As a former member of the Alabama State School Board (2003-2019), I would like to share my concerns about the ballot language for Amendment One. When voters get a ballot on March 3, this is all that is printed in the ballot summary about Amendment One:

*“Proposing an Amendment to the Constitution of Alabama of 1901, to change the name of the State Board of Education to the Alabama Commission on Elementary and Secondary Education; to provide for the appointment of members of the Commission by the Governor, subject to confirmation by the Senate; and to authorize the Governor to appoint a team of local educators and other officials to advise the commission on matters relating to the functioning and duties of the State Department of Education (Proposed by Act 2019-345.)”*

This brief summary is misleading and totally unacceptable. It’s the classic “bait and switch.” Totally missing from the ballot is the very important content of SB 397 in Section 5 beginning at the bottom of page 4 and continuing on to page 5 mandating the new commission (which replaces the current state school board) to adopt five things. The first is “Course of study standards that ensure nationwide consistency and the seamless transfer of students from within and outside the state in lieu of common core.” The ballot summary for March 3 does not include any mention of standards.

Last December before the summary for the ballot was available, a legislator contacted the Legislative Services Agency Legal Division to confirm what the ballot language would be. He was given this information: “If the Amendment passes, the (new governor-appointed) commission will have to develop new standards which “ensure nation-wide consistency and the seamless transfer of students.”

A representative of the AL State Department of Education said they were are not aware of any other nationally recognized standards for math and English Language Arts other than the Common Core Standards. Unfortunately voters would not have any way of knowing this since it’s not included on the ballot.

Any assertion that Amendment One will free Alabama of the much-detested Common Core State Standards aka College & Career Ready Standards is false. Voters who rely solely on the ballot summary will not realize that the Common Core standards will be permanently written into the Alabama constitution. We would have to pass another constitutional amendment to ever get rid of them. Although the Secretary of State’s office was asked to add necessary information from the bill onto the ballot for clarity, this was not done.

On Monday several organizations including the Alabama Farmers’ Federation (ALFA) , Forestry, Manufacture Alabama, the Alabama Realtors Association and perhaps others began running hundreds of thousands of dollars worth of ads endorsing Amendment One. The ads complain about our low test scores and how elected board members are too political. Apparently the Amendment One proponents think having a state school board made up of members who all were appointed by one person will not be “political.”

For those too young to remember or who have forgotten, many years ago the Alabama State School Board was an appointed board. However, it was changed to an elected one because the appointed board was not doing a good job. Right before the Common Core standards were implemented, former state school superintendent Joe Morton spoke frequently about how students’ scores had increased, moving Alabama up to the middle range of states. Then after a few years of using Common Core standards and assessments, our students’ scores plummeted to the bottom in math and close to the bottom in reading. I remember student progress declined all across America both in states with appointed state school boards as well as those with elected boards after the Common Core State Standards were implemented nationwide. If we are serious about improving learning, we need to start by actually replacing the much-hates Common Core aka College and Career-ready Standards with some that are more traditional and have been proven to work . Perhaps returning to the ones we were using immediately before Common Core would be a good start–at least when we were using them, our students’ performance was going in the right direction.

I know I’m not the only person who thinks there has been some legislative chicanery going on with this amendment. If the legislature and governor are so proud of it, why are they hiding so much of it, especially the information about Common Core, from the voters on election day, and why would it take so much media time to convince voters that it’s a good idea.

Link to the actual bill language which is not available on the sample ballot:

https://legiscan.com/AL/text/SB397/id/2049734/Alabama-2019-SB397-Enrolled.pdf

]]>July 13, 2019

*“The epidemic of supposed gender dysphoria among children and adolescents—“transgenderism”—has often been described as a cult. The designation is in some ways apt. Though lacking a charismatic leader usually found in such movements, other expert descriptions of cults certainly apply: “designed to destabilize an individual’s sense of self by undermining his or her basic consciousness, reality awareness, beliefs and worldview, [and] emotional control.” Cults also lead the target to believe that “anxiety, uncertainty, and self-doubt can be reduced by adopting the concepts put forth by the group.” The promise is a “new identity” that will solve all problems, even as it separates one from family and previous life.”*

Please read more: The Cracks in the Edifice of Transgender Totalitarianism

]]>On the other hand, AL’s State Charter School Commission readily approved Tarim’s Unity School Services’ application to run both the Montgomery and the Washington County Charter Schools. AL’s poorly written charter school law of 2015 allowed for the incompetent oversight given by the state charter school commission. This commission is composed of members selected from a list of nominees presented by the governor, the speaker, the Senate pro-tem, etc. The state school board has the job of rubber-stamping one of two names for each position. That is their sole responsibility when it comes to charter schools. With only a very brief paragraph on each candidate and no opportunity to question any candidates, the board was forced to rubber stamp one person for each position. Ironically, Charlotte Meadows, a friend of Rep. Terri Collins of the House Education Committee, was one of the two names Sen. Marsh nominated. Although she did not get appointed in 2015, Meadows has been very much involved in charter schools, and particularly in Montgomery’s LEAD Academy. Members of the appointed AL Charter School Commission approved the charter schools listed above even though the national board which had been hired by AL to evaluate charter school applications refused to approve them. So, why did the elected state school board in Texas refuse Tarim while AL’s charter school commission approved him?

Charlotte Meadows has been pushing appointed boards for a long time. At the 2017 winter meeting of the AL GOP state executive committee, I spoke in favor of a resolution to keep an elected state school board. Charlotte Meadows was one of only two or three people who spoke in favor of changing to an appointed state school board. The result was overwhelmingly in favor of maintaining an elected board.

In next March’s primary, a constitutional amendment to change to an appointed board will be on the ballot. Those legislators who voted for the amendment have been trying to convince voters that it will insure that the much-detested Common Core State Standards will be replaced if the amendment is approved. Many detractors- including me–think this is just a “bait and switch.” The Constitutional Amendment actually requires that Alabama’s standards must ensure a nation-wide consistency and a “seamless transfer” between states. In other words, AL would have to share standards with 40+ other Common Core-aligned states, essentially forever locking Alabamians into Common Core (or whatever name might be used), through our state Constitution. Simultaneously, we’d be giving up our voice in education by approving the change to an appointed board.

Several reporters including Josh Moon, Kyle Whitmire and Larry Lee as well as the noted columnist Valerie Strauss of the Washington Post have been doing some dynamite reporting on the misadventures of the AL Charter School Commission. A simple internet search (something the AL Charter School Commission and Charlotte Meadows obviously did not conduct) will give you a clear understanding of what is really at stake.

]]>Former AL Gov. Bob Riley said at his last AL State School Board meeting in November of 2010 that he wanted to set up an education/economic development type foundation in AL just like former NC governor Jim Hunt’s. That was the same meeting where Gov. Riley said he’d been “waiting six years for this day” (the day the state school board voted 7 to 2 to approve Common Core in AL. Stephanie Bell and I both voted NO.)

Soros’s millions or perhaps even billions have had enormous influence on moving America to the far LEFT including the area of education.

George Soros Funds Activists Pushing Euthanasia and Assisted Suicide Worldwide

]]>Joe Warren’s recent letter to the editor expressed the concerns I have been hearing about Dothan City Schools’ new education plan. However, Mr. Warren did not include one major item — the International Baccalaureate (IB) program. This global program from the United Nations is almost totally under the public’s radar. Those who have mentioned it to me were very concerned and full of questions. Since it was first mentioned by the previous superintendent, perhaps our new superintendent does not realize how little we had been told about IB.

Dothan has, unfortunately, had a history of introducing a string of unsuccessful, controversial, and often expensive “innovations” over the years: whole language; new math; Common Core math; open classrooms; “Pumsy;” “Peace Education;” block scheduling; and so on. The pattern has been to build up consensus for a pre-selected outcome after a series of meetings and then bring in the new program. I’d like to suggest we slow down and have some serious, open, and comprehensive discussions.

Here are some of the questions that I think need to be answered about IB:

>> What will be the total cost to get started and then what will be the annual cost? How will this program be funded? If the answer is “raise taxes,” what is Plan B if the public votes no? What are the odds that people with no children in Dothan schools or those parents whose children go to private, county, or home schools will vote to raise taxes especially for a “global” school? ”

>> Will the IB school(s) in Dothan teach the UN/UNESCO aligned content used in other IB schools?

>> Does the IB content align with the current Alabama content standards? If a student transfers in or transfers out of Dothan’s IB program, will it be difficult to adjust?

>> How will IB impact AP in Dothan? Which southeastern colleges and universities give credit for IB?

>> What exactly are the beliefs and values embraced by IB? From what I can find, they are UN/UNESCO-aligned, the values that drove President Ronald Reagan to withdraw America from UNESCO. Unfortunately President George W. Bush supported those values and rejoined. Will the IB program in Dothan be modeled after the one in Decatur, Georgia, where Dr. Edwards apparently served as the first superintendent?

Here are some excerpts from an interview with their current principal: Fostering Global Citizenship

*“When our students initiate fundraising for hurricane victims or write letters to state senators to express their concerns about budget cuts for space programmes (sic) or the US’s commitment to the Clean Air Act, you see the embodiment of the IB learner profile as well as the attitudes of a global citizen. The school explores and celebrates cultural differences in a challenging, nurturing, and intentionally multi-ethnic educational environment to foster global citizenship , helping students grow as individuals without parochial biases and with critical thinking skills necessary to improve their world.”*

The principal’s predecessor said, *“Internationalism and open-mindedness are innate in our school. You see it and you feel it, and the combination of both results in being global thinkers. For example, the library serves as a quiet refuge for our Muslim students to pray each afternoon at 2 pm. Their recognition of, and respect for, other people’s religious customs demonstrates they are globally minded.”* The principal also said *“At its core, PYP (Primary Years Program) has six transdisciplinary themes, which are visited each year in increasing complexity. These six themes are global in nature…”*

**So the $64,000 question is: Do Dothan parents and other voters want our graduates to be “global citizens” or American citizens with the education and training to be successful in a global market? It seems that we have been pushed along a bit too fast, leaving the community unclear about what is about to come down the pike. I know I would feel less uneasy if I knew more details.**

—

*Betty Peters of Dothan is a former state Board of Education member serving Alabama’s 2nd Congressional District.*

Dear Mr. Gates,

You recently wrote, “Math is one area where we want to generate stronger evidence about what works. What would it take, for example, to get all kids to mastery of Algebra I?”

I believe I can answer your question. There have been two significant math studies done in the last decade, reaching very similar conclusions. The first was the National Mathematics Advisory Panel Report of 2008 commissioned by President George W. Bush. Here are some of their conclusions: students’ difficulty with fractions (including decimals and percents) is pervasive and a major obstacle to further progress in mathematics including algebra. The panel suggested curriculum should allow sufficient time to learn fractions, and teachers must know effective interventions for teaching fractions. Preparation of elementary and middle school teachers in mathematics needs to be strengthened; using elementary teachers who have specialized in elementary mathematics could be an alternative to increasing all elementary teachers’ math content knowledge by focusing the need for expertise on fewer teachers.

Another problem is that many textbooks are too long (700 to 1000 pages) and include non-mathematical content like photographs and motivational stories. Key topics should be built on a focused, coherent progression, and continual revisiting of topics year after year without closure should be avoided.

Lack of automatic recall in addition, subtraction, multiplication and division is a serious deficiency as is a lack of proficiency with whole numbers, fractions and certain aspects of geometry and measurement, which are the foundations for algebra. Of these, knowledge of fractions is the most important foundational skill not developed among American students.

The panel advised that algebra problems involving patterns be greatly reduced in state tests and on the NAEP assessment. Also districts should ensure that all prepared students have access to an authentic algebra course by 8th grade, and more students should be prepared to enroll in such a course by 8th grade.

The second important study, “Early Predictors of High School Mathematics Achievement” was published in June 14, 2012, and an article about it, entitled “Fractions are the key to math success, new study shows,” was posted at the Univ. of Michigan’s Institute for Social Research on June 18, 2012. Robert Siegler, a cognitive psychologist at Carnegie Mellon University, was the lead author of this study which analyzed long-term data on more than 4,000 children from both the United States and the United Kingdom. It found students’ understanding of fractions and division at age 10 predicted algebra and overall math achievement in high school, even after statistically controlling for a wide range of factors including parents’ education and income and children’s age and I.Q.

Univ. of Michigan researcher Pamela Davis-Kean, the co-author of the study, said, “These findings demonstrate an immediate need to improve the teaching and learning of fractions and division.”

Dr. Siegler stated, “We suspected that early knowledge in these areas was absolutely crucial to later learning of more advanced mathematics, but did not have any evidence until now.”

I know how interested you and your wife are in improving education, especially in math, for our students. As a state school board representative, I understand the importance of getting our teachers and students on track immediately. I believe we can succeed, though, if we will follow the advice given in these two studies. I would certainly be glad to discuss this subject with you or your staff.

Sincerely,

Betty Peters

]]>*“There are some good things in there, but some of them are in there at the wrong grade levels,” she said.”*

Read more.. Alabama Developing New Standardized Student Achievement Test

]]>At a middle school in California, the state testing in math was underway via the Smarter Balanced Assessment Consortium (SBAC) exam. A girl pointed to the problem on the computer screen and asked “What do I do?” The proctor read the instructions for the problem and told the student: “You need to explain how you got your answer.”

The girl threw her arms up in frustration and said, “Why can’t I just do the problem, enter the answer and be done with it?”

The answer to her question comes down to what the education establishment believes “understanding” to be, and how to measure it. K-12 mathematics instruction involves equal parts procedural skills and understanding. What “understanding” in mathematics means, however, has long been a topic of debate. One distinction popular with today’s math reform advocates is between “knowing” and “doing.” A student, reformers argue, might be able to “do” a problem (i.e., solve it mathematically), without understanding the concepts behind the problem solving procedure. Perhaps he has simply memorized the method without understanding it.

The Common Core math standards, adopted in 45 states and reflected in Common Core-aligned tests like the SBAC and the PARCC, take understanding to a whole new level. “Students who lack understanding of a topic may rely on procedures too heavily,” states the Common Core website. “… But what does mathematical understanding look like?” And how can teachers assess it?

“One way … is to ask the student to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.” (http://www.corestandards.org/Math/).

The underlying assumption here is that if a student understands something, she can explain it—and that deficient explanation signals deficient understanding. But this raises yet another question: what constitutes a satisfactory explanation?

While the Common Core leaves this unspecified, current practices are suggestive: Consider a problem that asks how many total pencils are there if 5 people have 3 pencils each. In the eyes of some educators, explaining why the answer is 15 by stating, simply, that 5 x 3 = 15 is not satisfactory. To show they truly understand why 5 x 3 is 15, and why this computation provides the answer to the given word problem, students must do more. For example, they might draw a picture illustrating 5 groups of 3 pencils.

Consider now a problem given in a pre-algebra course that involves percentages: A coat has been reduced by 20% to sell for $160. What was the original price of the coat?”

A student may show their solution as follows:

x = original cost of coat in dollars

100% – 20% = 80%

0.8x = $160

x = $200

Clearly, the student knows the mathematical procedure necessary to solve the problem. In fact, for years students were told not to explain their answers, but to show their work, and if presented in a clear and organized manner, the math contained in this work was considered to be its own explanation. But the above demonstration might, through the prism of the Common Core standards, be considered an inadequate explanation. That is, inspired by what the standards say about understanding, one could ask “Does the student know why the subtraction operation is done to obtain the 80% used in the equation or is he doing it as a mechanical procedure — i.e., without understanding?”

**Providing instruction for explanations—the road to “rote understanding”**

In a middle school observed by one of us, the school’s goal was to increase student proficiency in solving math problems by requiring students to explain how they solved them. This was not required for all problems given; rather, they were expected to do this for two or three problems per week, which took up to 10 percent of total weekly class time. They were instructed on how to write explanations for their math solutions using a model called “Need, Know, Do.” In the problem example given above, the “Need” would be “What was the original price of the coat?” The “Know” would be the information provided in the problem statement, here the price of the discounted coat and the discount rate. The “Do” is the process of solving the problem.

Students were instructed to use “flow maps” and diagrams to describe the thinking and steps used to solve the problem, after which they were to write a narrative summary of what was described in the flow maps and elsewhere. They were told that the “Do” (as well as the flow maps) explains what they did to solve the problem and that the narrative summary provides the why. Many students, though, had difficulty differentiating the “Do” section from the final narrative. But in order for their explanation to qualify as “high level,” they couldn’t simply state “100% – 20% = 80%”; they had to explain what that means. For example, they might say, “The discount rate subtracted from 100% gives the amount that I pay.”

An example of a student’s written explanation for this problem is shown in Figure 1: Example of student explanation.

For problems at this level, the amount of work required for explanation turns a straightforward problem into a long managerial task that is concerned more with pedagogy than with content. While drawing diagrams or pictures may help some students learn how to solve problems, for others it is unnecessary and tedious. As the above example shows, the explanations may not offer the “why” of a particular procedure.

Under the rubric used at the middle school where this problem was given, explanations are ranked as “high”, “middle” or “low.” This particular explanation would probably fall in the “middle” category since it is unlikely that the statement “You need to subtract 100 -20 to get 80” would be deemed a “purposeful, mathematically-grounded written explanation.”

The “Need” and “Know” steps in the above process are not new and were advocated by Polya (1957) in his classic book “How to Solve It”. The “Need” and “Know” aspect of the explanatory technique at the middle school observed is a sensible one. But Polya’s book was about solving problems, not explaining or justifying how they were done. At the middle school, however, problem solving and explanation were intertwined, in the belief that the process of explanation leads to the solving of the problem. This conflation of problem solving and explanation is based on a popular educational theory that being aware of one’s thinking process — called “metacognition” — is part and parcel to problem solving (see Mayer, 1998).

Despite the goal of solving a problem and explaining it in one fell swoop, in many cases observed at the middle school, students solved the problem first and then added the explanation in the required format and rubric. It was not evident that the process of explanation enhanced problem solving ability. In fact, in talking with students at the school, many found the process tedious and said they would rather just “do the math” without having to write about it.

In general, there is no more evidence of “understanding” in the explained solution, even with pictures, than there would be in mathematical solutions presented in a clear and organized way. How do we know, for example, that a student isn’t simply repeating an explanation provided by the teacher or the textbook, thus exhibiting mere “rote learning” rather than “true understanding” of a problem-solving procedure?

**Requiring explanations undoes the conciseness of math**

Math learning is a progression from concrete to increasingly abstract. The advantage to the abstract is that the various mathematical operations can be performed without the cumbersome attachments of concrete entities — entities like dollars, percentages, groupings of pencils. Once a particular word problem has been translated into a mathematical representation, the entirety of its mathematically-relevant content is condensed onto abstract symbols, freeing working memory and unleashing the power of pure mathematics. That is, information and procedures handled by available schemas frees up working memory. With working memory less burdened, the student can focus on solving the problem at hand (Aditomo, 2009). Thus, requiring explanations beyond the mathematics itself distracts and diverts students away from the convenience and power of abstraction. Mandatory demonstrations of “mathematical understanding,” in other words, impede the “doing” of actual mathematics.

**“I can’t do this orally, only headily”**

The idea that students who do not demonstrate their strategies in words and pictures must not understand the underlying concepts assumes away a significant subpopulation of students whose verbal skills lag far behind their mathematical skills, such as non-native English speakers or students with specific language delays or language disorders. These groups include children who can easily do math in their heads and solve complex problems, but often will be unable to explain — whether orally or in written words — how they arrived at their answers.

Most exemplary are children on the autistic spectrum. As autism researcher Tony Attwood has observed, mathematics has special appeal to individuals with autism: it is, often, the school subject that best matches their cognitive strengths. Indeed, writing about Asperger’s Syndrome (a high functioning subtype of autism), Attwood notes that “the personalities of some of the great mathematicians include many of the characteristics of Asperger’s syndrome.” (Attwood, 2007)

And yet, Attwood adds (ibid.), many children on the autistic spectrum, even those who are mathematically gifted, struggle when asked to explain their answers. “The child can provide the correct answer to a mathematical problem,” he observes, “but not easily translate into speech the mental processes used to solve the problem.” Back in 1944, Hans Asperger, the Austrian pediatrician who first studied the condition that now bears his name, famously cited one of his patients as saying that, “I can’t do this orally, only headily” (Asperger, H., 1991 [1944]).

Writing from Australia decades later, a few years before the Common Core took hold in America, Attwood adds that it can “mystify teachers and lead to problems with tests when the person with Asperger’s syndrome is unable to explain his or her methods on the test or exam paper” (Attwood, 2007, p. 241). Here in post-Common Core America, this inability has morphed into an unprecedented liability.

Is it really the case that the non-linguistically inclined student who progresses through math with correct but unexplained answers — from multi-digit arithmetic through to multi-variable calculus — doesn’t understand the underlying math? Or that the mathematician with the Asperger’s personality, doing things headily but not orally, is advancing the frontiers of his field in a zombie-like stupor?

Or is it possible that the ability to explain one’s answers verbally, while sometimes a sufficient criterion for proving understanding, is not, in fact, a necessary one?

**What is really being measured?**

Measuring understanding, or learning in general, isn’t easy. What testing does is measure “markers” or byproducts of learning and understanding. Explaining answers is but one possible marker.

Another, quite simply, are the answers themselves. If a student can consistently solve a variety of problems, that student likely has some level of mathematical understanding. Teachers can assess this more deeply by looking at the solutions and any work shown and asking some spontaneous follow-up questions tailored to the child’s verbal abilities. But it’s far from clear whether a general requirement to accompany all solutions with verbal explanations provides a more accurate measurement of mathematical understanding than the answers themselves and any work the student has produced along the way. At best, verbal explanations beyond “showing the work” may be superfluous; at worst, they shortchange certain students and encumber the mathematics for everyone.

As Alfred North Whitehead famously put it about a century before the Common Core standards took hold:

It is a profoundly erroneous truism … that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.

Katharine Beals is a lecturer at the University of Pennsylvania Graduate School of Education and an adjunct professor at the Drexel University School of Education. She is the author of Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School.

Barry Garelick has written extensively about math education in various publications including The Atlantic, Education Next, Educational Leadership, and Education News. He recently retired from the U.S. EPA and is teaching middle and high school math in California. He has written a book about his experiences as a long term substitute in a high school and middle school in California: “Teaching Math in the 21st Century”.

—

**References**

Anindito Aditomo. Cognitive load theory and mathematics learning: A systematic review, Anima, Indonesian Psychological Journal, 2009, Vol. 24, No. 3, 207-217

Hans Asperger. “Problems of infantile autism,” Communication: Journal of the National Autistic Society, London 13, 45-32), 1991 [1944]).

Tony Attwood. The Complete Guide to Asperger’s Syndrome, Jessica Kingsley Publishers, Philadelphia, PA, 2007. (p. 240)

G. Pólya, How to Solve It: A New Aspect of Mathematical Method, Doubleday, Garden City, NY, 1957

Richard Mayer. Cognitive, metacognitive, and motivational aspects of problem solving, Instructional Science, 1998, March, Vol. 26, Issue 1-2, pp 49-63

]]>Common Core Math Standards Encourage Dubious Inquiry-Based Approaches

Purveyors of the inquiry-based and student-centered math agenda, which has persisted for more than 20 years, argue traditionally taught math has never worked for the vast majority of the nation’s student population, and they say mental math is the key to “understanding,” as opposed to what they consider to be rote procedures.

The mantras of “students shall understand” and “explain” appear in the Common Core standards and are, according to Tom Loveless of the Brookings Institution, “dog whistles” that serve as a signal to proponents of the inquiry-based and student-centered math agenda to see Common Core’s math standards as requiring those approaches.

It is ironic how inquiry-based math approaches seem to spend more time showing students strategies they might discover on their own than on teaching the standard algorithms they almost certainly won’t learn on their own.

The analytic, problem-solving, and critical-thinking capabilities inquiry-based math proponents tout as the stated goal of Common Core only develop after students master facts and procedures. Understanding works in tandem with procedural fluency, but the current emphasis on conceptual understanding places the cart before the horse. Proponents of inquiry-based math point to students’ procedural fluency as evidence “they can do it but they don’t know what they’re doing,” but the reality is the students cannot do the math if they do not master the procedures.

**Once Is Never Enough**

The inquiry-based thinking that dominates interpretation of the Common Core standards holds one indication of “understanding” is if a student can solve a problem in multiple ways. Thus, the proponents of inquiry-based math insist on having students come up with more than one way to solve a problem. Forcing students to think of multiple ways to get the same answer, however, does not in and of itself cause understanding. It is as if the reformers are saying, “If we can just get them to do things that look like what we imagine a mathematician does, they will be real mathematicians.”

In my experience, and that of many math teachers I know, delays in understanding are normal and do not signal a failure of the teaching method. Students learn to do something; they learn to apply what they’ve mastered; they learn to do more; they begin to see why; and eventually the light comes on. The inquiry-based math community fails to understand that what they deride as “procedures devoid of meaning” is hard to accomplish with elementary math because the very act of learning procedures is itself informative, and the repetitious use of them conveys understanding to the user. Placing the cart before the horse by insisting on “deeper conceptual understanding” prior to teaching standard algorithms and procedures is simply not effective.

**Standard Procedures Delayed**

Unfortunately, the Common Core math standards delay the teaching of standard algorithms for addition and subtraction, as well as other key operations. The standard algorithm for multi-digit addition and subtraction does not appear until the 4th grade.

It’s important to note Common Core does not prohibit the teaching of the standard algorithms prior to the grade level in which they appear in the standards. This has been confirmed by the lead writers of the Common Core math standards, Jason Zimba and Bill McCallum. Zimba recommends the standard algorithm for addition and subtraction be taught sooner. Zimba would introduce the standard algorithm for addition late in 1st grade, with two-digit addends. He would then increase the complexity of its use in subsequent grades, continually providing practice toward fluency. The goal would be complete fluency by 4th grade. Zimba also would introduce the subtraction algorithm in 2nd grade and increase its complexity until 4th grade.

Despite admonitions from those in the know, such as Zimba, the word does not seem to have reached school districts, administrators, policymakers, publishers, or test makers. Nor do such recommendations appear in the Common Core background discussion on its website.

Morgan Polikoff, assistant professor at the University of Southern California’s Rossier School of Education, was quoted in a recent article in The Florida Times-Union, and his comments show the widespread disdain for teaching the standard algorithms.

*“Common Core… put[s] the algorithm last and the conceptual understanding first,” Polikoff said. *

*“They want you to understand how the tool works before they give you the tool. If you understand the concepts, then when you get to higher levels of math problems, you’ll be thinking like a mathematician and you can do it.”*

Such thinking manifests itself in many schools and school districts where teachers have gone so far as to issue warnings to parents not to teach their children the standard method at home because it would interfere with the student’s learning. Many parents are choosing to ignore such warnings. More power to them.

—

*Barry Garelick (barryg99@yahoo.com) has written extensively about math education in various publications, including The Atlantic, Education Next, Educational Leadership, and Education News. He recently retired from the U.S. Environmental Protection Agency and is teaching middle and high school math in California. Garelick is the author of Teaching Math in the 21st Century, which recounts his experiences as a long-term substitute in a high school and middle school in California.*