Replace Algebra 2 with Fundamentals.

Now there's an idea. Let's think about this a second.  I'd like to develop a curriculum that is, indeed, "Fundamentals."  I interpret that as "life skills."  But more than that, 13-16 year olds (and older) are still in the process of discovering who they are and what they want with their lives.  It seems to make sense to spread the net wide and let them see lots of different options.  It would be nice to have the "fundamentals" be the basics of different fields so they'd have a realistic taste of what's available.  It also would be good to give them a strong enough foundation so that his/her career options are not limited.   

Let's start with the list on this meme. 

1. Financial Fundamentals. This meme does not identify what "financial fundamentals" they are considering, but let me guess.  Balancing a checkbook, says a friend of mine.  Ok, that will take 5 minutes.  But's lets be real.  I think our banks, phones, apps, computers do that now for us. Here's an important financial fundamental idea:  Interest rates and saving money. The name of this topic is "Exponential growth."  (Hint: that appears in Algebra 2. Every single one of the eight Algebra 2 textbooks on my shelf teaches interest rates in their "exponents" section of the text.) Interest rates and mortgages and college loans and car loans.  Mortgage payments are calculated by a formula derived from the sum of a finite geometric series.  (Hint: formula use and geometric series appear in Algebra 2.) How to play the stock market. (Ok, that's not an Algebra 2 topic, but the stock market is studied in many college economics classes -- many of which require calculus as a prerequisite; remember a prerequisite to calculus is Algebra 2.)  

2. Teach kids about careers (not just college.)  You bet.  But is this just mathematics or does this belong in all classrooms?  This is a larger topic that each subject needs to address in the classroom of each course.  Each idea, each topic, each skill could and should be connected with a career that uses that skill.  For example, when I teach analytic geometry (included in many Algebra 2 classes), I'm sure to address how that skill is important for rocket scientists or planners of solar panels.  Or when I teach trig (included in most Algebra 2 courses), I ask the kids to research the pitch of a roof or grade of a road (construction, surveying, engineering, architecture).  I've been a little bit of a weasel when I teach my Algebra 2 students graphing or statistics; a project I ask them to complete includes finding erroneous graphs in the newspapers. When we study logarithms, we consider log scales used in pH, in earthquake measurement, and the like: topics relevant to literacy about living on earth and relevant to different career possibilities.   English teachers, history teachers, ....all teachers need to do the same. 

3. Salaries?  I'm a little confused.  What about salaries?  Maybe given a $15 hourly rate, how much will you make in a 40-hour week?  That would be 4th grade math, I think.  Does that need repeating in high school? I'm betting my kids would say, "Ms Peaches, we got this."  

4. Credit.  Do we show them how to look up their credit score on Experian?  Did any of us learn that in school?  I think we did just fine without that.  Maybe if we taught them responsibility, then they'd pay their bills on time and have good credit.  I'm all for teaching responsibility: In a typical Algebra 2 class, I give 30 minutes of homework each night and ask that that homework be turned in on time and with a legible name at the top of the page. 

5. Budgeting (I think that's just adding and subtracting, isn't it? ) taking out a loan (see #1 above) investing (#1 above) college debt (isn't that also a loan?), buying a house (also a loan, called a mortgage, listed under financial fundamentals in #1)

6. Filing Taxes. Seriously?  Our tax code is such that completing the forms for a student's summer job is easier than the formula practice (oh, another Algebra 2 topic), and practiced by following a grading rubric for a project OR it's so complicated we have tax specialists and tax attorneys who spend years in school to learn this -- and who make a whole career out of completing tax forms for individuals and companies.  It's not really the kind of topic that can be put into a couple weeks or months of an Algebra 2 curriculum.  Just as we can't have "surveying highways" or "the architecture of a skyscraper" as a reasonable topic in the Algebra 2 curriculum, the tax code night get to be a little much.  

In short, the current standard Algebra 2 curriculum includes these topics.  And more.  We just need to be sure the teachers help the students make these connections meaningful and linked to a career opportunity. 

Tracking.

Amelia struggled in Algebra 2.   A math teacher even told her, "You'll never be any good at math, but you need this to graduate."  She was persistent, and completed the course with good grades and with pride. Her lesson of persistence and of the difficult lesson that, "I can do this, it just takes effort" as well as the mathematics had a profound effect on her life. She's now the CEO of a major company she founded, developed, and has made successful.  Her company has contracts with hotel chains and airline companies.

Allery Yazzie was placed in a lower level math class as an 8th grader.  As a member of the Navajo (Dinee) Nation living on the res, his style was different. His 8th grade teacher didn't see his abilities through the cultural differences. An admissions officer from Stanford was directed to him early in Allery's senior year of high school; he recently graduated from Stanford University.

Brian Gonzales was placed in a lower level math class in 9th grade.  In 10th grade, his ability to reason abstractly kicked in and he was shooting the lights out in his lower-level class.  But he was unable to double-up in math and remained a year behind his peers in math, eliminating the possibility of taking Calculus as a senior, reducing his college choices (selective colleges ask for a year of Calculus on student transcripts), and making the possibility of majoring in mathematics a more distant goal.

Edwina thought she didn't need math at all (and had been doing poorly, so why take it?) but found the Algebra 2 teacher attractive, so she took the class so she could spend an hour looking at him each day.  In college, she discovered that she was pretty good at math and was able to include a minor in mathematics with her Engineering degree.

Who determines tracking?  The higher paid careers require more math and STEM classes -- so when we make tracking choices, we ultimately determine who will be in that higher paying career.  Edwina's thinking clearly illustrates one of the problems with having students consider their curricular choices prematurely; teachers may have an unconscious or conscious bias that does not serve the people of color or the girls who populate their classrooms.  Yes, I'm going there: I am saying that tracking students can be racist and sexist or perpetuate erroneous notions that girls or people of color "can't do math." Furthermore, there are times when students are "tracked" prematurely.  Tracking prior to Algebra 2 is clearly too early for most students; many people acquire abstract reasoning closer to their 18th year instead of their 15th year.  Tracking can limit students whose abilities are not yet fully realized by themselves or their instructors. 

Ode to Shakespeare

I've never used the information gleaned in "The Merchant of Venice," in my life.  Nor have I used information I learned about the War of 1812 or Latin declensions.  I've never needed how to write a lab report.  My life is certainly full even though I don't remember Hamlet's soliloquy.  (Or how to spell soliloquy -- I had to look it up.)

But no one -- no one! -- asks us to eliminate Shakespeare from the curriculum.  Why is math under fire here?  Or perhaps we should eliminate Shakespeare and other studies that folks never use.  What would the result be?

We'd lose our culture. We would lose ourselves.  We'd loose the essence of being human.  Isn't the study of mathematics part of that cultural literacy too?  Perhaps a bigger and unanswerable question is why -- in the US at least -- do people not see mathematics as part of our valuable culture?

Oh, the irony!  I named this blog using a Shakespeare reference.

Further, I never would have known I'd made the right career choice in mathematics if I didn't have a study of history or English to which I could compare my studies of math.  I'm glad that all options were presented to me; I'm glad I can be at least somewhat literate regarding the subjects I did not choose.

Where are the Mathematician's Voices in this Discussion?

Quite simply, they aren't there.  The discussion is between parents, legislators, people who are over 50 and have been students. 

I'm so bewildered by this.  

I trust my dentist to make good decisions about how to deal with my tooth pain even though I've had teeth for 56 years.

I rely on a tax preparer, even though I've paid taxes for over 40 years.  

Just this morning, I asked the advice of the gentleman behind the counter at the post office what the best way to send a package to Michigan would be.  I've mailed and received packages hundreds (maybe even thousands) of times before, but I don't presume to know what's currently best.  My specific experience is simply not as full or as complete as the man behind the counter.  

Why is it that people think their experience as a student many years ago or as a liver-of-life makes them more qualified than a career math educator to determine what's best to have in the curriculum?   

Polynomials. Do we Really need to Teach/Learn them?

So why do we study polynomials? A Forbes author writes about how silly this is. https://www.forbes.com/sites/tomvanderark/2019/03/19/bad-bargain-why-we-still-ask-kids-to-factor-polynomials-and-how-we-fix-it/#7b98686063c1

The funny thing is, the study of (and more specifically, the factoring of) polynomials, including DesCartes Rule of Signs, finding upper and lower bounds of roots, determining end behavior, and the like used to fill up at least one-third of a standard Pre-Calculus class (not Algebra 2, btw, but Algebra 2 gets blamed for having this topic in its curriculum.)  But that was prior to about 1992. Currently I spend, maybe, a week at most in a PreCalculus class considering the behavior of polynomials so that students can progress to Calculus where they see applications of polynomials in economics (maximizing profit, minimizing loss) or physics (projectiles and quadratics, for example).  "Polynomials" has not really been a dominant topic since the advent of graphing calculators in the classroom -- about 1992.  Those of us over 40 remember factoring dominating the curriculum -- an accurate memory for that era-- but not accurate for what's currently taught.

In Algebra 1 (and some in Algebra 2), we teach factoring of quadratics, which are special polynomials. There's a bunch of reasons for teaching factoring of quadratics. 1. there's a good deal of number sense and problem-solving as well as organization of thinking that goes into this skill. (Number sense is important for things like understanding your bills, bank statements or making a budget.) 2. There's applications all over the place: projectiles, revenue maximization to name the most basic. 3. Students learn, at this level and in this place, how to symbolically represent expressions and equations in mathematics, a skill generalizable to science and even essay-writing.  4.  The graphs help all people understand how graphs work and what those graphs mean. It's hard to open a newspaper and NOT see a graph.  Many of those graphs actually show some level of embarrassing illiteracy regarding graphing, so these journalists could actually use a refresher course in Algebra 2 so they could represent that data well.  Each year when I see "factoring of quadratics" in the curriculum, I consider the fact that German high school students never learn factoring.  And they do fine.  So to be honest, I don't spend much time factoring quadratics.

Instead, "Dial Dallas," I say.  (Dallas is the home of the TI graphing and programmable calculator).  Students pull out their TI-84 and press Y=, 2nd Calc, and a few keystrokes later they have the roots.  Or the maximum value.  Or a specific value for a given independent value.  Anyone over 40 doesn't understand this process; those under 40 are all over it and can follow the routine in their sleep, answering complex questions that include interpolation and extrapolation.  One parent hired his son to do some analysis that I'd taught the son in class "for the office." The student returned to the classroom with a $300 check from his dad, letting me know his dad thought he'd gotten a good deal on information much more swiftly and less expensively than with a professional consultant.  "30 minutes," said the teen, "It took me 30 minutes."   I thought $600/hour was pretty good pay for a 16-year-old.

So what's my point?  People over 40 THINK they know what's in an Algebra 2 curriculum based on what they experienced over 20 years ago, but they don't.  How can they make good decisions when they simply do not have the necessary information?

Eliminate Algebra 2 from the Curriculum, they say.

Irrelevant, they say.

Out of touch, they say.

Not useful, they say.

Hurt my GPA, they say.

I function quite well without any Algebra 2, thankyouverymuch, they say.

This blog includes posts that are my musings as I consider their indignation stemming from their wasted their time taking Algebra 2 in high school.

(Editorial note: "they" is purposely left without a referent.)

Legislation has been introduced to eliminate Algebra 2 as a graduation requirement in some states (Michigan in this source, but Florida and California have also fallen in-step with the idea).  https://www.record-eagle.com/news/local_news/legislation-proposed-to-drop-algebra-as-graduation-requirement/article_5b786758-5ac5-5fc2-b068-28e8935eaa77.html

A thoughtful commentary on the issue was published in blog form in March 2019 http://rtalbert.org/what-to-do-about-algebra-2/.  Some of these topics in his blog will be addressed in this blog.  Read on! Additional posts forthcoming.