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News from the North House Weekly News & Reflections from the Middle School

Week of November 5th, 2018

“Pure mathematics is, in its way, the poetry of logical ideas.” Albert Einstein

Dr. Montessori believed in the necessity and importance of mathematics in education. The ability to solve mathematical problems comes from the abstract part of our human minds that constantly seeks out ordered patterns in all the information we receive through our senses. This type of thinking--mathematical thinking--is at the core of all our intellectual activity.

In her educational syllabus for adolescents, Dr. Montessori placed math alongside language and moral education, understanding that the brain goes through the same processes when it works to solve math problems, to articulate thoughts into language, and to make ethical judgment calls. Our ability to think, to reason, and to make decisions is itself mathematical in nature.

“Mathematics is a linguistic activity: its ultimate area is preciseness in communication.” William Schaff

In education, many schools emphasize math’s unique importance in our modern world by increasing instructional time and testing. The goal for many becomes to encourage young people to race their way through the different levels and categories we have created for math over the centuries. Many young students in this ‘race’ are left to perceive that math is about speed, memorization, and tests. But, young people today also need to see that the problem-solving nature of math is a process, not just a final answer. The process of solving a problem is the key, and it should be respected. Within the process, failure is most certainly going to come on occasion. What a great learning opportunity! Young people will fail once in a while as they struggle to discover the correct ways to solve problems. They need to know and feel these moments so that they may experience what it is like to rise out of that feeling into one of accomplishment through hard work and dedication to a task. These are valuable experiences that will truly help them in adult life— further strengthening their overall reasoning and resilience.

In Montessori schools, math is fully integrated into all that we do, and mathematical knowledge builds naturally as students move from Children's House through adolescence.

The constructive triangles, for example, are materials that can be used in Children's House, Lower Elementary, and Upper Elementary.

Middle students recently brainstormed ideas of how these materials can be extrapolated to demonstrate more advanced concepts.

Integrating hands-on experiences and materials helps abstract concepts to become more concrete in the developing mind. Geometry students used a paper technique to prove some of the postulates and theorems in the current chapter.

Algebra tiles are used to model like terms, distributive property, and solving equations. Students may use them to discover a concept or to practice a skill until it is mastered.

Some students used ratios to create scale models for their end-of-unit math projects.

“Good mathematics is not about how many answers you know; it is how you behave when you don’t know.” Anonymous

While dedicated time for math work is necessary, it does not always need its own separate instructional time in order to exist within all that an educational program offers. Our students must calculate and solve real-world problems when they work do work for their small business, when they are taking inventory of supplies, when they are carefully taking measurements for timelines, maps, models, and art projects in the Humanities or Expressions.

In micro-economy, students apply math skills almost every week.

They do cost analysis on each product they make to determine how much profit they can make from their products. And, they use numbers from previous years to project how many items we need to make this year.

The Finance committee keep detailed records of all incoming and outgoing money, while dividing profits into different budgets that students can use to grow their business. Mathematics becomes more real and more meaningful when it is recognized as a constant in all of life’s activities.

In Montessori education, mathematics is highly valued. So much so that we strive to provide our young people with opportunities to get deep into the process, to really understand its meaning and purpose in life, to fearlessly embrace the struggles that come with it and to strive for the accomplishments that await. It is a deeper form of math education than is found in many traditional settings, and its value is beyond measure.

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