MacKenzie Guynn PRO HARKNESS For the past few years, Honors Pre-calculus has been taught using the Harkness Method. For those of you who don’t know what it is, the Harkness Method was developed at Phillips Exeter—- a boarding school in New Hampshire— as an extension of the Socratic Method. It is based off of the idea that students will better learn the material if they are responsible for teaching and finding ways to explain it. A typical Honors Precalculus class consists of students discussing the 4-7 homework problems they did the night before, presenting designated problems to the class, and ensuring that their peers understand the concepts before moving on. This leaves no time for a planned lesson by the teacher. Daniel Schwartz, a junior in Honors Precalculus confirms that “the teacher lets the students teach themselves as much as possible, but when something needs to be addressed, then the teacher will jump in.” People say that you haven’t mastered a subject until you are able to teach it to someone else. By this logic, having the students teach their peers deepens their understanding of the subject. But it also creates a more interesting environment in class than when a teacher is merely lecturing you on a new chapter, as many math classes do. Annabel Edwards, a current Harkness Method student, notes that class “is challenging sometimes because there is no teacher to help and you have to figure out the new material each day as a class. Despite this, the discussions we have make it more fun and interactive than a normal math class.” The challenges that come with having to come up with a way to solve an equation on your own rather than have a teacher lay out a specific set of steps to take often makes the class seem daunting. But in the end, learning how to solve things in a way that makes sense to you and learning how to challenge the process are two valuable lessons for life in general. High school is supposed to prepare you for college and life after schooling, where there is most likely not going to be one way to solve a problem, nor will there be an instructor to offer a step-by-step procedure. Also, keeping with our theme of leadership this year, these two lessons are key values for a good leader to have. I mean, think about it—would you rather work with someone who doesn’t offer new ways to do things or someone who challenges the status quo and offers a different outlook on a problem? With that having been said, don’t think that if you never take a class taught with Harkness you will never learn these skills. You can develop them through various avenues, but taking a Harkness class definitely wouldn’t hurt both in your high school and life careers. Hannah Korach ANTI HARKNESS My first encounter with the Harkness Method was in my freshman year Algebra 2 Class. Applying this method to Algebra 2 wasn’t conventional— it was used to show us what math classes would look like for us in the future. Although our experience with it was brief and only covered one unit, the outcome was a variation of reviews and feelings about the learning structure. Many of us didn’t perform well on the first test. We were unsure of what caused our poor performance. Were we bad at teaching one another? Were we missing the point of Harkness itself? It seemed like we just weren’t used to learning new material through this new, dynamic system. We would go home, complete our respective problems in the homework packet, and discuss them in class with little teacher-interruption. Class would move slowly, and apprehension to present problems would build. But, more often than not, we were just stuck. Even reaching what we considered collaborative break-throughs did not suffice as a complete understanding or reasoning for why our math worked. Lily Campbell, my classmate in Algebra 2, explains that “forcing kids to teach each other things they don’t fully understand is ineffective. They need some sort of guidance from the teacher and work on the topics collaboratively.” Although Harkness includes some teacher input, I find it easier to learn one specific solution for a complex problem. A lot of appreciation for math comes from the fact that there’s little to interpret. One simple solution reigns. Harkness essentially takes this away, forcing you to reconsider the one method you felt solid about. Leave that imaginative thinking for English class. My brother, Daniel Korach, also believes that the Harkness teaching method left him feeling lost. “Harkness’s emphasis on a student-led environment leads to many instances of equally confused students playing the role of teacher, which often left me feeling uneasy about the material.” Students should be able to have their teachers as a leader and resource in the class, not a lifeline who you only ask the most vital questions to. Teachers are consistent instructors whose consistent presence is integral in the classroom setting. Harkness is a method that often leaves the students feeling unsatisfied, unsure of their work, and lacking direction. ]]>
zmcarthur • Nov 7, 2017 at 8:21 pm
Come by sometime, Hannah! Your feelings about this style of learning are certainly not alone at Latin — it is uncomfortable at first for many (and for some students, simply not the best structure to learn the most). But I think there are many advantages to learning this way – seeing unfamiliar problems and trying to solve with different techniques learned previously, connecting concepts, recognizing patterns, hearing a variety of voices on what your peers “see” in a problem, and figuring out, as a class, what methods work best for certain situations. I would also generally push back on that the teacher is not that involved in Harkness learning – I find it’s often my most challenging class to teach, deciding how to direct conversations, what student ideas to delve into, and when to fully “jump in” (as Mackenzie wrote) and give more direct instruction.
zmcarthur • Nov 7, 2017 at 5:49 pm
Interesting article! A couple sentences that stood out to me, from Hannah’s half, and a math teacher’s reaction to them:
1. “A lot of appreciation for math comes from the fact that there’s little to interpret.”
From my perspective, appreciation for math comes from the fact there’s so much to interpret! Problems that have little to interpret are boring. Problems that have a LOT going on, nuanced questions, problems that have many ways to solve them, like many in the Honors PreCalculus “Harkness” class, are the reason I love mathematics. Who wants to just be asked to find the y-intercept of a line? Yes, there’s an answer. It’s clear. There’s nothing to interpret, unless some context of the problem leads the y-intercept to have meaning. That kind of problem is, in my strong opinion, not mathematics. Mathematics is looking at a problem, taking time to understand the problem, attempting a solution, interpreting the solution, and deciding whether that solution is meaningful… and then trying to solve the problem another way. Mathematics is far from black-and-white – the best problems are shades of gray where different students can take different approaches based on their particular skills and everyone can defend their own solutions.
2. “Leave that imaginative thinking for English class.”
Hannah Korach! (side note: I don’t know Hannah at all but did love teaching her brother last year in Honors Pre-Calc.). MATH IS ALL ABOUT IMAGINATION!!! Math is not about memorizing rules and applying them. Math is about recognizing patterns and making inferences and trying new ways of looking at things – it is about CREATIVITY and taking risks and running into dead ends and understanding why you’re at a dead end. Problems that have straightforward solutions and processes to get to those solutions are barely math. Only when you need to use your brain to really work to solve problems are you starting to do math.
p.s. I think Harkness is a great way to spark the imaginative interpretation that makes math as fun as it is, but do understand the structure of the class can make some uncomfortable at first. Based on end-of-year student feedback, 90%+ of students that go through a full year of Harkness learning like it as much or more than a more “traditional” math classroom setup. I hope you give it another chance someday!
hkorach • Nov 7, 2017 at 7:40 pm
Yeesh alrighty! Math is my favorite subject. I think it is awesomely creative and I get legitimately excited to see the math section on standardized tests, regardless if I know how to solve it. I’d be very open to practicing the Harkness method further and hope I get to take a class where it is taught because I can totally see the good in it. I wrote the article because I could also see the negative parts of it that other students felt and wanted to try writing about it in the forum! (I mean, it feels pretty good when something you write is good enough to be published next to all the elite, unreal student writers). But if you would like to discuss anything further I would be happy to! Thanks for reading.