One of the many decisions parents and families grapple with as their children reach 5th and 6th grade at MUS is where to send their children next? In our community, that includes a variety of public and private school options. For years, we have been able to create a system that allowed students to seamlessly flow into either the public or private school setting. In 2013, the shift to the Common Core State Standards made that more challenging, specifically in the area of mathematics.
The Common Core State Standards are essentially a checklist of skills and behaviors that students need to be able to do or demonstrate at each grade level. The change from the previous California State Standards to the Common Core State Standards was a revision of that checklist that guides teachers and curriculum makers. In K-7th grades, those changes were mostly minor revisions. Maybe a skill or two moved down a grade level, but the list of skills stayed the same. A major shift was the added expectation that mathematics was to make sense. Memorizing the steps to solve a problem is no longer sufficient. With the addition of the Standards of Mathematical Practice, students are expected to understand why the math works and when to apply it.
An additional shift that has had a significant impact on 7th-11th grade is the choice to teach math in the traditional pathway where each domain (algebra I, geometry, algebra II, and precalculus) or in an integrated pathway where algebra, geometry, and statistics are taught in each grade level 6th-11th grade. Essentially the standards from the traditional pathway are shuffled together to teach a fraction of each of the individual domains each year, in an integrated way. Rarely does an individual domain show up in the real world in isolation. By teaching in an integrated way, teachers have the opportunity to provide more sense making opportunities for their students and more opportunities to apply mathematics to the outside world.
The decision to continue with the traditional pathway or shift to the integrated pathway was left up to each individual district in California. The majority of the districts in California, under the recommendation of the California Math Framework and many leading math educators, shifted to the integrated pathway. This is also the methodology chosen in most other parts of the world. In fact, the American “traditional” system is not used in many other places as it makes these connected “maths” seem like separate subjects rather than parts of a whole. At this point, the majority of the private schools have maintained the traditional pathway, which has made it much more difficult for schools to align with both the public and private schools at the same time.
As mentioned above, the changes in K-7 were relatively minor. So, why would this affect the transition to 7th grade in private or public school? For most of our students, it does not. Most students seamlessly transition to either the integrated pathway in the public schools or the traditional pathway in the private school. Our students excel in both.
The shift does have an impact on our extremely advanced students compared to their peers who graduated MUS before the introduction of Common Core. This small group represents students that score near perfect on state testing and are our Math Superbowl finalists. Before Common Core, these students would entirely skip 5th-grade content standards. In 5th grade, they were grouped together all year and taught the 6th-grade curriculum. In 6th grade at MUS, they were taught the 7th-grade curriculum. These students left MUS and fed into 8th-grade Algebra I as 7th graders in public or private school. Around 2015, with the adoption of the Common Core State Standards, the local public school that our students feed into, developed the integrated pathway, where all income 7th graders enter into 7th-grade math. In that pathway, students choose to enter into 7th-grade math, 7th-grade honors, or 7th-grade compaction were 3 years of content standards are taught in 2 years, instead of 3.
Besides the change in our local feeder district, as stated earlier, the Common Core State Standards added a layer of complexity with the Standards of Mathematical Practice. Students are now expected to understand the math at a deeper level as opposed to just memorizing steps and shortcuts to compute. We have decades of international research to prove that the traditional approach to teaching left Americans behind most of the world in the area of mathematics. Just think, if you were given an Algebra II final exam today, what score do you think you would get? That score is not a reflection of your abilities but rather a byproduct of how we learned math. Providing opportunities for critical thinking and real-world application has required us to slow down. Entirely skipping 5th-grade math is no longer an option as we would undermine the critical foundation that our students need to succeed in advanced mathematics. That is the major issue still challenging the 7th-grade math compaction teachers in the middle schools.
Also around 2015, many new research studies were presented about the negative consequences of leveling students by ability. In those tracking systems, all subgroups underperformed compared to similar subgroups taught in mixed ability classes. With study after study showing similar results, and with the endorsement of the California Mathematics Project, National Council of Teachers of Mathematics, and leading researchers at Berkley, UCLA, Stanford, and Harvard, it forced us to evaluate our longstanding practices of how we grouped kids in mathematics at MUS.
Influenced heavily by the new pathways from our local public schools, new expectations set by the Common Core State Standards, and by new research on grouping students in mathematics, we changed our program at MUS. Starting in 4th grade, we stopped leveling our students entirely in mathematics. Instead, we created opportunities for differentiation within the classroom around depth instead of acceleration. After two years of positive state testing data, we slowly graduated out the leveled math classes and acceleration from our math program. We now teach math in all grade levels (K-6) in mixed ability classes. This shift has increased the workload for teachers as they now have to plan each lesson in new ways, thinking about different ability levels.
Looking at local data, state data, and data from our local math competition, MUS has either maintained or increased our performance in all measures compared to our leveled math classes of the past. All areas except one. The one measure that has decreased is the number of students that are entering 8th-grade Algebra I at local private schools as 7th graders. By not teaching 7th-grade math to our advanced 6th graders, less of our most advanced students that enter into private school are able to skip 7th-grade math and succeed in 8th-grade Algebra I as 7th graders.
On the surface, that looks like we are disadvantaging some of our top mathematical thinkers. Digging deeper, we have learned that some of the local private schools have also shifted their approach to allowing 7th graders to enter into 8th-grade math. They shared stories and data around students that accelerated too quickly and sacrificed the depth of understanding for getting ahead in coursework. Their findings are that students who complete Calculus AB as a junior compared to those that complete Calculus AB as a senior are not as likely to get admitted into the top universities. They also are not creating or encouraging pathways within their own schools for students to enter 8th-grade math as 7th graders.
Their findings are consistent with data present by our local district five years ago and with feedback from mathematics professors from many UC schools. In 2013, the UC and Cal State schools issued a joint statement called the Statement on Competencies in Mathematics Expected of Entering College Students. They have found that the majority of students entering mathematics related studies were strong at computation and completing formulas but lacked the depth and understanding required to excel in mathematics at the university level. Many of those students skipped math their senior year because they competed Calculus AB as a junior. They have since changed their admission expectations to encourage depth, understanding, and high performance over acceleration.
I often get asked from parents, what math class should my child take once they leave MUS. My only advice that I give is to backwards map so that their child has the opportunity to take Calculus AB as a senior. This advice keeps all doors open for students to be able to earn a spot in math-related majors at our top universities. The short term bonus is that students have time to see the beauty of mathematics and the real world application of mathematics. They get to love and appreciate mathematics because of that, not just because they are good at it. Long term, more of those students will want to major in math-related areas, will excel in their university courses, and go on to apply their skills to impact the world after graduation. Sometimes when you rush to get to the end as quickly as you can, you miss out on why you were on the journey in the first place.