March 28, 2018
On August 2nd 2010, the California State Board of Education (BOE) officially adopted the Common Core State Standards (CCSS) for all California public school children in grades K-12. California’s Department of Education (CDE) soon began to develop an implementation plan for CCSS, which was presented to the California state legislature, Governor Edmund G. Brown Jr., and to the people of the State of California on the BOE’s official website on March 19, 2012.
The CDE developed and released the California Common Core State Standards: Mathematics (CCSS-M) document in August 2013, with corrections published in February 2014. Even before 2014, the La Canada Unified School District (LCUSD), as a Local Educational Agency (LEA), had begun implementing a transition plan to faithfully adopt the new Common Core standards in LCUSD schools.
The CDE’s 2013 Mathematics Framework was developed for LEA’s to support and implement the CCSS-M standards. The Mathematics Framework was adopted on November 6, 2013. The Framework describes in greater detail the difference between the two “higher mathematics” (i.e. high school) pathways:
Higher Mathematics Chapters
The higher mathematics chapters are organized into courses according to two pathways:
- Traditional Pathway — consists of the higher mathematics standards organized along more traditional lines into Algebra I, Geometry, and Algebra II courses. In this sequence, almost the entire Geometry conceptual category is separated into a single course and treated as a separate subject. Although these courses have the same names as their traditional counterparts, it is important to note that the nature of the CA CCSSM yields very different courses. In the past, the label ‘Geometry’ referred to a specific course, but now it may also refer to the conceptual category. Care will be taken throughout the higher mathematics chapters to make the distinction clear.
- Integrated Pathway — consists of the courses Mathematics I, II, and III. The integrated pathway presents higher mathematics as a connected subject, in that each course contains standards from all six of the conceptual categories. For example, in Mathematics I, students will focus on linear functions. Students contrast linear functions with exponential functions, solve linear equations, and model with functions. They also investigate the geometric properties of graphs of linear functions (lines) and model statistical data with lines of best fit. This is the way in which most other high-performing countries present higher mathematics, and it maintains the theme developed in kindergarten through grade eight of mathematics being a connected, multifaceted subject.
[Source: Overview of the Standards Chapters from 2013 California State Mathematics Framework. ]
Appendix F of the 2013 Mathematics Framework maps the CCSS-M higher mathematics content standards to the courses in the two different pathways:
Click on the table above for the entire standards comparison.
As you can see, there are substantial differences, with the Integrated Pathway incorporating fewer CCSS-M Algebra standards in the Mathematics I course, but more Geometry standards. Similarly, the Geometry course in the Traditional Pathway covers almost all CCSS-M Geometry standards for Higher Math, while the Integrated Pathway splits the teaching of CCSS-M Geometry standards over the Mathematics II and Mathematics III courses.
Given the CCSS-M standards allowed LEAs to choose one of two different pathways, it was not unexpected, then, that different districts chose different pathways. A survey conducted by the educational journal EdSource of the top 30 public school districts in California by high school student enrollment showed that half had chosen the Traditional Pathway, and half had chosen the Integrated Pathway by 2015 [Source: “California districts moving to new ‘integrated’ high school math pathway”, EdSource, Oct. 27, 2015.]
Meanwhile LCUSD officials adopted the Traditional Pathway for its new CCSS-M aligned HS courses, but bizarrely gave them Integrated Pathway course names. Further, the district decided to phase out old, traditional pathway courses starting in the 2015-16 school year. Thus for a period of three years, LCUSD taught two sets of classes, phasing in new CCSS-M aligned courses (LC Math 1, LC Math 2, and LC Math 3) one course per year, and phasing out old traditional pathway classes (Algebra 1, Geometry, Algebra 2, Advanced Math Topics and Pre-Calculus). 2017-18 is the final year that Advanced Math Topics, Pre-Calculus, and Honors Pre-Calculus will be offered in LCUSD.
Of the 15 districts identified in the EdSource article as adopting the Traditional Pathway, NONE chose to name their courses with Integrated Pathway names. For example, the following high-performing districts with whom LCUSD is frequently compared named their high school courses as follows:
| District | Pathway | Grade 9 | Grade 10 | Grade 11 | Grade 12 |
|---|---|---|---|---|---|
| Palos Verdes Peninsula USD | Traditional | Algebra 1 (Honors) | Geometry (Honors) | Algebra 2 (Honors) | Precalculus |
| Palo Alto USD | Traditional | Algebra 1/1A/1.1 | Geometry A, Honors | Algebra 2 (& Trig A or Trig H) | Pre-Calculus or Intro to Analysis & Calculus |
| Fremont Union HS District | Traditional | Algebra | Geometry (Enriched) | Algebra 2/Trig | Pre-Calculus |
| Capistrano Valley USD | Traditional | Algebra 1(Honors) | Geometry (Honors) | Algebra 2/Trig (Honors) | Precalculus (Honors) |
| La Canada USD | Traditional | LC Math 1 (Honors) | LC Math 2 (Honors) | LC Math 3 (Honors) | LC Math 4 (Honors) |
So why did LCUSD choose to give Integrated Pathway names to Traditional Pathway courses? When asked, an LCUSD administrator explained “we were looking for something different to distinguish them from the pre-Common Core names.” The logic behind the course name change is befuddling on several levels. The first problem is that words and names are carefully chosen because they convey specific meaning. Misusing words leads to misunderstanding. This has already occurred in LCUSD. Save a single HS math teacher, every other teacher and parent interviewed for this story wrongly believed that LCUSD had chosen the Integrated Pathway for its LCHS math courses. Even today teachers and parents who have children in the LC Math 1, LC Math 2, and LC Math 3 courses believe their children are taking Integrated math courses.
The confusion becomes even more problematic when one realizes that college admissions officers, scholarship committees, and counsellors are making decisions based on the same misunderstandings of the course names.
To compound the problem further, based on the misnaming of courses, students and parents are making incorrectly informed decisions about tutoring, supplementing, acceleration, and intervention outside of school. Given LCHS is using the Traditional Pathway, students and families should have no problem taking summer or online courses in Algebra 1, Geometry, and Algebra 2, or purchasing supplemental books or seeking out online resources in these traditional math topics. Yet several parents interviewed for this story avoid traditional mathematics courses because they wrongly believe they won’t be as applicable to our “integrated” math courses. Students transferring in or out of LCHS will make erroneous decisions as well.
And how do LCUSD families benefit from this very strange, peculiar, and singly unique decision to give Integrated course names to Traditional courses? The question remains unanswered.