Harkeness Math

Which schools use harkness table for Math? I know Exeter uses in math.

@winworld123 - I suspect this is a harder question to answer straightforwardly than you might think. It depends what you mean by Harkness table (literal table v approach) and even teacher by teacher.

From what I understand, there is the Exeter math curriculum, used by many. It doesn’t use a traditional math textbook. It doesn’t require a Harkness table, per se, but it is discussion-based. Kids do the homework - a set of problems without instructions - then bring their solutions and failures to class for group discussion. The idea is that students will see there are multiple ways to get to the same result and become more comfortable with muscling through hard problems- it is ok to not know immediately how to do something. You know, like how life really is. But it can be very uncomfortable for people who do better with knowing the rules up front.

The other part that is confusing is that the instruction isn’t strictly divided up into neat self-contained slices of only geometry or trig or algebra, etc. There is a mix in each course- all concepts you have learned are fair game and can come up at any time, within the progression of the problem sets. If your approach to a problem uses trig and someone else uses algebra, that is cool and will be great fodder for class discussion.

At Cate, the honors math classes follow this model, but not all classes. Within the honors classes some teachers more than others will give students direction. But the classrooms don’t all have Harkness tables. The ones I have seen the kids arrange their desks in a circle.

I think many of the boarding schools are adopting this way of teaching math at least in part, but others will have to chime in. The school websites often have info about their approach- and they can all be quite different. It isn’t “either-or” Harkness or no Harkness.

Also, from what I gather, the problem-based curriculum sort-of maxes out with calculus. After that, the method doesn’t work so well.

When DS was at George, the more accelerated math classes used this approach. He started in this track. While he really enjoyed the energy of the class, it wasn’t a great way for him to learn. He was always a step behind, it seemed, needing to hear everyone else’s approach before actually grasping the concept. He dropped down a level sophomore year, opting for the more "traditional " approach of getting an explanation first, then practicing with problems, and getting more creative only after that. For him, this was a better fit.

I think this is very personal. My sense is that the kids who were naturally gifted at math really enjoyed this approach while kids who were simply “good at math” were more split. It’s hard to know in advance if it’ll work well for you or not.

Honestly, my mathy kid gets stumped all the time, so he uses a combination of the internet (!), help from classmates, and advanced friends when working on homework problems. For him, it was a blast and very social (A true math geek he is). All of that independent work - even YouTube videos on math concepts - was done with the blessing of the teacher. So long as there was real understanding come test time, however the student gets there, it is all good. It works for him because he does math for fun in his spare time. He is weird that way. If you aren’t so self-motivated, it can still be a great way to do math. But a traditional approach may work better than it would for my kiddo.

That level of freedom (aka students self-teaching during homework) might vary from school to school, too. Dunno.

If approach matters to you, then it is definitely something to research deeply. My experience was the schools were very open to discuss theIr math curriculum.

Fwiw, it will be interesting to see what happens next year for kiddo’s cohort of advanced math students. They are the first cohort to max out the problem-based curriculum (they started phasing it in with the freshman class before his, and his advanced Freshman group (those placing out of honors geometry) skipped a year of pbl - so they finished the pbl 4 “calculus” class as sophomores and there is no pbl 5). They are re-tooling the traditional calculus BC class for them as juniors to dive deep into theory and proofs (the school insists it won’t be repetitive), and then they will move into multivariate/linear/probability as seniors. This is a small school issue. The larger schools have a lot more baked-in options for the advanced math kids. Just something to be aware of.

Having spent 2 years doing Harkness math at Exeter so far, my personal experience with it has been excellent. I came from a public middle school where I had skipped math levels, but my middle school’s math curriculum was quite weak and didn’t really prepare me for Exeter. My initial Exeter math placement may have been a slight overplacement, but I was able to catch up, and I think that the Harkness method was what made that possible.
Here’s what I love about Harkness math: It really forces you to understand what you’re doing, because you have to figure out how to do it for yourself, or at least begin that process. Through explaining your solution methods to your classmates, you both come to understand them better yourself and learn how to communicate reasoning and complicated processes. Through discussing with your classmates, you get to see multiple and creative ways to think about and solve the same problems, and it feels great to figure something out together. It’s a method that really encourages creativity, communication, problem solving, and understanding.
That said, not everyone loves it. I happen to enjoy thinking about solving problems and I think that math is interesting. In the beginning, I did have to allot a considerably greater amount of time to my math homework than is recommended, although I don’t anymore. If you’re only in math to get your graduation requirement, it may not be loads of fun, although it is hopefully more interesting than more rote methods. For people who don’t enjoy problem solving or the sorts of creativity that Harkness math encourages, it can be extremely frustrating.
Nonetheless, there are also people who have never enjoyed math before in their lives who discover joy in it through Harkness, and in a lot of ways, Harkness math practices skills that many STEM vocations require better than learning methods and then practicing them: solving problems before you know exactly how, collaborating on creative solutions, and applying skills to unique challenges rather than repetitive practice problems.

My kid who is really mathy ( perfect score on SSAT math) really detested the “Harkness” style of learning math. And this kid loves collaboration. One of the reasons was my child liked having a lesson laid out and then diving in. This seemed to work even in the highest level classes. The teachers would often add bonus or tough questions that took the learning to another level and kids who were strong would often work in groups to solve it.

The Harkness Method for math, on the other hand, isn’t direct. For some kids that really impedes learning. Some kids like to have a lesson and then go from there. Not every kid wants to sit through Harkness especially if they are the type who can already solve things in multiple ways quickly. It’s redundant. As kids move beyond Calc, the lessons return to more of an instructional style and again delve into different sections. There can still be time for kids to solve things differently on the board so someone can see multiple approaches.
I think it’s just a style/preference thing. I can see some kids who like the method and some who detested it. My kid hated it and couldn’t wait to move on. Maybe one of the reasons was s/he was the student always doing the alternative, unusual method by request so others could see a different way to solve it. My kid also wasn’t a fan when they used this type of method in middle school for the math team.
I’d love to know if the strongest math students prefer Harkness or another method. My kid said that the strongest math students often sat at a table and were given other problems while the others worked on the Harkness style on the board. So at least there was differentiation within the class. This was the highest level class so obviously there are variations within a classroom.

Kiddo liked the Harkness method because he would only do the problems he thought were fun (thankfully math is fun to him - so usually they were the harder or novel ones) then sit back in class to pick up the bits he needed to learn that weren’t in the problems he did. So it was a time-saver for him, although admittedly it isn’t how the class is supposed to work. It would have driven him nuts if he had to do all the problems, especially after having to sit through a lesson first. But then, he is an “only need to hear it once” kind of learner.

If you are the kind of kid who wants to be the good citizen and complete all of the homework, then the class can eat up your study time and then some. And then I can see the discussion being frustrating if you already “got it” while other people worked through issues.

I think it is pretty essential that you have at least a small cluster of equally mathy kids in the class who respect each other’s brains and want to see what they came up with. A kid hovering above the pack as you describe your DD , @Happytimes2001 that would be frustrating. Kiddo is lucky because he is in a group of about 5 students that all get along and are all mathy-brilliant in their own ways. Kiddo couldn’t tell you which one was the top of the class. Now they have been together for two years, they are a well-oiled machine getting through the material.

@Happytimes2001 , I am wondering as I read your post if part of DS’ distaste for this approach had to do with his less than stellar organization (and attention span).

Following someone else’s plan eliminated some of the chaos (non linear explanations) inherent in a Harkness math class. It wasn’t up to him to "organize " the various approaches into something that ultimately made sense to him. And admittedly, his feeling about math homework was that you did it to get it done. While it wasn’t necessarily unpleasant, it was not “fun”.

@gardenstategal I think it was partially due to how s/d had taken math previously ( mainly directed classes with deeper learning done in class and help provided if needed). Kiddo has stellar organizational skills but does get bored when things are repeated. We barely survived the circular learning that was taught for math in grammar school. Ok, I got it already was a common thing.

Kid loves math and does think it’s fun but also tends to finish it quickly. Has become a math tutor and in that regard has more patience and understanding. ( This is a good way, I think for kid to see how people learn and at what speed in various areas). I’m glad they asked.

No I think the issue was kid was leaning towards the higher end of the class ( maybe in the top 3) in a class of 12. So was bored by students, going over things in too much detail. I get this. I am also impatient if things are explained more than once or in too much detail. Not so much about managing chaos but about getting it and ready to move on ( impatience/boredom).

Also, I think like many things Harkness works best in math for the middle kids. Those on the bottom might not be able to keep pace and those on the higher end might be bored. I’d love to hear how other kids who are generally in the top tier within a class feel about it. Guess all learning is hard to fathom. Harkness seems to work very well in other subjects.

@Happytimes2001 Kiddo is going to tutor next year too - hoping that will help him appreciate the process others go through.

@CateCAParent Last night kiddo was filling out a long form and exclaimed, “This is so frustrating. It must be like what people some feel like when they do math.” The tutoring is great because apparently some things work with some kids and others with other kids.
My kid wasn’t good in Chem so has learned the lesson of working hard in a subject and not getting it easily. But still needs to work on it.

At some point everyone hits a wall and has to go over it. So it’s a life lesson.