Somehow I got from Megan Golding's audacious idea (see here) to the blog Gas Station Without Pumps's discussion of eliminating age-based grade level instruction in math, and instituting placement by achievement.

This approach to placing kids has long been popular with parents of gifted children (though for some reason not with school teachers and administrators). It has gone by many names (subject acceleration, readiness grouping, grouping by ability or skill or mastery, … ). I prefer the name placement by achievement, since we are not accelerating students but letting them move at whatever velocity best suits them, and we can’t measure “readiness” but only what has already been achieved. Ability is not the point, achievement is. I guess that “grouping by mastery” is ok, but “mastery” seems to me a more cumbersome word than “achievement” and “mastering” a subject seems to me appropriate for post-baccalaureate studies.

Personally I prefer "placement by mastery", but reasonable people may differ.

In another post, GSWP discusses the recent article by Bill Evers and Ze'ev Wurman, advancing the idea that the California state math standards are superior to the proposed Common Core standards. (I believe California adopted the Common Core standards -- if Evers and Wurman are correct, look out, afterschooling! -- but I digress).

GSWP goes on:

My opinion is that the whole notion of age-based grade levels is wrong and twiddling with the standards won’t fix that. There is value to having standards that all schools and curricula must meet, but I wish that the standards were not labeled with grade levels. There are students ready for algebra long before 8th grade, and students who are barely ready for it by the end of high school. Having students progress through the standards based on mastery, rather than age, would be greatly helped by not labeling the standards with grade levels.

One specific criticism of the Common Core that Evers and Wurman raise, that there is a big jump at 8th grade because the K–7 standards are too weak to provide sufficient support for the 8th grade algebra standards, is probably a valid one and should certainly be considered by the State Board.

Discussions on the Common Core:

## 19 comments:

I've thought about this often, especially since I taught in a K-3 school many years ago that did this in reading. There were about 12 levels in those 4 years, and children progressed through them at varying rates.

I do think that there would be one problem with "mastery placement" or "achievement placement:" the fear of being retained is one (out of many) factors that can keep some kids working harder than they otherwise might. Especially in the upper grades. If we basically tell kids, you can progress as fast or slow as you feel comfortable with, I'm worried that some will say to themselves, "slow is fine by me."

The placement-by-achievement post is at

http://gasstationwithoutpumps.wordpress.com/2010/07/21/placement-by-achievement/ if anyone wants a direct link.

Slow

isfine. You just put the graduation level as mastery at the level you want to insist that everyone gets to. If some get there at age 8 and others at age 18, what difference does it make?And if they don't get there, then what? The problem with getting rid of age-based grade levels is there is NO MINIMUM PROGRESS below which a teacher or a school is held accountable.

I'm not suggesting the current system of age-based grade promotion rather than mastery is good. I'm saying that how does this not become just the large blank check for blaming students?

Because if a student can't going to master algebra 1 by the end of high school, are you really do anything but suggesting it's the student's fault?

"And if they don't get there, then what? The problem with getting rid of age-based grade levels is there is NO MINIMUM PROGRESS below which a teacher or a school is held accountable."My son's martial arts dojo groups by ability and also has a typical/expected amount of time for each level. This seems to work pretty well. Kids can go faster than typical, especially if they attend more than the minimum number of classes per week or if they practice at home. Some kids go slower. And some go slower for part of the year when other activities interfere.

Grouping by ability doesn't have to eliminate the possibility of having an idea of what is typical.

-Mark Roulo

The analogy is awfully different. If after 2, 3, 5, or 12 years of martial arts, none wants to continue, and none knew how to break a board, disarm an opponent, or evade an attack, what's the harm, other than the parent's money and the child's time?

But if you can't READ or compute a percentage after 12 years because you went too slowly to ever put it together, there's a lot of harm.

No, it doesn't HAVE to eliminate the possibility of having an idea of what's typical: but is a teacher or school going to have a bare minimum per year, and accept accountability if the student doesn't meet it or not?

Since most schools don't now claim that kind of accountability, getting rid of grade levels isn't going to suddenly create it.

It's the culture. Until a school decides they aren't going to let kids fail or continue to fall backwards as their peers accelerate away from them, no reorganization of the deck chairs will change it.

Who determines what is mastery? Would it be like like the minimum proficiency cutoff our state uses on its test? In the old days, if you didn't master the material in a grade, you were held back or had to go to summer school. That's a form of mastery placement. It was also set very low.

Mastery placement will not solve issues with low expectations. You can raise the cutoff level, but coming from that direction, the mastery level will always be too low. I can't imagine K-6 schools setting the minimum mastery placement level high enough to assure that the students will get to algebra in 8th grade. This implies the need for two (or more) mastery placement tracks. It's not just a matter of speed through the material.

I'm with GSWP -I've had this scheme in preAlgebra, on contract via independent learning at a DoDDs Europe school when I was of middle school age and in a midwestern public high school for Alg.I up. The issue of low expectations is resolved by the contract. A certain amount of work must be completed with end of chapter tests averaging to determine a certain letter grade each quarter. Doing the minimum chapters perfectly gets a B. Average chapters -> standard grading system. Max chapters gave a little bit lower percent needed for each letter, however the students that did that option weren't the type to need the boost.

Texts were Dolciani & Brown series, high school option was independent study or traditional lecture w/board work. Decision was the students as far as is./lecture and min/avg/max. Geo could not be taken i.s.

My current district uses mastery placement for ms and hs, but they won't allow pretest or i.s.. 85 or higher on each unit is needed to advance.They must attend afterschool tutoring until they get the pass while simultaneously working on the next unit in class. Final grade of 65-80 puts the child in remedial, same class, the following year. 80-85 puts them in bridge. 85-100 allows them to progress. Placement is by math dept, all classes lecture.

I like the option I grew up b/c the student has much control over his success. The current district tends to block capable children by adjusting the behavior portion of their grade so that they are forced into remedial.

The true problem here is K-5. Whole class full inclusion does not work. We need to go back to ability/acheivement grouping before middle school starts. We need to pull students who are disruptive due to medical and pyschological conditions out of the mainstreamed classroom permanently so that others can see and hear and think during academic class time.

Sorry, Gas Station Without Pumps! I'll go back & fix it.

I am the math specialist at a charter school that ability groups and we use Singapore as our core text. Because it is split into two books for each grade level Singapore is ideal for ability grouping. We roughly have a low, medium, and high group at each grade level, but we teach math at the same time so some kids are going to higher grades for math. One way we handle the "low" groups is that they tend to be smaller and we put two staff members with the lowest groups, so kids are getting more one-to-one instruction. So far it is working and the parents are mainly happy. Anytime parents complain that their kid should be in a higher math group, we tend to give it a try. I find that if kids and parents are really motivated it is a good thing to let them stretch.

I am the math specialist at a charter school that ability groups and we use Singapore as our core text. Because it is split into two books for each grade level Singapore is ideal for ability grouping. We roughly have a low, medium, and high group at each grade level, but we teach math at the same time so some kids are going to higher grades for math. One way we handle the "low" groups is that they tend to be smaller and we put two staff members with the lowest groups, so kids are getting more one-to-one instruction. So far it is working and the parents are mainly happy. Anytime parents complain that their kid should be in a higher math group, we tend to give it a try. I find that if kids and parents are really motivated it is a good thing to let them stretch.

And how much yearly progress is the low group expected to make?

Why should the goal be to get every student in Algebra I by 8th grade? Obviously that is the minimum required for students aiming for an elite college, or for a STEM major at any college. But those students are only a small percentage of the overall student population (at most 25%). The average student only needs to finish Algebra II by graduation.

"Why should the goal be to get every student in Algebra I by 8th grade?"One argument is that the majority of Europe, as well as Japan and Singapore (I think) get their kids to Algebra in 7th grade. The push for Algebra by 8th grade here is an attempt to make the US typical curriculum as fast-paced as the European remedial curriculum.

"The average student only needs to finish Algebra II by graduation."I'd suggest that the average student doesn't need Algebra II at all. And that if we are insisting on a non-watered-down Algebra II as a requirement for high school graduation (as we do in California), then maybe 30-40% of the kids won't be graduating.

Consider that the next class after Algebra 2 is Trig --- which is a 1 semester course at best --- and after that you are ready to start Calculus.

Requiring everyone to be one semester short of starting Calculus as a requirement for graduating high school???

-Mark Roulo

I think the algebra by 8th grade premise is flawed as well. It's based on data showing that students that had algebra in 8th grade did better in college. But was it the algebra in 8th grade that made them do better in college, or the fact that the students that took algebra in 8th grade were harder working, smarter, traits that would also make them do better in college.

From the standpoint of STEM careers, for my chemistry degree I needed to be able to start calculus when I entered college to graduate in four years. So if I'd had algebra 1 in 9th grade I still would have been able to complete enough math to start calculus at college.

Although I think all students should have the option of algebra in 8th grade, pushing all students into just seems to result in watered down courses. Regarding other countries, I've taken a look at the Singapore math textbooks, and they seem to spread out algebra I, II, and geometry over 7-10th grades. So it's not like 7th graders in Singapore are taking a full on algebra course, they're taking a course in basic algebra and geometry principles.

In Europe and Japan, students are explicitly tracked into separate high schools based on the results of one high-stakes exam. Most students do not attend the college-prep high school but rather a vocational one. So we're comparing ourselves against only the highest-achieving of the Europeans & Japanese. Apples to oranges.

I'm not sure that's completely correct (algebra I & tracking). There are multiple opportunities, at least in some countries, to change tracks (yes, via test). Also, was just looking at the mathematics sequence for one country w/tracking (& approx 30% on top track) and looked like algebra 1 content was mostly in first year of secondary school across all secondary school types. That would be approx. 7th grade. Not sure about others but would caution against assuming that the "lower" tracks are completely lacking in academics.

The goal of algebra (a proper version) in 8th grade should not have to be such a key target, but it is. Arguments against it hide the huge issue of poorly taught math in K-6. I'll accept 9th grade for a proper course in algebra, but for many, the damage is done. You are either at a base camp for climbing a larger mathematical mountain or you are struggling to reach a mathematical plateau.

The inability to get more kids into algebra in 8th grade is indicative of a much larger problem. You can't claim that only some of the kids in K-6 need to be led along this path. Which kids are you talking about? Is this done by careful selection or by trusting the spiral? If they don't make it to algebra in 8th grade, where does that leave them? Unfortunately, many just see the difference as speed, rather than an issue of hitting a mathematical wall because of bad teaching and curricula.

The goal is to push and keep all educational doors open as long as possible. Most kids don't even need Algebra II by the end of high school, but you can't decide that in K-6. Getting all kids prepared and through a proper course in algebra (8th or 9th grade) is much more important that torturing them to get through a lifetime terminal course in algebra II in high school. That's not preparing them for anything.

This is a core issue of what we're fighting for. There has to be some force driving proper math education back into K-6. Even if you think that only 25% of kids should ever get to algebra in 8th grade, who are these kids and how will they get the proper preparation? And for the rest of the kids, how do you prepare them properly rather than set them up for remedial mathematical torture in high school and making them feel that it's all their own fault?

"Some might be surprised that although I push for the target of a proper course in algebra by 8th (or 9th) grade, I'm not a supporter of algebra II (real or pseudo) for high school graduation. After algebra, math requirements should be based on what the student wants to do after high school. We don't need some sort of generic "workplace analysis" to torture all kids through algebra II in high school. If students want to major in journalism, they can easily go online and check the department requirements at their favorite college. If students want to become electricians, they can check the math requirements at their local vocational school. If students want to keep all options open, they can continue with the geometry, algebra II, pre-calculus, and calculus sequence as far as necessary. At least they will working from a proper base."

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