STANDARD 13 — ALGEBRA K-12 We develop an understanding of algebraic concepts and processes and use them to represent and analyze relationships among variable quantities and to solve problems.
Meaning and Importance The Language of Algebra Algebra is the language of patterns and relationships through which much of mathematics is communicated. It is a tool which people can and do use to model real situations and answer questions about them. It is also a way of operating with concepts at an abstract level and then applying them, often leading to the development of generalizations and insights beyond the original context. The use of algebra should begin in the primary grades and should be developed throughout the elementary and secondary grades.
Descriptive Statement
Algebra is a language used to express mathematical relationships. Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. Modern technology provides tools for supplementing the traditional focus on algebraic techniques, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a reallife situation.
When we get it, it: (“Why study algebra?”)
Algebra provides methods for moving from the specific to the general. It involves discovering the patterns among items in a set and developing the language needed to think about and communicate it to others. Algebra provides procedures for manipulating symbols to allow for understanding of the world around us. Algebra provides a vehicle for understanding our world through mathematical models. Algebra is the science of variables. It enables us to deal with large bodies of data by identifying variables (quantities which change in value) and by imposing or finding structures within the data. Algebra is the basic set of ideas and techniques for describing and reasoning about relations between variable quantities.
The development of manipulates, graphing calculators, and computers have made a more intuitive view of algebra accessible to all students, regardless of their previous mathematical performance. These tools permit and encourage visual representations which are more readily understood. No longer need students struggle with abstract concepts presented with very few ties to real-life situations. Rather, the new view of algebra offers real situations for students to examine, to generalize, and to represent in ways which facilitate the asking and answering of meaningful questions. Moreover, inexpensive symbolic processors perform algebraic manipulations, such as factoring, quickly and easily, reducing the need for drill and mastery of paper-and-pencil symbol manipulation.
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the contract was amended the following year, Vheru was entitled to 20 percent of all revenues generated by sales of the textbook and related materials. In early 2004, LAUSD gave Vheru a temporary position as supervisor of Central Office Mathematics Department, which gave him the authority to issue book purchase orders without any oversight. Several months later, LAUSD notified Vheru that it intended to replace him as the supervisor of the Mathematics Department with another individual. The indictment alleges that before he was replaced as the supervisor, Vheru executed a scheme that caused the district to issue $3.7 million worth of purchase orders for his Algebra book in violation of California conflict of interest laws and the district's code of ethics. He subsequently caused the District to pay for the book and related materials with federal funds that were specifically provided to the district under Title III of the No Child Left Behind Act for programs for students with limited English proficiency. The federal government provides Title III educational funds to the State of California, which transmits some of the money to the school district. The district is required to spend the money on programs that are designed to increase the academic performance and English
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proficiency of pupils who have difficulty reading or writing English. The indictment alleges that Vheru attempted to conceal his scheme by, among other things, having the purchase orders for the algebra books describe the items being purchased as materials that were intended to help students prepare for the California High School Exit Exam, and taking other steps to prevent the publisher from disclosing to the district the true nature of the course materials that were being purchased and Vheru's financial interest in the deal. In July 2004, the school district paid nearly $4 million to the publisher for Vheru's textbook and related materials, and for a small amount of exit exam materials. Soon after, the publisher paid Vheru approximately $676,000 in royalties and a $255,000 consulting fee. Vheru worked for LAUSD in several roles from 1982 until he resigned approximately two years ago during the course of the District's dismissal process. Vheru is specifically charged with 11 counts of "honest services" wire fraud for allegedly depriving the school district of his honest services and misuse of the funds that were used to finance the purchase. The indictment also contains one count of misapplication of funds that were under the control of a federally funded government
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agency. If convicted of these 12 felony charges, Vheru agency. If convicted of these 12 felony Vheru faces a maximum possible penalty of 230 charges, years in federal faces a maximum possible penalty of 230 years in federal prison. prison. An indictment contains allegations that a defendant has An indictment contains that a defendant has committed a crime. Every allegations defendant is presumed committed crime. Every defendant innocent untilaand unless proven guiltyisinpresumed court. innocent until and unless proven guilty in court. The case against Vheru is the result of an investigation by The case against Vheru is theofresult of an investigation by the United States Department Education, Office of the United States the Department of Education, Office of Inspector General; Los Angeles School District, Inspector General;General; the Los the Angeles School District, Office of Inspector Los Angeles Unified Office of Inspector General; the Los Angeles School District, Office of the General Counsel; Unified and the School District, Office of the General Counsel; and the United States Postal Inspection Service. United States Postal Inspection Service. Release No. 07-034 Release No. 07-034
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Bo b Mo s e s s e e s a l g e br a a s a l e a di n g c a u se o f hi g h s c ho o l dr o po u t t h e p re s s u re of t ry i n g t o p a s s A lg e b r a . “ I t ’ s a c i v il r i g ht s is s ue — if po o r c h il dr e n d o n’ t l e a r n hi g h- le v e l m a t h , h e a r g u e s, t h e y ’ ll n e v e r g e t t he jo b s t h e y n e e d a s a d u lt s t o pu l l t he m s e lv e s o ut o f po v e r t y . “ We r e c og n i z e t h a t s uc c e s s i n m a t h a n d s c ie n c e l a y s t h e f ou n da t i on fo r s u c c e ss in n s c ho o l a nd b e y on d ”