Reply to Interesting Article about Math in the World Today.

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[quote=Anonymous][quote=pettifogger][quote=Anonymous][quote=pettifogger][quote=Anonymous][quote=Anonymous]The article is pretty spot on. This is probably the largest root cause:

[quote]One likely reason: U.S. high schools teach math differently than other countries. [b]Classes here often focus on formulas and procedures rather than teaching students to think creatively about solving complex problems involving all sorts of mathematics[/b], experts said.[/quote]
I highly doubt the above will change anytime soon. Most teachers and parents do not even know what mathematics is, they think it is procedural and rote and it's all about calculations. In fact the exact opposite is true. Math is about imagination, creativity, problem solving and proof (i.e the art of explanation). In general our culture does not support thinking deeply and creatively about things, it instead opts for acceleration coupled with a superficial understanding (certainly in math class, if not in school in general). As a teacher, I can find and pose numerous examples of elementary problems (i.e given/shown to elementary students and only requiring the most basic tools) to many high school students and they would have a very hard time solving them, or not be able to at all. This proves that problem solving in our math classes is almost nonexistent, which is corroborated by the abysmal average SAT scores nationwide.

Oh, and the "geometry sandwich" is absolutely real:

[quote]Most American high schools teach algebra I in ninth grade, geometry in 10th grade and algebra II in 11th grade – something Boaler calls “the geometry sandwich. Other countries teach three straight years of integrated math – I, II and III — in which concepts of algebra, geometry, probability, statistics and data science are taught together, allowing students to take deep dives into complex problems.”[/quote]

The lack of understanding of geometry (by both students and teachers) is so bad that it was hilariously featured in a chapter from a famous problem solving book a couple of years back called "Geometry for Americans" :

https://imgur.com/a/76qSUlh[/quote]

Although MCPS still calls the sequence Algebra 1, Geometry, Algebra2 it actually is integrated math and should be renamed--there are algebra topics all three years, there are geometry topics all three years. Plenty of other districts actually have renamed the classes.  Plenty of other school districts, e.g. California, have renamed the classes.  Now, the topics covered in MCPS are more cursory compared to what was covered in algebra/geometry a generation ago, but students are hitting the classes younger--the target is 80% in Algebra 1 by 8th grade.

There's plenty wrong with math education in the US but the article sounds out of date.[/quote]

There is definitely no geometry being done in algebra classes, that is a myth.[/quote]

In the MCPS algebra packets, it's quite common to have a problem that looks at area or perimeter of a simple figure as a function of side length.  These are concepts, introduced in IM and revisited in geometry.  Later in the year there's some discussion of optimizing area given constraints on perimeter.

The bigger question is how much traditional geometry is in geometry.  The unit on proofs is one packet and about three weeks, straight edge and compass constructions are about the same.  But there are frequent problems that use algebra.  E.g. there will be a figure with two unknown angles, and geometric relationships such that a system of two variables needs to be solved--algebra review.[/quote]

Right but that's not really geometry, it's more of an algebraic afterthought. And constructions by themselves would not make sense without proving why the construction works, which is done using geometric principles. Those geometric principles (parallel lines, angles relationships, similar/congruent triangles, etc.) are not taught until geometry class. Without having these basics down, just doing a construction is akin to following a recipe without knowing why it works at all.

I also have reservations about proofs, I highly doubt an isolated proof unit will be helpful in understanding how to argue about what is/isn't true. Learning how to prove something (i.e. logically explaining why something is true via deductive reasoning) is something that should be done in all areas of mathematics throughout the school year (and kids in elementary school can handle it if developed correctly). Proof writing cannot be taught in a matter of weeks, since the development of the skill is highly dependent on doing lots of various types of problems from all subjects.[/quote]

I don't disagree, but I'm not sure how familiar you are with the MCPS geometry curriculum.  There's a little lip service to constructions, a little to proofs--which mostly amounts to filling in a blank in an otherwise completed two-column proof.  In fact most of euclidean geometry is swapped out for studying transformations in the coordinate plane: translations, reflections, and rotations by 90 degrees (arbitrary angle is too advanced).  This is all a ground work for studying functions, and a direct continuation of the way lines and parabolas are introduced in MCPS algebra 1.  This is applied further in algebra 2. The course are taught on a spiral and topics are revisited and expanded each year.

I agree proofs could be incorporated through out math education, but they are not.  My DC is in calc now, and still not seeing proofs--there are some in the book, but none presented in class.  There are very few teachers with the experience to model proof technique, even the most basic.  Concise definitions aren't modeled either, and that's necessary for proofs. There aren't even textbooks before pre-calc, so where would the teachers get clear definitions, much less the students.  I know for a fact my DC's teacher last year didn't know that a counter example suffices to show a statement is false, DC almost lost points on a test because of it, and when arguing was told grudgingly there could be points this once.[/quote]

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