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In considering how to approach having a CCSS Algebra 1 course in 8th grade and who should take it, the document, “ Appendix A: Designing High School Mathematics Courses Based on the Common Core State Standards” is well worth looking at.
Here is the link:
http://www.achieve.org/files/CCSSI_Mathematics%20Appendix%20A_101110.pdf
The document includes detailed proposals for compacted courses. It is worth studying them to make a considered decision of exactly which students would be capable of moving at the required speed.
The document explains that moving faster can’t be done at the expense of skipping content. The authors explain this idea of not skipping CCSS content because of the need to maintain the coherence of the CCSS. Coherence, or the closely interlocking nature of the CCSS standards across grade levels and domains, is a key component of the strength of the CCSS and can’t be damaged without undermining the quality of the mathematics education.
The document suggests many paths to acceleration including waiting for high school before attempting acceleration. As a middle school teacher I am addressing only the middle school acceleration here.
For example the compacted 7th grade course has every one of the CCSS 7th grade standards and in addition 15 CCSS 8th grade standards. Given there are only 28 standards in the entire CCSS 8th grade course this is a very, very, substantial amount of additional material.
The compacted Algebra 1 course has every one of the CCSS Algebra 1 standards and in addition 13 CCSS 8th grade standards. Again, given there are only 28 standards in the entire CCSS 8th grade course this is a very, very, substantial amount of additional material.
I think a very important question is developing clear objective criteria for how to decide near the end of 6th grade exactly which students should be encouraged to attempt one of these compacted courses.
If anyone is aware of any work in this area I would very much like to hear about it.
I’d also be interested to know of efforts in this area. CCSS is already more substantial than many previous middle school curricula, so accelerating it has to be done carefully and should be a matter of choice, not mandate. An alternative to acceleration is enrichment; instead of rushing on to the next topic, do harder and more complex problems on the current topic. For many students, having solid grasp of ratios and proportional relationships by the time they reach high school will serve them better than having been exposed to quadratic equations.
In my district we have middle schools with grades 6-8. We are trying to decide if we should begin to accelerate students in grade 6 or grade 7. In either case we will provide many other ways for students to “jump into” acceleration as late as their 10th grade year. Also in either case we would not be skipping content but would be compacting the content. We would either be compacting 4 years into 3 years or 3 years into 2 years.
My question specifically concerns appendix A on Page 81. Following the logic of the first recommendation on this page, compacting 4 years into 3 years would be preferable to compacting 3 years into 2 years. Therefore, leading one to believe that accelerating and compacting the curriculum beginning in grade 6 would be not only ok but preferred. However in recommendation number two, it states that the Achieve Pathways Group does not recommend starting acceleration until grade 7.
After using some of my ELA Common Core skills and closely reading this second recommendation, I think the intent of this recommendation was not to track students too early and choose the fate of their high school mathematics as early as the 6th grade, not that there is an issue with the mathematics of compacting prior to grade 7.
I contend that beginning to compact the curriculum for grades 6-8 and Algebra I into the three years of middle school and providing multiple opportunities for students to enter this accelerated pathway along the way through middle and high school is preferable to waiting until 7th grade and compacting 7-8 and Algebra I into two years.
I would love feedback from Bill, the Achieve Pathways Group, and anyone at large on this idea.
Thank you.
From my fading memory, your analysis of the rationale behind the recommendation in Appendix A is correct. I also remember there was an active debate about this, and your point of view also had supporters. My personal view is that enrichment should be considered before acceleration. That is, students who are eating up the material should be given harder problems on grade level material rather than an accelerated and possibly superficial treatment of material from later grades. Acceleration should be an option for students who are truly prepared for it, and hopefully that fraction of the population will increase over time. This doesn’t, of course, answer your question about whether to start acceleration in Grade 6 or 7 … sorry!
In the Catholic Diocese of St. Augustine, FL, we are struggling with the issue of Advanced 7th grade and Algebra 1 8th grade, too. We don’t WANT to offer these courses because we believe enrichment is the way to go for the few truly gifted students we have in each of our 23 elementary schools and the Common Core is already advanced, both in its content and its critical thinking expectations. But, we compete with public schools offering IB programs, 8th grade Honors Alg. 1, etc. and our tuition paying parents insist that their students be placed in “accelerated” courses in 7th and 8th grades. For now, we will need to accommodate.
On that note, does anyone know of a “placement test” that might reliably tell us if an incoming 7th grader is capable of handling the Common Core 7th Grade Advanced course and also one for the 8th Grade Algebra 1? And, are there already tests available that we might give quarterly in each of these courses that could be used as formative assessments to help us figure out what to do with students who might be having difficulty? The PARCC assessments will likely tell us what we need to know, but we can’t wait until 2014-2015.
Also, ALL teachers in the Diocese, including those in the 4 high schools will be using the problems from illustrativemathematics.org in their daily lessons. Thank you for these excellent problems! They are awesome.
As we were working on curriculum planning with the new CCSS, a question came up about how standard form fits into the CCSS in both The functions and expressions and equations domain and what the expectations are for the students. For instance, in the current TN curriculum, it is an expectation for students to rewrite equations that are in standard form in slope-intercept form. Is this an expectation in CCSS? Also, what are the expectations when solving systems and the methods used to solve systems? Thanks for your time!
Putting equations and expressions in particular forms comes up under a variety of headings in the Algebra forum: http://commoncoretools.me/forums/forum/public/hs-algebra/.
A general principle of the Standards is described in the Algebra Progression, p. 4, http://ime.math.arizona.edu/progressions/:
“The Standards emphasize purposeful transformation of expressions into equivalent forms that are suitable for the purpose at hand. . . . Each is useful in different ways. The traditional emphasis on simplification as an automatic procedure might lead students to automatically convert the second two forms to the first, before considering which form is most useful in a given context.”
In the quote above, for “simplification” one could substitute “putting the equation of a line into standard form” or “putting the equation of a line into slope–intercept form.”
Re systems of equations: there is the beginning of discussion here: http://commoncoretools.me/forums/topic/a-rei-5-what-does-it-meanlook-like/. I’ll try to contribute more to that thread.
All,
I’m a district math coach and coordinator in WV and have great interest in this topic. I have been a passionate advocate in the last few years for allowing middle school acceleration as we transition to common core standards. It matters SO much in states like mine what the folks at the top are recommending and I’d love to have comment on my rationale…
In a state with the one of the least well-educated populations in the nation, with over half of our students living in poverty, where better than 1/5 of 9th graders failed 2 or more subjects, with less than 40% even proficient in math, I am concerned that it’s more important than ever to give future leaders every possible opportunity for brain stretching.
I totally buy the argument that, with common core standards, content is deepening and that students do not need to ‘skip’ so much as they need to deepen. However, it really only resonates in a theoretical context. What I can’t wrap my mind around is that as the theory morphs down into practice, learners will continue to need different amounts of time to own and personalize ideas. Next year, we will begin to implement these new standards with the students that we have with a great mix of ability, need and desire. Even while working at elite Southern private schools, where 100% of the students finished Algebra by the end of 8th grade, the hungry, naturally gifted learners finished Geometry by the end of 8th.
I worry that changing curriculum can get confused with changing audience. In my (granted, limited in comparison!) experience, the most naturally gifted learners easily learn at both a pace and depth two times greater than the average. In addition, I find that these learners struggle mightily at the beginning of a truly rigorous course surrounded by their peers. But after a short adjustment period, as the sore muscles in their brains transform into stronger cerebral muscles, their potential for engagement and depth grow exponentially.
In short, there’s a difference between the local community college where I have taught and Haverford, where I went to school myself (and where my thesis advisor and lasting friend, Jeff Tecosky-Feldman, still speaks highly of you, Bill!). The institutions don’t serve the same audience, and thus don’t use the same strategies. In our most educationally disadvantaged areas, it’s so important to do the very best by the higher-level students. The ratio of need for highly qualified leaders to availability thereof in all fields is much higher here than in those states lacking our dismal stats.
As one teacher put it… “are we not just moving from no child left behind to no child pushed ahead?” We should continue to delve deeper into these standards, to strive to make our curriculum fertile ground for learning. As our classrooms improve and deepen, the hope is that the learning potential of ALL students will rise, leaving the group of mathematically gifted still with needs beyond the grade level.
My idea in regards to middle school advancement is not to leave out a middle school course, nor to identify kids as 5th or 6th graders. Instead, 8th graders who are ready, willing and able to go an extra mile could take an elective math class in 8th grade in addition to their regular class.
I appreciate feedback, insight, and the opportunity to join the conversation.My Best,
JoannaJoanna, very interesting thoughts (and nice to know the connection with Jeff, who I still see regularly at our Harvard consortium meetings). It’s a complicated problem, and I don’t have a neat answer. Like you, I would like to see more students get further ahead in mathematics, and I wouldn’t want the Common Core to be interpreted as a barrier to acceleration. In fact, I believe that in the long run the Common Core is an engine for acceleration. Students who experience a faithful implementation of the Common Core in elementary school are more likely to be ready to take off. But we have to wait for that, and in the meantime we have to eliminate phony courses that give the illusion of acceleration without the reality of.
Hello wise math folks,
I am reviving this topic in the hopes that people can share back what they have tried regarding Algebra 1 and 8th grade standards (compaction, enhanced HS pathways, etc.) and what the challenges and successes of doing this have been.
Also hoping that folks have found/established other “go to” resources for this topic beyond Appendix A.
Thank you!
Jen Spencer
HS Algebra teacher
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