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Both the math and English Common Core standards have their share of critics but it’s math that gets special condemnation, as the new problem worksheets land on kitchen tables across the country.

Parents are taking to the Internet to air their frustrations by posting puzzling problems from the new standards. And even writers of the Common Core – a set of standards in math and English adopted by over 40 states – have agreed some of the questions were a bit bizarre and say teachers should also send home traditional problems.

Common Core math

So the question on the minds of many of the educators who gathered for the 25th annual conference of the Association of Mathematics Teachers of New Jersey was, what does a good common core question look like? The answer, according to many presenters, is to pose them with enough ambiguity to require students to think creatively to problem solve.

“Students should grapple with language,” said David Wees, who designs Common Core aligned math questions at New Visions for Public Schools. “You have to choose the right level of ambiguity, enough language so that students know what to do without making it obvious what they need to do.”

RELATED: Why is this Common Core math problem so hard? Supporters respond to quiz that went viral

Jamie Wall, lead math teacher at Brooklawn Middle School in Parsippany, New Jersey, spent the summer revising her school’s math curriculum in anticipation of the state’s new end-of-year exams. Starting this year, New Jersey will be using tests developed by PARCC, a consortium of about a dozen states that are developing tests to align with Common Core.

A sign of a good math problem, according to Wall, is that kids are able to approach it in many different ways. “Going over all the ways might be boring for an advanced student, but the less advance students need to be exposed to all the ways to do something,” she said.

Wall suggested ways to get kids to think about math that includd drawing pictures and crafting narratives. “Write me a math story,” she said.

Many of the presenters at the New Brunswick conference focused on the eight math practices outlined in the Common Core standards. They were particularly interested in two – making students persevere through difficult questions and having them construct and critique math arguments.

Linda Gojak, president of the National Council of Teachers of Mathematics, presented several problems she liked. One set she called, “always, sometimes or never.” The question asked if multiples of five have a five in the ones’ places always, sometimes or never and asked students to justify their answers. The answer is sometimes, as multiples of five always either have a zero or a five in the ones’ place.

As one the authors of the Common Core math standards, Phil Daro showed a problem he liked. He said, have students solve 15 divided by three in six ways: as a multiplication problem, by constructing equal groups of numbers, using an array, using an area model, using the multiplication table, and through writing a word problem. Students could learn about remainders by having them do the same thing for 16 divided by three, he suggested.

Linda Furey, National Educational Consultant at Triumph Learning, likes a problem that has students pick between four possible field trips to see caves. The students are given the costs of tours, lunch, and admission fees for each trip and given a budget of $700. All but one of the four options comes in under budget. Students’ judgment then comes in when the activity asks the students to make an argument for which trip the class should go on.

RELATED: More teachers are souring on Common Core, finds one survey

Jason Zimba, a founding partner of Student Achievement Partners and a member of the Common Core math standards writing team, doesn’t think teachers should throw out age-old math problems like seven plus eight. The standards, for example, still require that students memorize their times tables by third grade.

“If I were managing it in my own classroom,” says Zimba. “I would be sending home fairly traditional-looking problems, not only because that’s what parents are going to be able to work with, but because that’s part of the standards. They’re the end point. That’s the goal.”

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  1. This story highlights what is good and what is terrible about Common Core.

    One of the mantras of education over the last 30 years has been teaching in “multiple and diverse” ways. When doing this, the teacher realizes that students think differently, and that the teacher will try and present skills and material in many ways, with the hope being that a student who didn’t learn one way might learn better a different way.

    Common Core takes this to a nightmarish conclusion: force all students to learn all of the ways. In the past, students could find a way that suited them without penalty. Now, virtually every student will be penalized because very few students will adapt to every strategy.

    Common Core also flies in the face of current brain research by introducing advanced problem solving long before the brains of most young students have developed to handle that level of learning.

    I guess the good news for the students is that they can just blame the teachers and complain to the person hired to replace them at half the cost and none of the experience.

  2. The architect of Common Core math was Jason Zimba. The other two lead writers of CC math were, William McCallum, and Phil Daro.

    Jason Zimba, told us CC does not get students ready for selective colleges.

    William McCallum said,
    “While acknowledging the concerns about front-loading demands in early grades, [McCallum] said that the overall standards would not be too high, certainly not in comparison [with] other nations, including East Asia, where math education excels.”

    Phil Daro said,
    “And remember that the reason we have standards is because of the social justice agenda to make sure all kids get enough math to have a decent opportunity.”

  3. Educators hardly support other educators, that’s why so much chaos and mismanagement take place in the industry.

  4. Oh I wish I could modify the quote above just ever so slightly.

    “You have to choose the right level of ambiguity, enough language so that students know what to do without making it obvious what they need to do.”

    “You have to choose the right level of ambiguity, enough language so that students know WHAT to do without making it obvious HOW to do it.”

  5. the common core standards do not require the memorization of the multiplication tables by the end of third grade. They ask that students be FLUENT in multiplication which is a very different thing.
    Fluency can be defined as ‘knowing how a number can be composed and decomposed then using that information to be flexible and efficient with solving problems.’ (Parish 2014, p 159).
    The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense.

  6. Paula,

    The standard in question actually reads:

    CCSS.Mathematics.3.OA.7 “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.”

    If you read closely, you will notice that the last sentence does call for knowing the product, or the solution to a multiplication problem, of all single digit by single digit multiplication problems FROM MEMORY by the end of Grade 3.

    That said you are correct in that the standards are set up in a way that the numeracy is developed prior to the rote memorization.

    BTW for context, I am a mathematician by trade that has two children in a public grade school, and I support my state’s adoption of the CCSS. In my state as well as in others, there are issues with local curriculum choices, but as most of the CCSS detractors seems to forget (or gloss over because they can not find anything wrong with the actual standards) standards =/= curriculum. The CCSS do not tell teachers how they must teach, they state what the students must know by the end of the year (teachers get to choose how to get them to that level of understanding).

  7. I must concur with Richard and the nightmare that has been created. I believe a common set of standards is a good thing with such a transient population and the expectations set by our major colleges and universities. With that being said, I have personally witnessed students losing points because they did not “solve” a problem in the way the Common Core calls for. Far worse is the result this is having on our children and their confidence level in Mathematics.

    Differentiation has been a practice implemented by good teachers for years – it is the way we teach. When requiring a student to gain
    “conceptual understanding” of division of fractions with models, then communicating to the child they have “fallen short” if this is not the way their brain solves a problem, is detrimental to the education of our children.

    Educators have been trained to identify different learning styles and to present activities to address all different styles, however, they are now being told that ALL students must solve the problems in ALL ways presented, which is the antithesis of good teaching practices.

    I would also like to respectfully disagree with Paula’s comments regarding memorization of multiplication facts. As a middle school educator I see first hand how the lack of this “memorization” cripples a child’s ability to move into Pre-Algebraic and Algebraic concepts – many times students understand the underlying concepts, but due to poor basic computation skills, they often get the incorrect answer(s). This is self-defeating in two ways: 1 – students become discouraged and stop attempting the work if they are constantly incorrect, and 2 – the time necessary to work each of these problems is more than many students are willing to invest.

    Our brain’s ability to memorize starts to diminish at the age of 10 years – which is why, historically, memorization of 0 – 12 multiplication facts was called for at the end of 3rd grade. Do students need to “break numbers down” and see them in many different ways? Absolutely – but our brain is a pattern-seeking device and that which we see, hear, write, and do repeatedly quickly becomes habit and automatic, which is what students need for their multiplication facts. Long division is simply an extension of multiplication, and as a middle school educator I see how many (well over 35%) of our children will say.” I am not good at long division.” When I start working on the students with their multiplication facts, and realize they do not even know that one odd factor and one even factor always yields an odd product, I know they have not spent enough time on multiplication.

    My biggest complaint about the Common Core standards is this: We discount how unique each brain is by assuming all students will acquire knowledge by a set age or grade level – many students are not ready for Algebra until 11th or 12th grade. Is allowing them to fail repeatedly in anyway preparing them for College and Career? My first thought would be – NO.

    When we start teaching, we are not the master teachers we will become – it is understood that a learning curve exists – that some people will reach this status at a much quicker rate, while others may fail to ever reach this status. Do we “flunk” these teachers out of the profession or do we tell them they have to go to “Reteach” because they “just are not getting it?”

    While the Common Core may have been written by educators, we can not deny that it was greatly influenced by NCLB. NCLB has stated that ALL students will be proficient – WOW – so I am guessing there is no reason for malpractice insurance, because if every member of each unique population is expected to achieve the same results, then all doctors are PERFECT. The Common Core was a knee jerk reaction to comparing our students’ scores with those of students from other countries. FYI – other countries don’t test entire populations, including SPED, ELL, etc. These countries track their students and decide which ones are going to be highly successful in Mathematics and Sciences. Comparing our students’ Math and Science scores to those of other countries in like comparing a dog to a cat – yeah – they are both animals – but that is where they part company.

    Here is my final thought: We are the only profession in the world who are given a raw product we do not choose (our student population), told to deliver standardized instruction per grade level, yet expected to deliver designer originals when we have completed this “cookie cutter” process. We are controlled by individuals (politicians), the majority of whom have never taken a class on child pedagogy or brain-body development, whose primary concern is a talking point or a campaign election promise.

  8. The various methods being taught and which are in the spotlight, were also taught during the eras denigrated by many who criticize traditional math as having “failed thousands of students”. The difference is that the standard algorithms for the various procedures were taught in early grades and the alternatives to them were taught later–after mastery of the basic procedures. Thus, there was a distinction made between side dishes and the main course which is not being made in the current interpretations and implementations of CC.

    In contrast, what Common Core seems to insist on is akin to insisting that students continue to decompose words, syllables, and letters into their sounds long after they mastered decoding, phonics and reading. The purpose of learning to read is to allow students to use reading to learn other things; endless demand that they “demonstrate” they know the sound of “th,” or to repeatedly “explain” what’s the purpose of a period, are not conducive to development of fluent reading beyond the beginning stages. Yet that is what Common Core math effectively insists on doing years on end.”


    See also

  9. Thank you, Richard Patel. That is exactly the problem with how Common Core is being implemented.
    “The answer, according to many presenters, is to pose them with enough ambiguity to require students to think creatively to problem solve.” What on Earth makes them think that every person needs to think creatively, or even should think creatively, at every level of math? And again, some people are not creative at math at all, but they might need a standard way for creativity in another area (architecture, drafting). You don’t need 6 ways of doing a math problem in the real world. Just one way that works for you.

    A good math problem does not require you to problem solve. It requires you to learn how to do the math right. A challenge math problem might require you to problem solve, but that should only happen AFTER you learn how to do the math right.

    BTW, I liked Linda Furey’s cave field trip problem. Those are the kind nearly every kid understood and could eventually do. First you do the math, check to see that the math is correct, then make and educated decision (or problem solve) based on the math. That is some real world thinking.

  10. I agree with Tony: ” . . . as most of the CCSS detractors seems to forget (or gloss over because they can not find anything wrong with the actual standards) standards =/= curriculum.” Portraying the CCSS as a curriculum seems to be a common misunderstanding; it shows up in many articles written about the standards.

    If we could just get past that issue, we could move on to more interesting and useful topics, such as (1) why teachers find it so hard to attune their teaching to the CCSS; (2) what schools, teacher prep programs, educational organizations (including unions), and families can do to help teachers and support students; and (3) whether students taught via curricula that are aligned with the standards learn more, retain what they learn, and become more interested and invested in school and learning.

    After all, it’s about what’s best for the kids, not what’s hard for their teachers or their parents, right?

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