Acceleration

[jwburfeind]

 Jim Burfeind

[2/20/13: repetition of first paragraph deleted]

The 7th and 8th grade teachers at my school have been teaching some Common Core lessons using MARS problems and their rubrics for assessment. We have been surprised to find that our current groups of accelerated students are doing very badly. Our accelerated students are very good at formulas and procedures, but the problem solving, communicating reasoning, and thinking required by the Common Core is proving to be a big challenge.
 
In general, in looking at the Common Core it is important to remember the SMP (Standards for Mathematical Practice) are just as important as the Content Standards. SBAC for example will count the SMP for 60% of a student’s score.
 
We think that Common Core changes like focus, rigor and coherence are reasons to be very, very conservative in projecting acceleration for next year. Focus means there are fewer standards but the expectation is there will be more depth of understanding. Rigor means the national assessments will be very demanding. Coherence means you can’t skip standards in order to accelerate.
 
Some people have described the various proposals to “compact” three years of Common Core courses into two years. For example to teach Common Core grades 7, 8, and 9 in only grades 7 and 8. In the past we have had about 25% of our students accelerated. Based on our experience this year I see only 3% to 4% capable of maintaining the required pace. I think those few students might actually do better going deeper into a regular course instead of trying to go faster.
 
If you haven’t taught a Common Core standard in one of your accelerated courses and then used a MARS problem to evaluate how it went I suggest you try it. After teaching that lesson calculate how you would move fast enough to fit three years of Common Core into two.
 

[sunny]

We recently did some research in our district and uncovered interesting data. Every year about 1000 students are “accelerated” by being placed into the next math course, i.e. 6th graders are placed into 7th grade material, etc. The prevailing thought is that students will take calculus in 12th grade. By their senior year, only 20% of these accelerated students are actually in calculus. The majority are not even taking a math class. Also, we have found that state test scores drop the following year for 40% of the students who are accelerated, negating gains made by moving other students up to proficiency.

[Bill McCallum]

This is the sort of thing I worry about with acceleration that is either unwarranted by the student’s performance, or unsupported by adequate curriculum and instruction.

[swuttig]

We are working in our district to find ways to engage and challenge our gifted math students. Last year, we worked on a consistent curriculum across the district rather than a school by school decision. We compacted traditional 6th, 7th, and 8th grade curriculum since there is much repetition in 7th and 8th grade. Our district is in the process of implementing our new state standards which are very similar to the Common Core. We are trying to decide what we will be doing in the future about challenging our gifted students in addition to challenging problems. We don’t want them to skip grades/classes. We are a bit hesitant to compact the Common Core 8th grade math in the suggested accelerated pathway since it is an important foundation for later mathematics. We were wondering was there any discussion about other options of accelerating students by compacting, such as compacting 6th and 7th grade Common Core math.

[williamsl]

I continue to be very concerned that ALL students have a right to learn and mentally sweat in their math classes on a daily basis. We all know that students don’t learn at the same rate. I truly believe we can accelerate the learning of many who traditionally have struggled in math by using the CCSS with fidelity, providing those many representations and strong differentiate core instruction for all. This would fit with the RtI research that shows that if we teach this way we can really help all but a few learn during core instruction and then provide a little bit extra or a little bit different yet for those still needing more experiences to be successful. However, there are also those on the extremely fast learning end who don’t need to see things in many different ways to make the connections and truly understand. They don’t need the repetition and they have a right to go at the pace that is appropriate for them and not be slowed down so that they can teach others.

We have found that about 15% of our students, when provided with really good CCSS instruction don’t need two days on a lesson, they are making connections extremely quickly because this type of instruction is helping them as well. We’re using the CPM Core Connections curriculum and our accelerated group was able to complete all of the grade 7 curriculum and move through a chunk of the grade 8 curriculum in one year. This fall they will continue where they left off and move into the algebra curriculum. Effectively compacting three years into two without skipping anything, just by taking out repetitions that they don’t need that many students do.

Much of the research on heterogeneous groupings and taking away the slow paced classes makes sense. We can’t close achievement gaps by slowing some groups down and doing algebra in two years instead of one. However, in some studies the growth for the gifted students isn’t compared to the growth they make when they have appropriately paced curriculum. Reports say things like the top 10% were excluded because they were in other classes or had already been accelerated. So, the progress for the top students in the study was good, but the study didn’t actually include the top 10% of the students. Other times the gifted are reported as “no worse off” than when they were in undifferentiated classrooms with everyone getting identical instruction, again not compared to when they get what they need and can handle.

For more info please read Karen Roger’s book, “Reforming Gifted Education.” We need to make sure there are many options for all the types of students we have. We may need to work on making sure there are equitable pathways to all populations to all the options, but we shouldn’t be taking all the options away (especially when we are replacing it with undifferentiated one-size fits all teaching). Why would we stop offering IB High Level Math or AP Calc at the high school because we can’t figure out a way to increase the pace at which some students are able to experience curriculum?

[Bill McCallum]

I don’t have a lot to add here, but one comment I would like to make is that CCSS necessitates a rethinking of acceleration policies. Acceleration in middle school was often a response to the repetitiveness of the middle school curriculum. But CCSS in middle school is not repetitive; it is a dense and rich diet of important mathematics. So students who previously hungered for acceleration might now be quite satisfied with a solid implementation of CCSS.

[ttotorica]

Bill,

I just attended an Illustrative Math Conference and I am so energized by all I learned. Thank you for helping to provide this professional development for teachers! I especially appreciated hearing some of your thoughts about acceleration and compacting. We in our district have adopted a model of AP Calculus access for all, and as a result are developing course pathways that involve compacting Appendix A’s Math 7 and Math 8 courses into a single, one-year course along with a 4:3 model of compacting that absorbs the Fourth Course (Precalculus) into the integrated Math I, II, and III courses. These compacted courses are being built to provide entry points for calculus at both the junior high and high school levels and to also provide a double-accelerated pathway for those wishing to spend both their junior and senior years studying calculus.

My concern is that these courses are being built as the default courses for our general, non-gifted students. In an effort to send as many students to calculus as possible, my district is proposing the compacted 4:3 HS path for everyone, and I fear that by doing this, we will compromise both the depth of student understanding and the rigor of our courses. Do you share my concern that by compacting too much for the typical student, we will defeat the entire purpose underlying the CCSS development and generate thin and fragile mathematics competency as a result?

Given the district goal of providing access to calculus for all, do you know of any successful designs for high school acceleration that we might offer instead of the 4:3 model? I know of the “doubling up” model, where students simultaneously enroll in both Algebra and Geometry to gain a year for calculus study. But since we have adopted an integrated pathway, I’m not sure how that would look. I would like to propose a compacted, intensive summer course for precalculus, where the topics necessary for calculus success are offered to students after they have completed a normally-paced Math III course in their junior year. Do you think this could be a viable alternative to pitch to my district?

Thank you for your time and expert opinion; I appreciate it!

[Bill McCallum]

This is the most extreme example of acceleration I have heard of. Calculus for all is crazy. As a university professor I see the damage done by this sort of thing all the time: kids coming in with a fragile grasp of algebra or calculus because they have been raced through it, and being placed into remedial courses. This is a recipe for failure in college for many kids. There are some students who are ready for acceleration and they should have that opportunity. The rest are being done a disservice by this sort of thing. It’s an abdication of educational responsibility.

There used to be an excuse for it: the middle school curriculum was often sparse and repetitive and acceleration was the only way out of it. But with the Common Core students have plenty to do in middle school, and if they take it at the right pace they will be truly ready for college.

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