Reply to 100% on Iowa. Should DC take a summer math class?

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[quote=Anonymous][quote=pettifogger][quote=Anonymous][quote=pettifogger][quote=Anonymous][quote=pettifogger][quote=Anonymous]DC is really gifted in math and loves it.

Would a summer math class like geometry between 7th and 8th be worth it?[/quote]
There is only one reason why anyone would attempt such an awful thing, and that is purely because of acceleration purposes, which is a very superficial reason that is completely orthogonal to learning math for joy and understanding.

Based on your description, I frankly believe it would even actually risk [i]hurting[/i] your child's natural love for math. Additionally, practically speaking, K-12 students in the USA are [i]extremely weak[/i] in geometry because of how it is taught in school, and trying to do it all in a summer would almost surely hurt your kid down the road. Even worse, summer geometry barely passes as math, given that it will be very procedural and rote based, in addition to stress inducing because of the super frequent testing (I believe it happens on a daily basis due to the highly compressed schedule). Instead, you want your kid to slow down and cover math [b]slowly and deeply.[/b], with the goal of mastering a few select interesting topics, as well as increasing problem solving skills along the way. Discrete math such as combinatorics or number theory (AoPS offers both as others mentioned), are not only inherently beautiful, but they can also be used to introduce rigorous reasoning and formulating proofs. If you don't want an actual class, attend a math circle if you can find one (although there may not be anything in the summer), short of that try to introduce your kid to some of the math contest questions where they can learn from doing interesting problems as found in Mathcounts (although in my view that isn't as efficient as learning some of the subject material first). Brilliant.org also has a lot of wonderful and interesting material at their level, but does not have full blown classes like AoPS.[/quote]

Although this post is thoughtful, I disagree with the point of view. You can study mathematics slow and deep, but also fast and shallow if it fits your student’s goal. If the goal is to learn the tools for understanding science (physics, chemistry, biology) it can be argued that a shallow understanding of calculus is more useful than a deep exploration of number theory. I’d argue that the usefulness of geometry in science is far less than algebra, so skipping through it over a summer class would be ok.

Personally I am somewhat doubtful on how important contest math is for mathematical education. The skill of working on a problem under one hour time constraint, is almost never needed in a real job, and arguably working in a team, and good communication is a better skill to develop. [/quote]

My main point is that trying to learn all of geometry by forcing it into 6 weeks is horrible idea. The student will have an extremely shallow understanding of geometry and how to use it effectively to solve problems. But much worse, they will not even get a chance to learn math, as it it will be inappropriately presented as a bunch of steps to memorize and then immediately regurgitate on quizzes/tests, all without thinking or reflection, not to mention problem solving or learning how to put together a proof... Why would anyone want their child to go through an experience like that? It is obvious that it could backfire and kill their love or motivation to do math. Literally almost any other approach to doing math is better than this.[/quote]

If they don't do proofs in regular full-year Geometry, then what's the harm in taking summer Geometry without proofs?  Tbh, Geometry doesn't really make sense until you've gone through calculus anyway.[/quote]

Geometry basics can (and should) be learned starting in elementary school. Ideally it should be integrated into all aspects of math, which is how many other countries teach it. However, a full year of proof based Euclidean geometry would a next to impossible to understand or retain in a summer, and is what is normally covered in a summer course (I'm assuming OP meant the 6-week FCPS summer class, but they could be referring to another program as well). It would be fine to learn some geometry in the summer, whether by finding a more appropriate class that focuses on understanding, or perhaps by buying a good geometry book and work together with their child to learn a portion of it.

Regarding proofs, they are covered in both the summer class and the regular year geometry class, but they are done very badly. Instead of encouraging expression and creativity as well as logical connectedness, the way proofs are done in geometry class is via a focus on a constrictive 2 column approach, which is never then seen outside of the K-12 geometry class. Students typically walk out of a geometry class confused about what the nature of a proof really means, which is sad.

I think geometry is a beautiful subject for kids to learn and it would be wise to find a good quality approach to learning it for their kid. I don't believe summer school geometry as offered by fcps would be it.[/quote]

Some points of view are too math centric. As in real life the answer is almost always “it depends”. Between knowing how to write proofs, a scientific report, or a good essay, I’d rate the last two as more important. It also depends on the student goals, focusing in middle and high school exclusively on math would limit the options quite drastically. There’s never enough time to do well in everything so a student needs to choose an area of focus based on how useful a skill is (e.g. reading comprehension and writing is needed in every job), interest, aptitude, constraints etc.

If a student wants to learn more science, it’s better to take the physics, chemistry, biology sequence than the reverse that is usually taught in high school, but you can’t do it unless you finish algebra 2 early, as it is often a requirement for physics. In my view, class prerequisites is what drives the acceleration in math along with the desire to stand out among the student population for college admission purposes. Doing a six week geometry class that covers a bare minimum is fine if it fits with the student planning. I wouldn’t call a crash course in geometry a horrible infliction on your child, that’s a bit dramatic. This argument is only considering a stem interest, there is a whole other world of humanities, social sciences etc, where different skills are needed.

Doing contest math for developing problem solving, sure, but the same can be said about a solid science class, and even more so about an engineering extracurricular activity like coding or robotics.

To the OP question, it is fine to take a six week geometry class over the summer, but make sure you have a good reason for it. It’s probably better than taking summer algebra since it is less connected with the follow up math classes.
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