Algebra

Most students, parents, and teachers at the middle grades level have had at least one discussion about the hot topic—algebra. California Education Code (EC) 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." EC Section 51224 goes on to state 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 (refer to page 225 of the Mathematics Framework for California Public Schools Kindergarten through Grade Twelve (2005) (PDF; 3.19MB; 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) 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 Framework 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. Algebra Offered in the Middle Grades answers frequently asked questions about the algebra-readiness issue for eighth-grade algebra.

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 California Standards Tests 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. (Refer to page 225 of the Mathematics Framework for California Public Schools Kindergarten through Grade Twelve [2005] 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 grades 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.

In the Spotlight

Main Street Middle School, Soledad Unified School District
Student scores in Algebra 1 have improved steadily since 2005, when no Main Street students scored Advanced in Algebra 1 and only four percent scored Proficient. By contrast, in 2008 four percent of students scored Advanced on Algebra 1, and thirty-one percent scored Proficient. This progress in student math achievement has been the result of a concentrated schoolwide effort in a number of areas at the site.

Curriculum is segmented into six-week chunks.
Teachers use common assessments developed at the site.
Results from data analysis are consistently used to inform instruction.
Teachers hold mini-conferences during class with each student four times a year to discuss class work and test scores.
Students graph their success and write their academic goal for the next conference.
Teachers allow students who do not score well to participate in study sessions and then re-take the test to improve their performance.

Math teachers are located in the same area of the school and work in teams to incorporate strategies gleaned from lesson study. Math classes include a focus on academic literacy to provide necessary vocabulary to enhance understanding. Students are taught how to ask questions, including how to rephrase a question and how to ask for clarification. The process is working. Main Street Middle School is increasing the number of Algebra I sections and scores continue to rise.

Main Street DataQuest School Profile
Soledad Unified School District (Outside Source)

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, Elk Grove Unified School District, is a 2006 Schools to Watch™-Taking Center Stage Model School
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.

Toby Johnson DataQuest School Profile
Toby Johnson Middle School (Outside Source)
Schools to Watch™-Taking Center Stage—Model School-Visitor's Guide: Toby Johnson Middle School (Outside Source)
Schools to Watch™-Taking Center Stage

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 California Career Technical Education Model Curriculum Standards Grades Seven Through Twelve (PDF; 2.13MB; 441pp.). Chapter 9 of the Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve 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; 419KB; 23pp) (Outside Source), published by the Sonoma County Office of Education, contains suggestions about student uses of technology (page 9).

The U.S. Department of Education’s Doing What Works Web site contains a series of pages to help teachers prepare students for algebra. The site is organized to present research and strategies through three formats:

• Learn what works (research)
• See how it works (videos, Power Points)
• Do what works (use tools to improve your practice)

The National Math Panel: Critical Foundations for Algebra (Outside Source) from Doing What Works, contains videos, school profiles, and tools teachers can use to provide comprehensive instruction in algebra. The site also includes links to the report from the National Math Panel: Critical Foundations for Algebra.