[A Work in Progress] - on the Book of Isaiah - James E. Smith ...
4 pages
English

[A Work in Progress] - on the Book of Isaiah - James E. Smith ...

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4 pages
English
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  • expression écrite
An Expository Commentary on the Book of Isaiah [A Work in Progress] The translation used is the author's own unless otherwise indicated. James E. Smith January 2005
  • proud cities of sodom
  • judah for incorrigibleness
  • isaiah as a library of prophetic books
  • prophetic ministry
  • isaiah
  • chs
  • judah
  • books
  • jerusalem
  • book

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Publié par
Nombre de lectures 27
Langue English

Exrait

Algebra 1 YAG OverviewPurpose and Standards for Mathematics The National Council of Texas of Mathematics (2000) inPrinciples and Standards for School Mathematics states:Imagine a classroom, a school, or a school district where all students have access to highquality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning, and proof techniques to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it. (p. 3) The Texas Education Agency (2006)in the Texas Essential Knowledge and Skills for Mathematicsechoes these ideas in the Texas Mathematics Framework, providing focal points at each grade level and adds “problem solving, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics.”When the mathematics content, criticalthinking skills and processes are taught together, a greater depth of mathematical understanding and reasoning is attained. Algebra 1 is organized around three (3) strands: Foundations for functions; Linear functions; and Quadratic and other nonlinear functions. CSCOPE Mathematics CSCOPE Mathematics presents a constructivist instructional model, based on current research and national standards. For more information on related current research, refer to the CSCOPE white paper, “Taking a Closer Look”oo_leros.f)pdk.t_kapare_alcni_gscopcs/citepe_whe.csww5w:p//h(tte/doscopet/c13.nThere are recommended national standards for mathematics and for the separate disciplines within the mathematics curriculum. CSCOPE Mathematics units and lessons reflect these national standards where they align with the TEA Mathematics Texas Essential Knowledge and Skills. National standards referenced include the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), Principles and Standards for School Mathematics (NCTM, 2000), and the National Curriculum Focal Points (NCTM, 2006). CSCOPE Mathematics is both TEKScentered and conceptbased, and it integrates the mathematical strands. CSCOPE created “bundles of instruction” to form a focused, coherent curriculum that develops mathematics conceptually within the grade level and vertically among the grade levels. In each grade level, the focused “bundles” were mapped throughout the year allowing time for learning development. Once the “bundles” were completed and arranged in a logical order, CSCOPE next considered the concepts students must develop in mathematics at that particular grade. Performance indicators were written setting the expectation and the rigor of student performance after instruction. Key understandings were written to ensure that these concepts remain the center of instruction, that students view specific content details in terms of larger ideas, and that they develop relationships or connectedness between concepts. The exemplar lessons were then written as examples to provide teachers a model of instruction that targets the performance indicators and key understandings. Algebra 1 TEKS (From the TEKS Subchapter C. High School §111.32) The basics of algebraic reasoning and data representation which were developed in middle school are embedded throughout the Algebra 1 curriculum. The Algebra 1 curriculum addresses topics such as algebraic
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thinking and symbolic reasoning, function concepts, relationships between equations and functions, tools for algebraic thinking, and underlying mathematical processes (TEA, 2006). According to Driscoll (1999), algebraic thinking is facilitated by three habits of mind: doing and undoing, building rules to represent functions, and abstracting from computation. Doing and undoing implies that a student knows a process well enough to work a problem, but also to work backward from the answer. Building a rule to represent a function means that a student can find patterns in data and use those patterns to write an algebraic representation that represents it. Abstracting from computation means that a student has the “capacity to think about computations independently of particular numbers that are used” (Driscoll, 1999). One of the keys to developing algebraic habits of mind is the ability to translate among representations of data. CSCOPE Algebra 1 The first semester of CSCOPE Algebra 1 begins with the exploration of data relationships involving realworld functional situations, the relationships between variables and expressions, and the ways to represent these relationships. The development of the concept of function and the analysis of the characteristics of functions occur through the study of multiple representations of data. This functional approach to algebra is not unique to CSCOPE and has been promoted by the National Council of Teachers of Mathematics, the Dana Center in the development of the TEXTEAMS institutes, the Texas Education Agency math modules such as Mathematics TEKS Refinement (MTR), Mathematics TEKS Connections (MTC), and Teaching Mathematics through 3 Technology (TMT ), and other mathematics research. Beginning formal algebra with reallife situations that are naturally algebraic, students understand that formal algebra is not only a manipulation of symbols, but a logical way to approach mathematical situations in an effort to make sense of them. Experiencing reallife functional situations and their characteristics build algebraic habits of mind. Through careful instruction, teachers connect reallife with algebraic representation and build conceptual understanding before delving into algebraic manipulation. If students completely develop solving equations using symbolic manipulation before they develop a solid conceptual foundation for their work, they will be unable to do more than symbolic manipulation (National Research Council, 1998). After connecting the representations of one set of data, students begin to look at two sets of data and their commonalities. This gives rise to the idea of equality and leads to solving equations using tables and graphs. Then students use the properties of algebra to transform and solve linear equations and inequalities, and to determine reasonable solutions to problem situations with a focus on application to reallife situations. Through study of direct variation and proportions, as well as nonproportional situations, students explore the patterns that relate to linear functions, leading to the understanding of slope and intercepts and writing equations of lines (National Council of Teachers of Mathematics, 2000). Scatterplots and trend lines allow students to make predictions and draw conclusions based on data. Solving systems of linear equations (2 x 2 only) concludes the study of linear functions. Students begin the study of quadratics with an exploration of the properties of exponents, which allows a conceptual understanding of the rules for exponents. Students then apply rules of exponents with the properties of algebra to simplify polynomial expressions. “Students should be able to operate fluently on algebraic expressions, combining them and reexpressing them in alternative forms” (National Council of Teachers of Mathematics, 2000). This more general discussion of exponents leads to an exploration of quadratic functions. As in the exploration of linear functions, students first analyze characteristics of quadratic functions through real life applications and transformations. Building on concepts learned in prior units, students solve quadratics using tables, graphs, algebraic properties, and factoring. Using selected methods, students solve quadratic equations and determine reasonable solutions to problem situations. Linear and quadratic functions come together in a unit that explores algebraic models of realworld situations using the different representations to make predictions and critical judgments. Students collect and analyze other types of nonlinear data by exploring inverse functions and exponential growth and decay functions. Bibliography: Driscoll, M. (1999).Fostering algebraic thinking: A guide for teachers grades 610.Portsmouth, VA: Heinemann.
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National Council of Teachers of Mathematics. (2000).Principles and standards for school mathematic: An overview.Reston, VA: National Council of Teachers of Mathematics, Inc. National Council of Teachers of Mathematics. (2006).Curriculum focal points for prekindergarten through grade 8 mathematics.Reston, VA: National Council of Teachers of Mathematics. National Research Council. (1998).High school mathematics at work: Essays and examples for the education of all students.Washington, DC: National Academy Press. Texas Education Agency. (2006).Chapter 111. Texas Essential Knowledge and Skills. Subchapter C. High School. Retrieved April 4, 2008, fromhttp://ritter.tea.state.tx.us/rules/tac/chapter111/ch111b.html
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First Semester st 1 SixWeeks Unit 01: The Study of Functions(25 days)A.1ABDE; A.2BD; A.3AB; A.4AC
n 2 SixWeeks Unit 02: Linear Equations and Inequalities(15 days) A.1CD; A.3A; A.4AB; A.7ABC Unit 03: Investigating Linear Functions(10 days) A.1CD; A.2ACD; A.5ABC; A.6ABCEG
r 3 SixWeeks Unit 04: Linear Functions and Applications(16 days) A.2ACD; A.5ABC; A.6ABCDEFG Unit 05: Systems of Linear Equations(9 days) A.1CD; A.3A; A.4AB; A.8ABC
©2009, TESCCC
Yearat a Glance Algebra 1 – HS Mathematics Second Semester t 4 SixWeeks Unit 06: Exponents and Polynomial Operations(13 days) A.3B; A.4AB; A.11A Unit 07: Quadratic Functions(12 days) A.1D; A.2ACD; A.4A; A.9ABCD
t 5 SixWeeks Unit 08: Quadratic Equations and Applications(16 days) A.1D; A.4A; A.9ABCD; A.10AB Unit 09: Tying It All Together – Overview(9 days) A.1ABCDE; A.2ABCD; A.3AB; A.4ABC; A.5AC; A.6ABCDEFG; A.7ABC; A.8ABC; A.9BCD; A.10AB; A.11A
t 6 SixWeeks Unit 10: Inverse Variations(8 days) A.1BDE; A.11B Unit 11: Growth and Decay – Exponential Functions(12 days) A.1BDE; A.11C
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