Inert vs Generative Knowledge.

When we teach math, we usually seem to want to teach procedures without taking time to focus on having them see how everything relates.  The other day, when I read up on curriculum, I ran across a reference to inert and generative knowledge.  I honestly don't  remember hearing about either.  Knowledge was knowledge.

Briefly inert knowledge is knowledge that is not used while generative knowledge is used to solve a problem.  Remember back in elementary when you had to memorize all the state capitals and never did anything more with those?  That is inert knowledge but if you used the information to write to the governor of each state, then it becomes generative knowledge.

There are three types of inert knowledge.  The first is that the knowledge is there but not accessed while the second states there is a problem with the structure of the knowledge.  The knowledge is in a form that cannot be applied and the final is there is an issue with the situational usage of the knowledge.

In math, we often teach students process used to solve  various types of problems and we give lots of practice problems but we do not provide situations that require students to apply the processes to solve problems.  In fact, most real world problems found in textbooks are neat and only require students to apply the math learned in the section.  

Generative knowledge is often referred to as generative learning.  In generative learning, it is believed a student is not going to learn the material as well as when they are able to construct meaning by generating relationships between what is learned and it's usage. In other words, they are generating understanding.  If teachers do know help students generate their own understanding for each new topic or section, then they will know how to use it to solve problems, otherwise each topic or section will be treated as in isolated skill that cannot be applied to problems unless the student is taught to explicitly apply it.

This may explain why students seem to know what they are doing but are unable to apply it when they take the state test, or a district test.  This is because it remains as inert knowledge rather than being moved to generative knowledge.  Fortunately, there are ways to help students to this.  One way is to ask questions of students that make them look at similarities and differences between processes or topics.  Another way would be create discourse that encourages discussion, debating, or generalization.

In addition, it is important to create situations where students can apply the knowledge they are learning so it is no longer inert.  For instance, when I teach solving one and two step equations, I take time to show how the same equation written in a general form can be graphed as a line and how the solution for x and the answer (y) is a point on the line.  In other words take the problem 2x + 3 = 7.  We solve the equation to find x = 2. I teach that x = 2 and y = 7 and that point is on the general line 2x + 3 = y.  

I try to relate topics or concepts to things students have had before but I need to provide more activities and discussions to help students create their own understanding rather than trying to do it for them. It is hard sometimes because they arrive in high school not having had a lot of experience creating their own meaning.   Let me know what you think, I'd love to hear.  Have a great day.