As I sat in the Sheridan Cafe tapping my foot against the leg of a table and my pencil against the top of a desk, I looked down at the Pre-ACT in front of me. I flipped through the pages, scanning the 36 problems I had 40 minutes to complete. Two of the problems were geometry problems: finding the value of an angle and the ratio of two sides. The other 94% of the questions were a mixture of mostly algebra, with a few pre-calculus/trigonometry riddles thrown into the mix. It was at that moment, tapping my pencil in confusion and trying to recall the properties of imaginary numbers and hyperbolas, that I realized my understanding of algebra, and not geometry, was about to have a huge impact on the trajectory of my life.
Geometry is like a puzzle. The pieces are scattered across a table in an entirely random order, aching to be put into the right place. Solving the puzzle and mastering Geometry, develops critical thinking skills. However, unlike other activities that require critical thinking and reasoning skills, such as Socratic Seminars in English or Harkness discussions in history, all the critical thinking on the proper geometric solution can go south if you don’t see the right shape, trace the correct triangles, or make the right construction in your process. Unlike an English or history class, once you go down the wrong path in geometry it is nearly impossible to “reason your way” to finding the solution. Unlike algebra – which focuses on always finding the elusive “x,” something we, as consumers, do every day when determining how much time we need to get to Starbucks and back or how much money we need to add to our Apple wallet to purchase the Starbucks – the skills taught in geometry aren’t unique enough to necessitate a full year of math curriculum.
This isn’t coming from a place of bias or discontent towards the subject of geometry. In fact, grade-wise, I did better in the first semester in geometry than I did in the first semester of algebra. However, geometry to me feels black and white. You either see a shape or you don’t. You are either a visual-spatial learner or you are not, and if you are not, there is no amount of studying or preparation that can give you the natural eye necessary for success in geometry. For those without the natural gift to “see” the shapes, it can be a struggle to find a way to study for geometry assessments. From the first, most basic, test of the 18 theorems unit to the infamous circles test, I found myself staring at my notes and homework and hoping that reading each line of the 23 step proofs would be enough to carry me through the notoriously impossible quizzes. After being handed worksheet after worksheet filled with contorted shapes and lines, my first semester of geometry had me reminiscing about Algebra II and the linear relationship between preparation and performance.
While geometry can be confusing, at times even demoralizing, algebraic learning feels more like a steady climb up a mountain. Pieces of a puzzle weren’t flying all over the place. The goal was right in front of you, with each step planned ahead and easily distinguishable. Everything from the most basic mathematical concepts to complex graphing could be found in my Algebra II final artwork made on desmos. Geometry projects, however, tend to focus on one particular concept to explain the thought process behind a single angle without any reference to ASA, SAS, or AAA. While understanding how to find the single angle likely requires understanding the earlier theorems, the demonstration of that understanding is implied. Either you see it, or you don’t. Just like the rest of geometry.
Algebra’s formulaic nature also makes success more accessible to a wider group of students. Students who take good notes, students who seek sequencing, students who learn through repetition, can all succeed in algebra. My algebra folder is filled with countless study guides from each test and quiz, briefing me on precisely how to do the problem in front of me. I knew what was going to be put in front of me: I was guaranteed a string of numbers pertaining to a certain unit, possibly a graph, and the occasional curveball that took a little critical thinking. When a problem is written in the test, the course and lessons provide the instructions needed to answer the question. Geometry, in contrast, relies on the independence and the automatic understanding of the student. Examples and notes rarely help the cause. Automatic understanding isn’t something that we need to struggle with for a full academic year to prepare for life after Parker. For those students who excel in geometry or who want to pursue architecture, structural engineering, art, or other disciplines that apply geometry, Parker can provide an elective course and allow students to pursue their passions in the true meaning of progressive education.
Algebra remains the more functional, useful skill building mathematical discipline. The critical thinking skills of ground geometry are not found only in the realm of two column proofs and circles that make students see red. Parker’s mission is to educate students to be “responsible citizens and learners in a diverse democratic society and global community.” The fun logic puzzles and 18 theorems engraved in my brain just aren’t critical to meeting the mission that brings us all to Parker everyday.
Owen – Geometry
Throughout my academic tenure, I’ve never thought of myself as a math person. Year after year, I kept finding ways to make myself feel like I was out of place, that I didn’t fit with what math was. Math was always too formulaic, too one-size-fits all. I subscribed to the ideology that there were those who were naturally gifted at math and those who just didn’t fit in. Maybe this was due to my mathematical beginnings coming from such a rough place. In first grade at public school, every Friday was “Math Day” and we were timed while we did our times tables. I was never first to finish, so naturally I thought I sucked at math in general, and I would never “get it.” For a while I believed this lie – that was – until geometry.
Geometry never felt like math that was just memorization and a mindless, procedural action. It’s cumulative and more logical than anything else. Everything I need to see as part of the “puzzle” of a problem is right there. I just need to question myself a bit more or force myself to see a problem from a different angle. Geometry is almost entirely visual and the sense of accomplishment that comes with finishing a seemingly complex problem is something I can’t really find anywhere else. The greater concepts of geometry are also highly useful outside of the classroom, which makes it stand out more than algebra. Geometry is more a way of looking at the world in shapes and questioning how to compare these shapes to one another, how to see similarities between a triangle and a circle, or a 67-sided polygon and a trapezoid. These things don’t seem easily related, but geometry helps us get there. That sense of trial and error is something we face everyday and it’s something strongly represented in the medium of geometry.
As well, the way geometry rejects the memorization element so prominently in algebra makes it stand out that much more, as it provides an experience that is solely centered around using logic and brain power to figure out a problem. Since it’s less clean-cut, it welcomes creativity and innovation. What I love so much about geometry is the way three different people can solve the same problem in incredibly different ways. All valid and correct, it just depends on how you see it. Such is life. We see things differently from a different perspective everyday and our freedom of opinion and creativity is what makes life more interesting and enriching. eometry fosters this experience. In algebra, there is the right way of doing a problem and many, many, ways of how to do it wrong, or so I’ve learned. When I consider how my education will impact me five, ten, thirty years from now, I will not be remembering how a logarithmic equation changed my life and made me think differently. I will remember how using my logical thinking helped me persevere through puzzles that just happen to be geometric.
Considering geometry universally, it’s incredibly different learning geometry at Parker than it is at public school. This distinction is mentioned heavily in my Advanced Geometry class taught by Mr. Wilson, but it’s definitely a valid point. The way content is taught is important to how it’s interpreted and internalized. At public school, geometry is converted into an algebra-like structure: memorizing theorems and just copying and pasting them onto other problems. It’s like busy work. Not to be cliché, but you gotta teach these kids face to face. We’re lucky at Parker to have an opportunity to learn a different but no less effective method of learning geometry. It’s really smart. By focusing the course on more conceptual life skills by way of the course content, students get the chance to see the world and the daily logic puzzles we encounter at a higher level and therefore these logic puzzles seem more manageable. The course is designed to last longer than just high school. Algebra gets you some questions on some test or something later on in high school, maybe some calculus senior year and college, but unless you’re truly going into math as a career, algebra will be virtually useless moving forward in life. These conceptual ideas in geometry will last far into adulthood.
In general, geometry is not only a more useful skill for school, but it is more useful for life in general. In a society slipping into a system that no longer sees questioning authority (whether governmental or economic) as worthwhile, it’s of vital importance that we learn how to think critically and to see “the image” from all perspectives. For algebra, whether we like it or not, we’ll turn to Google. For geometry, it’s imperative we rely on the power of the human brain. We’re all made better for it.
