When we think about assessment, we want to figure out what students know, what students can do, and what students understand. Often, we focus on the first two because they’re easier to measure, easier to write, and frankly, easier to grade. Conversely, we think that we can only get at students’ understanding by having them give long written explanations in an essay style format. The good news is that by mixing up our verbs, we can assess deeper understanding even in short questions. We like to think about verbs in three categories.
Know and Do
To assess what facts students know or skills students have, we can use questions from this first column. These questions often ask students to simply know the definition of a word or apply a particular procedure. For example, students could be asked to solve a linear equation, identify the y-intercept of an exponential graph or classify a triangle as equilateral, scalene, or isosceles given its side lengths.
While every assessment will have some questions that fall under the “Know & Do” column, we want to provide some strategies for writing higher-level thinking questions corresponding to the final two columns of the table.
Understand and Apply
With these questions, we want to see if students understand the mathematical concept, or big idea, rather than just being able to perform a procedure or state key facts. An easy way to do this is to add a “How do you know?” or an “Explain” or “Convince me that you are correct” to the end of a know/do question. It could also entail asking students to represent their thinking using a visual or diagram. Application here, refers not just to real world application, but the ability to demonstrate understanding on a problem they have not seen before: for example, finding the value of a parameter in an equation to meet a certain constraint, rather than just being given an equation and asked to identify the y-intercept, zeros, asymptote, etc.
Connect and Extend
Using this set of verbs, we can assess deep understanding by asking questions where students must generate something new, break a complex problem down into smaller components, be “clever” in choosing a solution path, make connections among ideas that seem unrelated, make a prediction, or extend their thinking to consider other cases. The goal is to ask questions that connect learning across multiple lessons.
Examples
Topic: Key Features of Quadratics
