"Running the risk of inciting the ire of math teachers across the world, "What qualifies as "post-Geometric" math?" Does it have to be Pre-Calculus and Calculus? Does Statistics count? What about a class like Machinist Math, where the application of the mathematical concepts ties directly to the problem solving process directly related to operating and maintaining manufacturing machines? Is it possible to address the fundamental skills that math allows us to practice with a different kind of math curriculum than the "standard?"
Let's start with some background since this question really reminds me of a Rubik's Cube. Depending on the way you look at it there are several answers. There is little to no disagreement that Algebra 1 is necessary to understand for all students. It is a gateway, not only to math but other subjects. According to KnowRe, Algebra 1 presents students with academic challenges they have not yet had to face. Algebra is often the first course in which students deal with abstract reasoning and problem solving. This abstract reasoning helps connect the dots between historical events and what is currently happening in the world. It opens areas of science that cannot be explored without it. It has direct links to music and art along with a litany of applications in sports.
What about Geometry? Is that necessary. Prior to 2010 it would not be difficult to say yes. However, with the adoption of the Common Core State Standards, much of Geometry has moved into 5th - 8th grade where it is used as an application of current learning. This should remove a significant portion of the years learning as long as students are retaining knowledge (which is a major issue in all subject areas). The remaining portions of Geometry would be ground-level knowledge for trigonometry, applications in circles, etc... Knowledge that the current U.S. citizen walking down the street doesn't have. Should they have it? That is the debate.
What does the student need to succeed in their career/life?
Every time I am posed with student placement decisions this is my go to question. What makes this so hard is a few conditions we cannot change.
- Many students have no idea what they want to do after high school.
- If a student does have an idea of what they want to do, too many parents steer students away from their choice.
- Career choices are changing so fast most of the careers our current students will have don't exist currently.
- Some of the most growing fields are seen as "manual labor" when the reality is they are highly specialized (Machinist) involving lots of mathematics.
The Common Core State Standards do not require a student to pass Algebra 2. They require some of the skills in a typical Algebra 2 course but not all of them. Therefore, Algebra 2 is not required. In fact, most, if not all of the skills are taught in the 1st semester of a typical Algebra 2 course. The remainder of the skills are instructed as the next set of foundations needed for further study in mathematics. "Taking and successfully completing an Algebra II course, which once certified high school students' mastery of advanced topics in algebra and solid preparation for college-level mathematics, no longer means what it once did," writes Tom Loveless of the Brooking Institution in a blog post. "The credentialing integrity of Algebra II has weakened." Tom Loveless bases this statement on a correlation between the number of students passing an Algebra 2 course and the nations NAEP scores. The Algebra 2 barrier has been a sticking point with post-secondary education. For many institutions, it is required for entrance. Even for students with no interest in mathematics.
So if Algebra 2 is not something all students should have what is? The answer in my mind is nothing. This is not to mean no math class. It means there should not be one answer to this question. Lets face some facts. The important learning that happened in my life to get me where I am now did not happen in high school or college. It happened after several years in my field when I realized, "Wow, I really need to know more about that." I took courses, attended workshops, and read. When I was done I read some more. The constant for students who struggle in school is a lack of interest. It goes back to the question listed above. What does the student need to succeed in their career/life? Note, the question is not "What do we currently have that we can put the student in?"
By no means do I imply that students should not take Algebra 2, Pre-Calculus, Statistics or Calculus. I mean they should take what interests them. If a student has no interest in math but can't wait to corner someone in order to argue politics. They are more than likely not going into a field where Calculus will make a difference. It is quite possible their path may need to go through a more formal statistics course (which needs more math background than Algebra 1 but not a full year of Algebra 2). As the original questioner stated, what about a Machinist course? Definitely! Consider for a moment that student who doesn't do his/her homework but spends time in the wood/metal shop "playing" with materials. Currently they don't need Algebra 2. Although, it should be noted that much of a machinist job lies in content of a 1st semester Algebra 2 course. In my district we did a small challenge this year. The Machine Tool course was working on some models, determining the lengths and angles needed to make a part. It should be noted that the math is completely integrated into the course. The teacher took the same schematic to his Algebra 2 class and gave them a period to find the necessary measurements. After a period, they were no farther than when they started. The Machine Tool students, who would never pass an Algebra 2 class, had it all figured out.
Here is my answer to a long thought process. We don't need all students to take anything past Algebra 1. However, we need all students to take the math they need to move forward in what they want to do. We need instructional options for all students. An abbreviated upper algebra course for those students who don't now need everything Algebra 2 has to offer but yet might entice them to go farther if they so desire. We need courses such as Calculus for those students who know their path lies in mathematics. I once read a report that only 9% of college majors require calculus. Then why is that where the crown of mathematics is held. We need the upper level mathematics courses to continue to move innovation because that content will possibly be helpful in the next innovation. However, not everyone is an innovator in that way. The key is to find where that child wants to be innovative, then tailor the plan to set the student on a path towards their goal.
There are far too many resources available to not allow a student to tailor their own path.