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Bill,
We are having conversations about what course a 3rd year student (freshman) in an accelerated pathway and how it would differ from a 4th year student (sophomore). Do you have any thoughts about heterogeneous grouping versus keeping the accelerated students together? Asked another way, do you have a recommendation about whether curricula should include sections of “college prep” versions of a course which include, for example, stem denoted standards that go beyond the standard curriculum or should districts offer the same (one) version of the course for all students and mix ability/age, in your opinion?
Fred, well, this really is just a matter of opinion, so I’m speaking here as a private citizen, not as a writer for the Common Core. But, for what it’s worth, my opinion is that acceleration is greatly over-used, and that for most bright students it would be better to deepen within grade level rather than accelerate beyond grade level. That is, study harder and more interesting problems on the material in the current curriculum, rather than race through it and go on to the next grade. And I would add that the Common Core provides a structure of coherence and connections that make this easier to do than it might have been previously. All that said, I know that many parents demand acceleration, and school districts have to deal with that.
Bill, I believe I have read elsewhere that you agree that students who are ready earlier for higher mathematics should be introduced to that curriculum? For good or bad, this “acceleration” tends to happen in the middle level grades, and even Appendix A addresses this and points out that it would seem the option of teaching 3 years in 2 during 7th and 8th is maybe the option that should receive strongest consideration?
If this is the case (that we want students who are ready for a more advanced curriculum to receive that curriculum), then my question may still remain unanswered. There is debate here whether or not our 8th graders who would take Math 1 remain group together in Math 2 as freshmen or if they should be spread out amongst sophomores taking Math 2. The argument for keeping together may include an ability to explore appropriate STEM-denoted standards that may not or are not included in Math 2 that the sophomores would take; the idea being the “accelerated” students may be ready (more ready?) for additional advanced topics that may not be able to be covered in the general curriculum. The argument for mixing classes would be (I think this is the traditional argument here) that having the higher ability students (even if younger) mixed in may benefit the average students. This would create two versions of Math 1 (and Math 2 and Math 3) – a general curriculum version and a “STEM” version.
Thoughts?
Fred, sorry I wasn’t more helpful, but apart from my prejudices expressed earlier I don’t have much to say without knowing more of the specifics. If were at a PTA meeting at my kids’ school where this was being discussed, I would base my decision on all sorts of local considerations, including how the school handles the different tracks (does it take them all seriously or treat one of them as a dumping ground, for example).
Hi, I’m so glad you have provided this forum for questions. Traditionally, our district has provided Algebra I to 8th grade students who take a placement test and must meet other criteria. Typically, about 25% of our students fall into this category. This year, in order to increase rigor, our district has suggested we teach the Model 3:2 Accelerated curriculum to all 7th graders district-wide. There will not be any classes who only teach the 7th grade standards. It isn’t clear if the expectation is for all 8th graders to take Math I next year, or if some of them will take 8th grade math. From what I’ve researched and read concerning the Common Core standards, the rigor is built into the curriculum and the 3:2 Model is only for those students who are advanced and the acceleration would be appropriate. Can you give your thoughts on this?
As you say, Common Core in Grades 7–8 is already plenty rigorous. Mandating an accelerated curriculum for everybody is a bad idea, in my opinion.
Thank you. I also have a question concerning the 3:2 and 4:3 models for compacting the curriculum in 7th grade. My state has published a document for each model and both include geometry standards G.GPE.6 and G.GPE.7, while they are not included in the 8th grade standards. Also, they are not listed in the pathways overview in the CCSS Appendix A for Mathematics for 7th grade. Can you see any reason these standards would be needed in this course?
Well, it’s a bit hard to say without looking at the course; there may be some reasons of coherence that they wanted to put these standards in. G-GPE.6 connects with the work on ratios in Grades 6 and 7, and G-GPE.7 connects naturally with the Pythagorean theorem in Grade 8. So I can see why people might want to put them in. And, if these accelerated tracks are limited to the students who a really ready for them, then there is no harm done. But that’s a big if. The fact is, these topics can wait. Just because a topic fits naturally, doesn’t mean you have to put it in; that’s what got the U.S. curriculum into trouble in the first place.
Becuase of the Common Core we are redesigning our accelerated math courses (that begin in 5th grade). Currently we compact beginning in 5th. In all the research I have done over the last few years I know I came across, at some point, a position that states that compacting should not begin before 6th grade. I completely agree and can express my reasons clearly but am looking for some more evidence to use to support this idea. Is there a paper/appendix/video series to be referenced on this little tidbit I came across somewhere at some point?
I hope someone else can provide resources, I don’t know of any off the top of my head, although googling “acceleration versus enrichment in mathematics” brings up a few interesting-looking hits. But one point I would bring up is that the acceleration schedule will have to change for many states that have adopted the Common Core, because the Common Core is already accelerated relative to many previous state standards. So, if you previously started accelerating in Grade 5, you might well push that forward a grade or two under the Common Core.
Of course, my own opinion, expressed at the top of this thread, is that acceleration is greatly overused. It’s the modern equivalent of the insane speed-reading fad that was pervasive in my youth. It encourages all the wrong values: superficiality, thoughtlessness, expectation of a quick answer, lack of perseverance—all flaws that will cause problems when a student reaches college. The student who can survive acceleration with love of and ability to make use of mathematics is very rare indeed. Much better for gifted students to have extension materials that enrich on-grade topics rather than race through them.
But that’s just my opinion.
Are there any placement tests based on CCSS content and Math Practice expectations that can be used for these accelerated or “compacted” courses from Appendix A?
I am in need of three: for identifying mastery of fraction computation for an “Honors 6th grade”, for identifying who qualifies for the Appendix A version of 8th grade Algebra I, and who qualifies for the compacted 7/8 7th grade course from Appendix A?
Thank you!
Hi Bill,
We had a very brief conversation at the PAEMST training session in Philadelphia last year concerning acceleration. One of the pieces that is always in the back of my mind is the research regarding Gifted and Talented education and tracking that shares the importance of multiple pathways vs. a strictly once in always in and once out always out tracked system.
We have had such a system in Manitowoc for a number of years and I would like your opinion about how we are adapting it now with the knowledge of the rigor of the 6-8 CCSSM.
We know that approximately 10% of the students in any particular graduating class want (and enjoy) completing calculus 1 (or even beyond) their senior year in high school. In order to achieve that level of mathematics we have some students that begin their acceleration in grade 7. In the past they compacted grade 7 and 8 into one year (because the expectations had so much repetition) and then were mixed into the algebra classes at 8th grade. With the new standards we are using Appendix A’s 3:2 pathway for these students.
Some students didn’t realize their love and/or interest in mathematics until they reached junior high school and were taught math by the more specialized teachers in a secondary school (rather than the generalists at the elementary level). Some students didn’t mature enough to put a lot of effort into mathematics until junior high. For these students we had two different paths for them to catch up to the students who began acceleration in grade 7. First, they could take algebra and geometry, simultaneously in grade 9. (Very few chose this, but for the few who did they loved it.) Second, we have a course for grade 11 that combines the traditional adv. alg/trig/pre-calc into one year. Then students would go to calc 1 as seniors.
We plan to keep both of these pathways as well.
I saw a quote from Phil Daro saying that he believed that only about 10% of students would be ready for the new algebra standards in grade 8. That number would fit well with our 3:2 pathway.
I hope I have described things clearly. What do you think?
Thanks,
Lori
Thank you for discussing the notion of compacting and acceleration. I would like to begin the dialogue regarding tracking beginning in grade six. This will be a huge paradigm shift for a culture where there is status for being in the” A track” in our middle school. The teachers are very fearful of creating mixed ability groups in grade six. This may be due in part to the fact that differentiation is not something they are equipped to do. Additionally, it may be that they are afraid of the parent community. Your thoughts?
I’ve indicated elsewhere that I don’t feel comfortable commenting on various acceleration and tracking schemes without knowing what’s in the curriculum, and without knowing the particular circumstances of the school district in question. But I’ll just make one general remark here: there is plenty of mathematics in the CCSS Grades 6–8. It is completely different from the wasteland of repetitive curriculum that led people to consider all sorts of acceleration and tracking. So I would urge people planning to replicate previous schemes to give some thought to the possibility that they are no longer necessary.
I mentioned this thread to a mathematics education researcher of my acquaintance. She said that parents might be anxious about getting their children ready for calculus in high school given that acceleration traditionally lead to this track. If that’s the case, one way to reassure parents is to indicate pathways that lead to calculus in high school without acceleration in grades 6–8.
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