Saturday, April 6, 2013
Mortensen and Montessori - Mathematics Materials - Comments
I was recently asked to give my opinion on the following article:
http://pmswebsite.fatcow.com/teacherarticles/Townsend,Mortensen.pdf
Ok, I was asked quite a while back, and I was asked *again* recently ;)
My PERSONAL and PROFESSIONAL opinion are the same:
I am under the impression that the author of this article has a very limited training in Montessori, likely not the entire elementary sequence. Several times through the article, she makes statements about Dr. Montessori or the Montessori method that contradict Montessori's own writings.
Also, she states certain inconsistencies in the mathematics materials that are simply not present, at one point stating that the child isn't supposed to notice different sizes of the the various areas when doing square roots, multiplication on the checkerboard and the like... she misses the part where these materials tie into the stamp game - where "2000" is visually smaller than "9 units" - because we are moving the child to an abstraction based on the numeral present in a particular place, NOT emphasizing the visual size. We actually want what to the author appears to be a discrepancy and a confusion.
To her statement about no longer teaching division to 1st graders, I respond that the children should be working with the golden beads and stamp game in their primary years, whenever possible, as a sensorial experience - all four operations, including division. Now, it is up to the development of each child how far and how fast they are ready to proceed; it should never be up to an adult to make a blanket statement about not teaching a concept to a particular age.
The memorization work, when done in an AMI manner, will be done before a child reaches elementary; hence she is correct in its inappropriate place and tedious use in an elementary class. SOME children do fine with it into elementary; most will need to be done before entering elementary or work on memorization in other ways.
I won't say much more right now, because I want to get this posted.
I will say that I would love to compare notes as to scope and sequence for the elementary years; as well as further discuss specific materials and their purposes (there is a reason we limit what we do with a particular material - if we taught *everything* with just a tiny number of materials, our classrooms would require multiple sets and all elementary environments would have confused children - learning "too much" with just one material, they can lose their place - and using the same material many times over... well, it gets monotonous...).
Finally, I will say - if you need to shake things up and use another material - DO SO.
1) Follow the needs of the child.
2) Sometimes the adult can't provide for the needs of the child because of an emotional hang-up on something - that is FINE to recognize that and make accommodations for it, so that the child's needs are still fulfilled, if just in a different way. Just call it what it is: a modification for the sake of the adult. ;)
(UPDATE TO CLARIFY: My above opinion of the article is my opinion of the article and in no way reflects my opinion of the Mortensen Math materials which are probably truly very, very good if you can get past their website that is full of errors (ceator, insuctional, algibra) that attempts to look like a film production but instead comes off low-classy, advertisement-full (they're not really advertisements...), poorly worded and spelled; many things want to download to my computer and refuse to stop until I close the browser completely... and overall just looks like a gimmick --- all my red flags are up saying "stay away from this site" every time I visit it (although my virus protection says it fine). I have tried to contact them about the spelling errors at least but have not seen any changes. Their copyright is still 2011 as well. It just doesn't look professional is all. But I have heard good things about the *materials*.)
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Thanks for your thoughts! Some research has found that using many different types of manipulatives results in slower understanding, presumably because the learner has to spend time learning the new material rather than working with something they already understand. How relevant that research is to Montessori, however, is another question, as the classroom functions very differently from a standard class where manipulatives are just an occasional add-on to the work. More important, I would say, is the need to make sure that the way the concepts are taught is consistent from K-12, meaning that you do not later have to "correct" the concept the child learned earlier. I believe having some material that lasts throughout the years (e.g. Dienes multi-base blocks or an abacus), whether or not it is the exclusive material used, can have a unique benefit.
ReplyDeleteMortensen is an older fellow now. He created a great product, not a great company to continue his work. That said, you can check out the montessori album dot com article on his method, which links to two of his disciples who have continued his work and would be better sources to look at than the original Mortensen website. The article mentioned also has information about how Mortensen materials can be used for some Montessori activities.
Another question not considered here is whether subitizing using colors is the best method, as both the glass beads and Mortensen do. But that is another topic.