Mark Coté, CPM Project Manager, markcote@cpm.org
Does your school or district offer one or more accelerated pathways for secondary mathematics? How are students selected? Is the plan effective? To take the pulse of this controversial issue, these questions and several others were posed to the CPM nation via social media and email. The 32 responses I received from around the country offer an informal appraisal of putting students on a mathematical fast track.
The most common pathway reported was a middle school compacted class. A compacted class, in most cases, is designed to offer two years worth of math content during one year of instruction. Several flavors were mentioned, but the most frequent were either a Core Connections, Course 2/Core Connections, Course 3 class or a Core Connections, Course 3, Core Connections, Algebra class. The high school compacted classes were typically composed of either a Core Connections, Algebra 2, Precalculus hybrid or an Integrated II, Integrated III mix. Less common, by a 4 to 1 ratio (compacted : skipped), was the “skipped” option. In a “skipped” option, a student simply bypasses a course with no mechanism in place for acquiring the content. This occurrence was most frequent at the middle school level, with accelerated students skipping either 5th grade or 8th grade math.
As the chart to the right indicates, the selection process was fairly evenly split between student/family choice and school/district designation. In parallel with the ratio of pathways mentioned above, selection typically occurs during the middle school level. No universal selection process was reported, but test scores, grades, and teacher recommendations were mentioned as common data pools for decision making.
Feedback on this issue indicates that there are school systems experiencing success with acceleration. Upsides mentioned centered on the benefit to students and the increased enrollment in Advanced Placement courses. The following comments were representative of all submissions:
- Our system works well for those who are ready. It’s not right for everyone, but great for those who need more challenges.
- Kids who LOVE math can get way ahead and take so many math classes this way. They also often choose to tutor or aide in lower math classes.
- One of the positives is the few kids we get into Calc BC or even AB are pretty stellar mathematicians and have gone on to do some amazing things.
Many respondents reported a definite increase in the number of students taking advanced courses at their school, but several mentioned that they were unsure about the long-term impact of such participation. Input was mixed regarding student performance in these classes. A typical comment was, “Many students do go on to and do well in Calculus (many during their sophomore year), but I also see many promising math students burn out in math.” Parent choice was cited as having a positive impact on the process. When families were offered multiple entry and exit points coupled with a clear, substantial selection rubric, better results followed and fewer parents attempted to override the district’s decision about acceleration. Additionally, some systems have experienced success by offering a combination of online coursework and assessment to accompany the traditional classes.
While overall effectiveness was reported by about 30% of the respondents, the majority indicated that the acceleration program in their school/district had either mixed results or was not producing the intended outcome. The most frequently mentioned downsides included the selection process, the impact on student learning, the push from parents, and systemic repercussions.
Teachers cited a number of concerns about the selection process, especially at the middle school level. Many of the students selected were characterized as, “…being good at school and having social maturity, but also having no real passion for learning math.” Often, there were either no established screening criteria or, just the opposite, several rounds of stressful testing. In many cases, the late bloomers had no pathway as the culling occurred only once in the middle grades, offering just a single chance to move ahead. Several 6th grade teachers noted that the students selected for “advanced” math in 5th grade were often misidentified. Selection was based on how well they knew their number facts and how quickly they were able to produce answers in multiplication and division. As one teacher put it, “Rarely, if ever, do they look at perseverance, resiliency, problem solving, critical thinking or curiosity, which I think are key traits of students who are ready for more advanced mathematics.”
Skipping to accelerate was seen as the factor producing the greatest negative impact on student learning. It was frequently reported that students who skipped entire courses had large holes in their understanding of grade specific content; these gaps were magnified and then exposed as the students took Core Connections Algebra 2 and Precalculus. Such lack of preparation guaranteed failure for many students and set them on a course of prolonged, unproductive struggle throughout high school. Teachers also cited the following impacts of acceleration on student learning:
- Many of my students report losing motivation, feeling overwhelmed, and being done with math.
- I think most don’t have the developmental capability to really understand the math they are struggling to do.
- Accelerated students have trouble making connections because they don’t take the time to really go deep into the math.
- Students are missing out on key developmental areas in middle school and tend to be very good at the procedural part of math, but not so good at problem solving.
- The accelerated students I have worked with are very good at procedures. Once you step away from the procedure box, so to speak, they don’t know what to do. They have not gone through materials where they have to persevere and make sense of the problem.
Sadly, many teachers reported that a significant percentage of their accelerated students found the brisk pace too difficult to maintain and stopped taking advanced math altogether. Their juniors and seniors often stated that they had other hard classes and, “…something needed to give.”
If you build it, they will come.
This statement encapsulates the reaction from parents to systemic acceleration, as reported by many respondents. Advanced math classes have acquired a social status that many parents want to be connected to, either for their child’s benefit or their own. One teacher mentioned that the extensive public relations and marketing done by the district attracted two or three times the number of students who should be accelerated. Ivy League FOMO (Fear Of Missing Out) was also mentioned as a motivator from the parent’s perspective. “The parent push results in many students being driven too hard which in turn can make them feel like failures and hate math. This eventually can be detrimental to their overall progress and success in math as they move on to college.”
Acceleration has systemic repercussions as well. As mentioned above, teachers reported a decline in the study of mathematics for some students during the four years of high school. One teacher shared data collected over the past five years that illustrates the change in interest. The number of students is the average for each year.
freshman/sophomores: Integrated 2/3: 70 students
sophomores/juniors: Trig/Pre-Calc: 50 students
juniors/seniors: AP Calc AB: 10 students
seniors: AP Calc BC: 5 students
Many of this teacher’s students who would otherwise go to Calculus AB as seniors are opting not to because the accelerated Integrated II,III class has been so overwhelming. Another systemic issue reported is that the compacted classes are not truly condensed. Many teachers end up skipping important material because of the constant time crunch – especially sections covering probability and statistics. Likewise, the longer, more involved problems that require hands-on activities and take extra time, are deleted from the course. As students move forward through this abbreviated pathway, their teachers are expected to support those who do not have appropriate preparation, adding stress to an already demanding workload. Also, missing one or two days in a compacted course is the equivalent of missing a week in a regular course. Some students who are frequently absent never catch up. As one teacher put it, “A compacted class on a block schedule is a disaster.” Teachers also noted the following issues:
- Acceleration exacerbates the equity problems that come with tracking.
- No high school credit is offered when taking high school classes in middle school.
- Upper level math teachers complain about the lack of preparation of the accelerated students.
- Effectiveness depends on the teacher.
Finally, teachers noted that acceleration raises some sticky systemic questions. What happens when accelerated students fail? How do we have students repeat a course that they have already barely passed, and it is clear that they are unprepared for the next course in the accelerated sequence? How do we convince parents that their child needs to repeat a course to ensure long-term success? How do students complete their graduation requirements when they have fallen off the accelerated pathway?
As each school or district wrestles with the acceleration question, adjustments are often made. Several teachers reported such a learning curve and the subsequent modifications that were put into place. One teacher shared, “We took quite a bit of time educating parents on the benefits of learning concepts more deeply and sharing that the CCSS has added lots of rigor and no redundancy. This has helped slow the tide of excessive acceleration.” Another added, “We recently changed to not accelerating until 10th grade. In 10th grade, students have the option to complete Core Connections Geometry and Core Connections Algebra 2 simultaneously with the understanding that they will take four years of math – junior and senior advanced classes. We are still evaluating this acceleration program.” And a third offered this pathway, “Our feeder schools only teach through 8th grade math (no [algebra] option) so we’ve decided to accelerate in Integrated III, making it honors by embedding necessary precalculus concepts. Next year will be the first class of seniors to enter Calculus without having had a full year of Pre-Calc under their belts. From what I hear from students, the accelerated course has been a killer, even for exceptional students. We’ll see how this works.”
What will your school or district decide to do? Will you be involved in the discussion? If so, here are some additional resources to consider. This EdSource article brings up some of the equity issues involved. See the comments section for an interesting silent debate. In his blog, Robert Kaplinsky offers the case against acceleration.