Math help!

So I’ve received multiple questions from individuals who are planning out their course load and trying to determine whether to take Geometry or Algebra 2 after completing Algebra 1. It’s an understandable question, so in this article I’ll take a look at the arguments for both routes, but the short answer is either way is fine. Now let’s take a look at the reasons for each route…

A Short History (and a little about test preparedness)

Parents, chances are pretty good that you took courses in the order of Algebra 1, Geometry, and then Algebra 2. You probably also only had to take 3 math courses in high school, and there was probably very little integration of geometry into your algebra curriculum. Since students were required to take the ACT or SAT (and usually with little to no prep work), it made more sense for students to take geometry before algebra 2 for test purposes so that they had at least seen some geometry before they took the test.

But things have changed. Pretty much every state requires at least 4 credits of math in high school (some states even require for you to take math every year of high school, even if you got an early start on Algebra 1 in junior high), so basically all students have completed the core three math subjects that are on the ACT or SAT (neither test covers pre-calculus or higher level math) by their junior year. In addition, most high school math curricula has integrated at least some level of geometry into algebra, meaning students have likely seen some of the geometry on the ACT or SAT even if they have not taken a geometry course yet (and conversely, many Geometry programs have at least some algebra review incorporated). Finally, the average student is now doing some amount of test prep, so if there are holes in what they have covered mathematically they have the opportunity to fill those gaps in before the exam.

All this boils down to mean that the reason for taking geometry second, from a test-preparedness perspective, is basically gone. In fact, from my experience as a test-prep tutor for the past 14 years, I would say it is much easier to catch students up on the geometry on the ACT or SAT than the algebra (especially considering proofs are not covered on either test, which is by far the most challenging aspect of geometry for most students). Which brings me to my next point…

Proofs

Ugh. Yeah, most students are not fans of proofs. Very few teachers are good at teaching this component of geometry, where essentially math is merged with logic training (specifically, deductive reasoning). The integration of proofs into math has it’s foundation historically in geometry’s most famous book, Euclid’s The Elements. However, there is research that indicates that most high school students (and even a majority of college students) may not be ready cognitively to really deal with deductive proofs (see here for a more involved discussion with references). We see many educational systems abandoning traditional two-column proofs in favor of more descriptive, casual proofs that some hypothesize may be more appropriate for the average high school student.

How does this impact your choice of order for high school math courses? If you are utilizing a more rigorous (or a more classical) geometry curriculum, waiting a year by completing both algebra courses first may give your student’s brain a better chance of being cognitively ready for formal, classical geometry proofs. On the flip side, if using a curriculum that uses a more modern, less-rigorous proof approach (or if you are considering leaving out proofs altogether) then Geometry becomes a much easier course and therefore putting it before Algebra 2 could often make sense.

Struggling Learners

There is also the argument as to what makes sense in terms of course sequence, especially if a student struggles with math. If retaining algebra concepts is a challenge then taking Algebra 1 and Algebra 2 back-to-back makes the most sense. At the same time, if a student really feels beaten down and defeated by Algebra 1, taking a break to tackle Geometry (which most students who struggle with algebra will find easier and more refreshing) might be a wiser path to go.

Pre-Calculus

Finally, if a student is planning on going on to pre-calculus, it might make more sense to take Algebra 2 and Pre-Calculus back-to-back to have more continuity. For a student who’s strong mathematically and plans on continuing to Pre-Calculus and Calculus (versus going a less-rigorous route like consumer math, business math, college algebra, etc), it would probably be best to have continuity between the two more difficult algebra courses.

The Short Answer

So yes, there are arguments to be made for both routes. I know that can be both frustrating and confusing, but I hope it also frees you to know that it is fine to go whichever route seems to make the most sense for your situation, and that things will likely go fine either way.

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