California Department of Education
Taking Center Stage – Act II

Mathematics instruction

California’s mathematics content standards are divided by grade levels: kindergarten through grade seven and grades eight through twelve. The elementary standards are grouped into five categories called strands:

  • Number Sense
  • Algebra and Functions
  • Measurement and Geometry
  • Statistics, Data Analysis, and Probability
  • Mathematical Reasoning

As students move to higher grade levels, the problems require increasingly advanced knowledge and understanding of mathematics, greater use of inductive and deductive reasoning, and proof. The standards for grades eight through twelve are organized by discipline: Algebra I; geometry; Algebra II; trigonometry; precalculus, mathematical analysis; and probability and statistics.

The Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) (PDF; 4MB; 411pp.) refers to the mathematics standards students need to master in prealgebra classes. Chapter 2 of the framework states, “To allow local educational agencies and teachers flexibility, the standards for grades eight through twelve do not mandate that a particular discipline be initiated and completed in a single grade. The content of these disciplines must be covered, and students enrolled in these disciplines are expected to achieve the standards regardless of the sequence of the disciplines” (page 18).

Although not all eighth-grade students participate, results from the 2005 National Assessment of Education Progress (NAEP) (PDF; Outside Source), which is also known as The Nation’s Report Card, testing in the eighth grade show significant concerns about mathematics achievement in California. For example:

  • Of the 52 states and other jurisdictions that participated in the 2005 eighth-grade assessment, students' average scale scores in California were higher than those in five jurisdictions, not significantly different from those in four jurisdictions, and lower than those in 42 jurisdictions.
  • The percentage of students in California who performed at or above the NAEP proficient level was 22 percent in 2005. This percentage was not significantly different from that in 2003 (22 percent) and was greater than that in 1990 (12 percent).1

In contrast, results from the 2005 California Standards Tests (CST) (Outside Source) show that 26 percent of the eighth-grade students score at the proficient level or above in mathematics .

Whether educators look at NAEP or CST results, there is concern about mathematics proficiency. When discussing how to improve student achievement in mathematics, teams of teachers from Schools to Watch™-Taking Center Stage schools indicated that although their goal is to provide heterogeneous groupings for students in all electives and English language arts (ELA), they often resort to separate groupings for mathematics. For example, to provide geometry for advanced students, teachers find it necessary to separate those students from classmates still needing prealgebra since the content is so different.

However, a 2006 study on heterogeneous grouping of students in accelerated mathematics courses showed that mixed ability grouping could positively affect the academic performance of all students. The heterogeneous grouping did not appear to negatively affect the achievement of high-achieving students.2

In the Spotlight

Alvarado Intermediate School (Outside Source), a Schools to Watch™-Taking Center Stage 2004 model, Rowland Unified School District. Teachers use PowerPoint to teach mathematics. The program allows teachers to add new pieces of the equation after they walk around to see how well students are grasping the first part. It also allows the mathematics team members to develop parts of the lesson and share with each other, thus lessening the overall lesson development time required for each.

Bernice Ayer Middle School (Outside Source), a Schools to Watch™-Taking Center Stage 2005 model, Capistrano Unified School District. Resource teachers join the mathematics teachers as a team to help teach the concepts to students who need more help.

Rancho Cucamonga Middle School (Outside Source), a 2006 On the Right Track school, Cucamonga Elementary School District. Mathematics teachers found that they had more success in helping students pass the algebra test if they took chapters one through four in their state-adopted textbook after the testing window in the year prior to taking algebra officially. By giving early lessons in the spring, students were ready to start in chapter five in September, thus completing all the standards before testing.

Researchers who studied factors that led to Boston and San Diego having the highest gains in mathematics on the NAEP (Outside Source), found that educators in those districts relied on similar strategies. First, they built students’ conceptual mathematical skills. Second, the administrators in those districts invested in professional development to help elementary and middle school teachers learn how to use conceptual mathematics strategies.3

Conceptual mathematics helps young adolescent brains to attach significance to facts so they become stored in long-term memory. Rather than presenting mathematics as a series of equations and figures, teachers who use conceptual mathematics strategies also help students understand the meaning of the operations. Teachers build meaning from information by using:

  1. Feelings: Information must engage the emotional aspect of the brain—students must have feelings about what they learn in order to perceive it as meaningful. The brain releases a series of specific chemicals throughout the body during an emotional experience to signal that something important and meaningful is happening. Learners may perceive these signals either consciously or unconsciously.
  2. Relevance: Information must relate to something the learner already knows. The more relevant information is, the greater meaning it will have. For example, a mathematics lesson that draws parallels between daily life and the study problem helps students to see mathematics as being meaningful.
  3. Context: The brain always seeks to create meaning by fitting new information into a recognizable context or pattern that may be social, spiritual, intellectual, natural, et cetera.

In September 2006, the National Council of Teachers of Mathematics issued a report called Curriculum Focal Points (PDF; Outside Source). In consensus with many university professors, the report urges mathematics teachers in kindergarten through eighth grade to focus on a few basic skills. The report did not take a stand on instructional methods, but it did attempt to outline a curriculum narrowed to the most important skills in each grade.

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Footnotes
1The Nation’s Report Card State Mathematics 2005—California Grade 8 Public Schools Snapshot Report (PDF; Outside Source). Washington, D.C.: National Assessment of Educational Progress (NAEP), 2006.
2C. C. Burris, J. P. Heubert, and H. M. Levin. “Accelerating Mathematics Achievement Using Heterogeneous Grouping,” American Educational Research Journal, Vol. 43, No. 1, (2006), 105–136.
3Sean Cavanagh, “Big Cities Credit Conceptual Math for Higher Scores,” Education Week, January 11, 2006.


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