Thursday, July 12, 2018

ATM #beingmathematical. Cows eat grass

This is my 'homework' in advance of the ATM #beingmathematical session on 12 July 2018.

Here is the question:


The instructions were to think about how we thought about the problem.  Below are my ideas, including things I did wrong!  My thinking is in red and the maths is in blue.




Was there a way to do this without so much algebra?

Thursday, April 12, 2018

Ebbinghaus


I have some questions about the Ebbinghaus Curve.  

One example of the curve is linked to here:

While I am comfortable with the idea of needing to revisit material and that this can help with long-term retention (one of the authors of a 'Learn Spanish' podcast that I listen to says that you have to use a word in 6 different contexts before it becomes embedded), I find the Ebbinghaus Curve to be somewhat dubious. 

It looks rather specific, it has multiple copies of the same 'shape' of curve (subject to a stretch-factor) and it also still involves 'forgetting', so all we are doing is staving off the inevitable forgetting that will occur with everything.

I had a brief look at Ebbinghaus' work and was surprised by a couple of things:

1) Ebbinghaus had a single subject.  One person!  This seems to be a ripe and obvious field for research to be carried out with large numbers of people.  The idea that such an idealised curve can be produced after testing a single individual doesn't seem sensible.

2) The person was an adult.  The curve is now being used to predict how children might behave.  There are lots of differences between adults and children, but of particular relevance is that the adult knew they were part of a research study and presumably wanted to learn and recall things as well as they could.  This contrasts with some children in the classroom.

3) The adult learned strings of nonsense-words.  Again, this is vastly different to what happens in the classroom.  Is memorising strings of unconnected information related to learning connected information?  Is it linked to learning maths?  What about the role of understanding?

In summary: I don't have a problem with the idea of needing to revisit material to help with its retention.  I do think the 'Ebbinghaus Curve' is overly-specific and is an example of applying an idealised graph created from research carried out in a particular way to a completely different scenario.


Edit:
David Wees is exploring the data behind this in detail.  Worth looking at this thread: