Montessori 101 - Freedom and the Environment

True to Montessori form, two fundamental principles of Montessori education follow an overarching idea from the concrete to the abstract: the first is freedom and the second is the environment. How are these principles defined in relation to my personal belief system is the purpose of this essay. My reason for choosing to follow the Montessori path is that it follows natural laws that are in tune with who I am. It gives me great joy to work alongside the boundless energy of children, and to wrap myself in the meaningful endeavor of service to humanity. I am a natural, kinesthetic and visual learner. Montessori philosophy and methods endorse a natural environment, integrate freedom of motion, and harness sensorial means, including visual, into purposeful learning. I respect the free will of all people. I value creativity, self-discovery, and guide toward collaborative and independent, critical thinking. When paired with an open, respectful and socially responsible environment that recognizes and supports where students are developmentally, I see self-confidence grow, inner discipline flourish, and proud choices being made in preparing them to enter the world.

FREEDOM

There is no more powerful, intrinsic, motivating force than the fulfillment of one’s free will. A Montessori classroom provides the opportunity to unfold the child’s true self, by enabling their freedom of choice. Activity may be sustained for minutes, days or even a week at a time, as the child learns through repetition and self-motivated interest.

“The children in the Montessori class are given the freedom that is the liberty of the human being, and this freedom allows the children to grow in social grace, inner discipline, and joy.”¹

A result of this freedom is serious concentration that leaves an imprint of satisfaction, accomplishment and peace. After all that effort and hard work a child may feel remarkably rested.  I wonder, is inner-discipline simply an awareness to follow free will?  All people are free to regulate their behavior and to choose conscious control over their lifestyle. This is an empowering and liberating idea!

Promoting brain development, freedom of movement is intimately connected with learning. Montessori forewarns, “Man who does not move is injured in his very being and is an outcast from life.” ²
How can we participate with others if we fail to interact and move?  I enjoy seeing freedom of kinesthetic motion routinely integrated into Montessori practice. Golden beads, red rods, and sand paper letters are a few such examples. Effective teaching welcomes the child’s free will a uses all of our senses.

ENVIRONMENT

A Montessori classroom environment holds several key concepts for creative young minds to flourish. These include freedom, order, reality, beauty, materials and community. Freedom of choice provides the opportunity to lift a child’s independence. It is the child’s free will to choose which material to work with and for how long. It is not the adult’s role to interfere and perform acts that the child may learn to do for himself. A Montessori teacher protects the child’s choice and creates an environment for constructive work to surface. Montessori children are not forced to join group activities or compete with other students if they are not developmentally ready to show interest for that particular task. As a result,
this non-competitive environment gives rise to a natural human desire to help others.

                  Sequentially ordered across all content areas from easiest to most challenging, a Montessori environment is arranged from top to bottom and left to right. While appearing quite linear at first, this structure is extremely fluid as children move their bodies in and out, repeating the same works until fulfilled. Consequently, the child learns to trust the environment and interact positively with the materials. Importantly, the child is an integral part of this classroom structure. Students work diligently to maintain order when completing a cycle of activity by returning a work to its’ proper location.

                  Understanding the limits of reality and nature help students assign meaning to their new world and to separate the illusions and imaginative fantasy of role-play. Through contact with nature, inside and outside the classroom, children grow to appreciate order, harmony and beauty. Activities that are rich in natural content help the child to feel secure, maintain a sense of place, and feel free to observe life with exceptional detail. The benefit, according to Lillard is that children become an “acute and appreciative observer of life.” In addition, caring for living plants or animals helps children to coexist and live in awe of the natural world.

                  Beautiful Montessori environments typically include ample light, warm colors, glass walls, open space, and an inviting, relaxing atmosphere exhibiting high quality materials. Quality, in fact, permeates many aspects of this space. Well-designed activities of wood, metal, and natural elements encourage the child to treat the environment with care and to recognize that learning can be a sacred experience. Harmoniously arranged in ordered shelves, these activities invite participation.

                  Because many tasks in a Montessori environment are independent, the materials are designed to capture attention, promote self-construction and concentration. Through observation, a teacher may realize the child’s level of intensity and interest. Is this work meaningful? Is it at an appropriate level? Is it consistent with the child’s internal needs?

Lillard explains further (1972), “The teacher watches for a quality of concentration in the child and for a spontaneous repetition of his actions with a material. These responses will indicate the meaningfulness of the material to him at that particular moment in his growth and whether the intensity of the stimulus which that material represents for him is also matched to his internal needs.”³ (p. 60).

                  Clearly, when there is a quality of concentration, learning is most meaningful. Learning is suited to a particular stage of mental growth and matched to internal needs. Moreover, the child feels pleased with his/her accomplishment, peaceful and rested. In addition, the teacher should be flexible to alter the sequence or omit activities that the child shows no need for. At times, it is possible for a child to learn simply by observing another child, and to leapfrog activities.

A Montessori environment is a true community. Modeling respectful social behavior, people come to care for each other, solve problems together and consider the greater good of the group. Sitting beside a student and not only listening, but also hearing what they have to say, is a vital life skill for individuals. In this community, children learn to make choices that everyone can agree with.

Can You Prove It?

The process of learning is the polar opposite of a passive experience. Actively constructing knowledge, Constructivism, is rooted in Piagetian theory. Children construct meaning, building upon what they already know. Students are not empty vessels to be filled with our magic. They are their own shining stars that perform at center stage. As Kloosterman and Gainey suggest, students are “thinking individuals who try to make sense of new information.” (ch1, p.5). The cumulative effect of building upon prior knowledge has implications in all content areas, especially mathematics. According to the NCTM, Notional Council of Teachers in Mathematics,

    “The mathematics curriculum should include the investigation of mathematical connections…describe results using mathematical models…and use a mathematical idea to further their understanding of other mathematical ideas.”

Stated simply, this boils down to two simple words, explain and justify. Exploring problems together as a whole class and in small groups, a student’s job is to investigate and make connections, (to real life, to other mathematical models through a spiraling curriculum, and to a multiplicity of solutions). When we shape an environment that encourages sharing solutions and explaining what students believe and why they think the way they do, we help them recognize relationships and add meaning to their conceptual knowledge. 

Approaching mathematical problem solving in this way mimics the method of scientific inquiry. This process of discovery, followed by elaboration, discussion, and articulating a cohesive conclusion, provides structure for students to prove their thinking with evidence. It is hard for me to imagine students blindly following rules without reasons, yet, in some classrooms, I know it happens every day. I expect more from my students than the ability to get something correct and memorize a formula. They must be able to justify, explain, and prove, how they know what they know. I expect my students to engage in active learning, to process then apply their content knowledge, to question, share and reflect as they learn. When students reach this level of understanding in mathematics, they validate their own beliefs as they construct relationships to past and future conceptual meaning. Ah… but, can they prove it?

iTouch apps … to be continued …

Today, I am teaching myself to do more with iTouch applications by exploring literacy tools in the palm of my hand. For instance, imagine accessing the complete works of (insert your favorite author here). Recently, I discovered two apps worth mentioning. The first, Story Book Reading, offers the titles, “Three Little Pigs, “Waldo at the Zoo,” and “Black Ear Blonde Ear”. Each has beautiful illustrations to share and text that may be zoomed in for reading clearly. While the fables are ethnically diverse and maintain strong values, I have a hard time imagining sharing a 2-inch by 2-inch window with a class of 26 students. Where is the visual impact? How can this display be synched with projection on the ActiveBoard? I imagine this is only a matter of time.

A second app that I find useful for small group learning, is World Wiki. How demonstrative this would be for the World Geography unit I conducted last October. Differentiating instruction with a group of four students in a split 2/3-grade classroom, this app can quickly convey a myriad of statistics on any country from around the world. Students can learn that Vietnam, for instance, earned independence from France on September 2, 1945. In addition, the capitol city is Hanoi and the currency is the Dong. Advanced grade level students may chart, compare and contrast mathematical data between different countries, such as the G.D.P. of Vietnam in 2008 reaching 290 billion dollars. Today, information is literally at our fingertips. The mobility of these devices keeps us joined with knowledge. Is there really any excuse for ignorance? When we integrate these devices into the classroom, a key remaining question I have is: How do we design the experience to be equitable for all students? Does the “i”  in iTouch stand for independent, interactive, or irresistible? Certainly, I believe that it is far more than an iToy. I imagine the iTouch will evolve as an integrated educational tool, strategically shared with all students.

Forming a Healthy Self-Concept of Math

This week I learned to think about math in a healthier way. Before students can develop a healthy self-concept of Math, they must be given the opportunity to share their thoughts, beliefs, ideas, and perceptions on what math is and how they use math in their daily life. It is easy to take for granted how much mathematical reasoning goes into everyday activities.

Through open discussion and social context, the below mini-lesson from Leatham, K. (2010), helps students to recognize different patterns and to re-examine their definition of math. Simple everyday language is mathematically categorized and discussed. Examples: driving a car, quilting, playing the drums, hanging  a picture on the wall. In a second group lesson today, I was introduced a similar theme when I was asked to use a variety of atypical measuring tools (paper clip, post-it, poker chip), to measure a specific rectangular shape.

After plotting the length and width data points on an x, y graph, I came to realize that the slope was constant, forming a linear line. y = mx + b.  I found this to be surprising, as all data points were in different units of measurement. The implications for classroom practice in this 2nd exercise revealed a new way of seeing the x, y data when applying the concept of slope. Connecting the relationship to the content through experience, is a healthier way to see mathematics than memorizing and plugging in a formula without context.

I am reminded to continue asking what do the students know? What do I want them to know? How do I get them there? Did they get there and where do we go next?

The Largest Container

A vod presentation by Annenberg Media, Learner.org, by Suzanne Duncan a 7th and 8th grade class discusses length, width, and height of volume of a rectangular prism and area in a container.  shows a lesson “The Largest Container.”

Moving her arms in the air, Ms. Duncan defines the volume as a cylinder as a circle moving through space (height). Maximizing the idea of surface area and volume she asked the students to design the largest area possible out of a sheet of paper. What elements come to mind? Volume. Surface area. Once students had a possible solution they were encouraged to flatten out their shape, and write out the dimensions, and their computation of surface area and volume (so their thinking doesn’t get lost).

Causes for intervention in helping students correct for computational errors: 1) running out of time in the lesson, (stop where you are and move to the next phase), 2) adjusting to individual needs and learning dispositions. 3) redirect after students have had the opportunity to explore and discover on their own, preferably through small group engagement and whole class sharing.

As the topic of volume and formulas is too advanced for a 2/3 split classroom, I can restructure this lesson for my students by modeling and constructing a cube and a rectangle from a blank sheet of paper. An essential question may offer, “How many sides are in a cube?” Can you prove it? Can you build a cube? Sharing the many different possibilities in a class poster can encourage discussion and knowledge transfer. I can introduce vocabulary of length, width and height and touch upon concept of surface area.

Ms. Duncan holds a strong belief that mathematics is for all students. Moving from teaching a select few, who either understood the concepts or didn’t, to reaching and teaching all students, gave Ms. Duncan a sense of pride and accomplishment. Re-charging her batteries at the end of a 15 year career, she believes today that all students are naturally gifted learners. According to Gardner (1993), student intelligences can be categorized as follows: Verbal-linguistic (word smart), Visual-spatial (picture smart), Musical-rhythmic (music smart), Body-kinesthetic (body smart),  Interpersonal (people smart), Intrapersonal (self smart), Naturalist (nature smart). Considering the multiplicities of how all people learn, an important goal of education is to apply knowledge outside of school in the social and cultural settings of our greater life.

How can we make math exciting?

Ted Talk - Adora Svitak