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Register Online NowOver the past few weeks much has been said about the natural progression of learning and about the delivery and design of curriculum. It seems a good time to address the influence of intention. As educators and researchers in the classroom it is important for teachers to introduce skills and concepts that are necessary for students to function as contributing members of a group. To that goal we have intentionally made math and logical thinking integral to all aspects of our curriculum.
We believe math is a natural part of our everyday life; with this perspective we mindfully help students comprehend the power of knowing math facts and broader concepts. To this end we intermingle mathematical thinking and application in every class we offer.
In Book Club the students reading The Jungle Book constructed a Venn diagram comparing and contrasting the classic story we just read to the wonderful performance we attended at the Algonquin Theatre. Using this visual aid the children were able to recall many details and events from each versions. This led them to talk about the story as a whole and the distinct variants from book to play. Many of the children recalled specific details about each version. This mathematical concept of sorting, classifying, comparing and contrasting allowed the children to consider what each had in common and what differed.
Before being able to communicate directions about how to draw comics the students in the Comic Drawing class were introduced to many mathematical concepts. We talked about shape and size, relationships of shapes in space, distance and length in inches and centimeters, proportion and angles and directionality, amongst other ideas. When drawing a simple character the students need to draw two tapered ovals of differing sizes. They must place these ovals within a half-inch of each other with the smaller above and slightly to the left of the larger. They can then attach these ovals with parallel lines and draw more slightly curving lines that extend down from the top of the torso oval and bend at a 45-degree angle away from the body. The lines must be proportional to the size of the body; each line should be no more than an inch and a half in length before it bends. Drawing this character requires the thoughtful application of a number of geometric patterns until the process becomes instinctual.
In Poetry and Lyric the students count and clap syllables to write haiku and other poetic styles. When looking at rhyming we label patterns of end rhymes and then devise our own patterns to follow. We listen to music and label the verse and chorus patterns as we read along. We discuss the beat and meter of poems and tap along to verse read aloud. This links directly to the work some students are doing in their Dance Class where they are counting the beats and performing steps along with the music. They are using spatial thinking as they figure out how to use a three-step pattern to move about the room and how to do the foxtrot based around a square taped on the floor, all the while keeping their steps in time with their partner.
In Botany class children talk about germination time, planting and harvesting seasons and temperature zones on the earth. They understand why days, nights and seasons occur based on the tilting of the spherical-shaped Earth and why it is hotter at the equator. All of these address spatial relationships and cycles. Students often converse about the symmetry they see in nature; the radial symmetry of a spore print or sunflower and the linear symmetry of leaves. They are able to see the mathematical order in the world around them.
The participants of the Strategy Games Class focus on many mathematical concepts as well. Looking at the game board, the player uses their spatial awareness skills to assess the situation, looking for patterns. To play successfully, she must learn to think ahead and visualize what the board will look like several turns into the future. She has to devise a strategy but revise the strategy as she sees what her opponents are doing.
The study of physics relies heavily on algebra. Even the act of measuring the strength of the students’ paper bridges require them to count the pennies needed to break the bridge then convert that to a mass and then a force. The conversion of units is everywhere in our society from the lab to the kitchen to the grocery store.
In the Fossil class, getting children to understand just how old their shark teeth were the teachers had to use a more tangible approach. If 100 years were one millimeter on a timeline, the pyramids in Egypt would have been built only about 50 millimeters (2 inches) ago, our ancestors were hunting mammoths 100 millimeters (about 4 inches) ago. The animals that left the fossils we found were alive and swimming at least 650 meters away (that’s about the length of our driveway).
During a recent Problem Of The Day, students were asked to figure out how many triangles could be found in a geometric figure. All of the children and teachers started counting and guessing. Everyone developed his or her own strategy. When discussing the problem later, one of the teachers took the opportunity to point out that the figure was symmetrical and that if you counted the number of triangles in one piece you could then multiply it by the number of pieces. This made solving the puzzle easier. Then a student pointed out that sometime this could lead to the same triangle being counted twice. This sparked another round of counting.
In Moviemaking students aligned music, audio clip and voice-overs with their visual images. They manipulated the length and transition of each clip considering how the viewer assimilates information. The Money class is of course studying currency and has been introduced to the concept of “2 for” as a way of selling items. They use division, multiplication, subtraction and addition when they are asked to shop within a budget. Storytelling has involved sequencing, an activity that requires ordering from memory beginning, middle and end. The trout class is focused on tank temperatures and use of the calendar. As we continue our work a timeline will develop documenting the progression and the events that transpire over the course of months.
Even during the housekeeping it is easy to find ways that math is integrated. Each piece of laundry has a specific way it must be folded. The hand towels for the boys’ room are folded into thirds and then in half again, that is sixths, whereas the hand towels for the girls’ room are folded into a quarter size to fit properly into the bins. The napkins are folded into eighths and the dishtowels into sixths. The snack cart is labeled with the number of pieces each child is allotted to take and the snack preparers must figure out before hand how many to offer based on what is available and how many students are attending that day.
During Baking students are using the tablespoon and teaspoon measurements and multiplying that into cups. They are converting cups to quarts to gallons. They are halving, quartering and dicing vegetables and fruits. They are learning about baking times and temperatures.
It is clear that the black and white of a math textbook is extraordinarily limiting compared to the environment we are intentionally creating. Math skills that are develop organically because they are needed as a means to solving a problem stick a lot better. We do feel that children must learn math facts and that when addition, subtraction, multiplication and division are mastered a student is more likely to see herself as a capable mathematical thinker. This leads her to engage in critical thinking and to debate and prove her methodology when considering a problem with others. She is free and confident and more likely to join in wholeheartedly. We intend to continue our mindful inclusion of math across subjects. We also intend to call children mathematicians and great thinkers and problem solvers.
