From Thinking To Understanding Via Headlines

 In math webinars and trainings, I keep hearing that both we and the students must use visible thinking.  Of course the first thing that always pops up in my mind is the techniques used during reading.

When I taught reading, I had to make my "thinking visible" to my students.  In other words, I had to "think" out loud so they could see how I figured out the information.  That isn't always how we do it in math.

I've heard it said that understanding is the result of thinking and not a type of thinking at all.  Based on that, students have to use thinking to get to understanding.  It is also said that students are most engaged when they are involved with minds on thinking.

It is also said that learning is a direct result of thinking rather than memorizing steps or mathematical facts.  It is possible to solve equations while following algorithms but that does not guarantee understanding or learning. So let's look at some ways to help students develop from thinking to understanding.

1.  One way to do this is by using headlines which can be used in multiple ways.  This exercise uses the idea that students can capture an idea, concept, or topic in a few words.  Headlines are written with only enough essential information to give the reader an idea of what is being shared in the article  while capturing the attention of the reader.

To use it in the math class, you might have students write a headline which summarizes the most important idea on a particular topic at the beginning of class.  An example might be "Pythagorus quoted as saying "a^2 + b^2 = c^2Then later on, at the end of class or perhaps the next day, ask the students how they might change the headline after the lesson before having them explain how the headline differed.

A good way to implement this use of headlines is to have students think about the big ideas or important topic for the section.  Then let them brainstorm in groups as to what the big idea or central theme to help clarify thing.  Then in pairs, they create the headline.  Once everyone is done, they can share the headlines as a way of promoting understanding.

Two advantages to having students use this activity is that it provides a quick assessment of understanding and it means the students have to focus on the concept rather than using catchy phrases. In addition, this activity lays the foundation for students to be able to connect to other future topics.


Another way to use it is to create a short headline type story without the question.  Have the students read the story and then create possible mathematical questions that could be answered using the information.  An example might be:

1. "Worldwide, about 10 million metric tons of olives are produced each year.  A million metric tons are used for table olives and nine million (93 percent of the total crop are pressed for olive oil."

What mathematical questions could you ask that can be answered by the information in the headline?

Another way to use the headline story is to include the question but have too much or not enough information so students have to figure out what information can be used to answer the question if there is too much or what information is needed if there is not enough information.  If the story has too much information, have students pose other questions that can be answered with the information. If the story does not have enough information, ask students to create questions that can be answered with the information given.

This can easily be done in class or via distance.  Let me know what you think, I'd love to hear, have a great day.