The Math Task Force (MTF) was created to help inform decisions, to be made by the PUSD Board of Education later this school year, about the implementation of Common Core Math in this district. The MTF, which is made up of math teachers, parents, students, and administrators, is charged with considering and recommending options for math courses and math pathways in middle and high school. An MTF progress report follows.
Last year, the PUSD Board of Education approved a plan for the multi-year implementation of Common Core (CC) Math, starting with new middle school math courses in 2014/15. PMS is now offering three new courses: CC 6, CC7 and CC8. Students who were enrolled in Intro to Algebra through Calculus AB during the 2013/14 school year are continuing in the 1997 California Math Standards pathways, and are not affected by the implementation of Common Core Math. (Please refer to the District’s Common Core Math FAQ for more background information)
The Board decided that, during the transition to Common Core Math and after implementation is completed, the District will:
- continue to offer pathways to both Calculus AB and BC for qualified students; and
- offer at least one opportunity to “compress” math at both the middle school and high school level (students may compress at either or both points).
Later this school year, the Board will discuss the next phase of Common Core math implementation. The Board will adopt either traditional or integrated higher-level courses and course progressions. Under the traditional approach, students would take discrete, sequential courses in Algebra, Geometry, Algebra II, and Math Analysis. Under the integrated approach, the content of these courses would be mixed over a period of years. The courses implemented this year — CC6, CC7 and CC8 — are integrated courses.
The primary argument to adopt the integrated approach is that it allows for introducing the increasingly complex concepts in Algebra and Geometry over a period of several years, as students are more developmentally ready. A secondary argument is that the integrated approach lends itself to compression more so than traditional courses.
When the Board decides whether to adopt the traditional or integrated approach, the Board also will determine how and when students may speed up (“compress”) or slow down (“expand”) their progression through the new curriculum standards. These courses and pathways will be implemented starting in the 2015/16 school year.
The Board’s decision about courses and pathways will be informed by: input from the MTF; practical experience and insight gained by the math faculty during the first half of this school year; data about how PUSD students are doing in Common Core math during the first half of this year; input from the Silicon Valley Math Initiative; and input from the Alameda County Office of Education.
To date, the MTF met on September 8th, October 6th and 20th, and November 10th. The MTF will continue to meet monthly through February 2015, until it submits recommendations to the Board.
Learning About the Common Core Classroom
At most meetings, the MTF discusses a Common Core math problem, to gain a better understanding of how the teaching methods and lesson content of Common Core math differ from that of conventional math, and how math lessons can be differentiated for a range of learners. The purpose is to illustrate the classroom experience to the extent possible for the MTF members who are not math educators, and give context to MTF discussions about the organization of courses.
The MTF also hears a report of the ongoing professional development training for math teachers concerning the new Common Core Content Standards and Math Practice Standards, and an update on curriculum development. The math teachers are “piloting” new curriculum from a variety of sources, and continually assessing what works and what needs refinement. Teachers are piloting both traditional and integrated curriculum.
The math teachers also share observations about how students are responding to the new content and practice standards. In summary, some students need support for basic math, and others can go deeper and move faster through the lessons. “Problems of the Month” have levels A-E and each student can progress to his or her level of mastery. For this reason, these problems lend themselves to differentiation for a broad range of learners.
Investigating the Pros and Cons of Traditional and Integrated Math Courses
The MTF is divided into two subcommittees, one to consider the integrated math approach and the other to consider the traditional approach.
There are few research studies investigating the relative effectiveness of these approaches. The District is compiling articles and other resources on this topic. This District is identifying schools that offer Integrated Math and arranging site visits to learn about their experience.
David Foster, Executive Director of the Silicon Valley Math Initiative (SVMI), met with the MTF on November 10 to talk about how other districts are approaching this decision. SVMI is a consortium of school districts working together to implement Common Core math. SVMI was started in the 1990s to do research and development in math education, and has studied education practices in Japan, the Netherlands, and other high-performing countries. The Common Core math content and practice standards are intended to bring US math curriculum in line with these high-performing countries. SVMI supports districts in implementing Common Core math by providing professional development, curriculum, and other services.
Foster provided a brief history of the now-rescinded California mandate that all 8th graders take Algebra. Test data from that era indicates that many students did not do well in 8th grade Algebra and had to repeat the course. Foster advised, “Mathematics education should not be a race.” Racing contributes to the problem of superficial knowledge, poor retention, and math education that is “a mile wide and an inch deep.”
Foster cautioned that one cannot measure a district’s success by the performance of the most successful students. A 2013 case study of an unnamed Bay Area k-12 district with demographics similar to PUSD showed that many high-performing students did not retain math concepts, suggesting the students did not truly master the concepts. This study lends support to the Common Core approach of slowing down, to ensure deep conceptual understanding before advancing to higher level math.
Foster confirmed that there are no standard criteria used by districts to choose between the traditional and integrated approach. He also confirmed that, whether PUSD chooses a traditional or integrated approach, there is little ready-made, published curriculum for Common Core math, and the published curriculum is untested. Districts will have to pilot curriculum and develop curriculum by selecting from multiple sources.
While few studies compare the relative effectiveness of the integrated and traditional approach to high school math, Foster noted an international study by the University of Missouri,Curriculum and Implementation Effects Mathematics Learning From Curricula Representing Subject-Specific and Integrated Content Organizations on High School Students. This study finds that “students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum” based on several measures. Foster hesitated to rely too heavily on this research, because there are significant variables and cultural differences. Nonetheless, he noted that the five countries that are highest-performing in math (Singapore, Korea, Hong Kong, Chinese Taipei, and Japan) employ the integrated approach.
Investigating Math Pathways
Foster showed several sample pathways that allowed for compression of the math curriculum standards without doubling up math classes or relying on summer school. When considering math pathways and when/where to compress, Foster advised the district to consider what makes sense for student learning. He cautioned against sacrificing either practice and content standards. Under Common Core, none of the content standards are repeated — there is no longer spiraling or review. Also, by rushing though the content standards, the practice standards may be compromised.
Foster recommended that districts “go slow to go fast later,” and establish a strong foundation in middle school to support the study of more advanced math. Foster cautioned against prematurely trying to identify students for compression pathways. By delaying compression, “districts will achieve the best outcomes across the whole distribution of students.” Foster noted that in Japan, the opportunity to compress is in high school.
If PUSD is committed to offering a pathway to AP Calculus, Foster recommends the integrated approach because it lends itself to compression of CC8 and Algebra (allowing for a jump from CC8 to Math 2). Foster does not see a coherent way to achieve compression with the traditional approach. However compression is achieved, it is a fair question whether these students will know less math. Also, however compression is achieved, compression may be appropriate for only a small segment of students.
Foster concluded by noting that, historically, many believed acceleration was needed to be successful in math and the STEM fields. He observed that the system of acceleration may have in fact discouraged many students from STEM — either because they were later bloomers who did not accelerate and then perceived they were not eligible for STEM, or they did accelerate but then lacked the deep conceptual understanding needed for higher-level math. Our goal is to have all students truly understand math and be capable of applying math concepts, so they have the STEM fields available to them. Going slow and going deep can enable students to go farther.
The MTF has received input from SVMI staff, as well as PUSD teachers and will use these resources, as well as evidence from professional publications and site visits to form its recommendation to the Board of Education.
AB and BC Calculus
Currently, PUSD offers both AB and BC Calculus, and many students take them sequentially. AB Calculus is essentially the equivalent of the first semester college Calculus. BC Calculus is essentially the same as the first and second semesters of college Calculus. For many years, PUSD offered AB only. Six years ago, PUSD started offering BC as a follow up to AB, spreading the equivalent of two semesters of college Calculus over two years in high school. This year, there are 39 students in PUSD who completed AB Calculus and are now taking BC Calculus.
With the implementation of the new Common Core math, and the addition of the new CC 8 course, few schools are continuing to offer the opportunity to take both AB and BC Calculus. Instead, it is more common for schools to offer students the opportunity to take one or the other. Based on research by the District and the Alameda County Office of Education, Acalanes is the only school district in the area that still offers students the opportunity to take both AB and BC Calculus. This is made possible through the compression of Math Analysis and Algebra II (two-years-into-one) in 10th grade. Also, this may be a transitional pathway only, until Acalanes fully implements the new Common Core standards.
Currently, the District’s Math Analysis class prepares students for AB Calculus. District math teachers reported to MTF that the Math Analysis course could be modified to prepare students to go directly to BC Calculus if they choose BC over AB.
The MTF is now developing criteria for evaluating the traditional and integrated approach and making a recommendation to the Board. For example, the MTF will consider whether one approach or the other better supports: cognitive development of students; mastery of both the content and practice standards; opportunities for differentiation; and practical considerations about how to achieve coherent compression and expansion of curriculum standards.
The MTF have also discussed possible pathways for compression, and identified preliminary considerations including the following:
- There may need to be transitional pathways in addition to “final” pathways.
- The pathways should provide flexibility to compress and expand at various points, including the opportunity to take summer classes.
- Questions must be addressed about how to assess a student’s readiness for compression.
|Date & Time||Parent Engagement Events|
|Dec. 1st – 7pm||PUSD Parent Education Night – CC Math Update|
|Dec. 3rd – 9am||PHS Parent’s Club Board Meeting – CC Math Update|
|Dec. 3rd – 6:30pm||MHS Parent’s Club Meeting – CC Math Update|
|Dec. 9th – 3:30pm||PMS Site Council Meeting – CC Math Update|
|Dec. 12th – 9am||PMS Parent’s Club Board Meeting – CC Math Update|
|Dec. 18th – 3:30pm||PHS Site Council Meeting – CC Math Update|
|Jan. 7th – 7pm||PUSD Parent Education Night – CC Math Update|
|Jan. 14th – 7pm||PUSD School Board Meeting – CC Math Update|
|Jan. 22nd – 7pm||PUSD Parent Education Night – CC Math Update|
|Jan. 27th – 7:30pm||Education Speaker Series – Dan Meyer discusses Common Core Math and the importance and method of teaching students to formulate and solve problems rather than memorize and apply formulas.|
|Feb. 11th – 7pm||PUSD School Board Meeting – Math Task Force Presentation on Math Pathway Recommendations|
|Mar. 11th – 7pm||PUSD School Board Meeting – Math Task Force Presentation on Math Pathway Recommendations (2nd Reading)|