He notes that Quebec dominates the rest of Canada in math and have done so for many years. In spite of that, the other Canadian provinces don’t want to emulate Quebec’s success.
He highlights a study conducted by British Columbia’s Ministry of Education into Quebec’s success. I wanted to highlight a couple of the findings that he writes about.
The first finding is that Quebec has a clearer philosophy and sequence. Bennett writes:
The scope and sequence of Quebec’s math curriculum is clearer, demonstrating an acceptance of the need for clarity in setting out a progression of content and skills focused on achieving higher levels of achievement. The 1980 Quebec Ministry of Education curriculum set the pattern. Much more emphasis in teacher education and in the classroom was placed upon building sound foundations before progressing to problem solving. Curriculum guidelines were much more explicit about making connections with previously learned material.
Quebec’s grade 4 curriculum made explicit reference to the ability to develop speed and accuracy in mental and written calculation and to multiply larger numbers as well as to perform reverse operations. By grade 11, students were required to summon “all their knowledge (algebra, geometry, statistics and the sciences) and all the means at their disposal…to solve problems.” “The way math is presented makes the difference,” says Genevieve Boulet,a professor of mathematics education at Mount St. Vincent University with prior experience preparing mathematics teachers at the Université de Sherbrooke.
Did you catch that? A clear scope and sequence was key, but not only that, an emphasis was placed on building sound foundations before tackling problem-solving.
Now compare that to Common Core. We’ve noted Common Core’s Math Standards:
Delay development of some key concepts and skills.
Include significant mathematical sophistication written at a level beyond understanding of most parents, students, administrators, decision makers and many teachers.
Lack coherence and clarity to be consistently interpreted by students, parents, teachers, administrators, curriculum developers, textbook developers/publishers, and assessment developers. Will this lead to consistent expectations and equity?
Have standards inappropriately placed, including delayed requirement for standard algorithms, which will hinder student success and waste valuable instructional time.
Bennett then notes Quebec uses stronger math curriculum:
Fewer topics tend to be covered at each grade level in Quebec, but they are covered in more depth than in BC and other Canadian provinces. In grade 4, students are generally introduced right away to multiplication, division and standard alogrithms, and the curriculum unit on measurement focuses on mastering three topics — length, area and volume — instead of six or seven. Concrete manipulations are more widely used to facilitate comprehension of more abstract math concepts. Much heavier emphasis is placed on numbers and operations as grade 4 students are expected to perform addition, subtraction and multiplication using fractions.
Fewer topics, they go in depth and students are introduced right away to standard algorithms. Common Core puts conceptual understanding before they master practical skills. Barry Garelick wrote about this in The Atlantic in 2012:
Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings.
Yet Quebec does not do this.
Canadian provinces are wise to emulate Quebec’s success in math, but we in the United States would be as well.
Abt Associaties in a report they submitted for the state of Massachusetts did a cross-section of nine states that had gone through some process of revising the Common Core State Standards. They looked at Alabama, Arkansas, California, Florida, Georgia, Mississippi, New Jersey, Ohio and Utah.
The authors of the report, Jill Norton, Jennifer Ash, and Sarah Ballinger, acknowledged due to the states that were chosen it doesn’t give a full picture of what has taken place nationally, but essentially they found states that revise the standards didn’t really revise much at all.
They reported on changes with the math standards, “Across all grade levels in mathematics, the nine states revised 26.5 percent of the standards, with 73.5 percent of the standards were kept the same. The number of math standards revised ranged from 17 changes in one state to 282 changes in another. Moreover, eight of the nine states added math standards, with a total of 51 new standards added.”
With those changes we’re really talking minor tweaks.
With ELA standards it isn’t much different.
They write, “The story for ELA revisions was similar, with 23 percent of ELA standards revised and 77 percent left unchanged. Again, the number of revisions varied by state, ranging from 12 standards revised in one state to 330 standards revised in another. States added fewer new standards in ELA, with only six new standards added across all nine states. For example, one state added a new standard in sixth grade reading literature that requires students to ‘Differentiate among odes, ballads, epic poetry, and science fiction.’”
Takeaway…. bills or actions from the state board that just lead to revising the Common Core are generally worthless. We can’t really even note significant improvement in these states. We need to continue to push for a full repeal of the Common Core.
Depth of understanding was hailed by its architects as a cornerstone of the Common Core, a set of educational guidelines for what students need to know in each grade in English and math that have been adopted in 43 states and the District of Columbia. The problem is that most elementary school teachers did not learn math that way, and many now struggle to teach to the new standards.
An April 2016 study of a large urban school in Georgia reported the frustration of many elementary level teachers. Only two out of ten teachers there said they were very familiar with the standards and one out of four reported no training on how to teach to them. If the Common Core is to improve the math education of U.S. students as intended, experts agree that teachers who are meant to get students excited about math and become proficient in its basic concepts need more help and support. Yet the exact nature of that support and how to provide it are debated.
…“Elementary school teachers are generalists,” said John Ewing, president of Math for America, a non-profit that offers fellowships to teachers. “Their content knowledge is less than what a specialist would have so they don’t understand math in a broad way. Preparatory programs have to be more attentive and have a way to develop teacher expertise.”
So the onerous is on college elementary education programs to suddenly turn these teachers into specialists and learn math in a way they didn’t experience growing up.
This is the same reason parents struggle with Common Core math as well. The whole idea is completely asinine. For starters the math standards for elementary-aged students are not age-appropriate. Now they want teachers (and with some school districts – parents) to go back and learn all of these new methods when there was really nothing wrong with the way elementary school teachers and parents were taught.
We sent a man to the moon before Common Core, all of American innovation happened pre-Common Core. Now suddenly our kids need Common Core’s asinine approach to math in order to succeed?
The article also notes:
Susan Lee Swars, co-author of the April 2016 study of a Georgia urban school and a professor of math education at Georgia State University, said she was called in to provide professional development for the school and ran the study to see what kind of help the teachers would need. It was the school’s second year of Common Core instruction, and only 7 percent of the teachers surveyed strongly agreed that they were prepared to teach the standards and many voiced the sentiment that they needed to “unlearn” math and relearn it again. Other teachers spoke of encountering a lot of resistance in the classroom when they tried to modify math class to be more about the process than the solution.
Of course there is going to be rebellion when you focus more on the process than the solution. In real life the solution is what matters and using the fastest method to reach that solution. With all the talk of trying to prepare students for STEM they are using an approach that is the furthest from what is done on the job.
“I used to be against specialists because in time of budget cuts, they’re the first to go,” Ewing said. “But if you want to teach Common Core properly, we’ll probably move to a country of specialists. I’ve come around on this.”
Yeah, let’s just totally restructure school faculty to make way for unproven standards, more nonsense!
This is based on advice given from Jason Zimba, who was one of the lead writers for the Common Core Math Standards.
“The most important rule as a parent is to make sure it gets done. I may not have time to do an impromptu lesson on math but I can make sure everything is completed,” said Jason Zimba, one of the three lead writers of Common Core’s math standards and founding partner of Student Achievement Partners, a group that helps teachers with the standards. “It’s about managing work load and learning accountability.”
Although the father of two gives his children, ages 6 and 8, math tutorials on Saturday mornings, he says a parent doesn’t have to be a numbers whiz when it comes to homework.
“The math instruction on the part of parents should be low. The teacher is there to explain the curriculum,” said Zimba.
First as a parent I wouldn’t teach my kids Common Core math, I would teach them the fastest way to solve the problem so they will actually be prepared for life instead of what Common Core does. Second, this continues to feed into the mentality that teachers, not parents are responsible for a child’s education. I recognize that there are skill sets teachers have that parents don’t when it comes to classroom instruction. Our homes are not formal classrooms however, and it shouldn’t take “a math guru” to explain basic math to kids.
What Common Core has managed to do is drive a wedge between a student and their parents, and I think it is safe to say that this is by design.
The Boston Globepublished an article over the weekend that dealt with how the Common Core State Standards were impacting kindergarten students.
Here is one excerpt dealing with the impact of the ELA standards:
In two reports published earlier this year, the Boston-based nonprofit Defending the Early Years took aim at the kindergarten standards in ELA (focused on literacy at this age) and math. The first report singled out the expectation that kindergartners should be able to “read emergent-reader texts with purpose and understanding.”
Emergent-reader texts include repetitive lines like, “Brown bear. Brown bear. What do you see?” or, “The fat cat sat on a mat.” These are no trouble for some 5-year-old kindergartners and even some 4-year-olds, says Nancy Carlsson-Paige, an emeritus professor of early-childhood education at Lesley University and the report’s lead author. But, Carlsson-Paige adds, many normally developing kids won’t read these books on their own until age 7. “When we require specific skills to be learned by every child at the same time, that misses a basic idea in early childhood education,” she says, “which is that there’s a wide range to learning everything in the early years.”
Take walking as an example. An average child might learn to walk at 1 year, while some will be walking at 8 months and others might not take their first steps until they’re 15 months. They all end up walking just fine.
What does earlier reading in kindergarten predict for reading proficiency and academic success in later grades? Not much, according to the report, which cites study findings that by fourth grade, children who were reading at age 4 were not significantly better at reading than their classmates who’d learned to read at age 7. The report also points out that in Finland and Sweden, kids don’t even start formal schooling until they are 7 years old. Yet, Finnish and Swedish teenagers regularly trounce their American counterparts in international tests of reading, math, and science.
Given the wide developmental variation in young learners and the evidence that early reader advantages fade, the report concludes that a kindergarten literacy standard will simply crush the spirits of the late bloomers, linking school with “feelings of inadequacy, anxiety, and confusion.”
Here is another excerpt dealing with the math standards:
That’s the argument of Constance Kamii, a longtime professor of early-childhood education at the University of Alabama. Kamii wrote the second DEY report, published last month, attacking several of the Common Core’s kindergarten math standards, including that students should be able to count to 100 by ones and 10s, as well as compose and decompose numbers from 11 to 19 into 10 ones plus some further ones.
Kamii notes that the foundation of math is the ability to think abstractly about numbers — what five really means, beyond the numeral 5, or its place in a memorized sequence from one to 10 — as well as the logical relationships between numbers. “Not many 5- and 6-year-olds understand words like ‘forty’ and ‘fifty,’ ” Kamii writes in the report. So, while kindergartners can memorize the numbers from 1 to 100 with enough repetition, Kamii says that’s, “like making them memorize nonsense syllables.”
This leads to the other major criticism of the kindergarten standards — the pressure to meet them will intensify a push that began with No Child Left Behind for more academic drills, more lecture-style instruction and work sheets, and more testing in kindergarten.
“Young children learn best in active, hands-on ways and in the context of meaningful real-life experiences,” notes a statement of “grave concerns” about the kindergarten standards signed by hundreds of teachers and education scholars, including Howard Gardner, the Harvard developmental psychologist known for his theory of multiple intelligences and their importance in learning. “Overuse of didactic instruction and testing cuts off children’s initiative, curiosity, and imagination, limiting their engagement in school,” according to the statement.
NPR ran a profile on Jason Zimba that appears to be an attempt to change the narrative about Common Core. Here the writers of Common Core appear to be turned into victims, and curriculum companies and teachers are to blame for the poor roll out.
Every Saturday morning at 10 a.m., Jason Zimba begins a math tutoring session for his two young daughters with the same ritual. Claire, 4, draws on a worksheet while Abigail, 7, pulls addition problems written on strips of paper out of an old Kleenex box decorated like a piggy bank.
If she gets the answer “lickety-split,” as her dad says, she can check it off. If she doesn’t, the problem goes back in the box, to try the following week.
“I would be sleeping in if I weren’t frustrated,” Zimba says of his Saturday-morning lessons, which he teaches in his pajamas. He feels the math instruction at Abigail’s public elementary school in Manhattan is subpar — even after the school switched to the Common Core State Standards.
But Zimba, a mathematician by training, is not just any disgruntled parent. He’s one of the guys who wrote the Common Core.
And four years after signing off on the final draft of the standards, he spends his weekends trying to make up for what he considers the lackluster curriculum at his daughter’s school, and his weekdays battling the lackluster curriculum and teaching at schools around the country that are struggling to shift to the Common Core.
Zimba and the other writers of the Common Core knew the transition would be tough, but they never imagined conflicts over bad homework would fuel political battles and threaten the very existence of their dream to remodel American education.
Lest we forget, let’s remember that Jason Zimba himself said that if a student wants to take calculus as a freshman in college he or she will need more math than what the Common Core is required. He also said to the Massachusetts Board of Elementary and Secondary Education that the standards are “not only not for STEM, they are also not for selective colleges.”
You can watch that exchange below:
So let’s remember that there are problems with the standards themselves, but frankly when all of the Common Core-aligned math textbooks pretty much look the same it’s hard to say that they don’t accurately reflect how the standards are to be taught.
If curriculum publishers and teachers are getting it wrong, then there is a definite issue with a lack of clarity within the standards themselves as well.
Either way we circle back to the standards. This new narrative needs to be rejected.
I read an interesting article in the Sioux Falls Argus Leader yesterday. It was focused on how parents in the Sioux Falls, SD school district were fighting back against the Common Core Math Standards through pulling their kids out to homeschool.
That is probably the best thing that can be said about Common Core – it encourages homeschooling. I’m biased since my wife and I homeschool though.
The first thing that jumped out at me in the article is how a dad with a math degree saw problems with his daughter.
Rick Nath was tired of the emotional turmoil math homework was causing his daughter.
She was struggling with a new approach to old subjects, and Nath found there were fewer things he understood and fewer ways for him to help. It was a difficult realization for the 44-year-old Sioux Falls resident, who has a degree in math from South Dakota State University.
“By the time she got to sixth grade, that’s when it really got bad,” Nath said. “In sixth grade, it was tears.”
Surely he’s misinformed right? Doesn’t he understand these are more “rigorous” standards?
They then note the new trend with South Dakota parents.
In the four years since South Dakota schools began using Common Core, another movement has emerged: more parents are home-schooling. In Sioux Falls, the number of home-schooled students has more than doubled, and numbers statewide also are growing.
Parents choose home schooling to push their child academically, to teach beliefs not found in public schools or to avoid potentials for drug and alcohol abuse, according to the National Home Education Research Institute.
But some parents who have opted to leave public schools cite the new standards, which are benchmarks adopted by a consortium of states and embraced by the federal government: New homework, new lesson plans, new course material. And after piloting new state tests last spring, South Dakota will administer a finalized version later this year to thousands of students.
Parents may not understand what Common Core is, but they have noticed how it is being interpreted in the classroom through the asinine math that kids are bringing home. So they vote with their feet since the South Dakota continues to push these untested standards in the classroom. The sad thing in all of this is with all of the stress that the state of South Dakota is inflicting on their students they still will not be able to produce kids prepared for STEM programs in college.
Stanford University mathematics professor R. James Milgram included an informative e-mail in his packet of information for state legislators when he testified at a hearing on Common Core in Milledgeville, Georgia on September 24, 2014. The e-mail explains why presidents of many of the major mathematical organizations in the country endorsed Common Core’s standards in July 2013. The author of the e-mail seems to believe that the societies themselves would be unlikely to endorse Common Core’s standards, but that readers (i.e., the public) might be misled into thinking they had if they saw that the presidents had endorsed the standards. Consequently, the e-mail wants just the presidents’ signatures because they would “likely” be just as “effective.” The underlying assumption is that the members of these organizations would not be apt to learn what their presidents had done, much less know anything about the contents of Common Core’s mathematics standards.
The Common Core State Standards for Mathematics Table of Contents includes two types of standards. First listed are Standards for Mathematical Practice. Second listed are Standards for Mathematical Content. Before we explore the Standards for Mathematical Practice (SMP), let’s make a distinction between the SMP and Content standards. The SMP are process standards. They are a part of the CCSS. Most states have had similar process standards. As process standards, the SMP are probably as good as any others.
This table comes from slide 43 of a presentation at the Washington State School Directors Association conference in Nov. 2011. There are over 300 content standards in K-8. This above table presents one content standard and one of the Standards for Mathematical Practices.
Here are the eight Standards for Mathematical Practice.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
The Common Core State Standards lead off with Standards for Mathematical Practice.
The introduction to the Standards reads:
The standards for mathematical practice rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
To the casual observer, these words sound reassuring. For those who have been involved in the debate over how best to teach mathematics for the last two decades, this paragraph is extremely disturbing. NCTM’s process standards have been interpreted and implemented so as to downplay the importance of procedures and algorithmic involved in the debate over how best to teach mathematics for the last two decades, this efficiency in the name of “understanding”. It also favors finding more than one way to arrive at an answer that usually can be arrived at very simply in one way, and of eschewing word problems that provide the data that students will need to solve the problem in the belief that finding the data by themselves builds better problem solvers. We believe that the allegiance to the principles of the NCTM standards and ideology in Adding it Up will manifest itself in a student-centered, inquiry-based approach to math. We set out below attributes of the standards that are particularly weak and which lend themselves to such educational philosophy. As such, these standards in our opinion will diminish, not enhance, the mathematical proficiency and knowledge of students in K-12.
Possibly a little too esoteric but the concerns expressed regarding these standards manifesting in more student-centered, inquiry based approach to math are being realized.
Let’s take a close look at one of the SMP.
SMP 6. . Attend to precision.This sounds like they are calling for computational accuracy. One needs to look further and detect the nuance of emphasis in the narrative that gives more information about the meaning of this standard. Here is that narrative:
Mathematically proficient students try to communicateprecisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. (bold and color added for emphasis)
I have bolded the only phrase addressing accurate calculations. This does not come until the fifth sentence of the narrative. In the first sentence, “try to communicate precisely” is given a position of greater importance. While I am glad the writers thought to add “calculate accurately” into this standard, this standard appears to have more to do with attending to communicating with precision than calculating with precision or calculating accurately. Seven sentences… six related to communication, one about calculating accurately. How important is calculating accurately? What if the process of an inaccurate calculation is communicated precisely? And are you comfortable driving over that bridge or flying in that plane knowing that the engineers had great ability at communicating precisely about their inaccurate calculations?
The focus on communication was a problem with the old Washington math standards and other state standards influenced by the NCTM standards. This looks much the same, just a tad more sophisticated. Hey, it sure does sound great though. I’ll take a dozen… oh, there are only 8… that’s okay, I’ll still take a dozen.
Write or Wrong? The focus on communication in the SMP may, in part, be the source or justification for the emphasis in asking students to explain the process they use. The ability to explain may be given greater importance than getting the right answer. For many math problems, the work students show should be explanation enough and is a great indicator of understanding. There has been a shift in math it seems. Answers to straight-forward math problems used to be either right or wrong based on their being a correct answer to the problem. That no longer seems to be the case and an answer is deemed to be right if a group of students reach consensus about it.
Publishers of poor math textbooks/programs, professional development programs, and the SMARTER Balanced Assessment Consortium are emphasizing the Standards for Mathematical Practices (SMP) rather than the content standards. This emphasis on the SMP will influence local school district math textbook adoptions. The misguided but deliberate emphasis on the SMP rather than the content standards simply renders the CCSS as set of complex standards akin to the NCTM standards. The SMP flew in under the radar and few people were concerned about them. This emphasis will not serve the students across the country well.
The emphasis placed on the Standards for Mathematical Practice supports a constructivist approach. This approach is typical of “reform” math programs to which many parents across the country object. Programs like Investigations and Everyday Math are able to claim they address the CCSS SMP. Publishers of reform programs are aligning their programs with the CCSS Standards for Mathematical Practice. The adoption and implementation of the CCSS will not necessarily improve the math programs being used in many schools.
The emphasis on the SMP is driving professional development, textbook development, textbook selection and adoption, and assessment development. As a result of this emphasis, the SBAC may resemble a super sophisticated WASL rather than an actual assessment of student math skills.
Many math professional development programs for school administrators and teachers are focusing on the SMP. What is taking place in your local school district?
A couple of years ago I attended a meeting of math teachers at a middle school. None of the teachers had yet heard of the Common Core State Standards. The school principal was in attendance and was excited to share information about a seminar he attended the previous week. This principal distributed a one-sheet handout with the eight Standards for Mathematical Practice to the math teachers. He told the math teachers that these were the Common Core State Standards for Mathematics and this is what the school and the district will begin to focus on for math instruction. He gave no mention or indication of any awareness of content standards. These Standards for Mathematical Practice are what the school leadership has been told are the math standards and it is what leadership is telling teachers. Furthermore, administrators will evaluate teachers’ ability to deliver instruction on the SMP. Are the administrators in your local schools receiving similar training? For those who find the CCSS math content standards to their liking, and possibly an improvement over their old or current state math standards, I urge you and everyone else to beware of the deliberate emphasis on the Standards for Mathematical Practice.
Here are links to a couple of articles related to the emphasis on the SMP.