An Engineer Looks at the Common Core Mathematics Standards
An Engineer Looks at the Common Core Mathematics Standards
by Henry W. Burke
Common Core Standards for Mathematics and English Language Arts and Reading (ELAR) are being implemented in the Common Core states. In this report, I will focus on the Common Core Mathematics Standards.
Quality of the Common Core Math Standards
The Common Core Mathematics Standards have a number of basic problems. The CCS Math Standards:
1. Delay development of some key concepts and skills.
2. Include significant mathematical sophistication written beyond the level of most students, parents, and teachers.
3. Lack coherence and clarity to be interpreted by students, parents, teachers, and curriculum developers.
4. Have standards inappropriately placed; this includes delayed requirement for standard algorithms.
5. Treat important topics unevenly; this will result in inefficient use of instructional time.
6. Are not well organized at the high school level; the standards are not divided into defined courses.
7. Place emphasis on Standards for Mathematical Practice; this is a constructivist approach typical of “reform” math programs.
8. Publishers of reform programs are aligning with CCS Standards for Mathematical Practice; the CCS will not improve the math programs used in many schools.
9. Unusual and unproven approach to geometry. —
The Pioneer Institute recently published a report by R. James Milgram and Sandra Stotsky, “Lowering the Bar: How Common Core Math Fails to Prepare High School Students for STEM.” — http://pioneerinstitute.org/download/lowering-the-bar-how-common-core-math-fails-to-prepare-high-school-students-for-stem/
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.
Professor Milgram, who refused to validate the Common Core Math Standards, stated the following in the Pioneer white paper:
With the exception of a few standards in trigonometry, the math standards end after Algebra II. They include no precalculus or calculus.
The Common Core mathematics standards do not make high school graduates “college and career-ready,” as the Common Core proponents claim. The national mathematics standards will not prepare students to study science, technology, engineering, and math (STEM) in a selective four-year college.
The Pioneer report concludes by offering these chilling indictments:
At this time we can conclude only that a gigantic fraud has been perpetrated on this country, in particular on parents in this country, by those developing, promoting, or endorsing Common Core’s standards. We have no illusion that the college-readiness level in ELA will be any more demanding than Common Core’s college-readiness level in mathematics. — http://pioneerinstitute.org/download/lowering-the-bar-how-common-core-math-fails-to-prepare-high-school-students-for-stem/
Professor William McCallum, one of the three authors of Common Core’s math standards, said that “overall standards wouldn’t be very high” and “not up to the standards of other nations.” — http://educationnext.org/the-common-core-math-standards/
His opinion was supported by Jonathon Goodman, a professor at New York University. He also raised questions about the standards from an international comparison: “The proposed Common Core standard is similar in earlier grades but has significantly lower expectations with respect to algebra and geometry than the published standards of other countries.” (The Common Core websites have recently dropped the words “internationally-benchmarked” from their talking points.) — http://blog.heritage.org/2012/04/23/common-core-math-standards-fail-to-add-up/
Some experts have criticized the math standards for moving too slowly. If educators follow the Common Core through middle school, students will not encounter Algebra I until high school. That does not leave enough time to take Algebra II, Geometry, Trigonometry / Precalculus, and Calculus in the high school years. Most engineering colleges require incoming students to have four years of high school math, preferably through Calculus.
Under the Common Core Math Standards, students will not be ready for science, technology, engineering, and math (STEM) careers. Unless students can prepare for calculus in grade 12 or as college freshmen, they will not be prepared for STEM majors. — http://pioneerinstitute.org/featured/support-for-common-cores-fuzzy-math-doesnt-add-up/
Jason Zimba, lead writer of the Common Core Mathematics Standards, explained that Common Core’s version of “college readiness” means getting students ready for non-selective community colleges. Zimba recently acknowledged that “If you want to take calculus your freshman year in college, you will need to take more mathematics than is in the Common Core.” — http://theadvocate.com/home/6914390-125/common-core
Barry Garelick suggests that implementation of the Common Core math standards will actually make things worse. He said the math standards:
…will be a mandate for reform math — a method of teaching math that eschews memorization, favors group work and student-centered learning, puts the teacher in the role of “guide” rather than “teacher” and insists on students being able to explain the reasons why procedures and methods work for procedures and methods that they may not be able to perform. — http://www.educationnews.org/education-policy-and-politics/the-pedagogical-agenda-of-common-core-math-standards/
Ze’ ev Wurman has written extensively about the Common Core Standards (in Pioneer Institute publications and elsewhere). He served as a Senior Policy Adviser at the USDOE from 2007-2009. Garelick and Wurman found:
1. Common Core replaces the traditional foundations of Euclidean geometry with an experimental approach.
2. Common Core excludes certain Algebra II and Geometry content that is a prerequisite at almost every four-year college.
3. Common Core fails to teach prime factorization. Consequently, CCS does not include teaching about least common denominators or greatest common factors.
4. Common Core fails to include conversions among fractions, decimals, and percents.
5. Common Core de-emphasizes algebraic manipulation, a prerequisite for advanced mathematics. Instead, CCS redefines algebra as “functional algebra,” which does not prepare students for STEM careers.
Specifically, in the K-8 Grade span:
6. Common Core does not require proficiency with addition and subtraction until Grade 4 (a grade behind our international competitors).
7. Common Core does not require proficiency with multiplication using the standard algorithm until Grade 5 (a grade behind standard expectations).
8. Common Core does not require proficiency with division using the standard algorithm until Grade 6 (a grade behind our international competitors).
9. Common Core starts teaching decimals in Grade 4 (about two years behind the more rigorous states).
10. Common Core fails to teach in K-8 about key geometrical concepts (e.g., area of a triangle, sum of angles in a triangle, isosceles and equilateral triangles, etc.). –http://www.educationnews.org/education-policy-and-politics/the-pedagogical-agenda-of-common-core-math-standards/
There are hundreds of examples where young students are crying and becoming frustrated over the Common Core lessons and tests. Many times, the questions are not age-appropriate and fail to recognize the children’s cognitive abilities.
In an 11.9.13 article in the Washington Post, Valerie Strauss wrote “Why young kids are struggling with Common Core math.” — http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/11/09/why-young-kids-are-struggling-with-common-core-math/
A PARCC website directed viewers to the Mathematics Common Core Toolbox. Part B of the assessment included this question for fourth graders (age 9-10):
The San Francisco Giant’s Stadium has 41,915 seats, the Washington Nationals’ stadium has 41,888 seats and the San Diego Padres’ stadium has 42,445 seats.
The assessment then asks the following question:
Compare these statements from two students.
Jeff said, “I get the same number when I round all three numbers of seats in these stadiums.”
Sara said, “When I round them, I get the same number for two of the stadiums but a different number for the other stadium.”
Can Jeff and Sara both be correct? Explain how you know.
A very bright sixth grader gave this answer, which provides insight into how this age group thinks:
No, I know this because they all round to 42,000.
We know her response is typical for her age group (7-11) because of the work of one of the greatest childhood psychologists of all time, Jean Piaget. Piaget discovered that children go through distinct stages of cognitive development as they mature. Students at this stage (ages 7-11) have some inductive logic, but they do not have deductive logic (which this problem needs).
When they gave this same question to high school students, one 14-year old student provided this correct answer:
Yes, they can because it depends on the way a person rounds. Jeff is right if you round to the nearest thousand and Sara is right if you round to the nearest hundred.
The article explained:
But as Piaget told us, children are not “mini-adults.” If a child is not developmentally ready, these problems will likely lead to frustration, discouragement and negative emotional reactions—which is exactly what parents are reporting. — http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/11/09/why-young-kids-are-struggling-with-common-core-math/
Apparently, a good explanation is more important than the right answer in Common Core. When Chicago Curriculum Director Amanda August was explaining Common Core Math in a July 2013 meeting, she said that “the reasoning is a main goal, not just correct answers.” In a video, August said:
Even if they said 3 X 4 was 11, if they were able to explain their reasoning and explain how they came up with their answer, really in words and oral explanations and they showed it in a picture but they just got the final number wrong; we’re really more focusing on the how and the why. — http://www.breitbart.com/Big-Government/2013/07/19/Common-Core-Math-If-Kids-Say-3-X-4-is-11-If-They-Can-Explain-it-We-ll-Take-it
Oh really? As a Civil Engineer, I happen to think that getting the right answer is quite important! I doubt if the public would feel very secure if they had to travel over a bridge designed by a Structural Engineer who did not think exact calculations were very important.
Common Core Talking Points
The Common Core advocates have a number of standard talking points. These talking points might sound good, but they are myths! The common myths are:
1. Myth – Common Core was a state-led initiative.
Fact — The Common Core Standards (CCS) were initiated by private interests in Washington, D.C. To produce a facade of state involvement, the CCS creators enlisted the support of two D.C.-based trade associations — the National Governors Association (NGA), and the Council of Chief State School Officers (CCSSO). The bulk of the work to create the CCS was done by Achieve, Inc. (also a D.C.-based organization); massive funding was supplied by the Bill and Melinda Gates Foundation.
2. Myth – The federal government is not involved in the Common Core scheme.
Fact — The U.S. Department of Education (USDOE) was deeply involved in the meeting that led to the Common Core Standards. The USDOE is acting as the enforcer to lead states into the CCS scheme.
3. Myth – States adopted CCS voluntarily, with no federal coercion.
Fact — The states agreed to adopt the Common Core Standards as a condition of competing for the federal Race to the Top (RTTT) funding; the $4 billion RTTT competition served as a huge, persuasive carrot. In addition, the Obama Administration tied No Child Left Behind (NCLB) waivers to CCS adoption.
4. Myth – Under Common Core, the states will control their standards.
Fact — When a state adopts CCS, it agrees to accept the Common Core Standards verbatim! The Common Core Standards are copyrighted and states cannot change a single word.
5. Myth – Common Core is only a set of standards, not curriculum.
Fact — The standards will control the curriculum. Ultimately, every Common Core state will be teaching essentially the same curriculum. The two federally-funded assessment consortia will drive the curriculum through the assessments; teachers will be forced to “teach to the test.”
6. Myth – The Common Core Standards are rigorous and will make the students “college-ready.”
Fact — Several states had standards superior to the CCS. For example, Massachusetts had excellent standards in English Language Arts and Reading (ELAR) and Mathematics. CCS is best described as a “race to the middle.” Common Core will not make students “college ready!” — http://truthinamericaneducation.com/common-core-state-standards/myths-verses-facts/
Alternatives to Common Core Math
In my presentations before the Nebraska State Board of Education (SBOE) in November and December, 2013, I recommended that Nebraska utilize the Texas Standards for English Language Arts and Reading (ELAR).
I also suggested that Nebraska should examine the Texas Standards for the other subject areas. Texas has excellent Mathematics Standards, and these standards should be seriously considered for Nebraska.
Are there other alternatives to Common Core Math? In an 11.4.13 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.
Here are helpful links to Saxon Math resources:
To learn about Saxon Math – homeschoolers:
Donna Garner described the work of Niki (Naconia) Hayes, who wrote John Saxon’s Story: A Genius of Common Sense in Math Education.
In her article, Mrs. Garner wrote the following:
John Saxon was a very witty and brilliant scholar, and his passion for teaching students math the right way is a story that must be told. Niki has done just that.
As you read the book, you will feel as if you have crawled into Saxon’s marvelous mind; and you will come to understand why he fought so hard to publicize the math series he wrote and published — Saxon Math.
He showed how mathematics could indeed remain true to itself—a historically rich discipline—and still cause students from all academic levels (and races and genders) to say, ‘I love math!’ (Niki Hayes)
I treasure Niki Hayes’ diligence to present John Saxon’s colorful life in all its boldness and uniqueness.
“When Saxon died in 1996, Saxon Publishers had sales of $27 million in spite of major efforts by math education leaders and their political allies to destroy him personally and professionally.” (Niki Hayes)
Please go to either of these sites to order a copy of Niki Hayes’ book:
Common Core Math Links
4.23.12 – “Common Core Math Standards Fail To Add Up” by Evan Walter, The Heritage Foundation — http://blog.heritage.org/2012/04/23/common-core-math-standards-fail…
9.5.12 — “How To Indoctrinate Students’ Minds with Math” by Donna Garner –http://educationviews.org/how-to-indoctrinate-students-minds-with-m…
9.14.12 – “Fighting the Common Core Standards’ Social Justice Math” – by Oak Norton — http://www.utahnsagainstcommoncore.com/jordan-sd-rips-out-unsolvabl…
9.27.12 – “The Pedagogical Agenda of Common Core Math Standards” by Barry Garelick — EducationNews.org — http://www.educationnews.org/education-policy-and-politics/the-peda…
11.20.12 – “A New Kind of Problem: The Common Core Math Standards” – by Barry Garelick – The Atlantic -- http://www.theatlantic.com/national/archive/2012/11/a-new-kind-of-problem-the-common-core-math-standards/265444/
7.1.13 – “Common Core’s Cloudy Vision of College Readiness in Math” – by Dr. Sandra Stotsky — http://pioneerinstitute.org/news/common-cores-cloudy-vision-of-college-readiness-in-math-by-sandra-stotsky/
7.20.13 – “Common Core Math: Wrong Answers Acceptable” – by Warren Todd Huston — Breitbart.com — http://www.breitbart.com/Big-Government/2013/07/19/Common-Core-Math-If-Kids-Say-3-X-4-is-11-If-They-Can-Explain-it-We-ll-Take-it
8.11.13 – Video — “Example of Confusing Way Math Is Taught Under Common Core” — https://www.teachingchannel.org/videos/multiplication-division-in-the-core?utm_campaign=digest&utm_medium=email&utm_source=digest
8.13.13 — “Common Core: 3 x 4 = 11” — by Stanley Kurtz – National Review Online –http://www.nationalreview.com/corner/355713/common-core-3-x-4-11-stanley-kurtz
8.15.13 – “Common Core Math Leaves Students Without Clear Path to Calculus” – by Brenda J. Buote – Boston Globe — http://www.bostonglobe.com/metro/regionals/north/2013/08/14/reading-new-math-curriculum-runs-into-protests/pGcNh0mavGxkHiJuFoSKaO/story.html
8.23.13 – “ACT Study: Students Need 5 Math Classes (Starting with Alg. I in 8th Grade) To Survive College Algebra” – by Richard Innes – Bluegrass Institute — http://www.bipps.org/act-results-and-common-core-state-standards-for-math/
10.30.13 — “What’s 12 x 11? Um, Let Me Google That” – by David G. Bonagura, Jr., teacher — Wall Street Journal – http://online.wsj.com/news/article_email/SB10001424052702303471004579165310256329006-lMyQjAxMTAzMDMwMTEzNDEyWj
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