March 9, 2018 | Vol. 2 No. 17
Mathematics at Sparhawk School
Tree Tapping Math
By Suzanne Atkins, Lower School Director
We have arrived at a wonderful Sparhawk tradition of tapping our many maples at the Lower School! Sparhawk upper school parent, Chris Hicks from Morning Star Farm, started this tradition when his son was at the lower campus and he has generously returned every year since. Chris arrived with all his tree tapping equipment, his knowledge and his enthusiasm! Students identified their bright blue bags, grabbed their taps and were off to find a maple ready for tapping.
Maple tree tapping offers many cross curricular learning opportunities, particularly in math. Our youngest children learn that it takes 40 gallons of sap to make just one gallon of syrup and they have gathered 40 gallon jugs to get a real feel for this vast quantity. Maple trees should be at least 40 years old if we are to tap them, if teachers were maple trees, some of us could be tapped and some of us could not! In addition to measurement, maple sugaring also provides many opportunities for more sophisticated math such as geometry, data analysis and temperature variables: a maple tree must be 12 inches in diameter leaving us to figure this number using the circumference and pi; a sugarer must analyse diameters and circumferences in order to determine how many taps can go in any given tree; and the outdoor temperature at night and during the day are important factors in knowing how much and how fast the sap will flow to name just a few.
The kids get so excited to see the sap run from the spout into their personal bags and they vow to join the Tree Tapping Team and empty their bags daily. We will follow the process from tap to syrup throughout the next several weeks, culminating with the annual Maple Syrup Party at the Lower Campus!
To view all photos, click here.
Building 21st Century Math Literacies
By Casey Wright, Upper School Math Teacher
As an Upper School Math Teacher, I employ ideas I gleaned from my study of successful Finnish schools into my Sparhawk Upper School classroom. Those ideas include assigning less homework, having students collaborate more on quizzes and tests and employing a more Socratic system of wrestling with math concepts (instead of memorizing procedures). I am building a foundation of 21st century math literacies that allow students to solve the "puzzles" presented in more advanced mathematics classes.
Less homework and exploring math concepts with peers allow students to feel more refreshed in class while they discuss and navigate ideas in concert with other voices. I help students make sense of often arcane wording in the math text by "interpreting" concepts presented in each section of the text and writing a more cogent presentation on the white board to launch each new area.
Middle School Math Fair Showcase
By Diane Hichborn, Middle School Math Teacher
What a great way to have fun doing math! Sparhawk School Middle School held its annual Math Fair this past Tuesday. Students displayed mathematical problems and puzzles of all proportions for guests to ponder and solve. The purpose of the math fair was to give the students a meaningful experience in problem-solving, and an opportunity to share this experience with classmates and family through a visual presentation. This year each student researched a mathematician and learned about the type of math that they are known for. In turn, students chose a math puzzle with a similar concept to work on and present. The students become experts at their puzzles and projects through the preparation process and then present them with confidence.
Displays of various logic math problems such as Einstein's Fish Story, Fibonacci stones, or John Nash's The Hex, to ciphering and decoding number problems introduced by two women mathematicians; Elizabeth Freedman and Katherine Goble were present. From the interactive probability problem; Three Hats, to solving Blaise Pascal's Triangle and a Perelman-type 2D challenges were offered. Parents and families that came to the fair were afforded chances to brush up on their math skills when trying to find three fractions that were equal to 1, using numbers 1 – 9 only once. Some guests tried their hands at plotting parabolic curves on a graph, Sudoku, or worked their way through Ptolomy's concentric rings.
This year's Math Fair was a successful and enjoyable event: a way for students to practice leadership, initiative, and to find creative ways to solve and share problems with their community.
To see all math fair photos, click here.
Mathematical Project Based Learning
Statistical Analysis for Solving Real Life Problems
By Jennifer Esty, Upper School Stats Teacher
The Statistics class has activities throughout the year that bring a more realistic way to help students develop and apply their skills in examining data, reaching conclusions, and supporting those conclusions in a coherent fashion using graphical, numerical, and written analyses.
Projects are defined by the RAFT.
*R= role (reporter, researcher, manager, college TA etc.),
*A=Audience (newspaper reader, the "boss", employees, consumers, etc.),
*F=Format (written report, memo, presentation, poster, commercial, newscast, etc.),
*T=Topic (Race and the Death Penalty, How Much States Spend on Education, Sports Utility Vehicles insurance by model, creating Normal models for professor, smoking, etc.).
This challenges the student to get beyond the text, a list of problems or vocabulary words to connect with real world data and present data, and their conclusions, just as those working in the industry would. This allows the student the opportunity to bring their own perspective to the analysis and conclusion. Faced with the serious topic of smoking or the death penalty they are transformed from a math class to a member of our society facing the implications and responsibility of how data can be presented and the real ramifications found in conclusions. Training a critical eye towards both the data and how it is being presented helps sort through the complicated "fake news" world.
I Admit It, Math Wasn't My Favorite Subject In School
By Lisa Hughes, Lower School Teacher
Most of us adults recall being taught math one way: through algorithms listed in a book, solving equations step by step, with one approach and one answer. Oh, and make sure you "show your work" (any of you mental mathletes will cringe at that one). I was okay at memorizing the steps through oodles of practice, although I did not do well on math tests. Ugh. I never really understood the conceptual underpinnings of what math is or why following an algorithm worked. I was going through the motions, which led to one academic disaster to another straight through high school.
When I became a teacher and landed at Sparhawk in 2005, I vowed to myself and my students that I would do my best to make sure their experience was not the same as my own. And that goes beyond just having a year with a teacher who "gets" you as a learner - we can all recall having a year with a teacher with whom you felt no connection and learned little, and the teacher with whom you connected and learned a TON. For me, third grade was a year of tears as my teacher pulled her hair out attempting to teach me regrouping ("borrowing"); but fifth grade? Straight A's as I plugged into the math taught by a skilled and fun educator. Which, by the way, did not last. By sixth grade, I was back in a mathematics purgatory again, attempting to keep up with my peers, but failing.
Encouraging growth in math goes beyond having the right book and the right teacher - it's about providing opportunities for a student to develop their own intrinsic motivation and confidence around this subject. One looks forward to math class. One revels in it. One owns it. Gone are the butterflies in the belly when it's time to go to math, reduced is the feeling of dread when faced with an assignment. Most importantly, that inner voice that says. "I can't do this, I'm no good in math!" is no longer in control. Almost everyone can do math as long as the individual learner is considered and supported by the teacher, and even to some degree, his or her peers.
Which brings me to the Sparhawk Lower School approach to math - just what is the reality of our program on a daily basis? Sure, you can read our philosophy on our website, but what is it like in the trenches? Well, I can tell you from experience, our ultimate goal as teachers is this idea of student achievement. It's not getting through the material, nor is it teaching to the test. It's instruction that shifts and morphs according to what it takes to raise the bar for everyone in our class, even if everyone's bar is set at differing heights.
According to Steven Leinwand, author of Accessible Mathematics (Heinemann, 2009), instruction is what matters most. By making shifts in how teachers deliver the information, students can benefit the most from these interactions and empower themselves. I love this one small tidbit Leinwand offers in this fascinating book, and I will present it to you for consideration:
Teacher: Well, we've read the problem and now we need to ask: what is the difference between 31 and 12?
Student #1: 18!
Student #2: 19!
How do you proceed? It's a pretty simple problem. Do you acknowledge the correct answer and move on? According to Leinwand, no. What comes next from the teacher is to present it to the group: which answer makes the most sense? Do you know how to prove the right answer? How many different ways did people solve this? What do we do to check our answer? Why is it important to be accurate? Best of all, those less confident learners who may or may not have the answer are drawn into the discussion, rather than left passively listening to the "better" students rattle off the answers, which, again, may or may not be correct.
That is just one thread woven into the fabric of a typical class, where a myriad of techniques are present, designed to engage and encourage. In math, the answer to a problem (whether a student is correct or not) is not the end of the conversation, it's an opportunity to learn. Which brings me to our most recent event, the Math Fair. This is always a fun and interactive event, full of enthusiastic students who want to share their math puzzle with the world. According to SNAP mathematics foundation, the event is "like a science fair", the math fair has tabletop displays presided over by students, (and is):
"The purpose of a SNAP math fair is to provide a meaningful problem-solving experience for all students. The students will gain confidence in their problem solving skills, they will learn that enjoyment of mathematics is not confined to "elite" students, and it will create in them a favourable attitude towards mathematics. If our anecdotal evidence is to be trusted, they will improve their abilities in all aspects of mathematics." ~www.mathfair.com
It's also a way to shake up the normal routine and get parents involved in sharing the joy of exercising our brains with hands-on logic. I do hope you enjoyed the event - it's one of the most simple yet powerful displays of what we endeavor to generate with our math program: enthusiastic students who are confident presenters and owners of their own learning.
To see all math fair photos, click here.
Beyond the Textbook
By Mitch McDonald Upper School Math Teacher
Engagement in mathematics is critical to comprehension. Math textbooks can get dry and boring at times and at times like these we head in a different direction. Working together, students learn from each other's mistakes, assist one another with solving problems, and experience material from a different lens. Listening to your classmate explain a solution to you can be a nice change of pace from a teacher's explanation. Math class at Sparhawk while challenging is also fun as well.
In Algebra 2, students practiced for their upcoming test by using various methods of practice. One type was Kahoot, an online learning tool that is similar to the game show "Who wants to be a Millionaire?" Given four choices, students must race against the clock to solve complex algebra problems. This way of studying simulates the pressure of a timed test in a fun competitive way. Another approach was breaking into teams and racing to solve problems. Under the crunch time of a race, students realize how well they know the material. Working together allows discussion and debate over which strategies to use and helps students become confident in their approach. The comradery and excitement in these methods allows students to dive in and really engage the material.