As the November 20, 2015 deadline looms for the public to make suggestions to replace Arizona’s Common Core Standards, please consider making the following 8 comments. All of the data referenced in them comes from professional authorities with experience in K-12 education. These comments have been sent to the Standards Committee, but I cannot emphasize enough that the Committee and Arizona School Board need to "get the message loudly and clearly." Please send your comments, or use some or all of these! Send them to: https://k12standards.az.gov/comment-standards.
First. To the question "Is there anything better than Common Core"? the answer comes from a staunch Common Core supporter: Fordham Institute. Yes. (If you don’t have time to send specific comments to the Standards Committee, send the links to these superior standards!) The pre-2010 Massachusetts English/Language Arts Standards were rated A- by Fordham. (Common Core was given a B+.) Fordham stated: "As for the singular case of Massachusetts, there we find the state that has led the nation in achievement gains over the past decade, thanks in large part to its excellent standards—and their serious implementation." See page 4 of The State of State Standards—and the Common Core—in 2010.
One of the developers of the pre-2010 Massachusetts Standards, Dr. Sandra Stotsky, has improved them and offered them free to any state that wishes to use all or portions of them. Click HERE.
The pre-2010 California Math Standards were rated A by Fordham, stating "California’s standards could well serve as a model for internationally competitive national standards. They are explicit, clear, and cover the essential topics for rigorous mathematics instruction." (Common Core was rated A-.)
Click HERE for California’s pre-2010 Math Standards. Two addenda could be added that elaborate on the standards themselves and deal with pedagogical and organizational issues: 1) Mathematics Framework for California Public Schools, 2000 Revised Edition; and 2) Mathematics Framework for California Public Schools, 2006 Edition."
4 Comments Regarding Arizona’s Common Core English/Language Arts.
ELA Comment #1:
Thank you for this opportunity to comment on the current English/Language Arts (ELA) standards. First, please remove the highly prescriptive, bloated, 183 pages of Appendix B http://www.corestandards.org/assets/Appendix_B.pdf, including all references to it in the Standards. Appendix B is difficult to find on your website, however, it is still referenced in ELA 3-5, 6-8, and 9-12.
To truly allow Arizona’s teachers flexibility to use their skills, a list of suggested authors is preferable. New teachers soon learn which teachers are the best in their school, and they seek them out to help them hone their art.
Also, in the early grades, the current standards are not developmentally appropriate. They do not consider how young minds mature, and then present standards and material that correspond to the appropriate stage of mental development. For example, Arizona’s standards expect young children to “collaborate,” “engage in multiple discussions,” “express thoughts, feelings, and ideas clearly.” Forcing children to meet standards beyond their capacity turns them off way too early in their school career. They don’t care anymore and give up. They either think they’re stupid, or they think their teacher is. Either way, many of these children are unfairly labeled as behavioral problems, and many are misevaluated as in need of remediation.
I also don’t believe that the over reliance on straightforward “informational text” advances a student’s thinking abilities. I’m also concerned about expecting an English teacher to have a thorough understanding and appreciation for some of our Founding documents. Unless it is the remarkably short, powerful, and moving Gettysburg Address, in which context is critically important, much informational text taken from the pages of the federal register is sheer drudgery. What you see is what you get. Some of it has its practical place. However, there is far more classic literature that builds character. Isn’t that a goal of education?
Excellent, thought-provoking literature teaches us not just to think deeply and to grapple with our own and others’ humanity and depth of character, but it also serves to incidentally teach us spelling, grammar, and punctuation. Dry “information,” rarely forces us to wrestle with moral dilemmas. In fact, for sheer conscience provoking, good versus evil moral dilemmas, I give you Agatha Christie’s Murder on the Orient Express, compared to Eric Bonhoeffer’s My Soul Finds Rest. A murder mystery writer, multiple history lessons, problem solving, intrigue, vengeance, justice, courage, daring, truth and lies, a convicted pastor, biblical teachings, and the failed assassination of Hitler! Still. Those are choices best left to effective teachers who have their own ideas.
I have read the highly rated ELA standards developed by Dr. Sandra Stotsky: http://www.uaedreform.org/wp-content/uploads/2000/01/Stotsky-Optional_ELA_standards.pdf. They were judged superior to Common Core by Fordham. (http://edexcellencemedia.net/publications/2010/201007_state_education_standards_common_standards/Massachusetts.pdf).
They are sublime in their simplicity, beautifully organized and logically, age-appropriately sequenced. They won’t take hours and hours of teacher training to master, and they offer an extensive list of authors that corresponds to topics and learning levels.
Here’s an example of why I like Stotsky instead of Appendix B. Stotsky identifies both Louise Erdrich and Scott Momaday. Appendix B prescribes only one Erdrich book: The Birchbark House. Erdrich is a highly acclaimed Native American writer who has written some outstanding novels! Appendix B completely ignores Scott Momaday, of Kiowa descent. He is one of the most famous Native American writers of all time, as well as a recipient of the National Medal of Arts, as well as the Pulitzer Prize. If these incredible writers are so trivialized, what other writers are ignored?
It won’t do to attempt to “fix” the current standards. It would be like pulling out a few parts from a Toyota, and replacing them with some from a Lexus, and expecting the car to run.
ELA Comment #2:
Among the many flaws in Common Core ELA, here is one that should be eliminated: Emphasis on Informational Text. There is zero evidence to support the Core’s claim about the value of Informational reading instruction in English classes. The “research” rests on the opinions of two of the key players in the creation of the English Language Arts standards–David Coleman and Susan Pimentel–and their reliance on and many references to the “2009 reading framework of the National Assessment of Educational Progress (NAEP).” At the time they headed up the Common Core ELA Standards, neither Coleman nor Pimentel had ever taught reading or English in K-12 or at the college level. Neither has a doctorate in English, nor had either of them ever published serious work on K-12 curriculum and instruction.
Speaking of NAEP, the 2013-15 scores for states that adopted Common Core reveal that both reading and math have declined. See http://www.washingtontimes.com/news/2015/nov/11/david-anderson-common-cores-double-whammy/#.VkSx8CCX3UA.twitter.
The Introductions to K-2, 3-5, 6-8, and 9-12 endlessly repeat the call for a heavy emphasis on Informational Text. The term “Informational Text” is cited 30 times in the K-2 standards alone. Beginning in Kindergarten, literature standards are reduced by 50% to make way for 50% focused on Informational Texts. Per the Common Core Introduction, “In K–5, the Standards follow NAEP’s lead in balancing the reading of literature with the reading of informational texts, including texts in history/social studies, science, and technical subjects.” Again, NAEP’s opinion isn’t backed up by any evidence.
Studying and understanding classical literature is far more demanding, complex, and intricate than the “study” of straight-forward factual texts. Classical literature often deals with ambiguity, tone, paradoxes, inconsistencies, ironies, unclear intentions, subtleties, etc. Children are motivated far more by what attracts the imagination than by what appeals to reason. They are deeply concerned with serious questions. They place themselves into the stories they read, where they learn to behave properly and to discern right from wrong. Reading good literature also builds a more interesting vocabulary, and students are exposed to correct spelling, punctuation, and grammar.
English teachers are trained—by college English departments and teacher preparation programs—to teach the four major genres of literature (poetry, drama, fiction, and nonfiction) and the elements of rhetoric, not a large body of fragmented information on a variety of contemporary or historical topics.
Common Core finally removed “internationally benchmarked” from its list of assertions after the public began asking for the evidence. On the other hand, the pre-Common Core Massachusetts standards were in fact internationally benchmarked. See http://pioneerinstitute.org/news/wanted-internationally-benchmarked-standards-in-english-mathematics-and-science/
The pre-Common Core Massachusetts standards, updated and improved, are available online at no cost: See http://www.uaedreform.org/wp-content/uploads/2000/01/Stotsky-Optional_ELA_standards.pdf.
ELA Comment #3:
One of the best analyses of the serious flaws with CC Literature comes from Daniel Katz, Ph.D. in "Dear Common Core English Standards: Can we Talk"? See http://danielskatz.net/2014/09/19/dear-common-core-english-standards-can-we-talk/
Not only does he provide examples—“CC literature standards demonstrate that close textual reading is pretty much ALL that they contain; each of the anchor standard descriptors reiterates the anchors’ focus on the text—to the exclusion of the reader”–but he also provides examples of what Literature standards should be. “For example, Massachusetts has long been recognized as a high performing state on the National Assessment of Educational Progress (NAEP). In 2009, when Common Core was still twinkling in its authors’ eyes, Massachusetts’ 4th grade NAEP reading scores were higher than any other state in the nation. At the time, MA was still using its own English Language Arts framework, adopted in 2001.” These standards were "similar to principles articulated by the Nat’l Council of Teachers of English and the International Reading Assn (NCTE/IRA) in the standards for the English Language Arts that they released in the 1990s.”
Later improved upon by Dr. Sandra Stotsky, she offers the MA standards free, to any state that wishes to incorporate all or parts of them: http://www.uaedreform.org/wp-content/uploads/2000/01/Stotsky-Optional_ELA_standards.pdf.
What you WON’T see anywhere in Common Core ELA is this: “Young students enjoy the predictable patterns, excitement, and moral lessons in traditional and classical stories. In the middle grades, knowledge of the character types, themes, and structures of these stories enables students to perceive similarities and differences when they compare traditional stories across cultures. In the upper grades, students can describe how authors through the centuries have drawn on traditional patterns and themes as archetypes in their writing, deepening their interpretations of these and other authors’ works.”
According to Dr. Katz, even with "shaking the standards really hard," it is impossible to “get something other than close textual reading out of them…then they backwards engineer them from high school all the way down to Kindergarten…when students cannot be expected to have full fluency. “It represents a very specific purpose of reading literature, a purpose that does not serve the reasons why all children read. What Common Core does is take reading literature and purpose it entirely to close textual reading, which is a tool of literary criticism. In New Criticism, the text is treated as self-contained, and it is the job of the reader to investigate it as an object to be understood via the structure of the text and without reference to external resources such as history, culture, psychology or the experiences of the reader."
Citing the work of Louise Rosenblatt http://jlr.sagepub.com/content/1/1/31.full.pdf, he states: “This (Common Core) stands in stark opposition to Reader Response criticism where the role of the reader in creating meaning not only cannot be set aside, but also is absolutely essential for the words on the page to have any meaning whatsoever.”
Even when the standards suggest some form of reading that is connected to something other than the text, it circles right back to "close textual analysis." For example:
Grade 3: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text. (3.RL.2)
He ends his analysis with this statement: "Common Core, however, provides no explicit space for any other kind of reading or analysis, and it appears entirely uninformed by any framework of reading as a process that includes the reader in any capacity other than as faithful seeker of the text’s internally constructed meaning. Readers who want to understand society and history via the text? Readers who want to explore their own humanity across space and time with characters who live and breathe after centuries? Readers who want to enjoy the feelings of a work of art without picking it apart into its component parts?"
Space doesn’t allow me all of Dr. Katz’s examples, but here are a few. You can see the reverse engineering:
Grade 11: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. (11?12.RL.1)
Grade 6: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. (6.RL.1)
Grade 3: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. (3.RL.1)
Kindergarten: With prompting and support, ask and answer questions about key details in a text. (K.RL.1)
ELA Comment #4.
As stated in previous comments, Dr. Daniel Katz points out a fatal flaw that runs through all of the K-12 ELA standards. He noted numerous standards that narrowly focus on a “close textual reading" in which “the text is treated as self-contained, and it is the job of the reader to investigate it as an object to be understood via the structure of the text and without reference to external resources such as history, culture, psychology or the experiences of the reader.” See http://danielskatz.net/2014/09/19/dear-common-core-english-standards-can-we-talk/.
Follows are more statements from K-12 authorities:
Dr. Anthony Esolen: “It is as if Thomas Gradgrind had gotten hold of the humanities and turned them into factory robotics.” https://www.circeinstitute.org/blog/anthony-esolen-common-core-dante-and-more.
Thomas Newkirk, director of the Literacy Institute at the University of NH: “….the model of reading seems to have two stages—first a close reading in which the reader withholds judgment or comparison with other texts, focusing solely on what is happening within ‘the four corners of the text.’ And only then are prior knowledge, personal association, and appraisal allowed in. This seems to me an inhuman, even impossible, and certainly unwise prescription.” https://www.heinemann.com/shared/onlineresources/E02123/Newkirk_Speaking_Back_to_the_Common_Core.pdf.
Dr. Terrence Moore, prof. of history at Hillsdale College, author of The Story-Killers: A Common-Sense Case Against the Common Core: “Either there exists no coherent philosophy of education governing the arrangement of texts within the document, or there does exist a coherent philosophy: that of obscuring the high, powerful truths about virtue, freedom, suffering, and happiness found in great works of Western literature.” http://www.breitbart.com/big-government/2014/01/19/hillsdale-college-professor-terrence-moore-common-core-superficial-biased-embarrassingly-dumb/.
Stacy Stelmack Biscorner, teacher. “The lesson plans that are being required are not only ridiculous, cumbersome, and insulting, they are robbing children of what every competent teacher knows their students need most.. all the children are unique and shouldn’t be spoken to by a robotic adult who treats him as if he’s the next part on the conveyor belt of the public education system.” http://poeticjusticect.com/2015/07/29/its-common-sense-not-common-core-by-stacy-stelmack-biscorner/.
Dr. Sandra Stotsky, the premier ELA standards authority in the U.S. and a member of the Common Core Validation Committee: “Common Core’s division of reading standards make it impossible for Eng teachers to construct a coherent literature curriculum in grades 6-12. Common Core’s standards provide no intellectual base or structure for a literature curriculum and actually prevent one from emerging. A 50 percent quota for nonfiction and informational reading at each grade level means that test developers will shape the English curriculum by means of the kind of ‘informational’ texts they choose." http://www.uaedreform.org/wp-content/uploads/2000/01/Stotsky_Testimony_for_Colorado.pdf
Dr. Stotsky: “Most of Common Core’s college-readiness and grade-level reading standards are content-free skills. Skills training alone doesn’t prepare students for college. They need a fund of content knowledge. But Common Core’s ELA standards (and its literacy standards for other subjects) do not specify the literary/historical knowledge that students need. They provide no list of recommended authors or works, just examples of “complexity.” They require no British literature aside from Shakespeare. They require no authors from the ancient world or selected pieces from the Bible as literature so that students can learn about their influence on English and American literature. They do not require study of the history of the English language. Without requirements in these areas, students are not prepared for college coursework." http://www.uaedreform.org/wp-content/uploads/2000/01/Stotsky-Invited-Testimony-for-Hearing-in-Michigan-on-Common-Core.pdf.
March 2010, before the final CC standards were released, over 300 childhood development experts urged the NGA to suspend the standards for grades K-3, advising that Common Core was “too much too soon” and not supported by research. See http://www.edweek.org/media/joint_statement_on_core_standards.pdf
Clinical psychologist Dr. Megan Koschnick has made presentations regarding the problems with specific standards, especially in the early grades. See Crash Course in Early Child Development: https://www.youtube.com/watch?v=vrQbJlmVJZo and Common Core 101: https://www.youtube.com/watch?v=zs9_d8qFnIA
NY social worker and psychotherapist Mary Calamia testified to the NY State Assembly Education Forum, relating her experiences in treating children who were being subjected to Common Core. See http://stopccssinnys.com/uploads/Al_Graf_-_Mary_Calamia_full_text.pdf.
4 Comments Regarding Arizona’s Common Core Math
Math Comment #1.
According to internationally recognized mathematician Dr. R. James Milgram, math professor emeritus at Stanford University, the only mathematician on the CC Validation Committee, a mathematician so highly regarded that he’s on the NASA advisory council, and who also served on the ad hoc committee of California’s top-rated pre-2010 K-12 Mathematics Standards, students “educated” under Common Core math will be at least two years behind their peers from high-performing countries.
Even Jason Zimba, the lead CC Math developer, admitted that CC will not produce students who are ready for STEM studies: "Common Core is not only not for STEM, it’s also not for selective colleges. For example, for UC Berkeley, whether you are going to be an engineer or not, you’d better have pre-calculus to get into UC Berkeley.”
Marina Ratner, professor emerita of mathematics at Cal-Berkeley and one of the top mathematicians in the world wrote: “…students taught in the way that these standards require would have little chance of being admitted to even an average college and would certainly struggle if they did get in.”
She also stated, "For California, the adoption of the Common Core standards represents a huge step backward which puts an end to its hard-won standing as having the top math standards in the nation."
It is indisputable that Common Core math fails to prepare children for STEM studies and for admission to selective public and private colleges or studies in the humanities. This will hurt low-income students the most. Well-to-do families will enroll their children in private schools or pay for private tutoring or private summer school courses to ensure that their children have the proper preparation.
Some colleges will lower their standards and realign with Common Core. Selective universities will not; they will fill their student slots with children from states with high standards, from private schools, home-school, and foreign countries.
Ironically, one stated purpose of the RTTT competition was to prepare more students for STEM study and careers and to address the needs of underrepresented groups in these fields! To attain this goal, a full Algebra I course must be placed in the eighth grade – as agreed even by the Benchmarking for Success report that NGA and CCSSO used to justify Common Core in the first place!
If children are prepared to take Algebra I by the start of the eighth grade, they can progress comfortably to calculus in the twelfth grade. The experience of states that have placed Algebra I in eighth bears out the wisdom of this move. About 15 years ago, California moved Algebra I from ninth to eighth grade, and the number of students rated proficient and above in Algebra II increased by 240%. Moreover, the “achievement gaps” – the differences in scores for various demographic groups — narrowed. But despite this evidence, and unlike high-performing countries, CC delays Algebra I until ninth grade.
Any “accelerated path” allowed by CC — teaching three years of math in the last two years of grade school or the first two years of high school – favors students from well-to-do families, who can afford extra resources.
Beyond the delay in teaching Algebra I, CC math excludes certain Algebra II and geometry content that is currently a prerequisite at almost every four-year state college, as well as vast swaths of trigonometry.
So much content is missing from the CC algebra series that students will be unprepared for trigonometry, let alone pre-calculus. To make matters worse, CC math teaches geometry using an experimental system that has never been implemented successfully in K-12. Even Fordham Institute reported that “the geometry standards represent a significant departure from traditional axiomatic Euclidian geometry and no replacement foundation is established.”
That this failed approach is now, through CC, our national system of teaching geometry is bizarre.
The problems with CC begin in Kindergarten and extend through the eighth grade. In the lower grades, CC promotes “reform,” or “fuzzy,” math, thereby telling teachers "how to teach." It deemphasizes standard algorithms and confuses children about the best way for approaching a problem. The “learning progression” is delayed, so that children are not prepared to take Algebra I by the start of eighth grade.
The result will be an increase in the number of children who supposedly have some “conceptual understanding” of math but who can’t actually work math problems. This is a near certainty, because this happened in California in the 90’s when that state adopted essentially the same approach as CC. It was a disaster.
Why would Arizona now choose to go down a path that has been a demonstrable failure elsewhere? Under CC, this is a failure that puts each child in front of a train wreck twelve years in the making.
Math Comment #2: excerpted from a document by Dr. R. James Milgram and Ze’ev Wurman. See http://deltanewsweb.com/archives/images_2015/cc4.pdf.
Kindergarten – Grade 7
• CC does not require proficiency with addition and subtraction until Grade 4 (a grade behind our international competitors).
• CC does not require proficiency with multiplication using the standard algorithm (step-by-step procedure for calculations) until Grade 5 (a grade behind standard expectations)
• CC does not require proficiency with division using the standard algorithm until Grade 6 (two grades behind our international competitors).
• CC starts teaching decimals in Grade 4 (about two years behind the more rigorous states).
• CC fails to teach in K-7 key geometrical concepts (e.g., sum of angles in a triangle, isosceles and equilateral triangles, etc.).
• CC excludes fluent conversion between different forms of fractions – regular fractions, decimals, and percents.
• CC fails to teach prime factorization. Consequently, it does not include teaching about least common denominators or greatest common factors.
• Compound interest and the associated formula, (x A (n+l) – l)/(x-l) = 1 + x + x A 2 + … + x A n . This is or used to be a seventh grade or at latest, eighth grade topic.
Algebra 1: Missing components needed for Algebra 2 and Calculus
1. Division of monomials and polynomials (only addition/subtraction/multiplication are covered).
2. Derivation and understanding of slopes of parallel and perpendicular lines.
3. Manipulation and simplification of rational expressions.
4. Multi-step problems with linear equations and inequalities.
5. Multi-step problems with four operations between polynomials.
6. Multi-step problems involving manipulation of rational expressions.
7. Solving two linear inequalities in two variables and sketching the solution sets. The following were added to California’s Common Core version:
8. Solve problems with equations and inequalities with absolute value.
9. Solve problems with quadratic expressions.
Algebra 2: Some key topics missing
1. Writing quadratic polynomials in two or three variables as sums or differences of perfect squares. (KEY for the study of conic sections, which, in turn, underlies almost everything that is done in STEM areas.)
2. Detailed study of surfaces of revolution coming from quadratic polynomials as described above. In particular, the focus here should be on parabolic mirrors and their applications.
3. Introduction of the foci and the directorix for conies and their applications to parabolas and parabolic mirrors, and also for ellipses and elliptic surfaces with applications to things like whispering galleries and Kepler’s laws.
4. Definition and implications of the eccentricity for conic sections.
5. Structure of logarithms to base 10, e, or general base, b. Conversion between bases, calculation of explicit values in simple cases.
Geometry: Some key topics missing (Properties of triangles and circles)
1. Students should know that every triangle is circumscribed by a unique circle with center at the intersection point of the three perpendicular bisectors of the edges (also, that all three DO intersect in a single point).
2. They should know that every right triangle has the center of the circumscribing circle on its hypotenuse, and conversely.
3. They should know that the angle subtended by an arc on the circle (the angle obtained by drawing the two lines from the center to the ends of the arc), is twice the angle subtended by the ends of the arc and any point in the complement of the arc.
Pre-calculus and/or Algebra 2 and trigonometry: Key topics missing
1. Partial fraction decomposition of relatively simple rational functions and their graphs. Specifically, Understand that a function of the form (ax + b)/((x-r)(x-s)) can always be written as a sum (l/(x-r)) + (m/(x-s)), where, in this case 1 + m = a, and rm + Is = -b. Apply this to the determination of the graphs of such functions.
2. Graph functions in polar coordinates. Key examples, circles (r = 2cos(t)), Cardioids (2 + 2cos(t) = r), Rose petal curves (r = sin5t), lemniscate (rA2 = 4sin(2t)).
Algebra 2: Missing components needed for Calculus
• Composite functions
• combinations and permutations
• finite and infinite arithmetic and geometric sequences
• mathematical induction.
Note that all four topics above are quite "formal" in line with the overly formal treatment of algebra in Core Standards. The topics sketched in above are much more "realistic" in terms of the actual needs of students wishing to major in ANY technical area in college.
Math Comment #3:
Common Core’s math standards, like most of the Common Core standards, are verbose, indirect, and convoluted. They are also annoyingly prescriptive, telling teachers how to teach the standards. For example: “Represent addition and subtraction with objects, fingers, mental images, drawings , sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.” And another: “Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). Also, Common Core requires 5- and 6-year old’s to “think algebraically.” That requires a fully developed prefrontal cortex, a part of the brain that is not fully functional until early adulthood. See http://stopccssinnys.com/uploads/Al_Graf_-_Mary_Calamia_full_text.pdf.
The following simple, straightforward standards are taken from a set of standards that Fordham said: “…could well serve as a model for internationally competitive national standards. They are explicit, clear, and cover the essential topics for rigorous mathematics instruction." See California’s K-12 Math standards, rated “A” by Fordham, page 61 of http://edex.s3-us-west-2.amazonaws.com/publication/pdfs/SOSSandCC2010_FullReportFINAL_8.pdf.
Please note that these standards are just that: Standards. They don’t dictate curriculum, and they don’t require hours and hours of teacher training.
By the end of kindergarten, students understand small numbers, quantities, and simple shapes in their everyday environment. They count, compare, describe and sort objects, and develop a sense of properties and patterns.
1.0 Students understand the relationship between numbers and quantities (i.e., that a set of objects has the same number of objects in different situations regardless of its position or arrangement):
1.1 Compare two or more sets of objects (up to ten objects in each group) and identify which set is equal to, more than, or less than the other.
1.2 Count, recognize, represent, name, and order a number of objects (up to 30).
1.3 Know that the larger numbers describe sets with more objects in them than the smaller numbers have.
2.0 Students understand and describe simple additions and subtractions:
2.1 Use concrete objects to determine the answers to addition and subtraction problems (for two numbers that are each less than 10).
3.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones and tens places:
3.1 Recognize when an estimate is reasonable.
Algebra and Functions
1.0 Students sort and classify objects:
1.1 Identify, sort, and classify objects by attribute and identify objects that do not belong to a particular group (e.g., all these balls are green, those are red).
Measurement and Geometry
1.0 Students understand the concept of time and units to measure it; they understand that objects have properties, such as length, weight, and capacity, and that comparisons may be made by referring to those properties:
1.1 Compare the length, weight, and capacity of objects by making direct comparisons with reference objects (e.g., note which object is shorter, longer, taller, lighter, heavier, or holds more).
1.2 Demonstrate an understanding of concepts of time (e.g., morning, afternoon, evening, today, yesterday, tomorrow, week, year) and tools that measure time (e.g., clock, calendar).
1.3 Name the days of the week.
1.4 Identify the time (to the nearest hour) of everyday events (e.g., lunch time is 12 o’clock; bedtime is 8 o’clock at night).
2.0 Students identify common objects in their environment and describe the geometric features:
2.1 Identify and describe common geometric objects (e.g., circle, triangle, square, rectangle, cube, sphere, cone).
2.2 Compare familiar plane and solid objects by common attributes (e.g., position, shape, size, roundness, number of corners).
Statistics, Data Analysis, and Probability
1.0 Students collect information about objects and events in their environment:
1.1 Pose information questions; collect data; and record the results using objects, pictures, and picture graphs.
1.2 Identify, describe, and extend simple patterns (such as circles or triangles) by referring to their shapes, sizes, or colors.
1.0 Students make decisions about how to set up a problem:
1.1 Determine the approach, materials, and strategies to be used.
1.2 Use tools and strategies, such as manipulatives or sketches, to model problems.
2.0 Students solve problems in reasonable ways and justify their reasoning:
2.1 Explain the reasoning used with concrete objects and/or pictorial representations.
2.2 Make precise calculations and check the validity of the results in the context of the problem.
Math Comment #4:
Homeschool mother Gina Ray provided you with simple, streamlined, standards for Kindergarten math. She removed age-inappropriate standards; overly prescriptive "how to’s" that outrageously tell teachers how to teach; redundancies; and what she calls "goobly-goosh."
I recently sent you Kindergarten math standards taken directly from California’s A rated pre-2010 Kindergarten Math Standards, that Fordham said “…could well serve as a model for internationally competitive national standards. They are explicit, clear, and cover the essential topics for rigorous mathematics instruction." See page 61 of http://edex.s3-us-west-2.amazonaws.com/publication/pdfs/SOSSandCC2010_FullReportFINAL_8.pdf. However, these offered by Ms. Ray also look great.
Counting and Cardinality.
Know number names and the count sequence (0 to 100).
Count to tell the number of objects (0 to 100).
Know how to group numbers in tens.
Solve addition and subtraction word problems within 10.
Fluently add and subtract within 5.
Number & Operations in Base Ten
Demonstrate an understanding that numbers 11 and above are composed of tens and ones.
Measurement & Data
Describe and compare measurable attributes.
Compare two objects.
Introduce charts and graphs to compare two objects.
Identify and describe shapes. Correctly name them regardless of their orientations or size. Describe relative position of objects (such as above, below, beside, in front of, behind, and next to).
Compare shapes of all kinds (two-dimensional and three dimensional). Describe similarities and differences of the attributes of shapes (corners, number of sides, having sides of equal length, etc.)
Compose and decompose simple shapes (such as two rectangles forming a square and vice versa).
Ms. Ray has also suggested the following, which is taken from the Core Knowledge Sequence developed by Dr. E. D. Hirsh, Jr. In fact, all of the Core Knowledge standards are far superior to the CCS…easy to understand and have been time proven. See http://www.coreknowledge.org/mimik/mimik_live_data/view.php?id=1833&record_id=337
Patterns and Classification
Establish concepts of likeness and difference by sorting and classifying objects according to various attributes: size, shape, color, amount, function, etc.
Define a set by the common property of its elements.
In a collection of objects that includes a given set and an item that does not belong, indicate which item does not belong.
Moving from concrete objects to pictorial representations, recognize patterns and predict the extension of a pattern.
Extend a sequence of ordered concrete objects.
Identify pennies, nickels, dimes, and quarters.
Identify the one-dollar bill.
Identify the dollar sign ($) and cents sign (¢).
Write money amounts using the cents sign (¢).
Here’s the link to Ms. Ray’s complete analysis: http://www.gilbertwatch.com/tasks/sites/gilbertwatch/assets/File/The%20Common%20Core%20State%20Standards%2C%20My%20Suggested%20Revisions%20as%20a%20Homeschooling%20Parent%20(2).pdf