Common Core Pathways: Redefining Algebra

PathwaysI have fielded a great many questions lately regarding the creation of Common Core Pathways (course sequences), especially in regards to the big question: to accelerate or not to accelerate. I appreciate the curiosity, because in this last year I did a great deal of investigating in order to help my school district develop our own pathways. I recently had a request to share our pathways “with commentary.” This makes sense, since there are many misconceptions of the Common Core out there that I had to sort through, and the rationale for these pathways will help others decide if these will work for their system. So I share four things:

1) A primer for the Common Core Pathways, particularly in terms of Algebra content.
2) The needs of my district that led to the development of three pathways.
3) The actual Pathways that my district decided upon, with links to resources that helped us get there.
4) Student placement.

I hope this helps.

A Common Core Pathways Primer

The Common Core spells out clearly what students are expected to know at each grade level K-8. Then for high school it lumps the standards together in High School Domains (Number & Quantity, Algebra, Geometry, Functions, Statistics & Probability and Modeling). This is done in order to allow high schools to structure courses in a Traditional Model (Algebra 1, Geometry, Algebra 2) or an Integrated Model (Math 1, 2, 3). At first glance it looks like CCSS is now delaying Algebra until 9th grade, after years of states pushing it in the 8th grade. This is because CCSS does not define Algebra as a course, but rather a domain across grade levels. Understanding this is key to creating accelerated pathways.

Traditionally, an Algebra course is seen as starting with the arithmetic (integers & fractions) and the simplifying of expressions (which many consider to be Pre-Algebra), followed by solving of equations, then moving onto linear equations and systems by the end of first semester, with polynomials, quadratics and rational expressions rounding out second semester. In other words, we go from balancing a check book to racing cars to launching rockets in a single year. However, the Core spreads these concepts out over several years. Arithmetic, simplifying and basic solving is mastered in 6th grade. Solving multi-step equations and deeply understanding rates and ratios is the focus of 7th grade. The 8th grade standards focus on linear equations and systems. While Geometry topics like surface area, volume and transformations are spread throughout the middle school grade levels, along with probability & statistics, the key here is to see that the entire first semester of a traditional algebra course is covered by the end of 8th grade. This way, the students can be handed an exponential function when they walk in the door on the first day of their freshman Algebra class. So don’t get it wrong; students under the common core are still learning Algebra in middle school; they are just not finishing it. The Common Core does not delay the Algebra course for students; it simply redefines Algebra.

No More Than 3, Sometimes 4

Tim Kanold once shared with me the pathways created at Stevenson HS in Illinois. He claimed that they had two pathways… one pathway led to Calculus, another to Pre-Calculus. It was actually one pathway: Algebra 1, Geometry, Algebra 2, Pre-Calculus, Calculus. What made this sequence look like two pathways was the course that students enrolled in as freshmen (Algebra 1 vs Geometry). Stevenson HS offered a ride on a single train; the only variation was which boxcar a student boarded when arriving at high school. I ask Tim if every student graduated with a minimum of Pre-Calculus. He said that while 58% of the seniors graduated with Calculus, some only took three years of math. When I pressed for the pathway offered for special education students and the like, he conceded that those rare few were allowed to deviate from the given path. He stated, “Create only 1 path, no more than 2, and sometimes 3.”

My district embraced this idea, but we have one more level of need. My high school has an International Baccalaureate (IB) Program. In order for students to be able to reach its “Higher Level,” we need some students to come into high school taking Algebra 2 as freshmen. Furthermore, while California only requires two years of math, my district requires three, and the state still only requires Algebra 1 to graduate, not Algebra 2. Therefore, students on an IEP may take Middle School math classes through our Special Education Department, and anyone passing Algebra 1 may take Accounting to complete the third year.

With all that, my district adopted a “No more than 3, sometimes 4,” policy. These  3+ pathways are shown below.

The Pathways for Temecula Valley Unified

Pathways Math

Our district decided to stick with our traditional model. The scope and sequence of our “Common Core Pathway” is very similar to what the Dana Center of Texas produced. We also took some inspiration from Montgomery Schools in Maryland (scroll to the bottom of their page, and you will see a graphic very similar to ours) and Tulare County in California which beautifully laid out the scope and sequence for both the traditional and integrated models.

The Traditional Pathway allows students to reach Pre-Calculus or other similar 4-year college options. There are two keys to notice here. One, there is no remedial track. All mainstreamed students will be taking Algebra and Geometry. This is freaking out teachers who are anticipating having a significant number of “those kids” in college prep classes. They have told me that the kids won’t be properly prepared. I pushed back claiming that the kids will be ready, but I am not sure we teachers will be ready. (side note: Professional development training is imperative to make this work.). The second key to notice is that there are two types of Algebra 2 courses. Our Pre AP course was designed with the Common Core plus standards (+) included, for those students who intend to go beyond Calculus AB (Calculus BC or IB). For details on other courses shown in the diagram visit the Math Department at Great Oak High School.

The Accelerated Pathway was an easy adjustment. If we note the definition of Algebra explained above, then in 8th grade we teach a traditional Algebra course, substituting the Geometry and Stats topics for the Pre-Algebra topics. 6th and 7th grade remain untouched. Two years of math is condensed into one.

The Compacted Pathway was a bit trickier to create. In the past, students who wanted to take Geometry as 8th graders, simply skipped 6th grade math and got to Algebra 1 by 7th grade. That’s no so easily done now under the Common Core. So we have to compress 4 years of courses (6th, 7th, Algebra & Geometry) into 3 years as shown.

NOTE: Now that we have implemented these three pathways, I would only recommend the first two. Unfortunately, the Compacted Pathway is too much for both students and teachers. Since our high schools still need a means for students to reach Calculus B/C and beyond, it appears best to have that relatively small and uniquely talented population to accelerate in high school, through summer school, online options or Junior College courses.

Choosing a Pathway

The big question that follows after creating these pathways is “Which students are assigned which pathway?”  Or more to the point “Who gets to Accelerate?” We actually would like to see the majority of students follow the Traditional Pathway. For our upper level high school math programs to thrive, we need at least 20% of the middle school students on the Accelerated Pathway, and a little under 10% for the Compacted. Of course, we shouldn’t fit students to the needs of the school. The students are to be recommended by ability based on assessments and teacher recommendations. Our schools need to be watchful, though, because our community has parents who feel their child won’t be able to compete for a top college if they are in the bottom track. While some vigilance will be necessary, we also have an open access policy… students/parents may take any courses they wish. I am curious how these pathways portion out.

Furthermore on placement, another of Stevenson High’s policies that my district is adopting next year is the practice of moving students onto the next course … even if they flunk. I have also heard this same pitch from Bill Lombard. So, if a student flunks Algebra, the student enrolls in Geometry the following year, and makes up the class in summer school, online remediation or concurrently. Same thing is true when going from Geometry to Algebra 2. However, if a student fails Algebra 2, they may repeat, since these students have multiple options at this level (Trig, Stats, PreCalc, etc.). Needless to say, our teachers have a great deal to get done in terms of Intervention and Standards Based Grading to make this work.

I hope this helps those of you that are planning ahead. My district and its teachers still have a great deal of work ahead of us, so please share here what you learn in the construction of your own pathways.

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