Generative Knowledge
Although my profession revolves around teaching mathematics, I also have a deep appreciation for language. In fact, my bachelor's degree is in English, and I spent 4 years devouring literature. I was thrilled when I recently came across the term generative learning, which describes much of what I believe about education. I like the very sound of the word and all of the implications that go with it.
Generative knowledge is acquired when new ideas are integrated with a learner's existing schemata. The main idea of generative learning is that, in order to learn with understanding, a learner has to construct meaning actively (Osborne and Wittrock 1983). Generative learning is, therefore, the process of constructing meaning through generating relationships and associations between stimuli and existing knowledge, beliefs, and experiences. It is an active process, where the learner has the responsibility of engaging with the material and constructing understanding.
As educators, the goal of creating generative knowledge means that we must clarify how this new information can be used so that students can apply what they have learned to new topics and to solve new problems. Otherwise, "each new topic is perceived as an isolated skill, and skills cannot be applied to solve problems that are not explicitly taught." (Fackler 2010). In the pressure filled world of high stakes testing, data analysis, teacher evaluations, etc this distinction about knowledge is critical. We cannot possibly present every mathematical scenario to students. When we attempt to find every problem type, every vocabulary word, every possible way a student will be tested, we are setting ourselves up for frustration. The inevitable always comes around and we hear things such as, "Why didn't the skills transfer to the test?" and "I know I taught this, but they don't remember this 2 months after the test."
Perhaps the solution lies in thinking about this word - generative learning .... helping students to generate understanding. In mathematics, our Standards for Mathematical Practice ask us to focus on the structure of mathematics. Examples of this include questions such as, "What does it mean to add numbers and how is that different than subtraction? If fractions are numbers, how are they like whole numbers and how are they different?" Using mathematical discourse in our classrooms allows students to discuss, debate, and generalize mathematics. Providing students with real world situations and problems that they can relate to and where the solution path is not obvious will allow students to reach into their mental files of strategies and allow them to apply mathematics in meaningful ways. Finally, explicitly helping children to make connections from what they already to know to what they are learning will help them to generate understanding of new topics. Tools that have been successful in ELA can work here - creating K-W-L and anchor charts. Asking questions such as, "What does this remind you of? Have you seen this before? What do you already know that would help you solve this problem?"
We are all feeling pressure this year, maybe more so than other years, but if we take a step back and think about the bigger picture of education, the answer may just be there. If we teach children in environments that allow them to reason, connect, process and build understanding, then they will have the skills necessary to tackle the problems beyond just those that they will see on assessments. They will possess a powerful type of knowledge - generative knowledge - that is long term, lasting and meaningful.
Best of luck!
Sue Looney, Ed.D.
President - LMC
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