Taking Center Stage – Act II (TCSII)

A Portal for Middle Grades Educators

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 mathematics contenct standards for grades eight through twelve are organized by discipline:

• Algebra I
• Geometry
• Algebra II
• Trigonometry
• Precalculus
• Mathematical Analysis
• Probability and Statistics.

The Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) refers to the mathematics standards students need to master in prealgebra classes. Chapter 2, The California Mathematics Content Standards, 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).1

In Chapter 5, Mathematics Teaching for Understanding: Reasoning, Reading, and Formative Assessment (PDF; 154KB; 16pp), authors Paula Miller and Dagmar Koesling describe the role that literacy plays in three central elements of the math instruction. Readers see how a teacher helps students solve complex word problems and read difficult mathematical text, as well as how to assess students’ understanding.

The chapter emphasizes that literacy helps students with weak math skills develop the problem-solving and reasoning skills that make advanced mathematics courses accessible. The chapter also illustrates how to marry the mathematical reasoning process with a reading process to help students understand the context and concepts of math problems. The authors illustrate how teaching this way benefits students in terms of their engagement, understanding, achievement, and post-secondary options.*

*Reprinted by permission of the Publisher. From Suzanne Plaut, Editor, "The Right to Literacy in Secondary Schools: Creating a Culture of Thinking", New York: Teachers College Press ©2009 by Teachers College Columbia University. All rights reserved.

Although not all eighth-grade students participate, results from The Nation's Report Card: Mathematics 2009—National Assessment of Educational Progress (NAEP) at Grades 4 and 8 (PDF; Outside Source) continue to show significant concerns about mathematics achievement in California based on testing in the eigth grade. For example:

• The percentage of students in California who performed at or above the NAEP proficient level was 23 percent in 2009. This percentage was not significantly different from that in 2007 (24 percent) but was greater than that in 1990 (12 percent).2

Results from the 2010 STAR Tests Results show that 25 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 California 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, 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.3

English Learners in Secondary Mathematics: Rigor and Excellence, (Outside Source), is an archived SchoolsMovingUp Webinar which took place on November 5, 2008. Leslie Hamburger, Senior Program Associate in the Teacher Professional Development Program (Outside Source) at WestEd, demonstrates carefully structured secondary mathematics scaffolding tasks that challenge students while providing them with the necessary support to achieve the lesson’s specific learning objectives. These tasks enhance the linguistic and content knowledge needed to succeed in secondary mathematics.

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.4

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 for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (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.

Related Links

• California Mathematics Council (Outside Source)
• Mathematics Engineering Science Achievement (MESA) (Outside Source)
• Mathematics Teaching for Understanding: Reasoning, Reading, and Formative Assessment (PDF; 154KB; 16pp)
• Middle School Resources (Outside Source), National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics (Outside Source)

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Footnotes
1Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve (PDF; 3.19MB; 411pp.). Sacramento: California Department of Education, 2005, 365.
2The Nation’s Report Card: Mathematics 2009 Snapshot State Report—California, Grade 8, Public (PDF; Outside Source). Washington, D.C.: Institute of Education Sciences (IES), National Center for Education Statistics, National Assessment of Educational Progress (NAEP).
3C. 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.
4Sean Cavanagh, “Big Cities Credit Conceptual Math for Higher Scores,” (Outside Source) Education Week, January 11, 2006.

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