Acronym or Term ALD APLU CBMS CGI CCR CCR Anchor 1 Meaning Definition/ Meaning in terms of Common Core Common Core Terms -‐ General Achievement Level These articulate the knowledge, skills, & processes Descriptors expected of students at different levels of performance on the Smarter Balanced assessments. The Association of Public A research, policy, & advocacy organization representing & Land Grant 239 public research universities, land-‐grant institutions, Universities state university systems, & affiliated organizations. Conference Board of the An umbrella organization consisting of 17 professional Mathematical Sciences societies all of which have as one of their primary objectives the increase or diffusion of knowledge in one or more of the mathematical sciences. Its purpose is to promote understanding & cooperation among these national organizations so that they work together & support each other in their efforts to promote research, improve education, & expand the uses of mathematics. Cognitively Guided A professional development program based on an Instruction integrated program of research on (a) the development of students' mathematical thinking; (b) instruction that influences that development; (c) teachers' knowledge & beliefs that influence their instructional practice; & (d) the way that teachers' knowledge, beliefs, & practices are influenced by their understanding of students' mathematical thinking. College & Career The content knowledge, skills, & habits that students must Readiness possess to be successful in postsecondary education or training that leads to a sustaining career. College & Career Define the literacy expectations for students entering Readiness Anchor college & careers & provide the foundation for the K-‐12 Info. Source or For More Info: http://www.smarterbalanced.org/ac hievement-‐levels/ http://www.aplu.org/page.aspx?pid= 203 http://www.cbmsweb.org/ http://en.wikipedia.org/wiki/Cognitiv ely_Guided_Instruction https://www.epiconline.org/Issues/c ollege-‐career-‐ readiness/definition.dot http://www.cde.ca.gov/ci/cr/cf/docu ments/appendixesandreferences.pdf Acronym Meaning or Term Standards Standards CCSS CCSSO Cluster DOK Domain NAEP PARCC 2 Definition/ Meaning in terms of Common Core English language arts standards. They are essential to un-‐ derstanding the structure & cohesive nature of the CCSS. Common Core State A set of high quality academic expectations in English-‐ Standards language arts (ELA) & mathematics that define the knowledge & skills all students should master by the end of each grade level in order to be on track for success in college & career. Council of Chief State A non-‐partisan non-‐profit organization of public officials School Officers who head departments of elementary & secondary education in the U.S. states, the District of Columbia, the Department of Defense Education Activity & five U.S. territories. Groups of related standards inside domains Depth of Knowledge A reference to the complexity of mental processing that must occur to answer a question, perform a task, or generate a product. There are four levels as developed by Webb: 1. Recall and Reproduction 2. Skills and Concepts 3. Strategic Thinking, Reasoning 4. Extended Thinking Clusters of standards that address “big ideas” & support connections of topics across the grades National Assessment of The largest continuing & nationally representative Educational Progress assessment of what American students know & can do in core subjects. Partnership for the A Consortium of states working together to develop Assessment of Readiness assessments for CCSS Info. Source or For More Info: http://www.ccsso.org/Resources/Pro grams/The_Common_Core_State_St andards.html http://en.wikipedia.org/wiki/Council _of_Chief_State_School_Officers CA CCSSM http://www.google.com/search?q=S marter+Balanced+Assessments&ie=u tf-‐8&oe=utf8&aq=t&rls=org.mozilla: en-‐US:official&client=firefox-‐ a&channel=fflb&gws_rd=ssl#safe=ac tive&rls=org.mozilla:en-‐ US:official&channel=fflb&sout=1&q= depth+of+knowledge+definition CA CCSSM http://en.wikipedia.org/wiki/Nationa l_Assessment_of_Educational_Progr ess http://www.parcconline.org/ Acronym or Term SBAC SBAC Terms Claims Overall Claims CR ER 3 Meaning Definition/ Meaning in terms of Common Core for College & Career Smarter Balanced A consortium of states working together to develop a Assessment Consortium common set of K -‐ 12 assessments for CCSS (California belongs to this consortium) Info. Source or For More Info: http://www.smarterbalanced.org/sm arter-‐balanced-‐assessments/ http://www.smarterbalanced.org/wordpress/wp-‐ content/uploads/2012/09/Smarter-‐Balanced-‐Mathematics-‐Claims.pdf Grades 3-‐8 Students can demonstrate progress toward college and career readiness in mathematics Grades 9 -‐12 Students can demonstrate college and career readiness in mathematics Claim 1 Concepts and Procedures: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Claim 2 Problem Solving: Students can solve a range of well-‐posed problems in pure and applied mathematics, making productive use of knowledge and problem-‐solving strategies. Claim 3 Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Claim 4 Modeling and Data Analysis: Students can analyze complex, real-‐world scenarios and can construct and use mathematical models to interpret and solve problems. Constructed Response Prompt students to produce a text or numerical response http://www.smarterbalanced.org/sa Item in order to collect evidence about their knowledge or mple-‐items-‐and-‐performance-‐tasks/ understanding of a given assessment target. Extended Response Item Also referred to as an essay question. An extended http://teaching.about.com/od/A-‐ Acronym or Term Meaning PT Performance Task Item SR Selected Response Item TE Technology Enhanced Item CC Literacy across Disciplines RST Reading Science & Technical Subjects WHST Writing History, Science & Technical Subjects 4 Definition/ Meaning in terms of Common Core Info. Source or For More Info: response item is an open-‐ended question that begins with some type of prompt. These questions allow students to write a creative response that arrives at a conclusion based on their knowledge of the topic. An extended re-‐ sponse item takes considerable time & thought. It re-‐ quires students to not only give an answer, but to explain the answer with as much in-‐depth detail as possible.. Measure a student’s ability to integrate knowledge & skills across multiple standards—a key component of college & career readiness. Performance tasks will be used to better measure capacities such as depth of understanding, research skills, & complex analysis, which cannot be adequately assessed with selected-‐ or constructed-‐ response items. Prompt students to select one or more responses for a set of options. Take advantage of computer-‐based administration to assess a deeper understanding of content & skills than would otherwise be possible with traditional item types. Technology-‐enhanced items capitalize on technology to collect evidence through a non-‐traditional response type, such as editing text or drawing an object. ITeachingGlossary/g/Extended-‐ Response-‐Item.htm Just as students must learn to read, write, speak, listen, & use language effectively in a variety of content areas, so too must the Standards specify the literacy skills & understandings required for college & career readiness in multiple disciplines. Literacy standards for grade 6 & http://www.cde.ca.gov/be/st/ss/doc uments/finalelaccssstandards.pdf page 2 http://www.smarterbalanced.org/sa mple-‐items-‐and-‐performance-‐tasks/ http://www.smarterbalanced.org/sa mple-‐items-‐and-‐performance-‐tasks/ http://www.smarterbalanced.org/sa mple-‐items-‐and-‐performance-‐tasks/ Acronym or Term Meaning Definition/ Meaning in terms of Common Core Info. Source or For More Info: above are based on the expectation that teachers of ELA, history/social studies, science, & technical subjects use their expertise to help students meet the particular challenges of reading, writing, speaking, listening, & language in those content areas. It is important to note that the grades 6–12 literacy standards in history/social studies, science, & technical subjects are not meant to replace content standards in those areas but rather to supplement them. States may incorporate these standards into their standards for those subjects or adopt them as literacy standards in content areas. Common Core Mathematics K-‐8 Acronyms Domains & Clusters K-‐8: Info from Progressions Documents: http://ime.math.arizona.edu/progressions/ CC Counting & Cardinality Counting & Cardinality underlies Operations & Algebraic http://commoncoretools.files.wordp Thinking as well as Number & Operations in Base Ten. It ress.com/2011/05/ccss_progression begins with early counting & telling how many in one _cc_oa_k5_2011_05_302.pdf group of objects. Addition, subtraction, multiplication, & division grow from these early roots. This Progression page 2 involves important ideas that are neither trivial nor obvious; these ideas need to be taught, in ways that are interesting & engaging to young students. OA Operations & Algebraic The Progression in Operations & Algebraic Thinking deals http://commoncoretools.files.wordp Thinking with the basic operations—the kinds of quantitative ress.com/2011/05/ccss_progression relationships they model & consequently the kinds of _cc_oa_k5_2011_05_302.pdf problems they can be used to solve as well as their mathematical properties & relationships. page 2 Although most of the standards organized under the OA heading involve whole numbers, the importance of the 5 Acronym or Term NBT NF MD 6 Meaning Definition/ Meaning in terms of Common Core Progression is much more general because it describes concepts, properties, & representations that extend to other number systems, to measures, & to algebra. Numbers & Operation in Students’ work in the base-‐ten system is intertwined with Base Ten their work on counting & cardinality, & with the meanings & properties of addition, subtraction, multiplication, & division. Work in the base-‐ten system relies on these meanings & properties, but also contributes to deepening students’ understanding of them. Numbers & Operations The meaning of fractions In Grades 1 & 2, students use Fractions fraction language to describe partitions of shapes into equal shares.2.G.3 In Grade 3 they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision & measure-‐ ment. In Grade 4, this is extended to include wholes that are collections of objects. Measurement & Data Measurement: Geometric measurement connects the two most critical domains of early mathematics, geometry & number, with each providing conceptual support to the other. Measurement is central to mathematics, to other areas of mathematics (e.g., laying a sensory & conceptual foundation for arithmetic with fractions), to other subject matter domains, especially science, & to activities in everyday life. For these reasons, measurement is a core component of the mathematics curriculum. Data: As students work with data in Grades K–5, they build Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2011/04/ccss_prog ression_nbt_2011_04_073_correcte d2.pdf page 1 http://commoncoretools.me/wp-‐ content/uploads/2011/08/ccss_prog ression_nf_35_2013_09_19.pdf page 3 http://commoncoretools.files.wordp ress.com/2012/07/ccss_progression _gm_k5_2012_07_21.pdf page 2 http://commoncoretools.files.wordp Acronym or Term Meaning G Geometry RP Ratio & Proportional Relations 7 Definition/ Meaning in terms of Common Core foundations for their study of statistics & probability in Grades 6 & beyond, & they strengthen & apply what they are learning in arithmetic. Kindergarten work with data uses counting & order relations. First-‐ & second-‐graders solve addition & subtraction problems in a data context. In Grades 3–5, work with data is closely related to the number line, fraction concepts, fraction arithmetic, & solving problems that involve the four operations. Geometric & spatial thinking are important in & of themselves, because they connect mathematics with the physical world, & play an important role in modeling phenomena whose origins are not necessarily physical, e.g., as networks or graphs. They are also important because they support the development of number & arithmetic concepts & skills. Thus, geometry is essential for all grade levels for many reasons: its mathematical content, its roles in physical sciences, engineering, & many other subjects, & its strong aesthetic connections. This progression discusses the most important goals for elementary geometry according to three categories. Geometric shapes, their components (e.g., sides, angles, faces), their properties, & their categorization based on those properties. Composing & decomposing geometric shapes. Spatial relations & spatial structuring. The study of ratios & proportional relationships extends students’ work in measurement & in multiplication & division in the elementary grades. Ratios & proportional Info. Source or For More Info: ress.com/2011/06/ccss_progression _md_k5_2011_06_20.pdf page 2 http://commoncoretools.files.wordp ress.com/2012/06/ccss_progression _g_k6_2012_06_27.pdf page 2 http://commoncoretools.files.wordp ress.com/2012/02/ccss_progression _rp_67_2011_11_12_corrected.pdf Acronym or Term NS 8 Meaning The Number System Definition/ Meaning in terms of Common Core relationships are foundational for further study in mathematics & science & useful in everyday life. Students use ratios in geometry & in algebra when they study similar figures & slopes of lines, & later when they study sine, cosine, tangent, & other trigonometric ratios in high school. Students use ratios when they work with situations involving constant rates of change, & later in calculus when they work with average & instantaneous rates of change of functions. An understanding of ratio is essential in the sciences to make sense of quantities that involve derived attributes such as speed, acceleration, density, surface tension, electric or magnetic field strength, & to understand percentages & ratios used in describing chemical solutions. Ratios & percentages are also useful in many situations in daily life, such as in cooking & in calculating tips, miles per gallon, taxes, & discounts. They also are also involved in a variety of descriptive statistics, including demographic, economic, medical, meteorological, & agricultural statistics (e.g., birth rate, per capita income, body mass index, rain fall, & crop yield) & underlie a variety of measures, e.g., in finance (exchange rate), medicine (dose for a given body weight), & technology (kilobits per second). In Grades 6–8, students build on two important concept-‐ tions which have developed throughout K–5, in order to understand the rational numbers as a number system. The first is the representation of whole numbers & fractions as points on the number line, & the second is a firm Info. Source or For More Info: page 2 http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccssm_pr ogression_NS+Number_2013-‐07-‐ 09.pdf Acronym or Term Meaning EE Expressions & Equations SP Statistics & Probability 9 Definition/ Meaning in terms of Common Core understanding of the properties of operations on whole numbers & fractions. Mathematical expressions express calculations with numbers. Some of the numbers might be given explicitly, like 2 or 3/4 . Other numbers in the expression might be represented by letters, such as x, y, P, or n. The calculation an expression represents might use only a single opera-‐ tion, as in 4 + 3 or 3x, or it might use a series of nested or parallel operations, as in 3(a + 9)q -‐ 9/b. An expression can consist of just a single number, even 0. In Grade 6, students build on the knowledge & experi-‐ ences in data analysis developed in earlier grades. They develop a deeper understanding of variability & more precise descriptions of data distributions, using numerical measures of center & spread, & terms such as cluster, peak, gap, symmetry, skew, & outlier. They begin to use histograms & box plots to represent & analyze data distributions. As in earlier grades, students view statistical reasoning as a four-‐step investigative process: Formulate questions that can be answered with data Design & use a plan to collect relevant data Analyze the data with appropriate methods Interpret results & draw valid conclusions from the data that relate to the questions posed. In Grade 7, students move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. Info. Source or For More Info: page 2 http://commoncoretools.files.wordp ress.com/2011/04/ccss_progression _ee_2011_04_25.pdf page 2 http://commoncoretools.files.wordp ress.com/2011/12/ccss_progression _sp_68_2011_12_26_bis.pdf page 2 Acronym or Term F 10 Meaning Functions Definition/ Meaning in terms of Common Core Info. Source or For More Info: Because statistically sound data production is based on random sampling, a probabilistic concept, students must develop some knowledge of probability before launching into sampling. Their introduction to probability is based on seeing probabilities of chance events as long-‐run relative frequencies of their occurrence, & many opportunities to develop the connection between theoretical probability models & empirical probability approximations. This connection forms the basis of statistical inference. Eighth graders apply their experience with the coordinate plane & linear functions in the study of association between two variables related to a question of interest. As in the univariate case, analysis of bivariate measurement data graphed on a scatterplot proceeds by describing shape, center, & spread. But now “shape” refers to a cloud of points on a plane, “center” refers to a line drawn through the cloud that captures the essence of its shape, & “spread” refers to how far the data points stray from this central line. Students extend their understanding of “cluster” & “outlier” from univariate data to bivariate data. They summarize bivariate categorical data using two-‐way tables of counts and/or proportions, & examine these for patterns of association. Functions describe situations in which one quantity is determined by another. The area of a circle, e.g., is a function of its radius. When describing relationships between quantities, the defining characteristic of a function is that the input value determines the output http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_functions_2013_07_02.pdf page 4 Acronym or Term Meaning Definition/ Meaning in terms of Common Core Info. Source or For More Info: value or, equivalently, that the output value depends upon the input value. Since the elementary grades, students have been describing patterns & expressing relationships between quantities. These ideas become semi-‐formal in Grade 8 with the introduction of the concept of function: a rule that assigns to each input exactly one output.8.F.1 Building on their earlier experiences with graphs & tables in Grades 6 & 7, students a routine of exploring functional relationships algebraically, graphically, numerically in tables, & through verbal descriptions.8.F.2 Domains & Clusters 9-‐12: Info from Progressions Documents: http://ime.math.arizona.edu/progressions/ Number & Quantity N-‐RN The Real Number System In Grades 6–8 students began to widen the possible types http://commoncoretools.me/wp-‐ of number they can conceptualize on the number line. In content/uploads/2013/07/ccssm_pr Grade 8 they glimpse the existence of irrational numbers ogression_NS+Number_2013-‐07-‐ such as √2. In high school, they start a systematic study of 09.pdf functions that can take on irrational values, such as f(x) = x2 exponential, logarithmic, & power functions. page 9 N-‐Q Quantities There is no progression document on this topic N-‐CN The Complex Number That complex numbers have a practical application is http://commoncoretools.me/wp-‐ System surprising to many. But it turns out that many phenomena content/uploads/2013/07/ccssm_pr involving real numbers become simpler when the real ogression_NS+Number_2013-‐07-‐ numbers are viewed as a subsytem of the complex 09.pdf numbers. E.g., complex solutions of differential equations can give a unified picture of the behavior of real solutions. page 18 Students get a glimpse of this when they study complex 11 Acronym or Term N-‐VM Algebra OA-‐SSE A-‐APR 12 Meaning Vector & Matrix Quantities Seeing Structure in Equations Arithmetic with Polynomials & Rational Expressions Definition/ Meaning in terms of Common Core solutions of quadratic equations. When complex numbers are brought into the picture, every quadratic polynomial can be expressed as a product of linear factors. Info. Source or For More Info: There is no progression document on this topic Students have been seeing expressions since Kindergar-‐ http://commoncoretools.me/wp-‐ ten, starting with arithmetic expressions in Grades K–5 & content/uploads/2013/07/ccss_prog moving on to algebraic expressions in Grades 6–8. The ression_algebra_2013_07_03.pdf middle grades standards in Expression & Equations build a ramp from arithmetic expressions in elementary school to page 4 more sophisticated work with algebraic expressions in high school. As the complexity of expressions increases, students continue to see them as being built out of basic operations: they see expressions as sums of terms & products of factors.A-‐SSE.1a Students learn to use the properties of operations to write http://commoncoretools.me/wp-‐ expressions in different but equivalent forms. At some content/uploads/2013/07/ccss_prog point they see equivalent expressions, particularly poly-‐ ression_algebra_2013_07_03.pdf nomial & rational expressions, as naming some underlying thing.A-‐APR.1 There are at least two ways this can go. If the page 7 function concept is developed before or con-‐currently with the study of polynomials, then a polynomial can be identified with the function it defines. Another approach is to think of polynomials as elements of a formal number system, in which you introduce the “number” x & see what numbers you can write down with it. Each approach has its advantages & disadvantages; the former approach Acronym or Term A-‐CED 13 Meaning Creating Equations Definition/ Meaning in terms of Common Core is more common. Whichever are chosen & whether or not the choice is explicitly stated, a curricular implementation should nonetheless be constructed to be consistent with the choice that has been made. Either way, polynomials & rational expressions come to form a system in which they can be added, subtracted, multiplied anddivided.A-‐APR.7 Polynomials are analogous to the integers; rational expressions are analogous to the rational numbers Students have been seeing & writing equations since elementary grades, with mostly linear equations in middle grades. At first glance it might seem that the progression from middle grades to high school is fairly straightforward: the repertoire of functions that is acquired during high school allows students to create more complex equations, including equations arising from linear & quadratic ex-‐ pressions, & simple rational & exponential expressions;A-‐ CED.1 students are no longer limited largely to linear equations in modeling relationships between quantities with equations in two variables;A-‐CED.2 & students start to work with inequalities & systems of equations. A-‐CED.3 Two developments in high school complicate this picture. First, students in high school start using parameters in their equations, to represent whole classes of equations F-‐LE.5 or to represent situations where the equation is to be adjusted to fit data. Second, modeling becomes a major objective in high school. Two of the standards just cited refer to “solving problems” & “interpreting solutions in a modeling context.” & all the standards in the Creating Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_algebra_2013_07_03.pdf page 10 Acronym or Term A-‐REI Meaning Reasoning with Equations & Inequalities Functions F-‐IF Interpreting Functions 14 Definition/ Meaning in terms of Common Core Equations group carry a modeling star, denoting their connection with the Modeling category in high school. This connotes not only an increase in the complexity of the equations studied, but an upgrade of the student’s ability in every part of the modeling cycle. A written sequence of steps to solve an equation is code for a narrative line of reasoning using words like “if,” “then,” “for all,” & “there exists.” In the process of learning to solve equations, students learn certain stan-‐ dard “if–then” moves, e.g., “if x = y then x + 2 = y + 2. The danger in learning algebra is that students emerge with nothing but the moves, which may make it difficult to detect incorrect or made-‐up moves later on. Thus the first requirement in the standards in this domain is that students understand that solving equations is a process of reasoning.A-‐REI.1 This does not necessarily mean that they always write out the full text; part of the advantage of algebraic notation is its compactness. Once students know what the code stands for, they can start writing in code. Thus, eventually students might go from without intermediate steps. Building on semi-‐formal notions of functions from Grade 8, students in high school begin to use formal notation & language for functions. Now the input/output relationship is a correspondence between two sets: the domain & the range.F-‐IF.1 The domain is the set of input values, & the range is the set of output values. A key advantage of Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_algebra_2013_07_03.pdf page 13 http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_functions_2013_07_02.pdf page 7 Acronym or Term Meaning F-‐BF Building Functions F-‐LE Linear, Quadratic & Exponential Models F-‐TF Trigonometric Functions 15 Definition/ Meaning in terms of Common Core function notation is that the correspondence is built into the notation. The Building Functions group focuses on building functions to model relationships, & building new functions from existing functions This cluster of standards is very closely related to the algebra standard on writing equations in two variables. A-‐CED.2 Indeed, that algebra standard might well be met by a curriculum in the same unit as this cluster. Although students will eventually study various families of functions, it is useful for them to have experiences of building functions from scratch, without the aid of a host of special recipes, by grappling with a concrete context for clues.F-‐BF.1a Construct & compare linear & exponential models & solve problems involves distinguishing between situations that can be modeled with linear functions & with exponential functions F-‐LE.1a & turns on understanding their rates of growth & looking for indications of these types of growth rates (MP.7). One indicator of these growth rates is differences over equal intervals, given, e.g., in a table of values drawn from the situation—with the understanding that such a table may only approximate the situation (MP.4). Students begin their study of trigonometry with right triangles. G-‐SRT.6 Right triangle trigonometry is concerned with ratios of sides of right triangles, allowing functions of angle measures to be defined in terms of these ratios. This limits the angles considered to those between 0° & 90° In this progression the following ideas are added to the Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_functions_2013_07_02.pdf page 11 http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_functions_2013_07_02.pdf page 16 http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_functions_2013_07_02.pdf page 18 Acronym or Term Meaning Geometry G-‐CO G-‐SRT Congruence Similarity, Right Triangles, & Trigonometry G-‐C Circles G-‐ GPE Expressing Geometric Properties with Equations G-‐GMD Geometric Measurement & Dimension G-‐MG Modeling with Geometry Statistics & Probability S-‐ID Interpreting Categorical & Quantitative Data 16 Definition/ Meaning in terms of Common Core Info. Source or For More Info: notion of trigonometry: Extend the domain of trigonometric functions using the unit circle Model periodic phenomena with trigonometric functions Prove & apply trigonometric identities There is no progression document on this topic Students build on the understanding of key ideas for describing distributions—shape, center, & spread—de-‐ scribed in the Grades 6-‐8 Statistics & Probability Progression. This enhanced understanding allows them to give more precise answers to deeper questions, often involving comparisons of data sets. Students use shape & the question(s) to be answered to decide on the median or mean as the more appropriate measure of center & to http://commoncoretools.me/wp-‐ content/uploads/2012/06/ccss_prog ression_sp_hs_2012_04_21_bis.pdf page 3 Acronym or Term S-‐IC S-‐CP S-‐MD 17 Meaning Definition/ Meaning in terms of Common Core justify their choice through statistical reasoning. They also add a key measure of variation to their toolkits Making Inferences & Students move beyond analyzing data to making sound Justifying Conclusions statistical decisions based on probability models. The reasoning process is as follows: develop a statistical question in the form of a hypothesis (supposition) about a population parameter; choose a probability model for collecting data relevant to that parameter; collect data; compare the results seen in the data with what is expected under the hypothesis. If the observed results are far away from what is expected & have a low probability of occurring under the hypothesis, then that hypothesis is called into question. In other words, the evidence against the hypothesis is weighed by probability. S-‐IC.1 Conditional Probability & In high school, the relative frequency approach to Rules of Probability probability is extended to conditional probability & independence, rules of probability & their use in finding probabilities of compound events, & the use of probability distributions to solve problems involving expected value. As seen in the making inferences section above, there is a strong connection between statistics & probability. This will be seen again in this section with the use of data in selecting values for probability models. Using Probability to As students gain experience with probability problems Make Decisions that deal with listing & counting outcomes, they will come to realize that, most often, applied problems concern some numerical quantity of interest rather than a description of the outcomes themselves. Students should Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2012/06/ccss_prog ression_sp_hs_2012_04_21_bis.pdf page 8 http://commoncoretools.me/wp-‐ content/uploads/2012/06/ccss_prog ression_sp_hs_2012_04_21_bis.pdf page 13 http://commoncoretools.me/wp-‐ content/uploads/2012/06/ccss_prog ression_sp_hs_2012_04_21_bis.pdf page 18 Acronym or Term Modeling Meaning Modeling in High School Illustrative Mathematics Project Inside Mathematics 18 Definition/ Meaning in terms of Common Core understand that probabilities & expected values must be thought of as long-‐term relative frequencies & means, & consider the implications of that view in decision making. In high school, modeling involves a way of thought differ-‐ rent from what students are taught when they learn much of the core K–8 mathematics. It provides experience in approaching problems that are not precisely formulated & for which there is not necessarily a single “correct" an-‐ swer. Deciding what is left out of a model can be as impor-‐ tant as deciding what is put in. Judgment, approximation, & critical thinking enter into the process. Modeling can have differing goals depending on the situation—some-‐ times the aim is quantitative prediction, e.g., in weather modeling, & sometimes the aim is to create a simple model that captures some qualitative aspect of the system with a goal of better understanding the system, e.g. modeling the cyclic nature of predator-‐prey populations A community of educators dedicated to the coherent learning of mathematics. They share carefully vetted resources for teachers & teacher leaders to give our children an understanding of mathematics & skill in using it. They provide expert guidance to states & districts working to improve mathematics education. Provides a resource for educators around the world who struggle to provide the best mathematics instruction they can for their students. Too often, teachers who excel at reaching students have few ways of sharing these strong practices with others – & teachers who struggle, struggle Info. Source or For More Info: http://commoncoretools.me/wp-‐ content/uploads/2013/07/ccss_prog ression_modeling_2013_07_04.pdf page 6 http://illustrativemathematics.org/ www.insidemathematics.org/. Acronym or Term Meaning MARS Tasks Mathematics Assessment Resource Service Tasks MTEP Mathematics Teacher Education Preparation NCSM Great Tasks Progressions SMP SMP – Standards for Mathematical Practice AMTE Association of Mathematics Teacher Educators California Association of Mathematics Teacher CAMTE 19 Definition/ Meaning in terms of Common Core alone. Our classroom doors have remained closed too often & for too long. The Mathematics Assessment Resource Service (MARS), a project of UC Berkeley, Michigan State, & the Shell Centre in Nottingham England designed these formative performance assessment tasks. This partnership provides a coordinated research, development, & implementation effort for secondary mathematics teacher preparation programs in order to meet the challenges of the Common Core State Standards for Mathematics & to embody research & best practices in the field. This project is a collection of tasks to support implementation of the CCSS. Funded by the Brookhill Foundation, This project is organizing the writing of final versions of the progressions documents for the K–12 Mathematics Common Core State Standards. Describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Organizations that support Mathematics Education Info. Source or For More Info: https://www.scoe.org/pub/htdocs/c css-‐mathematics.html http://mathshell.org/ba_mars.htm http://www.aplu.org/mtep http://www.mathedleadership.org/c css/greattasks.html http://ime.math.arizona.edu/progres sions/ http://www.corestandards.org/Math /Practice/ Organization dedicated to the improvement of mathematics teacher education. http://www.camte.org/ Organization dedicated to serving those who provide professional development and or preservice education to http://www.camte.org/ Acronym or Term NCTM NCSM TODOS CMC3 CMC3-‐S CMC CMC-‐S 20 Meaning Definition/ Meaning in terms of Common Core Educators K-‐12 mathematics teachers in California. National Council of The public voice of mathematics education, supporting Teachers of Mathematics teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research National Council of Mathematics leadership organization for educational Supervisors of leaders providing professional learning opportunities Mathematics necessary to support and sustain improved student achievement. TODOS: Mathematics for A Mathematics education association that advocates for All equity and high quality mathematics education for all students— in particular, Latina/o students. California Math Council-‐ Organization that serves the needs of California Community Colleges Community College math educators in Northern and Central California. California Math Council-‐ Organization that serves the needs of California Community Colleges-‐ Community College math educators in Southern South California. California Mathematics Organization committed to improving mathematics Council learning in the private and public classrooms throughout California. California Mathematics So Cal's organization for pre-‐K to grade 16 Mathematics Council-‐South Educators, the California Mathematics Council -‐ South. A non-‐profit, all volunteer organization that serves to improve mathematics teaching and learning in public, charter and private school settings across eight counties (Santa Barbara, Ventura, Los Angeles, Orange, Riverside, San Bernardino, Imperial, and San Diego). Info. Source or For More Info: http://www.nctm.org/ http://www.mathedleadership.org/ http://www.todos-‐math.org/ http://www.cmc3.org/ http://cmc-‐math.org/ http://www.cmc-‐south.org/ Acronym or Term Meaning AVMC Antelope Valley Math Council GSDMC Greater San Diego Math Council, Greater Los Angeles Mathematics Council Imperial County Math Council Orange County Math Council Riverside San Bernardino Math Teachers Association San Gabriel Valley Math Council Ventura County Math Council GLAMC ICMC OCMC RSBMTA SGVMC VCMC CMC-‐C SMC 21 Definition/ Meaning in terms of Common Core CMC-‐S Affiliates Organization serving mathematics educators in the Antelope Valley. Organization serving mathematics educators in San Diego County. Organization serving mathematics educators San in the Greater Los Angeles area. Organization serving mathematics educators in the Imperial County area. Organization serving mathematics educators in the Orange County area. Organization serving mathematics educators in both the Riverside and San Bernardino County areas. Organization serving mathematics educators in the San Gabriel Valley area. Organization serving mathematics educators in the Ventura County area. CMC-‐C and Affiliates California Mathematics The Central Section serves educators from Paso Robles Council Central through the Central Valley of California to the Nevada border and south to Santa Barbara. Bakersfield Math Council Organization serving mathematics educators in the Kern County area. P-‐16 Math Council, San Organization serving mathematics educators in the San Luis Obispo Luis Obispo County area. SStanislaus Math Council Organization serving mathematics educators in the Info. Source or For More Info: https://www.facebook.com/pages/A ntelope-‐Valley-‐Mathematics-‐ Council/168634636493172 http://www.gsdmc.org/ http://glamc.org/ http://imperialcmc.weebly.com/inde x.html http://www.ocmathcouncil.com/ http://cmc-‐ math.org/organization/affiliates/RSB CMTA/default.html http://mysgvmc.weebly.com/ http://www.vcmc.org/ http://cmc-‐math.org/cmc-‐ organization/cmc-‐central/cmc-‐ central-‐home/ http://www.stanislausmathcouncil.o Acronym or Term CMC-‐N Meaning California Mathematics Council -‐ North Alameda Contra Costa County Math Educators AC3ME C3ASME Contra Costa County Association of Science and Math Educators CMSESMC Council of Math and Science Educators of San Mateo County MESC Math Educators of Solano County MLMC Mt Lassen Math Council MDMC MC-‐N NNMC SAME SFMTA 22 Monterey Bay Counties Math Educators California Mathematics Council – Far North Northern Nevada Math Council Sacramento Area Math Educators San Francisco Math Teachers Association, Definition/ Meaning in terms of Common Core Info. Source or For More Info: Calaveras, Mariposa, Merced, San Joaquin, Stanislaus and Tuolumne counties. CMC-‐N and Affiliates The northern section serves educators from the northern California border with Oregon, south to Monterey. Organization serving mathematics educators in the Alameda and Contra Costa Counties, and throughout the greater Bay area. Organization serving mathematics educators in Contra Costa County. rg/ Organization serving mathematics and science educators in San Mateo County. http://www.cmsesmc.org/ Organization serving mathematics educators in Solano & Yolo Counties Organization serving mathematics educators in the Mount Lassen area Organization serving mathematics educators in the Monterey Bay area Organization serving mathematics educators in the Humboldt, Del Norte and neighboring counties. Organization serving mathematics educators in the Washoe County and Reno, Nevada area. Organization serving mathematics educators in the Sacramento area. Organization serving mathematics educators in the San Francisco area. http://cmc-‐math.org/AC3ME/ https://www.facebook.com/MLMC. MtLassenMathCouncil http://www.cmcfn.com/ https://sites.google.com/site/nnevad amathcouncil/ http://edweb.csus.edu/projects/sam e/ Acronym or Term SCVMA WCMC 23 Meaning Definition/ Meaning in terms of Common Core Info. Source or For More Info: SFMTA Santa Clara Valley Math Association Organization serving mathematics educators in the Santa Clara area. http://www.scvmath.org/ Wine Country Math Council Organization serving mathematics educators in the Sonoma, Lake, and Mendocino County areas

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