The following problem1 demonstrates the impact of working memory limitations on processing information. Although there is no difficult conceptual thinking required to solve the problem, it has been reported that most university students require about 30 minutes to find the solution.
Three monsters, one small, one medium and one large, were each holding a globe. The globe came in three sizes only – small, medium and large, and each globe could be expanded or shrunk repeatedly to any one of these sizes but to no other size.
The small monster was holding the medium globe, the medium monster was holding the large globe, and the large monster was holding the small globe. They could change the size of the globes according to the following rules:
Only one globe could be changed at a time.
When two globes are the same size, only the globe held by the larger monster may be changed.
A globe must not be changed to the same size as the globe of a larger monster.
What sequence of changes would allow the monsters to hold globes proportional to their size?
Although each globe changing rule is easy enough to understand, the problem is difficult because it is difficult to hold the rules in working memory. The original creators of the problem (Kotovsky, Hayes and Simon – 1985) found memorizing the rules of the problem to the point where they could be repeated effortlessly made the problem much easier to solve.
While it is easy to assume that a student can’t solve a problem because he/she doesn’t understand what needs to be done, the monster problem indicates that working memory limitations are just as likely to be the cause of the difficulty.
1. from “Instructional design for technology” by John Sweller (1999).
In his book “Why Don’t Children Like School”, psychologist Daniel Willingham says that understanding is memory in disguise. Although this seems the exact opposite of the widely adopted strategy of making information memorable by making it understandable, his point is that memory and understanding are a pidgeon pair. Both are necessary for learning – memory improves as understanding improves, and understanding improves as memorizing improves. Any teaching strategy that neglects the role that memory plays in understanding is likely to be one where the students find conceptual understanding of the topic elusive.
Yup – I’m saying sometimes memorizing is an essential part of understanding, and sometimes it needs to come before you can understand enough to learn.
Yup – I know that’s not what they teach in teaching college, but then they don’t teach much cognitive science in teaching college either. Sure, plenty of Piaget, Vygostkty, Bruner and Gardner, but only a smattering of neurones and synapses.
Here it is – the crash course in cognitive science – a.k.a. “Your Memory, and Why It’s Important to Know More About It”.
Message understood doesn’t always mean message is remembered.
The brain apparently handles understanding (processing information) and memorizing (storing information) in totally different ways. Although (fortunately) it doesn’t happen very often, it is possible to have brain damage which makes it impossible to create new memories. Such an individual is able to reason and understand using any knowledge from memories acquired prior to the injury, but is unable to create new memories. Any newly acquired knowledge obtained from logical reasoning and understanding of already known information will not be remembered for more than a few minutes.
The long and the short of memories
Most theories about how brains think, reason, calculate and memorize involve the concept of two types of memory – working memory (sometimes referred to as short-term memory) and long-term memory. Although not yet fully understood, current theories about the interaction of these two memory types can help in the creation and design of more effective learning experiences for students, particularly those students with learning difficulties. Read more
Challenge: Is it possible to find a student who would not be engaged by Vi Hart’s brilliant math doodling videos.? These are about having fun while discovering mathematical relationships. Here’s a sample – there’s more on her site.
Doodling in Math: Sick examples
There’s plenty other mathematical stuff on Vi Hart’s blog. Stuff with balloons,and how to make platonic solids out of fruit. This is mathematics that meets Paul Lockhart’s1 description of the way mathematics needs to be taught – using playful “serendipitous exploration” to discover that mathematics is about weaving ideas into patterns.
The impulsive decision to make a trip to Africa was made shortly after an unsolicited email arrived in my inbox about volunteering in Uganda. I was already considering attending an Open Learning Exchange conference in neighboring Rwanda, so I decided to “volunteer” (by paying the prescribed fee to IFRE volunteers), and in no time at all a two week stay at a small and cheerful school was arranged for me, timed to follow on from the four day OLE conference in Kigali, Rwanda. It was an incredible experience. I found it amazing that the children learned as much as they did with almost no teaching resources (like reading books, or paper to draw on . . ), and (corny as it sounds), how well-behaved and infectiously happy the children were, as you can see from the videos further down the page.
Maybe, just maybe, Ken Robinson’s education revolution is starting to happen. Maybe the revolution is starting with classroom teaching time into homework time, and homework time into lesson viewing time. Sometimes it’s called flip-teaching, sometimes inverse-teaching, but whatever it’s called, the general idea is that teacher time is best spent interacting with students, and anything that makes more teacher time available for that interaction is going to improve the student learning experience.
Homework time and lesson time are flipped. By making a video of the lesson and making it available for students to watch as homework, everyone wins. With totally flexible viewing time, students are no longer penalized if classes are missed for whatever reason. What would normally be “homework” – applying the knowledge gained from the lesson – is done during class time, when there are opportunities to clarify any areas of confusion. Lesson time becomes quality teaching time as the teacher moves around the class, observing how students apply the knowledge and intervening or assisting as required. Read more
In an era that emphasizes the need for “deep understanding” in learning, it’s alarming that most of the students I meet requiring tutoring are totally reliant two ineffective strategies to find an answer – 1) guess and hope, or 2) don’t even try – that way you can’t get it wrong. Until recently my typical strategy would be to identify areas of misconceptions, and make students aware of what they needed to know to correct their knowledge of basic mathematical concepts . I stressed the importance of reasoning over guessing, and provided students with opportunities to practice and apply their new-found knowledge. I figured I was helping them acquire the “deep understanding” they had previously missed out on, and that this newly acquired knowledge would improve both their self-confidence and their motivation.