Today's thoughts came out of wondering if spiral learning and interleaving were the same. I stumbled across an article on spacing and interleaving from 2014 with a quote that made me sit up with a whoa.
The quote "We rely on memory rather than thinking" from Hattie and Yates, Visible Learning and the science of how we learn.
This quote perfectly identifies the overwhelming thought of teaching as it has been for so many years and seems to be continuing even now.
Why else would we teach students to follow processes when solving problems rather than looking for connections. I wonder if this is why so many of our students are unable to transfer knowledge from one situation to another or why they barely remember yesterday's lesson.
When teaching students to solve word problems, we often tell them to look for key words which may nor may not provide the correct information, make a plan, etc. Most of my student just look at the numbers, hoping to choose the correct operation. They don't stop to think about what the problems is asking or how they might solve it.
I know most teachers do not even ask questions designed to have students think. Usually the questions are "What is the first step?", or "How do we get rid of the constant?". Questions designed to ask about processes. In addition, most students do not know how to ask each other questions to open a discourse. Most students ask "Do you know how to do this?". If the answer is no, they quit and if the answer is yes, they want the other student to let them copy.
I found this list of 100 questions which can be used to move past the standard few used in the classroom. I like some of the questions such as "How did you reach that conclusion?" or "What is this problem about, can you tell me? Questions designed to make students think about their work.
Note, I am not saying Memory is unimportant. It is but too often students use the processes they've learned rather than thinking about the problem itself. I'm saying as a teacher, we need to encourage thinking through every facet of problem solving. Don't tell, ask questions to invoke thinking. Ask for explanations rather than steps. Ask why. Ask them to tell you. Ask, Ask, Ask.
Perhaps by encouraging more thinking, we can move past simple memorization, into real understanding of mathematics.