Prepare your rubric with student names and the few things you are looking for and you can quickly note a YES/NO during the lesson. This is particularly helpful if you want a snapshot of the group of students overall.
2. Interviews: Picking 2-3 key assessing and advancing questions, zero in on students you are seeking to understand better. Record their answers to each, calling back to the rubric to determine how they are developing understandings of the content.
3. Hinge questions: Posed at a key moment in the lesson, a hinge question is given to the whole class. A hinge question can determine whether or not the class is ready to move on, or needs additional time to explore the content at hand. It can be conceptual or procedural. Check these answers immediately and determine next steps.
4. Exit tickets: An old favorite, an exit ticket provides the opportunity for students to show their thinking on a similar problem or problem type that they explored during the task. Graded after the lesson, teachers then determine where the next lesson needs to go.
5. Show me: An obtrusive form of assessment that happens during the lesson. Stop a few students in their work, and ask them to show you their thinking physically, on the current or a different problem. Select these students intentionally.
The task cycle requires many opportunities for formative assessments throughout to determine where the learning goes next. Using rubrics and the formative five can help closely monitor student learning towards key mathematical goals!
Yours,
Ms. M
