Montessori Education Week - Testimonial Wall
Elementary Montessori Students Teach College Education Majors
A group of our upper elementary students spent the afternoon "teaching" a class of college students about Montessori. They were invited by a math professor to present the Montessori math materials to his math education majors. The chequerboard, flat bead frame, racks and tubes, the cubing material and other apparatus spent the day at KU opening a window into the Montessori world for these young soon-to-be teachers. Acting as ambassadors of Montessori, these children, as do Montessori children everywhere, provide the best reason to further explore the method. Their knowledge, skill and enthusiasm for math (for life!) is infectious! Maybe one of those young teachers will look at their future classrooms of children in a new way, or in the future send their child to a Montessori school. You never know the seeds of interest you plant in our journey as Montessorians and how these seeds will take root.
For the past seven years we have dreamed of the day when we could develop the back end of our property building a running path with bridges over the creek surrounded by wildlife
One of my former students, at that time 8 years old, had always wanted to build one of the bridges across the creek. He spent a lot of time designing, making models and doing experiments around the construction of this bridge.
Due to the recent fire at our school, the subsequent rebuilding and the change in zoning requirements, we were forced to completely resculpt the land. During the permit approval process, I told the city engineer we would be building wooden bridges. He said absolutely not citing the amount of water that rushes through the creek in a downpour. Instead, we were required by the city to construct low water bridges made of concrete and ugly metal tubes.
Enter my former student now a ninth grader and preparing for his Eagle scout project who made an appointment to talk with me yesterday. After reminiscing about the old days, I began the meeting by telling him about our construction projects (something I knew he would be interested in), how I wish we could have built the bridge he designed six years ago and so on. "Funny you should mention that bridge," he said as he spread his drawings out on my desk. "I talked to the city engineer and initially he said no, but after I showed him my sketches and he realized I would be incorporating 2 steel I beams in the construction, he said yes." Dumbfounded, I looked at his drawings. Before me were details of each section of the bridge from different angles. I couldn't believe it. Later upon reflection I could.
Of course, I don't know if he can write a paragraph with punctuation in the right place which was something he struggled with, but he can certainly design a bridge!
Those Montessori kids.
Gotta love 'em.
lleanna at raintree on a beautiful fall day in Kansas
Look Dad "It's a tetrahedron"
(the Montessori / Buckminster Fuller fans will especially like this one):
This morning, my daughter who had just turned 5, was playing with our magnet set, which is incredible for building structures.
She built a tetrahedron, and said "Look at my tetrahedron, daddy".
She built a cube and said "Look at my cube melt, daddy. "
(because a cube is incredibly difficult to stand by itself - it "caves in" on itself!!)
If you want to be proud of your children--
I'm not saying that is a very desirable thing--
there's nothing like having them go to a Montessori school.
When your 6-year old daughter talks with her grandmother about bones and muscles and knows the correct terms (like fascia latta or phalanges) it's fun to see the expression on granny's face.
When your 8-year old son visits a rock shop with you and the owner wants to impress him with the wonders of minerals so he asks him if he knows what's interesting about Iceland spar (a form of calcite) and without missing a beat your son says, "Yes, I know, it's doubly refracting," (and you don't even know what doubly refracting means,) It's fun to watch the owner's face.
When you read a news story with a dateline of Colombo, and you realize that you never until that moment knew that Colombo was a country's capital, and you ask your son (who, remember, goes this strange non-graded Montessori school) if he knows where Colombo is the capital of, and when your son instantly says, "yes, it's the capital of Sri Lanka." it makes you realize how much better an education he is getting than you yourself got.
And when your son at 18 owns his own apartment house and decides not to go to college, and at 20 he gives up a promising computer-related job at Paine Webber to take a volunteer job with Outward Bound (and you wonder about the wisdom of letting go such a promising position) but when at 24 he is one of the most senior and respected councilors with Outward Bound on the east coast, and when at 26 he is putting himself through college (and in the process, with more rental properties owned, he has more income per year than you do) and is poised to become a graduate fellow specializing in chemical physics, you understand that his Montessori education was the only one sufficiently broad in scope to properly prepare him to exercise his God given talents. And you also come to appreciate how we have to let that "inner teacher" that Montessori talks so much about be the child's guide, for every time we would have chosen instead for him, it would have kept him from blossoming into the wonderful, warm-hearted, multi-talented individual that was always there from the beginning (and we just didn't see.)
Read up on Montessori so that you will have the courage to choose it (and be a parent compatible with it--that's important too.) Then go for it. You'll never regret it.
Montessori - A Life Changing Event!
For most six to eleven year olds elementary school is a time for playing “chase” with the boys at recess, and cheerleading for the pee wee football team. For me it was a time of personal growth. To some the thought of an eight-year-old learning life lessons is outlandish, but for me it was completely natural.
My life changing elementary years were sparked by the intuition of my mother. She was the co-founder of Portage Collaborative Montessori School in North Canton. After I had gone to Canton Montessori School for pre-school and kindergarten, I attended Northwood elementary like most first graders. Although my mom thought this was a good school, she believed that the Montessori method created a better learning environment for me. Since no Montessori elementary schools were close to my home, she helped to found one here in North Canton.
In third grade I became one of the three guinea pigs in my class to attend this trial-based school. Montessori school taught me so many important lessons that I would have never learned until later in life if I had gone through traditional schooling. In Montessori School students were independent in the classroom and were free to walk around and talk with classmates.
The teacher would hold lessons to show the students how to use the Montessori materials, but it was up to the students to get it done. In fourth grade instead of learning the process to do long division, we had Montessori materials of little beads to represent numbers. The teacher would hold a lesson for five or ten students to show how the materials were used and the students would then have to work with that material three to four times a week. The Montessori materials would give the student something visual to represent the process that was taking place, instead of just working with pencil and paper. Later, after the students mastered the materials the concept would be applied without the aid of the material.
This process of learning eliminated listening to a teacher lecture, completing homework, and having tests. The students were expected to learn the materials without the threat of a test. This type of schooling promoted the student to be motivated to learn himself, instead of by the teacher. The classroom was filled with mixed ages of children. My class was a mix of first, second, and third graders, and one teacher and one assistant helped with any problems students may have encountered.
This idea actually worked for me. I loved school. Getting up in the morning to learn new things, figure out math formulas, and see my friends was the best part of my day. I was free from stereotypes of normal suburban public schools, and from being judged based on how involved my parents were in the PTA, or what I looked like. Instead of conforming to my environment, I became an instant leader. Everyone in the school looked up to my two other third grade classmates and me. Looking back, I enjoyed very bit of elementary school. Not only did we set a good example for the younger students we has a blast at the same time.
The four years that I attended that school taught me patience, motivation, leadership, and a love for learning that has never left me. I was beginning to find out what life was all about, something other students do not realize until the joy ride of high school is over. All of these skills helped me immensely when returned to public schools in seventh grade. Since I was so used to standing out and having people look to me, that was what happened. I wanted to be noticed: I never wanted to be that shy new girl, and I made sure people understood me. Instead of trying to fit into my surroundings, people adapted to my personality and found a fresh new outlook in contrast to monotony of middle school dramas.
I do remember a few times I complained to my mom about Montessori school, mostly because I was somewhat nervous switching back into public school. I feel bad about that now. My mother took a chance and gave me a gift that other moms criticized her for giving me. She helped shape me into the person I am today instead of letting my peers shape me into what they wanted. I am forever grateful for the perspective I gained by going to this school. I not only learned to love fractions and grammar; I learned to love who I am.
Junior at Hoover High School
North Canton, Ohio
Number of Handshakes
Tom had attended Montessori classes from preschool through sixth level. He now attended a small Catholic Junior high school in a small farming community in Northern Ohio. One of the math challenge questions from the eighth grade Math Book assigned by the teacher stated, “If there were 10 people in the room, how many handshakes could each person give and how many total handshakes would be exchanged. (If person A shook hands with person B that was counted as one exchange. You could not count it again; therefore, person B could not be counted as shaking hands with person A.)
Tom came home from school that day and asked me what the formula that we had discovered in our 9 – 12 Montessori geometry lessons as to how many lines could be drawn from one point on a Geometric figure and how many total lines could be drawn in that figured not double counting the lines. Not remembering the math formula and noting that my Geometry album that contained those lessons was at school, a 45-minute drive from home, I questioned why he needed to know that formula. Tom explained the handshake problem. I questioned how that related to the Geometry formula of points and sides. Tom proceeded to explain that the people were just the points to a ten-sided figure and that each handshake exchanged was a line drawn from them to the other person or point on the figure.
I suggested that we sit down and work through the steps of the Geometry lessons to find the total number of lines from each point and the total number of lines for the whole figure. We began with a three sided figured, a triangle, and made a chart to record the number of lines from each point and the total number of lines in the figure. We then worked with a 4-sided figure and moved on to a 5-sided figure and so on. Finally, we noted the patterns that were developing and discovered the formula. To figure how many lines could be drawn from a single point in a figure the formula was n – 1 where n was equal to the number of sides of the figure. Therefore, for a 10-sided figure, n – 1 results in 10 – 1 or 9 lines from each side. So as not to count the lines twice this would need to be (n - 1) / 2 times the number of sides in the figure. That results in a formula of n (n – 1) / 2.
For a decagon the formula would be 10 (10 – 1) / 2 or (10 x 9) / 2 or 90 / 2 or 45 total handshakes.
For a 20-sided figured the formula would be 20 (20-1) / 2 simplified to (20 x 19) / 2 or 380 / 2 which equals 190 total lines.
To me this an example of the mathematical mind about which Dr. Montessori spoke – putting together a problem involving handshakes with a geometric lesson involving the lines from each point in a figure.
Jim and Mike's Power Pattern
Two sixth level young men, Jim and Mike, were completing the squaring lessons in preparation for square root presentations. Mike and Jim had found the square of most of the numbers from 1 – 100 on the “Square Chart” by many of the squaring lessons - “Squaring Binomials”, “Cross Multiplication”, “From Square to Successive Square”, “From Square to Non-Successive Square”, or just multiplying a number to find its square. Today they were completing the “1-100 Square Chart” by calculating the square of any number for which they had not previously found the square.
As I worked with other students and presented lessons, I observed the Mike and Jim were having what I thought was “way too much fun working on this project”. Between lessons, I strolled to their work area and casually asked how they were doing. They replied that they were not finding the squares of the number the way I thought they should (multiplying the number by itself). “Oh”, I replied, “How were they finding the squared of the numbers?”
They proceeded to explain that they were just adding the next the next odd number to find the next square.
32 = 9, adding 7 to 9, sum is 16 which is 42
42 =16, adding 9, the next odd number after 7, to 16 results in a sum of 25 or 52
52 =25, adding 11, the next odd number after 9, to 25 results in a sum of 36 or 62
552 = 3,025, by adding 111 the sum is 3136 or 562
562 = 3,136, by adding 113, the next odd number after 111, the sum is 3,249 or 572
572 = 3,249, by adding 115, the next odd number after 113, the sum is 3,364 or 582
and so on for all the examples they could show.
My undergraduate degree was in Mathematics. I did not remember any rule, proof, or lesson where I had experienced this before, but I could not find any error in their thought process. In addition, it worked for every example what we tried. Since we had worked with the History of Numbers, we had created a space in the classroom called “Math Discoverers of Today” where we listed math discoveries that the children made. At group time, Jim and Mike explained their “Power Pattern” to their classmates, and added their names and discovery to our wall of discoveries.
My only question to Jim and Mike was, “if I knew that 772 = 5929, what odd number do I add to get the square of 78?” They did not know, nor did I, but they explained that they could count by odd numbers up to 78. That worked!
Several years later, after Mike and Jim had graduated from Montessori and moved into traditional Junior High School, I was presenting the 9 – 12 Montessori mathematics lessons for a group of trainees in Chicago. As I was completing the squaring lesson, “From One Square to Successive Square” and calculating what had to be added to the square of 4 to get the square of 5, I observed the result was 9. Then we tried from 52 to 62 and the result was 11. There where the odd numbers that Mike and Jim had noted. I exclaimed loudly to the class, “That’s where they got it!” Of course, the trainees looked at me a little funny. I proceeded to tell the trainees the story of Mike and Jim and their “Power Pattern”. Mike and Jim had completed activities “From Square to Successive Square”, always calculating what would have to be added to the first square to get the next. They were always odd numbers. They were always the next odd number.
From this lesson I learned and continue to share with Montessori 9 – 12 math trainees
The brilliance of Maria Montessori in the Math lessons
The importance of presenting the lessons even if we don’t always see their value. With all the push for Proficiency Testing, too often unless the Montessori lesson is directly related to teaching a concept that is on “The Test” many of us tend to skip it
How the lessons promote the development of the mathematical mind – a thinking figuring out, pattern observing mind
How the lessons and use to the Montessori concrete materials put pictures and ideas in the minds of the children that even they don’t know are there
That we, as the director/ress, can continue to learn – I now know what I what odd number, 157, to add to 78 squared = 6,084 to get the square of 79. The side of the square is 78 so to go to the next square, one must add 78 beads down one side, and add 78 beads across the bottom and then one bead in the corner to fill out the square. 78 + 78 + 1 = 157
to allow children to feel comfortable to experiment with activities and to share what they are thinking or observing.