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  #1  
Old 03-09-2007, 03:31 AM
HelenOfTroy HelenOfTroy is offline
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Montessori Maths question

Hi there,
I'm a student teacher and am currently training in Montessori for primary in New Zealand. As part of the requirements of my maths assignment I need to find out about Montessori teachers experiences with similarities, differences and complementary theories and practices of conventional and Montessori mathematics pedagogy.

I understand the main differences to be:
Montessori: Maths is presented with concrete, manipulative materials in a child-directed format.
Mainstream: Maths is studied as a separate subject and isolated discipline, in an abstract format, with the entire group of children moving together through the prescribed curriculum.

If anyone could take the time to talk about any experiences regarding the above, it would be gratefully received and appreciated. If you need clarification on anything please ask.

Thank you in advance.
Helen
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  #2  
Old 03-09-2007, 04:48 AM
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mommaruthie mommaruthie is offline
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Helen,
I am both traditional and montessori trained and would love to offer you an interesting perspective of your assignment....

I think the Mainstream is not entirely accurate and may be offensive to the amazing traditional teachers on this forum who use manipulatives as concrete proof to enstill their lesson to their students. Although the beauty of the montessori materials out shines the mainstream materials, there are still PLENTY of plastic manipulatives available to teach math concepts. Granted, there are no racks and tubes or checkerboards and REALLY should be as the concepts are better digested with these apparatus. If you do a search on the internet for math manipulatives, you should do a comparison of Montessori materials versus mainstream! Not to identify the quality of the material but to recognize that the Mainstream indeed has resources available that convey same function as Montessori. Example... Golden beads material are the same as the 'base ten'. Sure the hundred board is also available etc...
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  #3  
Old 03-10-2007, 01:12 AM
HelenOfTroy HelenOfTroy is offline
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Thank you for your feedback. On rereading my original posting I have realised that I had mistakingly missed the essential point that concrete materials are an important part of mainstream maths and I doubt there are any mainstream teachers who donít use concrete materials in maths. My intention certainly wasnít to disrespect anyone.

Iíve been reflecting on your comment that there are Mainstream resources available that convey the same function as Montessori. I am still in the process of understanding how all the Montessori materials work, but from what Iíve seen so far it seems to me that they are very purposefully designed and seem to have an underlying theme running throughout the materials to reinforce mathematical connections. For example the colours, one red bead represents one unit and if we look at the fraction insets the fractions are coloured red representing one whole unit.

Whilst there are many excellent resources available in the Mainstream that convey similar functions to Montessori, it seems that one advantage of using the Montessori materials is the underlying learning connections made between materials. What are your thoughts on this?
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Old 03-10-2007, 05:03 AM
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mommaruthie mommaruthie is offline
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I agree whole heartedly. I absolutely have NOT found any asthetically that can compare to Montessori's. The wood is gorgeous and the beads and colors are stunning. I have never taught in a 3-6 room but am very familiar with the materials- and have studied the sequence of materials so if needed from their room, I could 'borrow' for the child who is transitioning into the elem. room.
There are some mathematics materials in the upper elementary (checkerboard) that explain WHY you put the zero when multiplying with several multipliers. I havent found any tool in the mainstream that replicates that. I ADORE the division materials (racks and tubes) as you are able to bring to life each move. It makes the abstraction SO much easier to get to. The stamp game is entirely essential for the elementary program because I can use it for basics of addition to division! I have seen fraction materials that are similar as the triangle boxes. Are you talking about the three dimensional 'pawn looking' fractions materials? I know that in 6-9 room, the materials used for their math are able to be used in the 9-12 as continuation or progression of higher skills. In the 9-12 room, you would be only using for those who havent been introduced to abstraction yet such as, the child who may not be quite ready for it or HAS gone towards abstraction and needs to revisit the materials to reinforce the concept again.

I have made my own PAPER versions of the checkerboard and stamp games using Stock Paper and great hot laminating. This was originally out of necessity as one of the schools had a single apparatus and it was needed for many. The directress then made several checkerboards out of felt squares! (she used a sewing machine although I am NOT handy like that)

I have been teaching away from a montessori school but my environment is traditional. It is my montessori philosophy that allows me to integrate the lessons with pictoral representation of the montessori apparatus! For example, I draw out 'an array' as if its the multiplication board (red) and if I am demonstrating division, I will draw the (green) board with skittles/pawns and beads. I even draw a tiny cup to hold the remainder beads! Even the CUPS are color coded in the elementary montessori room!
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  #5  
Old 03-10-2007, 12:29 PM
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Yenna Yenna is offline
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Helen, I think your assessment of the differences is pretty close to the truth. While many traditional teachers may use manipulatives to illustrate a concept, that is quite a bit different than the Montessori materials whose purpose is to allow an individual to teach himself by becoming intimately familiar with the concrete representation of the abstract concept being presented. Also, as you noted, with the set up of traditional classrooms, there is no room for the individual to experience the trial and error or sustained concentration that Montessori affords. I think one of Montessori's biggest strength is the connections between materials you mentioned. Also, the same materials are utilized from primary up through the elementary classes - but the child is taught more complex lessons with the same materials, taking that understanding to a higher level.
Ruthie, while I think it's great you bring M philosophy into your class, you must realize that actually working with a mult. board and having one drawn on paper are two quite different activities, kinesthetically speaking. Also, FYI the hundred board is not a M material.
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  #6  
Old 03-11-2007, 03:26 AM
HelenOfTroy HelenOfTroy is offline
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Thank you Yenna and Ruthie for your replies.

I think the other thing that stands out for me is how the Montessori method caters for multiple intelligences.

For example interpersonal/intrapersonal intelligences are catered for through providing the choice whether to work on their own or work in a self selected group.

Verbal-linguistic intelligences are catered for through the Great Stories.

The manipulative materials cater for Logical/mathematical, visual/spatial, bodily kinaesthetic intelligences.


One thing I am not sure about is how a child relates say maths concepts learnt to his/her own world/culture. Is that up to the child to do or we should try and include this in our presentations?

In Mainstream I would tend to use materials that children can relate to, for example when teaching fractions I might use a pizza or a cake, or use something culturally relevant to an individual such as the use of natural materials.

Ok so I guess what I'm trying to say is I'm not clear on how we make the connection in Montessori with the child's own world? Any thoughts????

Last edited by HelenOfTroy; 03-11-2007 at 03:31 AM. Reason: want to add further clarification
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