California Department of Education
Taking Center Stage – Act II

Algebra

Most students, parents, and teachers at the middle grades level have had at least one discussion about the hot topic—algebra. Education Code Section 51224.5. (a) states, "The adopted course of study for grades 7 to 12, inclusive, shall include algebra as part of the mathematics area of study." Section 51224.5. (b) states that the requirement must be completed by grade twelve and that completion of an algebra course that meets or exceeds the rigor of Algebra I state content standards is a requirement for receiving a high school diploma. This requirement means that many middle grades students need remedial instruction if they are not yet proficient in prealgebra skills and concepts (see page 225 of the Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) (PDF; 4MB; 411pp.) for more information about readiness for algebra).

The organization of the standards raises questions at the middle school level: Should all eighth graders take algebra whether they are ready or not, or should those students who are below grade level in mathematics take prealgebra so that they are truly prepared when they enter high school? The Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) (PDF; 4MB; 411pp.) provides an answer to this important question. “It is imperative for students, whether in grade eight, grade nine, or even a higher grade, to master prealgebraic skills and concepts before they enroll in a course that meets or exceeds the rigor of the content standards for Algebra I adopted by the State Board of Education.”1 The Mathematics  lists 16 standards (13 from grade seven and three from Algebra I) that should be included in an algebra readiness program. This list along with the list of referenced standards from foundational skills and concepts provides a basis on which to build algebra-readiness instruction. Publishers will submit algebra-readiness programs for the 2007 Mathematics Adoption and the state-adopted algebra-readiness programs will be available for use in the classroom by 2008. (For more about the algebra-readiness issue, see the Frequently Asked Questions about eighth-grade algebra on the Middle Grades Web site.)

The California State Board of Education and the State Superintendent of Public Instruction agree that all students should have algebra early in their secondary phase of education. Algebra not only develops problem-solving and critical thinking skills, it also provides skills needed for higher mathematics and science classes that can ultimately lead to postsecondary education and higher-paying careers.

The decision to place students in algebra should be based on what is best for students. Schools that use the CST seventh-grade mathematics test as one of the predictors of success in algebra and place their “Basic” students in algebra will need to provide continuing support in order for students to gain proficiency on seventh-grade standards. Preparation for the California High School Exit Examination (CAHSEE) and algebra is needed. This support can be scheduled as a double block of mathematics for eighth-grade students, sometimes referred to as a “shadow” class. A shadow class reinforces and teaches standards not yet mastered and preteaches concepts in algebra so that students are exposed to new information, vocabulary, and preparation for algebra. Students who are not proficient or advanced in seventh-grade mathematics standards need support classes. These students are most at risk of not doing well in algebra or failing the CAHSEE, which is heavily based on seventh-grade standards. (See page 225 of the Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) (PDF; 4MB; 411pp.) for more information about readiness for algebra.)

In addition to algebra-readiness programs for students who are not yet ready to succeed in an algebra course, the 2007 Mathematics Adoption also calls for mathematics intervention programs for students in grades four through seven. These programs are intended to provide strategic and intensive support for students in grade four through seven. The programs are not intended to be full-year or full-course programs but to move students efficiently to grade-level instruction.2

Every student who takes the full-year algebra course must take the algebra standards test. Those students who take the course before attaining grade-level mastery of mathematics concepts have difficulty passing the CST algebra test. Their (low) scores affect the school’s overall totals, although the numbers may not be significant. To teach all the Algebra I standards, teachers need to cover them at a rate of about one per week up to the testing windows in April/May.

Many researchers argue that algebra is not just for the advanced students. In fact, one study found that algebra seems to produce almost as much achievement gain for low-achieving students as for their high-achieving peers.

The study of algebra, in particular, appears to serve as a gatekeeper to the college-preparatory track. Students who take algebra by the eighth or ninth grade are far more likely to take calculus in high school and pursue higher education than those who do not. Results are especially promising when ‘average’ students take high-level classes. Conversely, placing students in lower-level mathematics classes has never been shown to benefit them. This tends to suggest that accelerated curricula could make a difference for many middle grades students.3

In the Spotlight

Toby Johnson Middle School (Outside Source), Schools to Watch™-Taking Center Stage 2006 model, Elk Grove Unified School District. Teachers give quizzes and common formative assessments that help determine how well students are progressing toward proficiency on grade-level standards. After results from the common formative assessments come back, teachers help students develop a study guide for problems they did not understand. When students take common standards-based assessments, they must score 80 percent or more. If they do not achieve the 80 percent level, they must attend study sessions before, during, or after school. The times are flexible to ensure students have every opportunity to attend. Mathematics teachers also model good study skills that will help students keep up when they reach high school. In team meetings, mathematics teachers establish shared PowerPoint presentations of key concepts that they post on the school’s shared server. Bridge teachers and substitute teachers access these PowerPoint presentations to reteach and reinforce skills.


Technology applications for mathematics. Teachers can use graphing calculators, mathematics tutoring software, graphing sites, online mapping and graphing programs and Web sites, instant feedback student response systems, and timed practice programs for increasing student efficiency with basic mathematics facts. Technology standards are embedded in the mathematics content standards and in the Career-Technical Education Model Curriculum Standards (PDF; 2MB; 441pp.). Chapter 9 of the Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve (PDF; 4MB; 411pp.) contains helpful information about using technology in the mathematics curriculum. In addition, the booklet Math at Home: Helping Your Children Learn and Enjoy Mathematics (PDF; Outside Source), published by the Sonoma County Office of Education, contains suggestions about student uses of technology (page 9).

Additional resources to assist teachers in mathematics instruction are provided below.

California Department of Education Resources

External Resources

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Footnotes
1Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve (PDF; 4MB; 411pp.). Sacramento: California Department of Education, 2005, p. 365.
2Criteria for Evaluating Mathematics Instructional Materials (PDF; 110KB; 12pp.)
3Academic Achievement in the Middle Grades: What Does the Research Tell Us? (PDF; Outside Source) Atlanta, Ga.: Southern Regional Education Board, 2003, p. 4.
4Arlene Hambrick and Asta Svedkauskaite, "Critical Issue: Remembering the Child: On Equity & Inclusion In Math and Science Classrooms” (Outside Source). Naperville, Ill.: North Central Regional Educational Laboratory (NCREL), 2005.

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