Monday, December 14, 2009

Math in Traditional School

As a disclaimer - if you are unfamiliar with or new to Montessori, please understand that the following is not a representation of Montessori math and none of the activities shown are part of the Montessori curriculum. This is a chronicle of my attempt to help a group of students deepen their understanding of some math concepts by bringing a tiny sliver of what I have learned as a Montessori teacher into a very traditional setting.

As I mentioned in previous posts, I have suddenly found myself teaching 4th grade, not just in a traditional school, but in a traditional school on a military base! Yikes! ; ) Needless to say, it is different.

Dr. Montessori's math curriculum is one of the most beautiful things in the world as far as I'm concerned, so it hurts my heart to teach math from a textbook.

I was just wrapping up a chapter on multiplication with my class. I had used a modified version of Multiplication with the Golden Beads to introduce multiplication to begin with. I felt the best way to begin would be to demystify the operation itself. Multiplication can intimidate 4th graders (it still blows my mind that we're waiting until 3rd or 4th grade to introduce it for the first time, but that's beside the point), so I felt that introducing it as we introduce it in the early childhood classroom might help to create a clearer sense of what the operation of multiplication really is - simply taking the same number multiple times.

I set up an "Operations Table" and a "Bank," and designated a banker for our first lessons. The only difference is that the group was much larger than I would have liked, and we were using bright orange plastic "base ten cubes" instead of lovely golden beads. This did seem to help and the majority of the students seemed to really understand what multiplication was before we dove into the text. This chapter introduced a lot of terms, and some students were able to easily memorize all of them, but as we neared the end of the unit and prepared to test I observed that many students still didn't have the foundation necessary to understand the terms that were presented (and even those who had memorized them had done just that -memorize. They didn't necessarily have a concrete sense of the concepts taught). For example, we learned about Prime and Composite Numbers, and many students weren't even totally clear on the difference between odd and even! I wish I didn't have a textbook at all, but I do; and I wish I could do everything hands on all the time, but I can't. I decided that some work with concrete materials was absolutely necessary at this point, however.

I also wish I had enough materials and space to allow each student to work individually, but instead I set up the following in small groups and we worked through the following activities over the last week.

Odd and Even
To make sure that every student really understood the concept of odd and even numbers, I used the materials we have to give every student the opportunity to do the Cards and Counters as we do in the Montessori Early Childhood classroom. Unfortunately, I can't do one on one lessons in this environment, and the students are trained to do everything with worksheets, so I had to set the activity up with written instructions and a follow-up sheet for the students to fill out.

Below, you can see the instructions, the counters (I sure wish they were all one color! They're read on one side and yellow on the other), and the "Digit Deck" which contains the numerals 1-9.

Here's a close-up of the directions:

Another way in which all of this was beneficial was as an exercise in following directions. It was surprisingly difficult for some students to complete activities step-by-step. They often got ahead of themselves and became very confused about what was supposed to be next. I may need to reword my description of the layout if I do this again as well, as most students were confused as to what I meant for them to do with the last counter for each odd number.

After completing the activity, students had this to complete:

Not very Montessori at all, obviously, but I had to work within the system we're in.

Square Numbers

Prime and Composite Numbers
I am not aware of a Montessori material for teaching these concepts, although I've never worked in a school that had an elementary program, so maybe there is one. I tried to use concrete materials to demonstrate Prime and Composite numbers as they are defined by the students' textbook. The key difference here is that the concept had already been introduced, and only after the students learned it on the surface, were they given a concrete experience with the concept. If I were not just in this position temporarily, I would definitely change the way this was done for the future. Anyway, again, instructions, materials. Not a Montessori activity, but an attempt at using Montessori principles to better teach the material this class is working on.

The Properties of Multiplication
This one is really not very concrete, and it's not really Montessori at all either, but I'll add it in anyway.

So that's what I've been up to. After 6 years of teaching Montessori 3-6 this is really an odd and trying experience, but I love the challenge. I have never seen attempts at bringing Montessori principles into a totally traditional classroom and I have no real expertise in this area - I'm just trying what makes sense to me and modifying based on what I see working for my students. If anyone has suggestions or experience with such things - I would love to hear them! I'm going to spend Christmas break doing a lot of planning for our next chapter, which will be division. Hopefully I can bring in things like this earlier!


Annicles said...

I cannot believe how chair bound the american system is. My children go to mainstream schools and are american kindergarten, y 2 and y4 age (reception y3 and y5).

They do loads of practical work and do everything concretely first. They are also taught lots of methods so that they can find one that suits them best. It is interesting that the older 2 "do" their times tables in completely different ways.

I would have a look on some uk sites and see what you can find. I find them far more interesting and engaging than the endless worksheets on US sites.

Anonymous said...

Wow, I think you're doing everything right and are getting super creative with the tools you have! I was especially intrigued when you noticed that they had a hard time following directions. Interesting observation, and an obvious side-effect of an adult-driven educational system. Those kids are lucky to have you!

Anonymous said...

I know you posted this a long time ago, but I am in a similar situation (Montessorian in traditional school) and I'm wondering how this worked for you.

melissa said...

I do remember these activities being pretty successful, but I had a baby and left the classroom a few months later, so I did not have a long time to work with these methods and really see how they worked for the children. I think hands-on work with concrete materials is pretty consistently beneficial for children, though! I suspect with observation and tweaking, it would have gone well :)

Best of luck in your classroom!