Mary Rack, Mendocino High School, CA
As a member of the assessment writing team that met in Sacramento in July, I have dubbed us the Assessment Week Warriors. Working in teams by course, we were able to choose what we felt were the priorities for the week. Different course teams chose different areas of focus, but we all realized that writing quality assessment is a difficult, enlightening, and creative task. To help us get started, Judy Kysh presented some strategies for creating assessment tasks for students.
First, Judy suggested we ask students to show more than one way to solve a problem. For example, a student could use the rewrite, look inside, or the undo strategies to solve the equation (x – 7) 2 = 9. Different strategies create flexibility in math thinking.
A second strategy for creating an assessment task is to ask students to “Pause, Think, and Describe a Strategy”. Judy suggests a teacher should ask students to “Tell what the problem says and tell what you are going to do” before solving the problem. An example of this strategy is to ask students to identify the operation, and how they will “undo” the equation, all before solving. For example, given the equation (1/3 ) x =7, students should identify the operation, and use a full sentence to describe it, such as “The x is multiplied by 1/3” or ”x is multiplied by one and then divided by three.” For the “undo,” students might state “Both sides are divided by 1/3” or “Both sides are multiplied by the reciprocal, 3”. And lastly, the question “Why do you divide both sides by 1/3?” or “Why do you multiply by 3?” gives students an opportunity to communicate to their teacher mathematically, justify their thinking, and in a class discussion, critique the thinking of others.
The “Work Backwards” strategy gives students an answer such as x = 5/8, and asks students to write an equation that will take at least four operations to solve, that will give that answer. Another “Work Backwards” assessment task could ask students to write two pairs of linear equations: one set of equations that intersect at a specified ordered pair, and another set of equations that are parallel lines.
Judy’s other ideas include asking students to give an example of a mathematical concept, asking students to identify and explain errors in a solution, and confronting points of confusion students have about different math concepts by asking them to justify their solution and use multiply representations to justify their reasoning. This last one became known simply as Points of Confusion problems, or PoCs.
Buoyed by Judy’s suggestions, we set to work. Within our room, writers would talk about “Judy-fying” our problems so we could learn more about our students understanding. Due to the flexibility of the structure of the week-long assessment writing project, we were encouraged to think our tasks through, communicate our ideas to create an exemplary assessment product that would be accessible to diverse or marginalized groups of students, engage all learners in STEM related real-life problems, and assess the CCSS content and practice standards.
Our week closed too quickly. But I was happy to note that the teamwork was very similar to the teamwork we facilitate in our classrooms. We were independent learners using discussion and questioning to discover and experiment in a cooperative learning environment where we viewed, listened, responded, reflected, edited, problem-solved, summarized, and reinforced effort while producing our assessment tasks.
