Each Common Core Math Standard is taught only one time and is never repeated. Similar topics will reappear, but in greater depth and complexity. The Common Core Math Standards call on students to practice applying mathematical ways of thinking to real-world issues and challenges. In particular, problem-solving, collaboration, communication, and critical-thinking skills are interwoven into the standards. In addition, the Common Core Math Standards also contain Standards for Mathematical Practice. These 8 math practice standards describe varieties of expertise that should be developed in students. “These practices rest on important processes and proficiencies with longstanding importance in mathematics education.” (corestandards.org) Math Practice Standards can be viewed here.
Because each Common Core Math Standard is taught only one time, students can no longer skip content to accelerate or they will miss key foundational concepts. Based on guidance from the California Math Framework, our secondary math pathways provide for acceleration through compaction of courses rather than skipping. Acceleration pathways begin in 7th grade with a compaction of CC2 and CC3. The 8th grade compaction includes CC3 and Algebra 1.
A second opportunity to accelerate begins in high school with a compaction of geometry and algebra 2/trig in 9th or 10th grade and a compaction of algebra 2/trig with pre-calculus in 10th or 11th grade.
For students who wish to get to AP Calculus or Calculus by their senior year and who were not on the accelerated pathway, students may take a second math class as an elective. For example, a 10th grade student enrolled in geometry could take Algebra 2/Trig as an elective. The Math Curriculum Council is currently looking at creating additional access points into the accelerated pathway.
Many parents have asked for clarification about what content the 8th grade math class includes. The 8th grade Common Core 3 math class includes content from 6 of the 8 chapters from the 8th grade Algebra textbook used two years ago. The CC3 course includes a large portion of foundational algebra topics such as functions and linear equations as well as some geometry. As a result, the Math Curriculum Council recommends that CC3 be renamed Foundational Algebra and Geometry to reflect the content of the course.
Algebra 1 (9th grade math) will tentatively be renamed High School Algebra pending board approval. This course is significantly more rigorous than previous algebra courses and contains standards previously taught in Algebra 2.
Common Core Math Standards in a non-accelerated pathway are in alignment with the PSAT and SAT tests. It may be helpful to note that David Coleman, a lead writer of the Common Core Standards, is now the president of College Board. The new SAT and PSAT tests were created by College Board under Coleman's leadership. The new SAT test will be based more heavily on algebra concepts. Fremont's math pathways along with the Common Core Math Standards are designed to give students a deep, rich conceptual understanding of algebra. This will benefit them when they take these tests.
The Springboard junior high and high school Algebra 1 textbook series were also written by College Board, are aligned to the SAT tests and sequenced for the PSAT and SAT test taking timeframe.
Those concerned about STEM careers, should note that only Pre-calculus is a prerequisite for any sciences classes. AP Physics C (calculus based physics) can be taken concurrently with either Calculus or AP Calculus. And as noted above, students who are not on the accelerated path can take an additional math elective class in order to take AP Calculus and AP Physics C during their senior year.
In order to offer geometry in the 8th grade, students would either have to skip math content or beginning in 6th grade, have four years of math compacted into two years. The California Math Framework specifically recommends AGAINST this type of compaction because it would require skimming of content. Students would not be able to develop deep understanding nor would the students have an opportunity to become skilled in the math practice standards. In addition, and as noted above, the Common Core Math Standards are taught only one time. Skipping, therefore, is no longer a viable option. The California Math Framework and the math leadership in Fremont Unified School District recommend against either compacting or skipping content to provide a geometry course in 8th grade.
The Fremont Unified Math Pathways are grounded in brain research and are supported unanimously by the math teachers of our district who, based on their many years of first-hand experience, know what works in math education. In Fremont, our 6th grade classroom teachers are generally not math content experts. It is unrealistic to ask them to teach two levels of math which is where the first compaction would be required.
Nearby districts that offer an accelerated pathway often do so in a different manner, but the end courses are the same. In Fremont, students who are on the accelerated pathway can take AP Calculus either as juniors or seniors in high school. This outcome is the same for all surrounding districts. Some districts begin their acceleration earlier and also compact four years of math into two school years. This specifically goes against the recommendations of the California Board of Education, the writers of the California Math Framework, and university representatives. But even with this questionable hyper-acceleration, those students will still end at the same point- AP Calculus as juniors or seniors.
Fremont's plan for acceleration starts out in 7th grade and allows time for students to develop deep understanding of critically important foundational algebra concepts. Hyper-accelerating in elementary or junior high does not take into account research nor students developmental needs. The second high school acceleration allows for students to grow in maturity and cognitive development. In the past, when Fremont hyper-accelerated students by skipping content, teachers reported many students with significant knowledge gaps and often performing at mediocre levels. For example:
This data presents a compelling reason to avoid skipping content.
Fremont's Math Pathways are preparing a greater number of students for success in higher level mathematics. In the 2014-15 school year, approximately 150 students were enrolled in AP Calculus as juniors. These students participated in the skipping of content in junior high.
Also in 2014-15, Fremont had 376 7th grade students who earned A's at both semesters in the new secondary math pathways accelerated course. These students are currently on track to take AP Calculus as juniors. These students have not skipped any content. The course sequence compaction was recommended by the California Math Framework and agreed upon by Fremont Math Teachers. As a result of this accelerated pathway, nearly three times the number of students will potentially be ready to take AP Calculus as juniors and because they did not skip ANY content, we believe they will be much better prepared.
The American Management Corporation reports that employers want workers who can think critically, solve problems creatively, innovate, collaborate, and communicate. This skill set is exactly what the Common Core Standards and the Standards of Mathematical Practice will develop in our students. But these skills take time and practice. Fremont's Secondary Math Pathways are designed to provide students with this skill set in conjunction with a rich, conceptual math foundation.
FUSD Math Pathways 2016-17 (pptx - updated 2/4/16)
Math Pathways January 2016 (doc - updated 2/4/16)
Fremont Unified Secondary Math Pathways FAQ (pdf)
Jo Boaler - Memorizers are the lowest achievers (pdf)
Raising-Expectations Paper by Jo and David (pdf)
Professor Bill Jacob on Math Acceleration (pdf)