Accelerated, Advanced, and Intensified Classes: What's the Difference?
Editor’s Note: This is the first in a series of articles looking at the national debate on math instruction and its potential impact on Virginia and APS. The below is designed to kick-off the series by providing some background information for parents. Stanford Education Professor Jo Boaler has drawn national attention with her calls to decelerate math instruction, spawning a greater debate on the benefits of going deeper versus faster in coursework. It is important to note that different approaches may be better suited for different subject areas; we are currently seeing this play out in APS.
In SY 2023-24, APS will offer open-enrollment middle school honors classes in English, Social Studies & Science. This welcome development would offer courses in these subjects that are “advanced,” meaning they will cover the same material as regular classes but will go deeper. These classes differ in structure from existing APS middle and high school honors courses in math, which are accelerated and/or “intensified.”
Many parents may not perceive a difference between the terms ‘advanced’ and ‘intensified’, as used by APS. However, there is a difference and it matters for your child’s middle school math education. Let’s look at the difference:
“Accelerated”—the course is taken EARLIER than it would normally–6th grade Pre-algebra, 7th grade Algebra I, and 8th grade Algebra I are all accelerated a year or two.
For example: In APS, the base case is Algebra I in 9th grade. Any student taking Algebra I earlier than 9th grade is considered ‘accelerated’. Right now, APS only offers an accelerated pathway in math, and it offers up to ‘twice-acceleration’ for math–i.e., kids who place into it can take Pre-algebra in 6th grade, when the base case is Pre-algebra in 8th grade.
“Advanced”—applies to the proposed middle school honors courses in English, Social Studies and Science. They will cover the same content as regular classes and are therefore not accelerated. However, they will offer additional opportunities to deepen understanding relative to regular courses.
For example: writing more in-depth research papers.
“Intensified”—APS intensified courses are offered only for math in middle school currently and for a range of subjects in high school. These courses go both deeper and cover additional, accelerated content relative to their regular counterparts.
For example: The intensified math pathway accelerates Trigonometry into Intensified Algebra II, which is earlier than the regular math pathway which covers it in Precalculus. This acceleration opens up more space in Intensified Precalculus to begin covering Calculus concepts earlier, which is needed to prepare students for AP Calculus BC.
Intensified math courses also go deeper. For instance, Intensified Geometry emphasizes proofs more than Regular Geometry.
Why the Accelerated/Intensified Model Suits Math
The distinction between APS “advanced” and “intensified”/accelerated courses reflects the ongoing national debate over whether districts should offer classes that go "deeper" vs. "deeper and faster" (intensified/accelerated) in order to enhance student learning. Recent reform efforts, including the California Math Frameworkauthored by Jo Boaler and the National Council of Teachers of Mathematics’ Catalyzing Change, advocate that classes should move slower and go deeper on a narrower range of topics. As an example, they argue that delaying Algebra I until high school gives students more time to build a strong base in middle school math and enhances equity by delaying the jumping off point for different math pathways.
Boaler and Catalyzing Change both advocate getting rid of ‘accelerated’ and ‘intensified’ math pathways. However, in cases where honors courses are desired, they prefer that honors classes should be ‘advanced’ rather than accelerated; this could allow students to see how math is applied in real-life settings as opposed to moving on to learn additional concepts.
The proposed APS middle school honors courses in English, Social Studies, and Science are consistent with that latter philosophy (they will be 'advanced' not accelerated). These middle school courses are not part of a structured pathway per se and this construct works for them. However, current middle school math courses are part of a set math pathway that builds over time and where accelerated/intensified coursework is needed to reach calculus in high school in an unrushed manner. Thus, contrary to Boaler’s view, we believe it is critical that middle school math retains this accelerated/intensified structure even as its middle school counterparts in science and social science adopt an advanced format. That is why it’s really important to understand the difference between these three terms in terms of curriculum, and to know that they are not interchangeable.
Why Accelerated/Intensified Math Matters
Advocates of acceleration argue that students should be able to take on additional math content when they are ready. They also note that:
Students must take Algebra I in middle school in order to reach calculus by senior year without having to double up or take summer math courses, and
Students need intensified classes in Algebra I, Algebra II, and Precalculus to prepare them for the added material in BC Calculus.
In 2020-21, 60% of APS 8th graders were taking accelerated math (15% took Algebra I in 7th grade and another 45% took Algebra I in 8th grade). With the push to develop STEM skills, and the tremendous career opportunities in STEM fields, it is vital to provide students with an intensified and accelerated pathway to Calculus. Talented low-income students particularly rely on APS for accelerated options as they do not have the same access to outside programs as their wealthier peers. We applaud APS for being committed to offering both ‘advanced’ non-math and ‘intensified’/‘accelerated’ math honors courses at the middle school level and encourage APS to continue maintaining and increasing its high academic standards.
Given that Boaler's work is popular in the educational world, there has been increased pressure on school districts to decelerate math. But is there an evidence basis for it? Next installment: understanding the math debates in Boaler’s San Francisco and the impact on states and school districts across the US.
