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Math: Understanding WHY, Not Just HOW

Categories: Adolescent Program / Practical Life / The Montessori Difference / Why Montessori / WMS Programs

How many of us remember getting THROUGH certain subject in school, but not necessarily understanding the concepts?  Or as Mrs. Jonelis said she’d hear from struggling students in high school tutoring sessions: “I do fine grade-wise, but I don’t know what I’m doing.” Traditional models of education can fall into the trap of “teaching to the test” or teaching just enough for a student to “get by,” without actually ensuring that students are “getting it.”

How many of us remember muttering, “When am I ever going to use this?” When will I ever need to know this again?”  These questions get asked much more frequently at the Jr. High level, as students start to think more globally and about their own futures.   It needs to be useful and relevant for these students, beyond an exercise.

Students in the Elementary Classroom using concrete materials to determine the total number of valentines exchanged by the entire student body. Spoiler alert: it was a HUGE number.

Understanding the theory behind lessons is important.  In a conventional setting with pressure placed on grades and test scores, many teachers are forced to focus on the “how” of a lesson, but not the “why.”  With mathematics, this can make mastering increasingly complex areas even more difficult to understand.  And so a student memorizes the steps to take, without knowing why the steps matter in the first place.

When talking about this issue – understanding the motions and steps, but not why they actually matter – Mrs. Jonelis said, “Understanding the theory behind math is so important.  But in short 4o-minute classes, many teachers are forced to teach only the HOW.  There isn’t enough time to teach the WHY.  And the WHY is always the more important one.  If you understand WHY, you can instinctively puzzle out the HOW.

“For as long as I can remember, I wanted to teach.  In grade school, I discovered math.  It was ‘my thing’. I just got it.” – Kelly Jonelis, our incoming Math Specialist in the Jr. High Program.

Mrs. Jonelis, who joins our staff this Fall, is excited to have the opportunity to share her passion for math with the Junior High students.  She’s already planning with Dr. Bilezikian how they can work math into every day activities, beyond the classroom.  Dr. Bilezikian remarked, “She’s already thinking about exercises and discussions that never occurred to me.”  Her mornings will now be dedicated to sharing “the WHY” with our students.  She’ll be able to share when – and why – mathematics will come up in daily life.

Shopping for groceries, planning menus, and budgeting for class meals is a large part of the week for our adolescents. Comparing prices, determining cost per ounce, measuring and multiplying ingredients, and more come up during shopping trips.

In January, Mrs. Jonelis spent the morning with several of our adolescent students getting to know them a bit better.  One of the students was researching a crime wave and was talking to Mrs. Jonelis about the statistics in the research.  The 7th-grader noted that she wasn’t sure how confident she was in the conclusions that some of the authors were making.  An entire dicussion on having a true random sample for research, accurate statistics, and conclusive data ensued.  The adolescent student’s takeaway:  If you want to be confident in your own position, make sure your data and statistics are accurate.  (And how you can tell if they are!)

Other discussions that morning:  Figuring out which sledding hill will be the fastest (calculating slope).  Grocery shopping:  using the class budget efficiently, selecting recipes with ingredients that overlap for less waste, different types of tax for different items in the store.

“When will I EVER use this again?”  Mrs. Jonelis will be showing Jr. High students the WHEN, WHY, and HOW.   “Math is everywhere.  This is the age where students really start asking, ‘What am I ever going to use this for in real life?!’  In this particular environment, we can pursue to many areas that math IS useful and relevant.  I love math so much that I see it everywhere.  Being able to focus on where it comes up naturally instead of through a forced curriculum allows it to be more beautiful and interesting for these kids,” says Mrs. Jonelis.

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