This is it – my final Montessori class for the year. Our final topic is regarding mathematics education in a Montessori classroom. If students are self-paced, how does a teacher mitigate the range of student abilities, and how do they continue to integrate Montessori materials into those lessons to push student thinking?
From my understanding, the Montessori Math point of view is a holistic one. Math is integrated into everyday life and everyday dealings around the school. Mathematics is used to find order in the environment, especially when it is our human nature to find order and meaning within the world around us. The need to quantify things leads nicely into the language of science where math and science become part of a shared culture that work together to provide meaning.
In the Montessori classroom, math is not just numbers and shapes. It is a frame of mind that heavily borrows from Blaise Pascal’s theories of the mathematical mind and the theoretical mind in which one uses these frames of mind to make judgements and inferences about the world around them. Using this lens, the human mind, by nature, is mathematical. Finding patterns and relationships is the mind in action. These patterns give students the framework to have different experiences through different mindsets. In relation to patterns, geometry is seen as a sensorial entity that is the access point into math. The edges, angles, and corners all provide entry into larger conversations. In the Montessori classroom, math is for everyone in the sense that there will always be something to feed the “Psychoarithmetic mind” that offers the psychology of the student at each age milestone in tandem with the mathematical mind. A great entry point into Montessori mathematics is “The story of numerals”.
After understanding how mathematics works in the Montessori classroom, it is important to be familiar with the materials one might encounter in the class – things like beads, boards, rods, and cubes. When a student is ready to expand their knowledge and move into more complex mathematical concepts, transitional materials are introduced such as large bead frames, wooden hierarchy materials, fraction, and boards. Golden bead work is done with a large numerical base board and satisfies the need for repition. It is used to explore topics such as:
- rote counting
- writing 1-10 and values of 0
- describing movements in writing
- reading 1-4 digit numbers with decimal system cards
- writing 1-4 digit numbers
- counting numbers 0-10 with greater than (>) and less than (<) language
The golden board is presented in grades 6-12 differently because the psychology of the student changes and new items are added to the sensorial experience to satisfy their need for reasoning. In all cases, uses of Montessori materials need clear presentations for students to advance quickly through material. Often times, playing the math games with the materials in a social manner is preferred over independent work. Here, students can practice their social and reasoning skills with another at the same point in their mathematical journey. Some of the games that can be played socially include:
- introducing math language
- word problems using materials to solve
- word problems using paper and pencil to solve
- repeat for X (sensorial and symbolic)
- flash cards
- addition sentences with bead boxes
- math facts
- whole number operations
- symbol and quantity
Terry brought the Montessori Hexavium to our attention. It is a material he developed to illustrate how big topics can branch from the great lessons of Montessori. In the middle is the beginning of one’s Montessori journey. Each lesson then lends itself to topics and tasks that can be introduced. The outer layer lessons then compound on those lessons until you reach the final outer layers. This was a great visual to explore how Montessori works in a nutshell. I found this diagram really helpful when looking at how lessons and units can be sequenced to create a larger picture.
This Montessori series has opened my eyes to a completely different way of thinking, teaching, and learning. All of the discussions have leaned in a more cosmic education direction than I anticipated. I’m still very confused with the methodology in a practical situation. I would be very interested to observe how Terry practices Montessori learning with a classroom of students. At this point, we have not discussed working with students on IEPs, who are ELL, or are generally disengaged for whatever reason. How does a Montessori teacher approach educating children who may not fit the generalized role of what a student should look like? I don’t think I have totally bought into the idea of full Montessori integration, but there were some concepts that have sparked inspiration in me.
My major takeaways from this series that I think I could easily bring into my classroom are the more simplistic concepts of Montessori learning. I can adapt the physical environment to be more student accessible and encourage independence. I can create more learning experiences where I can conference with students one-on-one, or in small groups to discuss their next steps. I can reframe my lessons to adhere better to the Montessori “three part lesson” and have students explore and engage on their own more than having me talk about it. I can also try to be more methodical with my student observation. I love the idea of tracking a single student minute-by-minute to really understand what their priority is during a work period. If it is a student who accomplishes the daily learning task, how long does it take, and how long do they sustain focus before taking a break? If it is a distracted student, at what point do they become distracted, what are they doing instead, and for how long? I am a big data person, so numbers and graphs really help me understand how I can better help my students.
My wish for the future is to have the opportunity to try the idea of “going out”. I want to bring some students to a community space where the content explored in my course is applicable to their understanding of how an aspect of society works. Maybe if I am asked to teach gifted education next year, I can take a more Montessori approach to it.
I am not sure what will come of the Montessori series, whether it continues next year, or if the teachers who have participated in the class will be offered mentorship/resources on integrating Montessori in their classrooms. I am fortunate to have half of the staff at my school as certified Montessori teachers, so any immediate questions can go to them, and I can seek larger answers from Terry and Kelsey. If there are any updates to the Montessori program for teachers, I’ll be sure to update here and share some more thoughts. Until then, I will continue my studies into Montessori education as it pertains to modernizing the philosophy with the rise of technology, and I hope I can integrate my understandings into my final project on whatever it may be.
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