Wednesday, January 28, 2009

Algebra 2 as a Graduation Requirement? Related Issues...

The deadline for registering for the First MathNotations Math Contest on Tue Feb 3rd is drawing to a close but you still have an opportunity to register! Look here for details and email me if you want a team of your students to participate!

As I've reported for some time (look here), here in NJ the Commissioner of Education has been promoting higher standards and more ambitious graduation requirements, choosing Algebra 2 as the cornerstone. I've had misgivings about this as a requirement for all students for several reasons although I'm a strong supporter of the American Diploma Project's Algebra 2 benchmarks and the End of Course Test for all students who choose to take the course because of their educational goals.

A recent article (1-27-09) on the website gives an excellent account of the debate raging over this topic at the State Legislative level. I will reprint a good portion of the article and then reprint the comment I posted on the site. I strongly encourage my readers to read the entire article and all of the comments posted thus far. It is a microcosm of much of the current debate in math education. Several of the commenters provided a commonsense view of these issues and gave me food for thought.

Education Commissioner Lucille Davy and a panel of education and business professionals appeared Monday before the Assembly Edu-cation Committee to discuss the Department of Education's High School Reform project.

The requirement that all students take algebra II has been controversial, and on Monday it dominated a discussion that attempted to identify just what students need to know to succeed and compete in the 21st century.

Davy insisted the algebra II requirement would not be so rigorous that it would lead to high rates of failure or students dropping out.

She said it would be a continuation of algebra I, but schools could offer more rigorous honors courses to those who would need them.

But Rutgers math professor Joseph Rosenstein, of the New Jersey Math and Science Coalition, wondered if the proposed courses might then get so watered down they would no longer really be algebra II.

"Most of our students don't need algebra II," said Rosenstein, who supports requiring more practical applied math courses.

Rosenstein said if courses were tailored just to meet state requirements, students who should take a true algebra II course might not get the higher level of work they need.

The algebra II issue has also frustrated vocational high school officials, who worry that too many requirements will make it impossible for students to complete programs in high school.

"These are students who benefit from applied learning," said Thomas Bistocchi, superintendent of the Union County Vocational School, adding that their goal is to have students graduate as industry-credentialed professionals. "We just want students who want to become plumbers have the time to do it," he said.

Davy said there will be flexibility in how the coursework is offered, so that it could be integrated into vocational coursework, but opponents wonder if that could be done and still teach what would be tested.

Stan Karp, of the Education Law Center, said reform is needed, but the state needs better education, not just more requirements. He said teachers and students will need better preparation to meet the new requirements.

"Less than half of the high schools now require those courses," he said. "What is it going to take to get there?"

Asked about the cost of reforms, Davy said the state already spends the most of any state and should not need more money, just a better reallocation of existing funds.

Business representatives said they just need students who can perform modern jobs.

Dennis Bone, president of Verizon, said students need the foundation of skills to be able to adapt to new and changing technology.

"We are being revolutionized by technology," he said. "Billboards now are electronic, run by someone sitting at a computer, not climbing a ladder."

"So what does algebra II have to do with that?" Education Committee Chairman Joseph Cryan, D-Union, asked.

Dana Egresky, of the New Jersey Chamber of Commerce, said that if taking algebra II can help a carpenter solve more problems on the job, then that is the carpenter who would get the job.

Assemblyman Joseph Malone, R-Ocean, Monmouth, Burlington, suggested asking professionals ranging from carpenters to doctors how they actually use algebra skills.

"We need to do a better job at finding out what people actually need to know, not what we think they should know," he said.

Here was my comment:

I thoroughly agree with Prof. Rosenstein that not all students will need the skills/concepts of a more advanced algebra class. While I admire Commissioner Davy's desire to significantly raise the bar for NJ students there are some underlying issues that must be addressed first. How many of you believe that the majority of NJ students have demonstrated proficiency in the foundational arithmetic and prealgebra skills needed to be successful in a legitimate Algebra 1 course, never mind Algebra 2? As a retired math supervisor, believe me, that question was rhetorical!
However, we must clearly distinguish between the issue of a graduation requirement for all and the need for consistent, clearly stated and rigorous standards for a 2nd year Algebra course. Despite opinions to the contrary, I believe the latter is necessary for most college-intending students. The American Diploma Project (NJ is a member of this consortium) has developed precisely those kinds of world-class standards and the result is the new End of Course Test in Algebra 2. This test, which many NJ students have already taken, requires a deeper conceptual understanding of topics such as mathematical modeling which separates the Algebra 2 of the 21st century from the Algebra 2 course many of us remember. And, yes, there are still some mechanical skills which students need to master away from the calculator!
I strongly advocate that NJ adopt these higher standards for those students who will go on to take more advanced math courses. Clearly, it isn't for everyone and therefore we should reexamine it as a grad requirement for all.
Dave Marain

I felt it was important to make a clear distinction between Algebra 2 as a high school graduation requirement and the need for a high-quality curriculum which should be uniform for all students who need to take the course. Many commenter ranted about the evils of testing, the "who really needs algebra anyway" argument, allowing politicians to make educational decisions they know little about (imagine acknowledging that it should be left to math education professionals!) , the skills needed for the 21st century, etc. Fascinating stuff...

Is this same discussion happening in your district or state? Your thoughts are important to me. Do you take strong exception to my comments? Do you agree with the NJ Commissioner of Education or has she gone too far? What do you say to the many adults who argue that, in their occupation, they haven't ever used any of the 'stuff 'they learned in Algebra 2?


Sean Henderson said...

I have a comment coming, but I've decided to hold my tongue for now as I'm currently fuming about something else.

Dave Marain said...

I'm sure you have very strong feelings about politicians and special interest groups mandating what all students need to learn and what tests are prescribed for graduation or for each grade level up to 8th.

What I will never compromise on is the issue of standard content that must be included in a course called Algebra 2. How one chooses to present the material should be the sacred domain of the classroom teacher. But all this is pretty obvious by now, isn't it!

For the content of Algebra 2 and Precalculus (or whatever equivalent name you may have) to vary from district to district, even classroom to classroom, creates inequity for our students and I would add that makes it an iniquity!

Ok, Sean, I'll be patient now and wait for your reply!!

Matt said...

I teach high school math, and I tell my students that they probably won't even recognize the benefits they get from learning math as being such. One of my many responses to "When am I ever going to have to do this?!?" is "Do what, solve problems? Only every day of your life. They won't necessarily be math problems, but they will require some amount of problem-solving skills, and those that you develop in math class will most definitely help in other circumstances."

This idea that we should only have to learn something if we're going to "use" it "in real life" (and really, what do freshmen know about how their lives will turn out?)... well, it says a lot about our society. And not a good lot.

Jason Dyer said...

Davy insisted the algebra II requirement would not be so rigorous that it would lead to high rates of failure or students dropping out.

This is the part where my eyebrows twitched.

Dave Marain said...

Jason, I'm still twitching!
What is the current situation in most schools re Algebra 2? How many levels? Honors, Regular (CP), Fundamentals (Intermediate, other euphemisms)?? Are we thinking here that a non-rigorous Algebra 2 course is really just Algebra 1.5 or worse?

So, if students are "required" to take the EOC Test for Algebra 2, will this test be a lowest common denominator for the different levels of Alg 2? Of course not! This presents some issues then for that 3rd level mentioned above. Might have to do away with that course, but then what will happen to those students? Follow this train of thought and guess where it leads?

What a great answer! Imagine that - mathematics, algebra in particular, helps one to solve problems.

When one is thinking logically (and/or abstractly), one is using many of the principles of algebra without realizing it. Algebra sharpens the mind. So I guess that individuals who claim they never use algebra in their lives do not often engage in logical thinking!

Steve L said...

I read through both of the articles linked at the beginning of this post. One thing I noticed immediately was that all these articles use "algebra 2" (or some form thereof) as though it was a standard term, like meter or three, whose definition is pretty well set in stone.

Is there anywhere that lists what exactly the contents of the graduation-requirement level algebra 2 class would be? I can think of one definition of "algebra 2" where I would strongly disagree with requiring it for graduation; I can also think of another such definition where I would at worst mildly disagree.

Dave Marain said...

Algebra II (or 2) as is currently defined by Achieve and the American Diploma Project can be found on their website here.
The confusion about course names and content is precisely why I've been advocating for standardization for the past two decades and one of the reasons I started this blog.

While I do not believe that Algebra 2 is appropriate as a graduation requirement at this point, I strongly believe it is essential for a majority of youngsters, but not all. And if it's offered anywhere, the content and the expectations should be relatively uniform. If a student takes the course, that student should also take the EOC Test (or an equivalent) in my opinion and, even if not a graduation requirement, there should be some accountability for the student's performance. There are many ways to keep a record of this but that's for another day.

The usual arguments about this course or that course not being necessary for students opens up an important philosophical conversation about providing opportunities not limitations for students. Can anyone say for certain that an adolescent will NEVER need some course or program in their future!

jd2718 said...

Dave, please click over to Math Tales from the Spring. I especially recommend this post.

Texas has adopted a 4 year math requirement, and Algebra II is part of that requirement, and as day follows night... well, you can read it. You want to read it. You will not be surprised.


Dave Marain said...

Thank you for that link. You've now also made me and others aware of another excellent math teacher blog.

The "one size fits all" mentality of states' educational mandates has been and always will be foolish at best and harmful at worst. Whether it's CA's "all 8th graders must complete Algebra 1" (which is currently being challenged) or Texas' 4x4 math-science requirement or NJ's Algebra I or II graduation requirement (not yet a law), the fundamental assumptions in all of these decisions are flawed. Frontline teachers who deal with diverse populations of learners who come with a wide range of skill, ability and motivation are told to 'deal with it' and 'differentiate curriculum and instruction'. They are told this by administrators at all levels who couldn't possibly accomplish this themselves!

However, you also know my feelings about diluting the quality of what we teach. 'Watering down' is almost always the inevitable consequence of these kinds of mandates and making the passing of state assessments the goal of learning.

I reiterate: Standardizing the content of a particular math course is NOT equivalent to making that course a graduation requirement for all!

By the way, what I find really fascinating (and this should be another post) is the array of creative names used by school districts for the different levels of algebra or other math courses. Most agree on labels like Honors/AP but beyond that what are some of the adjectives used in your districts to describe the more 'paced' math classes? "Essentials"? "Fundamentals"? "Applications"? "Foundations"? How about naming a course "Watered Down Algebra for Passing the State Test"???

sabera said...

Mathematics of Linear Algebra