By Michael Telek
Deep in the heart of Music City USA, Dr. Ricki Gibbs and his team at Warner Arts Magnet Elementary are engaged in some professional development with the Institute for Learning. Gathered in small groups, they are shown this picture and asked, “Which one does not belong?” (WODB) It seems like a simple question, but is it? Check it out and consider which you think doesn’t belong.
Did you eliminate 4 because it is an unfamiliar diagram? Or, maybe you eliminated 3 because the expression contains parenthesis. You may have elimated 2 because it contains 3 factors. It’s possible that you struggled to eliminate any of them because they all equal 60.
So, what’s the point of asking a room full of educated adults, adults just like you, a question like this? A question that can also be posed to students. Well, it has to do with the cognitive effort employed to make connections among the different representations and reason how they may or may not be related. The mental acrobatics a person uses to connect and reason is unique to them because it is based on their existing knowledge and set of experiences. No matter which you eliminated or kept, the work of coming to a decision is the critical part!
More About “Which One Doesn’t Belong?” and Similar Activities
These types of activities are beneficial for many reasons, e.g., they can be used for formative assessment purposes before, during, and after the study of a concept.
Additionally, they
- offer opportunities to apply existing knowledge.
- provide low risk engagement opportunities with no/few wrong answers.
- afford opportunities for every student to answer, to weigh in, to vote.
- require the use and connection of representations.
- require making and supporting a claim.
- focus on the “why” of the claim, not agreement or disagreement with the claim.
"If we see entry points and how to solve this problem differently, think about how our scholars, who don’t have the knowledge background that we have, see it” said Dr. Gibbs “That ‘a-ha’ moment was, how are we going to find ways to onboard, give entry points, to scholars that show them how to attack the problem but not show them just one procedure to do it.”
IFL Math Fellow Kristin Klingensmith explains, “We use Which One Doesn’t Belong? activities and other similar activities for a variety of reasons. The activity is not routinized or procedural in nature. Their design provides an opportunity for students to draw on their prior knowledge and from their experiences in and outside the classroom.” She goes on to say, “One of the most important things about activites like this one is that there is more than one way to reason about how the represenations are connected and which can be eliminated. The mental process that a person, school-aged or adult, uses to make a determination is one that is unique to them. The beauty of activities like this is the rich conversation that grows out of making connections between and among the four representations.”
Purposeful Questions and “Which One Doesn’t Belong?” Activities Using purposeful questions can help tie the discussion to the mathematical structures that are illustrated by the representations. Here are some that could be used with this WODB.Questions to Elicit Student Thinking
Questions to Connect Representations and Explain Mathematical Reasoning
|
|---|