The previous 19 posts have touched upon a few of the key recent advances in cognitive science. It is time to begin consideration of:
1. The impact of cognitive science on teaching and learning mathematics,
2. Modification of what should be taught in early algebra courses.
To set the stage for this shift in emphasis I suggest that you review the previous posts beginning with the March 6, 2018 post: “What is Teaching and Learning.” In the event you do not have time to actually review the previous posts, I will point out a few key points from that first Post.
Intent of Blog: My avowed intent for this blog is to improve teaching and learning of mathematics.
Key Definition: When we talk about learning we mean acquiring knowledge and skills and having them readily available from memory.
Learning Process: Learning happens when external stimuli are perceived, stored in memory, and a retrieval process is established.
Key Definition: Instruction is a deliberately arranged set of external events to support internal learning processes.
Past Weakness: Instructional developers have produced no end of trivial rearrangements of external events without any real understanding of the internal events important to learning.
Important Advances: During the last 20 years or so cognitive scientists, assisted by technology as amazing as neuroimaging, have discovered a lot about what happens inside the brain during learning activity.
Key Understanding: We now have the advantage of better understanding both external and internal events in the process of learning.
Exuberant Anticipation: As science further informs us of internal events we should look forward to an extended time of improvement in teaching and learning.
Clear Vision: Herbert A. Simon, one of the founders of the field of Cognitive Science, Nobel Laureate, and University Professor (deceased) at Carnegie Mellon University maintained:
“Learning results from what the student does and thinks and only from what the student does and thinks. The teacher can advance learning only by influencing what the student does to learn.”
Student Inclusion: It is imperative that the student be informed of the advances in cognitive science.
Previous Mistakes: Recent research contradicts some commonly accepted beliefs, is sometimes counter-intuitive, and shows that some teaching and learning methods we have used and encouraged our students to use are just plain wrong and mostly a waste of time.
Call to Action: Please approach these writings with an open mind, be ready to change, and be ready to discard some of your “truths.” Study references such as listed in the Pages section of this Blog