NEBRASKA’S NEW MATH STANDARDS — TWIN SISTER TO COMMON CORE
3.13.15 — “Nebraska’s New Math Standards – Twin Sister to Common Core”
In an attempt to share his concerns about Nebraska’s new math standards which are “twin sisters” to the Common Core Math Standards, Nebraskan Henry W. Burke (a civil engineer) presented both his written report and oral comments to the Nebraska State Board of Education (SBOE) on March 6, 2015.
Mr. Burke’s oral comments to the SBOE begin at marker 17:10 and end at 27:08:
LINK TO VIDEO CLIP: http://www.education.ne.gov/Movies/Stateboard/mar_2015_board_meeting.mp4
Mr. Burke’s written report follows.
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Nebraska Math Standards and NCLB WAIVER
By Henry W. Burke
3.4.15
Math teacher (and former principal) Nakonia Hayes described how Americans’ eyes glaze over at the mere mention of the word “math.” She said:
Too many claim they don’t like math, can’t do math, or don’t want even to think about math. This phenomenon is found only in America. Interestingly, such attitudes are not heard in Third World countries that produce strong math students.
http://www.educationviews.org/recognizing-american-hero-john-saxon/
Is the State of Nebraska, through the Nebraska Department of Education, improving students’ math abilities or is the State losing ground? Are the Nebraska Math Standards getting better or worse?
- Henry Burke Presentations to the Nebraska SBOE
Table 1. – Henry Burke’s Presentations to Nebraska State Board
Item
No. |
SBOE
Meeting |
Subject |
1 | Oct. 2013 | Common Core Standards |
2 | Nov. 2013 | Suggested Texas TEKS for NE ELAR Standards |
3 | Dec. 2013 | NAEP Results, Evaluated NE ELAR Standards |
4 | Jan. 2014 | Common Core Math in Nebraska |
5 | Feb. 2014 | Suggested English Success Standards for Nebraska |
6 | Mar. 2014 | Suggested Saxon Math for Nebraska |
7 | Apr. 2014 | Nebraska Is Building on the Wrong Foundation –
Nebraska ELAR Standards |
8 | May 2014 | Reject and Replace NE ELAR Standards with English Success Standards |
9 | Sep. 2014 | Nebraska Should Not Seek NCLB Waiver |
10 | Oct. 2014 | Reject AP U.S. History (APUSH) |
- Nebraska Math Standards Are Behind Schedule
Nebraska law (State Statute 79.760.01) requires that academic content standards be reviewed every five years. The current Nebraska Mathematics Standards were approved by the State Board of Education on October 8, 2009. If my “non-Common Core math” is correct, the new math standards should have been approved by October 2014. English standards were updated last year, but the math standards were postponed until 2015.
Based on last year’s actual revision schedule for the English standards, I can guess that the Nebraska Department of Education (NDE) will release the Proposed Nebraska Mathematics Standards this spring (within a few months), and the Math Standards will be adopted by the State Board at the August 2015 SBOE Meeting. Therefore, the Nebraska Math Standards will be revised and adopted one year late!
- McREL Alignment Study for Math
The Nebraska Department of Education contracted with McREL (Mid-Continent Research for Education and Learning) to conduct an alignment study between the 2009 Nebraska Standards and the Common Core Standards (CCS). In May 2012, the NDE issued a contract for $47,900 to McREL to perform the comparison for Nebraska’s English and Math Standards; the reports were issued in September 2013. These are the links (URLs) to the McREL Executive Summary and full report for Mathematics:
http://www.education.ne.gov/documents/HomePage/Math_Executive_Summary_McREL_Alignment_Study.pdf
http://www.education.ne.gov/documents/HomePage/Math_NE_to_CC_Final2013.pdf
Table 2. — McREL Alignment: 2009 Nebraska Math Standards with CCS
Grade | Percent of CCS
Addressed by NE |
K | 86 % |
1 | 100 % |
2 | 96 % |
3 | 100 % |
4 | 100 % |
5 | 100 % |
6 | 100 % |
7 | 96 % |
8 | 100 % |
High School | 61 % |
Algebra 1 | 83 % |
Geometry | 88 % |
Algebra 2 | 68 % |
Advanced Topics | 13 % |
As the percentages show, strong agreement was observed between the 2009 Nebraska Math Standards and the Common Core Standards (CCS) in K-8 grades; agreement dropped off somewhat in High School. Nearly all of the Advanced Topics in CCS Math were not addressed by the Nebraska Math Standards. The chief differences between the two sets of standards were mainly in the (1) organization and placement of concepts and (2) specificity.
Clearly, Nebraska’s weak, Type #2 Math Standards are very similar to the very poor Type #2 Common Core Standards. It is like comparing one dilapidated car to another car that barely runs; one might be better, but they are both clunkers!
The NDE has a long track record of wasting taxpayer money on contracts with biased organizations. In 2008, the NDE awarded a $50,000 contract to McREL and a $50,000 contract to Achieve, Inc. to evaluate the Nebraska Standards. (Achieve was a primary author of the Common Core Standards.) Because those organizations promote poor Type #2 education, they gave a predictably mild evaluation of the Nebraska Standards. Both groups offered few substantive comments for change, while they included enough empty language to justify their $50,000 fees.
- Fordham Evaluation of Nebraska Math Standards
The Thomas B. Fordham Institute evaluated all of the state standards in 2010. In this survey, Fordham gave the 2009 Nebraska Mathematics Standards a grade of “C” and called the Nebraska Standards “mediocre.” On Clarity and Specificity, Fordham scored Nebraska 2 out of 3; on Content and Rigor, Fordham scored Nebraska 3 out of 7.
http://edex.s3-us-west-2.amazonaws.com/publication/pdfs/SOSSandCC2010_FullReportFINAL_8.pdf
Because Fordham has taken over $7 million in Gates Foundation funding, Fordham has developed a distinctly pro-Common Core bias. Accordingly, Fordham is no longer considered to be an objective, un-biased organization; and we should not use any of their evaluations after 2009 or 2010.
- Common Core Math Is Horrible!
- Kansas Math Scores Drop under Common Core
Ze’ev Wurman, former U.S. Department of Education official under President George W. Bush, recently refuted the Common Core talking points that the standards are “higher” and more “rigorous” than others. (Wurman testified before the Kansas Legislature in February.) Wurman stated the following about Kansas’ experience with Common Core Math:
Just this Monday I testified in Kansas about the fact that while Fordham rated the old Kansas standards at C for English and F for mathematics, Kansas student achievement on the NAEP under those “undemanding” standards was solidly in the upper half in Reading and solidly in the top 5 in the nation in math (remember that “F” grade?).
On the 2013 NAEP however, Kansas took a dive under the new “excellent” Common Core and now is barely in the upper half in math, and below the national average in Reading. And the performance of minorities in Kansas was hit much worse — Hispanic 4th graders plummeted from #14 on Reading in the nation to #28, and Black 8th graders went from being #10 to #38. In math Black and Hispanic 4th graders went from being numbers 2 and 3 in the nation, to being numbers 12 and 10 respectively. Kansas students from low-income levels went from #3 in 2007 to #8 under Common Core.
In other words, Fordham’s presumption that its grading of the standards is meaningful, and that its pinning the medal of excellence on the Common Core — or medal of shame on states like Kansas — justifies its support for federal and state education bureaucracies lacks empirical evidence. Kansas did rather well with all of its students until the Common Core came along, and then the bottom fell out.
Under Kansas’ old standards, Kansas students were in the top 5 in the nation on the 2007 NAEP math tests. Under Common Core, Kansas students were barely in the upper half in math on the 2013 NAEP tests. Clearly, Kansas students did more poorly once Common Core was introduced in the schools.
- Common Core Math Hurts Minority Students
I wrote about the NAEP and ACT test scores in my December 2013 report to the Nebraska State Board of Education (SBOE). When I made this exhaustive study of the national tests, I was struck by the huge achievement gaps between White students and Minority students (primarily Blacks and Hispanics).
On the national level for NAEP Mathematics, the achievement gaps between Whites and Minority students have remained essentially unchanged for the last three tests (2005, 2009, and 2013). The achievement gaps for Whites-Blacks in average scale scores were 31 in 2005, 30 in 2009, and 30 in 2013. For Whites-Hispanics, the achievement gaps were slightly less at 24 in 2005, 23 in 2009, and 21 in 2013.
http://www.nationsreportcard.gov/reading_math_g12_2013/#/changes-in-gaps
For Nebraska, Grade 8 Math students, the White-Black achievement gap for 2013 was 42 (292 – 250 = 42). The White-Hispanic achievement gap was 25 in the 2013 NAEP tests (292 – 267 = 25).
Competent math teachers know that students excel in math when the students are prepared to take Algebra 1 in the 8^{th} grade. Because the Common Core Standards (CCS) delay Algebra 1 until high school, the CCS students will not reach the higher math courses. An excellent report by Ze’ev Wurman determined:
…preparation of all K-7 students to take an Algebra 1 class in grade 8 benefits the minority and disadvantaged students the most. The explanation seems pretty obvious. When grade 8 Algebra is considered an accelerated course, students that get the required acceleration—tutoring, home support—come mostly from advantaged households. Only when everyone is prepared in grades K to 7 to reach algebra in grade 8 do the disadvantaged students get their chance to shine.
…early Algebra-taking translates directly into increased successful taking of advanced mathematics in high school—not only Geometry and Algebra 2 but even Advanced Placement Calculus AB and BC courses.
But the true travesty of the Common Core is its failure to deliver on its promise of a genuine Algebra course in grade 8, and the devastating impact that failure is bound to have on the achievement of minorities and disadvantaged students.
- Common Core Math Does Not Support STEM Careers
The Common Core proponents often tout how the standards will prepare students for careers in STEM (Science, Technology, Engineering, and Math). Common Core Math basically ends with a very incomplete Algebra 2 course. Because Common Core Math does not include trigonometry or calculus, students will not be prepared for STEM studies when they enter college.
Jason Zimba, one of the lead authors of Common Core Math, even admitted that CCS does not prepare students for STEM. Zimba told the Massachusetts Board of Elementary and Secondary Education that the new standards would not prepare students for colleges to which “most parents aspire” to send their children.
I recently checked the engineering requirements at a number of colleges and universities. Almost all of them required incoming freshman students to have taken four years of high school math, preferably through calculus. This means entering college freshmen with a Common Core background will have to take “remedial,” non-credit courses before they can begin their engineering studies (hence, more time and money).
- Common Core Math Is Not Internationally Benchmarked
The most outrageous statement by the Common Core advocates is that the Common Core Standards are internationally benchmarked. They are not! The Common Core Standards fail miserably when compared with the standards of high-achieving countries.
Dr. James Milgram of Stanford University was selected to be on the Common Core Validation Committee. Because he found the Common Core Standards to be so deficient and without merit, he refused to validate the CCS Math Standards. Both Dr. Milgam and Dr. Sandra Stotsky were on the Common Core Validation Committee; and both refused to sign off on the Common Core Standards. Milgram and Stotsky never received any proof to support the “internationally benchmarked” claim.
[R. James Milgram is professor of mathematics emeritus, Stanford University. He was a member of Common Core’s Validation Committee 2009-2010. Sandra Stotsky is professor of education reform emerita, University of Arkansas. She was a member of Common Core’s Validation Committee 2009-2010.]
Dr. Milgram frequently points out how the Common Core “reform math” techniques stand in stark contrast with the traditional techniques employed by the highest-achieving countries. The U.S. lags other countries and will fall even further behind under Common Core.
One of the Common Core authors (Bill McCallum) has admitted that CCS does not compare very well with other countries. Marina Ratner, a mathematician, wrote in the Wall Street Journal:
I learned that at the 2010 annual conference of mathematics societies, Bill McCallum, a leading writer of Common Core math standards, said that the new standards “would not be too high” in comparison with other nations where math education excels.
The Common Core standards will move the U.S. even closer to the bottom in international ranking.
- Common Core Authors Have a Poor Track Record
In testimonies around the country, Dr. Milgram has said that one of the authors of the Common Core Math Standards was one of the writers of the 1992 California Math Standards. Those standards caused California to fall to 49^{th} in the nation; the unfortunate students learning under those standards could not recover; and they would never reach adequate math levels.
http://www.nevadaappeal.com/news/14623693-113/common-core-debated-in-carson-city
According to Professor Milgram, only a third of those California students could graduate from college and only two percent could earn a degree in STEM (science, technology, engineering, or math). Because the Common Core Math Standards are the equivalent of those horrible 1992 California standards, the future looks rather bleak for the United States.
Dr. Susan Berry recently said this about the Common Core authors:
There is no official information about who selected the individuals to write the Common Core standards. None of the writers of the math and English Language Arts standards have ever taught math, English, or reading at the K-12 level. In addition, the Standards Development Work Groups did not include any members who were high school English and mathematics teachers, English professors, scientists, engineers, parents, state legislators, early childhood educators, and state or local school board members.
- Common Core Math Is “Reform Math” under a New Name
Common Core Math is simply a rehash of concepts from yesteryear (e.g., “reform math,” “new math,” and “fuzzy math”). Because those Type #2 techniques were dismal failures back then, why would we think they could be successful this time?
Common Core Math includes fewer standards than many good state standards. To counter its critics, the CCS proponents claim the math standards are “deeper” and more “rigorous.” With Common Core Math stopping somewhere in Algebra 2, these claims are factually wrong. Simple concepts are made artificially more complex, with the pretense of being deeper.
The Common Core writers were enthralled with models and model drawing. With all of the model drawing, little time is left to cover geometry and other important topics. The students are constantly told to draw models to answer trivial questions, such as finding 20 % of 80. A student who gives the correct answer right away (and does not draw a picture) loses points. Of course, Common Core textbooks are saturated with pictures, diagrams, and elaborate word problems.
- Common Core Math Is Very Expensive
I have devoted much time to calculating the costs to implement the Common Core Standards in each of the CCS states. This work is based on an excellent Pioneer Institute white paper. Professor Ratner (professor emerita of mathematics at California Berkeley) made these insightful comments about the cost of Common Core:
The teaching of math in many schools needs improvement. Yet the enormous amount of money invested in Common Core—$15.8 billion nationally, according to a 2012 estimate by the Pioneer Institute—could have a better outcome. It could have been used instead to address the real problems in education, such as helping teachers to teach better, raising the performance standards in schools and making learning more challenging.
- Build the Nebraska Math Standards on a Strong Foundation
I covered many of the basic concepts about the writing and organizing of standards elements in previous reports and in presentations to the Nebraska State Board. In this case, I will apply these concepts to the Nebraska Math Standards.
Attributes of Good State Standards
Very few state standards are truly exemplary. As I have previously demonstrated, the Common Core Standards and the Nebraska English Standards definitely fail to make the grade.
In order to have excellent state standards, they need to be:
- Explicit
- Knowledge-based
- Academic
- Clearly-worded
- Grade-level specific
- Measurable
If state standards comply with the six criteria listed above, teachers will not have to second-guess the standards writers. School districts will not need to hire expensive consultants to “interpret” the standards nor to develop curriculum; it will be readily apparent what is required for each and every grade (and course). Similarly, the school districts will save money that otherwise would be spent with Educational Service Units (ESU’s).
Type #1 and Type #2 Education
Long-time, experienced educators know that there are basically two philosophies of education (i.e., Type #1 and Type #2). Nearly all educators, curricula, vendors, lobbyists, organizations, and advocacy groups fall into either Type #1 or Type #2.
Basically Type #1 means the curriculum standards are traditional/knowledge-based/academic, emphasize back-to-the-basics core knowledge and skills that grow in depth and complexity from one grade level to the next, are specific for each grade level (or course), and can be tested largely through objective questions that have right-or-wrong answers.
Exemplary education standards must be Type #1!
Common Core Standards as well as school-to-work, outcome-based education, CSCOPE, etc. are examples of Type #2.
With Type #2 education, students work in groups, receive group grades, and receive project-based learning (constructivism). Tests (assessments) have many subjective questions with few if any right or wrong answers; the people scoring the tests determine what is correct.
A handy chart provides the characteristics of Type #1 and Type #2 education:
Start the Standards Development Process with Exemplary Standards
Because I have criticized the existing and proposed Nebraska Standards, I believe it is important for me to offer some positive suggestions to do it the right way. The first suggestion is to start with exemplary Type #1 Standards.
- Use the Texas Math TEKS Standards as a Base
- At the November 2013 Board Meeting, I suggested that the SBOE adopt the Texas ELAR Standards. I also suggested that Nebraska should examine the Texas Mathematics Standards. Links to the Texas Math TEKS (Texas Essential Knowledge and Skills) and related articles:
http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
http://www.educationviews.org/nakonia-hayes-texas-math-standards/
http://www.educationviews.org/drill-2012-teks-math-process-standards-strike-traditional-bedrock/
- Incorporate Saxon Math into the Math Standards
At the March 2014 State Board Meeting, I suggested that the Board should include Saxon Math in the Proposed Math Standards. In an article, “Making the Simple Complicated — Common Core Math,” education expert Donna Garner stated:
What was wrong with the math that our American astronauts learned when they were the first to put a man on the moon?
I still stand by Saxon Math as the best way to teach students. Saxon Math introduces concepts in tiny pieces and then spirals students’ mastery through continuous practice on new and previous concepts. Reform math programs take concepts in bigger chunks but do not bother to establish mastery as students proceed along.
Resources for Saxon Math:
http://www.educationviews.org/hayes-saxon-math-fuzzy-common-core-math-wrong/
http://news.heartland.org/newspaper-article/2014/02/26/nakonia-hayes-john-saxon-and-math-wars
http://saxonhomeschool.hmhco.com/en/resources/result.htm?title=Placement
http://www.amazon.com/Math-54-Saxon-4/dp/1565772970/ref=sr_1_3?ie=UTF8&s=books&qid=1229091864&sr=1-3
Make the Standards Writing Team Focus on Type #1
The NDE should assemble a writing team of experienced classroom teachers and educators, made up preferably of those who are currently in the classrooms each day. Tell them that the final standards must be traditional, classical Type #1 standards. Make sure that they clearly understand the differences between Type #1 and Type #2 educational philosophies.
Focus on the six attributes of exemplary Type #1 state standards. The standards must be: explicit, knowledge-based, academic, clearly-worded, grade-level specific, and measurable. Do not let the writing team wander away from these basic tenets. For example, do not let the standards fall into the Type #2 trap (how the student feels about something, the student’s opinion on an issue, personal beliefs, etc.). Standards must be knowledge-based!
Give the Math writing teams the two documents mentioned previously (Texas Math TEKS and Saxon Math information); and encourage the writing team to go through the Texas document, pulling out the elements that would be good for Nebraska students.
As the writing team is preparing the standards, members must constantly be reminded to follow the six tenets of good Type #1 standards, checking constantly to see that proper scope and sequence are occurring within each grade level and between each grade level.
Assumptions about the NDE
Based upon the past, I assume the Nebraska Department of Education (NDE) is taking the same approach that it has always used – revising the existing standards rather than starting with a clean slate. For the new Proposed Math Standards, I expect the NDE will simply revise and tweak the existing 2009 Nebraska Mathematics Standards.
Because the 2009 Math Standards are weak Type #2 standards, they make a poor foundation for the new standards.
- The 2009 Nebraska Mathematics Standards Are Type #2
I will briefly examine the existing 2009 Nebraska Mathematics Standards to illustrate their weak Type #2 nature. I will include actual examples from the 2009 Standards to illustrate how the existing document fails to meet the six tenets of good standards.
- Explicit
This standard is repeated for Grades K-2:
Students will demonstrate the meaning of addition and subtraction with whole numbers.
How can students demonstrate the concept if they cannot make the computations?
- Knowledge-based
Under Computation, this standard is repeated for every grade from K-High School:
Students will compute fluently and accurately using appropriate strategies and tools.
This general standard does not exemplify good, knowledge-based standards.
- Academic
This standard was listed for Grade 1:
Use objects, drawings, words, and symbols to explain subtraction as a separate action.
This standard is not academic and appropriate for a first grade student.
- Clearly-worded
This standard is shown for Grade 1:
Use concrete, pictorial, and verbal representations of the commutative property of addition.
Would teachers and students consider this standard clearly-worded?
- Grade-level specific
When the same standard is listed for every grade, it is not grade-level specific. Also, the 2009 Math Standards include standards for Grades K-8 and High School. As in prior years’ standards, the NDE does not list grade-level specific standards for Grades 9, 10, 11, and 12. Without specific standards for each grade, teachers will have to guess what should be covered in a particular grade; and there will be no real accountability at each grade level for teachers nor for their students.
- Measurable
This standard appears under Grade 6:
Represent a variety of quantitative relationships using symbols and words.
This is a Grade 5 standard:
Students will determine theoretical probabilities.
These standards are not measurable and are not age-appropriate for 5^{th} and 6^{th} grade students.
If the NDE builds the new proposed Math Standards on the weak, Type #2 foundation of the 2009 Math Standards, a flimsy structure will be created. How can we improve the outcomes for Nebraska students when we provide weak state standards?
- NCLB Waiver Request
The Agenda for the March 2015 State Board Meeting includes the following item:
7.3. Approve the ESEA Flexibility assurances and authorize the Commissioner to complete and submit a Waiver from NCLB requirements by March 31, 2015
This makes it very clear that the NDE will submit an NCLB Waiver Request (ESEA Flexibility Request), presumably to avoid the onerous provisions of the No Child Left Behind (NCLB) law.
In my 9.3.14 report to the State Board, “Nebraska Should Not Seek a No Child Left Behind Waiver,” I stated:
The NCLB waiver pact is a ruse! Any short-term relief that the states gain will come at the expense of yielding unprecedented amounts of authority to the U.S. Department of Education (USDOE).
I also explained that a state applying for this illegal waiver must choose either Option A – Common Core Standards or Option B – College and Career-Ready Standards. Presumably, Nebraska will not opt for the Common Core Standards; that leaves Option B. To be eligible for Option B, the state must have College and Career-Ready Standards that have been approved by the Institutions of Higher Education (IHE) in the state.
Nebraska obtained the IHE “College and Career-Ready Standards” designation for the new English Standards last year. I do not think the Nebraska IHE organization would grant the College and Career-Ready Standards designation on the existing 2009 (out-of-date) Math Standards. How will this problem be handled in the Nebraska Waiver Request?
I made the following points in the Conclusion to my 9.3.14 report:
Nebraska should not seek a No Child Left Behind waiver (or ESEA Flexibility Request) for the following reasons:
- Nebraska scored very poorly in the Race to the Top competitions (No. 39 in Phase 1 and No. 31 in Phase 2). The state will likely get a low score in the ESEA Waiver Request.
- Nebraska might be “forced” into adopting the Common Core Standards to score some points on the ESEA Waiver Request.
- Through the waiver and Common Core, Nebraska would completely lose state and local control over the schools.
- The NCLB waiver will drastically increase federal intervention in our schools.
- Because Common Core is curriculum, Nebraska’s possible adoption of Common Core would usher Common Core curriculum, assessments, teacher evaluations, and CCS indoctrination into our public schools. Nebraska should have no part of it.
- Nebraska’s accountability system will not measure up to the USDOE criteria.
- The NCLB waiver is illegal and a classic case of federal overreach.
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Bio for Henry W. Burke
Henry Burke is a Civil Engineer with a B.S.C.E. and M.S.C.E. He has been a Registered Professional Engineer (P.E.) for 37 years and has worked as a Civil Engineer in construction for over 40 years.
Mr. Burke had a successful 27-year career with a large construction company.
Henry Burke serves as a full-time volunteer to oversee various construction projects. He has written numerous articles on education, engineering, construction, politics, taxes, and the economy.
Henry W. Burke
E-mail: hwburke@cox.net
I have been a math tutor at a school for kids who have failed miserably in public schools. I can attest to the excellence of Saxon math. With Saxon, even kids who may have been mathematically illiterate when they entered, leave the eighth grade knowing Algebra. The Saxon program was bought out by Houghton Mifflin. I can’t verify that they haven’t tampered with it, so I can only endorse the original Saxon program.
The new owners of Saxon Math have not tampered with K-8, although they are offering supplements of Common Core information to “support” Saxon. (No Saxon teacher will bother with such stuff.) The high school algebra texts have been changed, so I encourage people to buy the third editions, published in 2003, or even earlier editions. The newly-created Saxon Geometry is not a John Saxon product, so I would not use it. The Algebra 1/2, Advanced Math, and Calculus textbooks are still okay.
Henry,
This is a masterpiece of clarity, resources, and examples of why Nebraska’s Board of Education should pay honest attention to your suggestions. Also, thanks for giving John Saxon the respect he is due as a true hero of K-12 math education and the one resource that could help pull American kids from the lower rungs of mathematics performance.
I want to add a couple of comments regarding Nebraska’s present EXTREMELY fuzzy math standards that you quoted near the end of the article:
1) “This standard is repeated for Grades K-2: Students will demonstrate the meaning of addition and subtraction with whole numbers.”
First, this could simply mean that children can demonstrate their knowledge (or meaning) by counting on their fingers. Second, to explain the “meaning” of something requires understanding its purpose or significance. A primary school child would be correct by simply saying, “If I can add and subtract correctly, I can get the right answer.” The fuzzy folks want a more “nuanced” answer, however, which is unfair to ask of a primary student.
2) “This standard was listed for Grade 1: Use objects, drawings, words, and symbols to explain subtraction as a separate action.”
According to this standard, a teacher MUST have EVERY STUDENT use objects, drawings, words,AND symbols to explain subtraction as a separate action.” By using the word “AND,” the standard requires that EACH of those methods be used by EVERY student. Do the teachers, curriculum directors, and “leaders” understand that is a MANDATED requirement because of that one word? (If they had written OR instead of AND, and said “as appropriate,” they would have allowed teachers to make judgment calls on the best method(s) for teaching his/her particular students.
And what in the world do they mean “explain subtraction as a ‘separate action'”?
3) “This standard is shown for Grade 1: Use concrete, pictorial, and verbal representations of the commutative property of addition.”
Again, by using the word AND, the writers have declared ALL students must use concrete, pictorial, AND verbal representations…”
The time and energy do not exist for teachers to have every student do each of these methods, at least not proficiently. It therefore causes teachers to ignore the standards.
4. “This standard appears under Grade 6: Represent a variety of quantitative relationships using symbols and words.”
“This is a Grade 5 standard: Students will determine theoretical probabilities.”
I am not trying to be disrespectful toward elementary teachers, but if you were to ask them to give “a variety of quantitative relationships using symbols and words,” OR if they had to “determine theoretical probabilities,” I think there would be a long pause in their responses–if any responses at all.
Mathematics does indeed have a language of its own (which is the language of science), but writing K-8 math standards, in particular, in user-friendly language is the way to get fewer students (and teachers) afraid ot it.
That means standards writers need to remember they are also writing for parents as well as teachers, if we are sincere about having more parent involvement with children’s education.