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We have each year a cohort of students who study high school math in the middle school grades. To align to a change in course sequence 9 years ago at our sending district, we changed our sequence for these students to Algebra I in 7th and Algebra II in 8th. These students take Geometry in 9th grade at the high school and then go on to Pre-Calculus, etc. We recognize that most schools instead follow the Algebra I- Geometry- Algebra II sequence.
We are looking for information regarding whether the standards are constructed to prefer one sequence over another, or if PARCC testing requires that instruction follow one of the two sequences in order for students to be properly prepared. Would you be able to provide some guidance based upon your work with Common Core and PARCC that could inform my process and stake-holder decision-making?
The high school standards do not specify any arrangement of the mathematics into courses; that is up to states and districts. I’m not an expert on PARCC, but I believe they will have end of course tests for Algebra I, Geometry, and Algebra II. These should be relatively independent of each other, but there could be places where they assume that an Algebra II student has had Geometry. For example, the Geometry domain Expressing Geometric Properties with Equations (G-GPE) is in Algebra II in the PARCC framework. You can check out the frameworks here.
The biggest question I have about your proposal is not the order of those courses, however, but the preparation of the students entering Algebra I in Grade 7. The K–8 standards were designed to gives students a solid preparation for algebra. How do you handle acceleration in Grades K–6 for these students?
We along with many other middle schools with rigorous course offerings offer acceleration to talented students and have for many years. This acceleration has occurred for many, many years and it requires careful development of placement criteria, and curriculum mapping and compression. Things indeed have changed with Common Core, yet the meticulous mapping is similar. In terms of our current procedure, students are identified for initial acceleration at the end of 5th grade using a multi-dimensional and multi-modal analysis of mathematical achievement, algebra readiness/potential and progress in developing the mathematical practices. Those students who are determined as eligible undertake a Pre-Algebra Accelerated course in 6th grade. The curriculum includes the 6th grade CCSS standards as well as 7th and 8th grade CCSS standards pertinent to Pre-Algebra. For these students, the curriculum connects the more concrete concepts in 6th grade with algebraic extensions from Pre-Algebra. We benchmark to follow progress and mediate any gaps. These sixth grade students take the state-mandated 6th grade level assessment, NJASK and soon to be PARCC, as well as local course exams. As seventh graders, these students take Algebra I Accelerated in a similar fashion, and have taken seventh grade level state assessments and course-specific local exams. During the Achieve Algebra I EOC years, they took also took that high-stakes assessments.
Until about 8 or 9 years ago, as eighth graders, these students would have taken Geometry as eighth graders, until our sending district changed their middle school accelerated sequence to Alg I- Alg II- Geometry. Currently, these students undertake Algebra II in eighth grade, with respective state mandated eighth grade level assessments and course-specific local exams; beginning next year, the state has advised us that once students reach Algebra I, they will no longer take assessments by grade level, but by course. We will still ensure that students achieve all the standards, but at least students won’t lose twice the instructional time in standardized testing.
We are not unique in offering middle school mathematics acceleration; it is common at least in our region. It allows competitive NJ students looking to apply to selective schools to reach Calculus I by their junior year. We are considering reverting to the more traditional Algebra I- Geometry- Algebra II sequence for these students– Algebra I in 7th, Geometry in 8th and Algebra II in 9th. It seems more developmentally appropriate to integrate the visual support for complex mathematical ideas earlier, and save the more abstract content of Algebra II for 9th grade. We have been unusual in our Alg I-Alg II- Geometry sequence. We are concerned as to whether being out of the typical sequence will disadvantage our students in achieving the standards or in demonstrating mastery in high-stakes assessment, as part of the larger discussion about the sequence, especially since our sending district will not be changing the sequence this year.
We are planning on examining the frameworks documents in detail, but I was hoping for availability of some additional expertise to take under consideration.
Dear Dr. McCallum,
You had inquired the following:The K–8 standards were designed to gives students a solid preparation for algebra. How do you handle acceleration in Grades K–6 for these students?
I am an NJ parent of a child who is slated to be radically accelerated in 6th grade so as to be ready for AP Calculus BC in 11th grade(!) In our NJ district, there is no acceleration at all in grades K-5 for math. Since I am also a math professor, I supplement whatever is needed for my kid at an appropriate developmental level. I see topics rushed through at a speedy pace in 6th grade and beyond, with lots of concept gaps. Even the “standard” track kids are rushed through so that almost all can take some version of calculus as seniors. Competitive school districts feel that this is the way to gain admission to top universities, so I am not sure that compactification is going to go away.
The proper way of acceleration – to teach on-grade topics in depth by using materials such as the ones written by the Art of Problem Solving group – requires a fairly sophisticated understanding of mathematics. Also, many universities still use the traditional high school math curricula as the benchmark for their placement criteria. Thus, as far as districts like mine are concerned, I do not, unfortunately, foresee much change in the approach to secondary school math.Forgive me, but this mode of acceleration seems awfully excessive, especially with the new standards. I hope that this rush through standards isn’t at the expense of the students love or like for math, or conceptual understanding of math. I am also left to wonder of the preparation of the middle school and K-5 teachers. Are they prepared to teach high school courses? Do your K-5 and MS teachers have math degrees? Are they prepared to teach these new standards, which are already radically more rigorous? “Algebra 1” and “Algebra 11” are just the names of the courses. In our district, the standards that are in these courses are radically different and more rigorous than we had in the past.
I am curious about your data… do many students who complete this mode of acceleration enter an elite university in a STEM field? or complete a degree in STEM field? Lots of questions….Forgive me, but this mode of acceleration seems awfully excessive, especially with the new standards. I hope that this rush through standards isn’t at the expense of the students love or like for math, or conceptual understanding of math. I am also left to wonder of the preparation of the middle school and K-5 teachers. Are they prepared to teach high school courses? Do your K-5 and MS teachers have math degrees? Are they prepared to teach these new standards, which are already radically more rigorous? “Algebra 1″ and “Algebra 11″ are just the names of the courses. In our district, the standards that are in these courses are radically different and more rigorous than we had in the past.
I am curious about your data… do many students who complete this mode of acceleration enter an elite university in a STEM field? or complete a degree in a STEM field? Lots of questions…Middle school acceleration made some sense when the middle school curriculum was impoverished, as it often was under previous state standards. It makes less sense when the middle school standards are as rich and demanding as they are under the Common Core. I certainly understand all the forces driving middle school acceleration and I also understand that those forces are not going to go away overnight. But parents and schools do not have to submit to those forces. I didn’t with my own children, and they are all happy and successful.
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