Sometimes, Always, or Never.

 

I have occasionally run across activities involving statements that students classify as sometimes, always, or never true.  In other words, is the mathematical statement always true, only true some of the time, or never true.  An example might be "A cube has the same length for all edges."  This is always true.  

They were always interesting but I wondered why one should use an activity such as this.  It turns out, there are good reasons to use this type of activity, especially for assessing student knowledge, especially  when students are expected to provide justification for their answers.

First of all, this activity is a good way to determine if a student is over generalizing or under generalizing a mathematical concept based on their justifications.  It also provides them the opportunity to think about their own understanding. In addition, this activity can help students improve their understanding of various concepts. 

When students have to come up with examples or counter examples as they try to prove their answer, it encourages mathematical thinking.  If this is done in a small groups, students have to use mathematical conversation when explaining their choices. 

The sometimes, always, or never can be used at the beginning of a concept to establish how much students know about the topic, or it can be used later on after they've had a chance to learn the material to see how much they really understand about the concept.  If the activity is used before, look at statements that focus on the concepts that will be taught.  If used after the lessons, choose statements that focus on what they learned.

One of the best ways to do this is to give students access to the statements so they can answer the questions individually.  Then place them in small groups so students can discuss their answers using the conversation to come to a consensus on the answers of always, sometimes, never.  Finally, go to a whole group so the students can discuss the statements as a group, sharing their examples and counter examples.

Another way to use sometimes, always, or never is to use it as part of journaling in math. Provide the statement for students to determine if it is always true, sometimes true, or never true.  Let them write their answer in their journal but it must include examples and or counter examples to explain their thinking.

Where the sometimes, always, or never activity offers itself as a better choice over true or false activities because there always seems to be the concept or topic that shows up is sometimes true so its hard to determine whether you want to use true or false.  

It is possible to find or develop statements for all levels and types of mathematics.  It might cover properties, the application of definitions, patterns, and so much more.  This activity is one that can be done as needed and is a wonderful way of having students practice mathematical thinking and mathematical conversation.  In addition, it helps students learn to express their thinking in an understandable way.  Let me know what you think, I'd love to hear.  Have a great day.