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Math Lessons: To the Bat Cave!

Categories: Adolescent Program / General Knowledge Fund / Going Out / Practical Life / Trips

From Mrs. Mayhugh: 


Many of us will have uttered, “When will I ever need to know this??” while attempting to solve pages of equations for math homework.  We didn’t see how anything we were doing could be relevant to “real life.”  Seeing a formula in a text book, calculating the answer, and handing the page in for grading was the entirety of the lesson.  We were just supposed to know how.  Rarely did we know why. 


In her article “Math and the Adolescent Mind,” Catherine McTamaney discusses how math in a Montessori Adolescent Community can differ from a traditional environment.  One of the biggest areas of difference is in the application of the lesson.   Montessori Adolescent Communities are immersed in the “real world,” applying mathematical concepts and formulas to situations they’re encountering daily as a part of their curriculum.  They design their own spaces; they cook their own lunches with groceries they’ve shopped for and planned for given their recipes.  The students are going on trips that ask them to explore the world around them, make budgets, set up temporary housing for their classmates, build structures, and do things independently that they haven’t tried before.


They ask questions and WANT to find answers.   How does this relate to math?


Math in our Adolescent Community is applied mathematics at a lofty level.  While the physical Montessori materials are available, students at this age are capable of seeing broad, abstract, “big picture” concepts.  They’re looking for patterns and connections – for formulas that will give them answers and make sense of their world.  


Kelly Jonelis, our Math Specialist in the Adolescent Community, expanded on the importance of relevance for her particular area of study.  She noted that when this age group sees the relevance of what they’re being asked to do, the struggle and the fight just doesn’t happen.  Yes, there are still frustrations, but the battle to get going on their work isn’t as prevalent as it is in a traditional setting.  Students are looking for an answer to a question that THEY have asked.


A few examples of applying math to every day life in our Adolescent Community include:


Every week our Adolescent students plan lunch for 14 students.  They vote on recipes (that must meet a nutritional guideline).  They then create a grocery list while consulting their grocery funds (collected every month).  When you’re cooking for 14 hungry mouths, but your recipe only serves 4, how do you know how much to buy?  Math.  Every week students multiply quantities when scaling up recipes to serve a group of 14. This often involves converting to different units (think 12tsp = 4tbsp = 2oz = ¼ cup). Students care about these conversions because it makes their food preparation easier. When the students shop, they calculate and compare costs per unit; determine the total cost of their items, including tax; and ensure that they, as a group, have stayed within their weekly shopping budget.


During an outing, the students saw an excavator moving rocks across a river and observed a several second sound delay.  They later calculated the width of the river based on the length of the sound delay.  The students were out and about; they experienced the sound delay firsthand.  They wondered about the actual distance.  And then calculated it.


After debates on their recent camping trip about which tent was larger, the students calculated the volume of each tent.  Why calculate the volume of the tent?  Because they WANTED to know.  Like most adolescents, they were debating.  How do you solve this debate?  Math. Each student tackled the question in a different way and then they compared solutions.  Were the answers from different methods similar?  If they weren’t similar, why weren’t they?  The class makes a point of discussing and addressing different ways to solve each question.


While gardening and setting up the tomatoes that they would care for all summer: Students measured the raised beds and calculated the surface area to determine how much paint was needed for full coverage as well as the volume of mulch necessary to cover all beds at a given depth.  These students want a successful garden so that they can later sell the produce.  What will they need?  How do they know how much to buy? How do they figure it out? All of these calculations are not only relevant, but helpful. It makes the students’ jobs easier.


While touring caves in Hannibal, Missouri, the tour guide pointed out large circular marks on the ceiling.  The markings?  Footprints left by the oils on the feet of the bats as they clung to the ceiling, making a “bat chandelier” (layers upon layers of bats clinging to each other down from the ceiling).  Given the immense amount of markings in a pattern on the ceiling, the students wondered just how many bats could fit into this “chandelier.”

When the students returned from the trip, they researched native species of bat for the Hannibal area.  They researched the shapes and sizes of each of the species likely to inhabit that particular cave.  They asked the tour operators of the cave to measure the diameter of the circle where the markings were seen.  Now the students knew the diameter of the space, the size and shape of the likely mammal inhabiting it, and a general idea of how many bats were clinging to the ceiling.

With this information, each student set pencil to paper to try and puzzle out: How many bats could fit in the CONE that they form in the cave?  In other words, what is the volume of the cone that the bats are filling in the cave and how can that volume translate to a quantity of bats?


Wait.  Is Mrs. Mayhugh actually trying to say that finding the volume of a cone of bats clinging to a cave ceiling in Hannibal, Missouri is “relevant”?


Back to that memory we all have of our early years uttering, “When will I ever need to know how to do this??”… 

When will you ever have to calculate how many bats could fit into a conical shape in a cave in Hannibal, Missouri?  When you VISIT the cave and ask that question.  The relevance to the students’ lives comes from their direct interest.  It’s not an assigned hypothetical.  They’re experiencing the math problem in real-time, focusing on it in real life.



CommuniTEA: FAQs with Mrs. Mayhugh
Sep 24 @ 8:15 am – 9:15 am

Please join Mrs. Mayhugh for coffee and community as she goes over your “frequently asked questions.”

CommuniTEA: Parent-to-Parent
Oct 10 @ 8:15 am – 9:15 am

Join fellow Wheaton Montessori Parents (past, present, and future) for a morning of socializing and connecting.  Refreshments provided!