kitchen table math, the sequel: Paved with Good Intentions

Monday, April 12, 2010

Paved with Good Intentions

UPDATE: I guess I wasn't clear. Here's the gist of the post:

In order to meet the "algebra 1 in 8th grade" state requirement, the St. Paul school district has made algebra 1 a two year course that begins in 8th and ends in 9th.

Since the NMAP final report suggested that states move as much as possible to a math curriculum that taught Algebra 1 in 8th grade (thereby matching many international countries' standards), many states have decreed Algebra 1 will be taught in 8th grade. Like many states, Minnesota has mandated such.

The new law states that by the 2010-2011 school year, all public schools will offer "algebra 1" in 8th grade. That course will no longer be available for credit in high school--if a student needs it again, it will not count toward grad requirements.

The MN standards for this 8th grade course, however, are not a full year of algebra 1. They instead cover the algebra of the line: linear functions, linear equalities. At least one of the authors of the standards told me himself that he felt a full fledged algebra 1 course was not appropriate in 8th grade. The standards for an "authentic algebra" course are actually defined by the end of an algebra sequence--including algebra 2.

So what of the gap between?

The rest of an "authentic algebra" course as defined by NMAP
must go somewhere right?

Well, here's St. Paul's solution:

Grade Level: 9 High School

Subject Area: Mathematics

Course Number: M403011

Course Title: Intermediate Algebra (Reg 9)

Course Length: 1 Year

Prerequisite: Algebra 1

Course Description:
This course covers the second half of a traditional Algebra 1 course. It extends from polynomials, through quadratic and exponential functions.
Topics covered include:

1. Exponents and Polynomials
2. Factoring Polynomials
3. Quadratic Functions and Equations
4. Data Analysis and Probability
5. Exponential and Radical Functions
6. Rational Functions and Equations

To recap:

the first half of algebra 1 is now taught for an entire year in 8th grade. The second half of algebra 1 is now taught for an entire year in 9th grade. Why, we've sure accelerated our math program up to that international standard, haven't we!

To the parents, though, this is a fraud. Their children are taking 8th grade algebra 1, they think. But they do not know that algebra 1/2 is now being taught for a year, and algebra 1/2-1 is another year. Their kids are still not going to reach AP calc.

And if you're interested in how you get to algebra in 8th grade:
Unfortunately, MN didn't change the standards leading up to 8th grade. Those changes to curricula in grades 4-7 are required by 2014. No changes in teacher certification have been mandated at all.


Allison said...

Oh, and Minneapolis?
Well, they use CMP2, Connected Mathematics Program for grades 6 through 8. And their algebra course for 9th grade?

Discovering Algebra, Key Curriculum Press. Yes, the one Seattle Adopted. They use the whole sequence: Discovering Algebra, Discovering Geometry, Discovering Advanced Algebra.

Bostonian said...

Related stories: 'Algebra-for-All' Push Found to Yield Poor Results and
The Misplaced Math Student: Lost in Eighth-Grade Algebra

What fraction of people will ever grasp Algebra I, even if they are well taught? I'd guess no more than 1/2.

momof4 said...

I am convinced the whole 8th-grade-algebra-for-all would be less of an must-happen issue if those really PREPARED for it didn't break down along racial/ethnic lines (although the Hmong in MN may not fit that).

Of course, the idea is based on a flawed assumption from the start. When the data came out, decades ago, that those kids who took algebra in 8th grade did better on whatever measure of later accomplishment, the fact that 8th-grade algebra was HONORS-ONLY, taken ONLY by the top kids was ignored. It was essentially a proxy variable for identification of the top students; of course they continued to to well.

We should be PREPARING far more kids for 8th-grade algebra, but it is unreasonable to the point of impossibility to expect that ALL can be ready. Half the kids in the country are below average. There are certainly Lake Woebegon places (Edina, for instance; to continue the MN theme), but there are also the opposite places.

Anonymous said...

Well, my son was ready for pre-algebra in the 4th grade and algebra 1 by 5th grade. He took accelerated algebra 1 (which mirrored honors algebra 1 at the high school) in 6th grade. He isn't a genius.

He lucked up, though. He got to be taught alone by the gifted teacher since he was moving faster than the gifted pullout, so he got to skip all of the junk.

He was the first kid in the district to be sent over to the junior high from the grade school, but since then, they have had one or two sent from each grade school. So far all have been boys.

Again, he's just your garden variety gifted kid. But, he was taught a proper sequence leading up to algebra. That's probably the difference.


Bostonian said...

Regarding the comment of "Anonymous", the question is whether algebra can be taught to students with IQ < 100 (and if they can retain it), not whether students with IQ > 130 (a typical threshold for a gifted program) can learn it.

Anonymous said...

My point was that if a gifted kid can learn it earlier than 8th grade, then bright kids who don't make the gifted cutoff can probably learn it by 8th grade.

My other point was that if the sequence of topics leading up to algebra isn't correct, it won't make a bit of difference what your IQ is.


Linda said...

I taught 8th grade Algebra 1 in California for 2 years- a high school level class- not watered down or half of the material. MIddle School kids can do it if they have appropriate preparation, such as 7th grade PreAlgebra. A few of my students did have to take Algebra 1 again as freshmen because they weren't ready for the pace of the entire Algrebra 1 class in one year. I lost them half of the way through. With a little more time they probably could have gotten through 3/4 of the material at a level of mastery. I see no reason not to do a real Algebra 1 class for most 8th grade students if the middle school math program is set up well.

Also, I've looked over Key Curriculum Press' Algebra 1 text and found it to be lacking in way too much of the material necessary to teach a comprehensive Algebra 1 class. It does graphing really well, but most of the equation material is missing.

Catherine Johnson said...

Singapore Math starts algebra in 4th grade for all kids.

Catherine Johnson said...

Wayne Wickelgren said that a school should have 80% of its students mastering algebra in 8th grade. That was his floor, as I recall.

Math Coach

Catherine Johnson said...

Take the guideline that most college-bound students should proceed through the K-12 math curriculum--a hierarchy of classes stepping from simple arithmetic to calculus--at a pace that lands them in algebra in ninth grade. This is too easy for most children. In a regular middle school two of my children attended, all of the students took algebra in or before eighth grade and over 80 percent mastered it, putting them one or more years ahead in math.

Entire countries of students accomplisih this routinely. The Third International Mathematics and Science Study, conducted in 1996, found that the material taught in U.S. eighth-grade math classes was taught in the seventh grade in many other developed countries and even earlier in Japan and Germany. As a result, U.S. eighth graders performed significantly poorer on a standardized math test than eighth graders in twenty other countries, and far poorer than Japanese students, who scored highest. Overall, U.S. elementary and middle school math education lags a full year behind that in dozens of countries and one and a half years behind Japan and Germany.

Math Coach by Wayne Wickelgren, p. 4

That was the passage that made me accelerate C's math learning.

Right there.

SteveH said...

There shouldn't be anything magical about (authentic) algebra in 8th grade. The reason it's important is that this defines the entrance to the top math track in high school. If you don't hit this checkpoint, then your STEM career prospects drop greatly.

It shouldn't have to be this way. What's wrong with algebra in 9th or 10th grade? It probably means that the kids were not prepared properly, and that all math after that point is remedial to a large extent. You are peaking in terms of math, not setting up a base camp for the big climb up a larger math mountain.

If kids are taught math properly in K-6, then I don't care much if they get to algebra in 8th or 9th grade. And, after they have completed a proper algebra class (sometime), I don't much care if they get any other math ... as long as they know the consequences.

You can't just proclaim that all kids need to take algebra in 8th grade. Maybe they think this decree will force change into the lower grades, but I don't see that. It will just force schools to water down the definition of algebra.

So, in MN, does this mean that they have eliminated (did they ever have one?) two tracks for math in 7th and 8th grades? Around our parts, schools don't assume that all kids can get to algebra in 8th grade, so they split up the kids and don't worry about the fact that they (now) offer the same honors algebra course as the high school. If we were mandated to have all kids get to algebra in 8th grade, then I can see the honors algebra going away and everyone having to take a CMPish form of algebra. Then again, our split track method means that as long as some kids get to the top track, they will never try to find out why they got there and whether more kids could get there.

Does MN mandate that 7th and 8th grade teachers have to certified in math? Our state now requires this for all 7th and 8th grade teachers in all subjects. Overall, I think this is good, but it makes the jump from 6th to 7th grade much more difficult. They've turned on the filter.

Genevieve said...

I think if districts are not preparing most students for Algebra in eighth grade, then they need to find a way to open new avenues to Calculus in 12.

I talked to a district last month that is able to do this because they offer block scheduling. They allow students to take Algebra 1st semester and geometry 2.

They also offer an Algebra 1 class that has one semester double period and the second semester single period to help students that need to go a little slower.

While this doesn't fix the K-8 math, at least students aren't having doors shut way to early in their schooling.

Allison said...

--So, in MN, does this mean that they have eliminated (did they ever have one?) two tracks for math in 7th and 8th grades?

No, it's more vicious than that.

There are still two tracks, but the courses both have the name "algebra 1".

In St. Paul schools, there is an honors algebra 1 track called "Pre IB/AP Algebra 1" taught in 8th or 9th grade. It is a 1 year course and teachers one year of algebra 1.

To be on that track, you start in 7th grade with pre algebra (called "Pre-AP/IB Pre algebra")

But parents don't know the difference. They see that their child has an A in Algebra 1 in 8th grade, and burst into tears when their prospective 9th grade school tells them their child is on the remedial science track--a year down because they are a year away from taking chem, and can't take the chem-bio-phys-APcourse offering, and are on the remedial math track, too.

--Does MN mandate that 7th and 8th grade teachers have to certified in math?

Nope. The certs are for either elementary teachers or seconday teachers, and 7th and 8th are elementary. Now, some schools hire 2ndary certified teachers for their junior high slots, but most do not. And there's absolutely no new prep to help those teachers teach algebra.

momof4 said...

Given the experience one of my kids had with block scheduling, I am not sure how well it would work to "catch up" those kids who did not have real 8th-grade algebra 1. All of my child's classes were honors level, in an affluent suburb, but his complaint was that half of each period was wasted in every class because too many kids couldn't handle the pace of double-period instruction. A teacher relative said the same thing; most kids can't handle a full year's material in one semester. Those most likely to be able to do so would be the kids already at the top, who usually have more background knowledge and require less repetition, but those are the kids most likely to enter HS already on the AP calc BC path. I would think it likely that those who did not make the cut for 8th-grade algebra would need average-to-slower pace, not faster, to master new material.

lgm said...

>>I would think it likely that those who did not make the cut for 8th-grade algebra would need average-to-slower pace, not faster, to master new material.

LOL. My kid was dropped for executive functioning and slow handwriting (not bad enough for a label). He has no trouble with the pacing, but needs sufficient time for notes and test taking. He's officially on the low end of normal, but the teachers don't want to provide notes or time in an accel class. Other dropped capable kids are LD, and those that were too poor to make up for the school-induced gaps brought about by full inclusion. All wasted potential due to politics.

Genevieve said...

I don't know how the block scheduling works out for students that are trying to catch up.

It sounds as though the option of doing a one year algebra course at a pace that is more like a year and a half (first semester block, second semester regular) would be a good idea for students that just need a little more time to understand Algebra without sacrificing two years.