Advice on the Teaching of Standard Algorithms Before Common Core Says it is Safe to Do So Dept.

EdReports.org is an organization that rates textbooks/curricula with respect to how well they align with the Common Core standards. There are no ratings on the effectiveness of a curriculum or textbook–just whether it adheres/aligns to the standards.

They published a guideline for how to use EdReports’ reviews of texts.  Of interest is that under “Focus” for K-8, the key criterion to be assessed via their gradated ratings is: “Major work of the grade and no concepts assessed before appropriate grade level”

What captures my attention about this is the “no concepts assessed before appropriate grade level”.  Sounds similar to “no wine before its time” but it has more sinister implications in my opinion.

In my investigations and writing about Common Core standards, I have heard from both Jason Zimba and Bill McCallum, the two lead writers of the math standards. They have assured me that a standard that appears in a particular grade level may be taught in earlier grades. Jason Zimba also wrote an article to that effect.  So for example, the standard algorithm for multidigit addition and subtraction appears in the fourth grade standards. This does not prohibit the teaching of the standard algorithm in, say, first or second grade. A logical take-away from this would be that students need not be saddled, therefore, with inefficient “strategies” for multidigit addition and subtraction that entail drawing pictures or extended methods that have been known to confuse rather than enlighten.

Nevertheless, the interpretation of the “focus” of Common Core is used as a means to judge whether a textbook is aligned.  The term “focus” is discussed on the Common Core web site in a description of instructional “shifts” expected from implementation of CC. The instructional shifts do not appear as a standard anywhere within the Common Core content or the 8 Standards of Math Practice.

This means that if a publisher wishes their math book to sell, they will make sure that their assessment packages (otherwise known as tests and quizzes) do not include standards for later grades than for which the test/quiz is intended.  The result is that students will be tested on the inefficient convoluted and pictorial methods that are used in lieu of the standard algorithms.

While there are teachers who can overlook this, and accept a student’s use of a standard algorithm, there may be teachers new to the profession who adhere to the pre-packaged assessments. Furthermore, such practices may be reinforced by Professional Development vendors who specialize in Common Core.

The Common Core website insists that pedagogy is not dictated by Common Core:

Teachers know best about what works in the classroom. That is why these standards establish what students need to learn, but do not dictate how teachers should teach. Instead, schools and teachers decide how best to help students reach the standards.

In view of all this, my advice is to allow students to use the standard algorithms on a test even if it appears in a later grade. As far as alternate strategies, be aware questions on state assessments may include them. While scores on the state tests are not used in figuring the grade a student receives in a class, they may be used to qualify students for gifted and talented programs.

Bottom line advice: Teach the alternate strategies. Just don’t obsess over them.

 

5 thoughts on “Advice on the Teaching of Standard Algorithms Before Common Core Says it is Safe to Do So Dept.

  1. Have you ever taken a look at non-math public school textbooks? They are so bad! Every page is a distracting mess of separate boxes and graphics and photos. How can anyone learn anything? Actually they math books are the same way. I’m glad as a homeschooler I have access to other curricula.

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  2. The end result is that some outstanding curricula are punished by EdReports in their reviews primarily on the fact that they introduce topics that align to Common Core standards above grade level. For example, all three variants of Singapore Math, the “Primary Mathematics – Common Core Edition”, “Dimensions Math” (2013-15 & 2016-17), and “Math In Focus: Singapore Math by Marshall Cavendish” (2013) receive ridiculously low scores for Gateway 1 alignment in most grades because Singapore Math introduces topics well before Common Core prescribes them. For example, in our public school district when we were considering “Math In Focus” (MiF), those opposed to Singapore Math cited EdReports’ low scores as reasons against MiF. For example, in the EdReports’ review, MiF Grade 7 received a score of just a 4 out of 12 (i.e. “Does Not Meet Expectations”) in “Gateway 1: Focus & Coherence” because:

    “The instructional materials reviewed for Grade 7 do not meet expectations for assessing material at the Grade 7 level. There are too many concepts assessed that are beyond the Grade 7 CCSSM, and the alteration or omission of these items would significantly impact the structure of the materials. In chapters 1, 6, 7 and 8, there are assessment items that most closely align to standards above Grade 7 grade, and their inclusion is not mathematically reasonable for Grade 7. The alteration or omission of these items would significantly impact the underlying structure of the materials.”

    Source: https://www.edreports.org/reports/detail/math-in-focus-2013-7

    What is worse is that EdReports will not evaluate a curriculum for Gateway 2 “Rigor & Mathematical Practices” if the curriculum doesn’t meet the minimum Gateway 1 score (i.e. at least an 8.) Thus, almost none of the Singapore Math reviews are reviewed for their rigor. And actually EdReports’ reviews for Gateway 2 are often just cross-checking how well the textbook aligns w/ CCSS-M’s dubious “Standards of Mathematical Practices.” As Barry has discussed in other articles on this blog, many of the Mathematical Practices encourage “rote understanding” and not “deeper conceptual understanding” as CCSS-M aspires to.

    Given the CCSS-M standards push Algebra 1 standards out to 9th grade, this implies that almost all math curricula that use pre CCSS-M standards will be punished for introducing concepts too early.

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  3. Few talk about the fundamental change in education since I was in school in the 50’s and 60’s. That’s the idea of full inclusion. While this is a nice goal, it increases the range of abilities and willingness of students. In my son’s high school, it’s handled as a full inclusion environment, but with three academic levels for each course. However, in his K-8 schools, it’s handled in an age-tracking equal academic environment. They claim that differentiated instruction (differentiated learning) deals with the difficulty and claims on top of that that they achieve a higher level of understanding. It doesn’t happen. Some schools offer grade level academic grouping for part of the time, but that just groups the kids who get needed (mere) facts and (rote) skill mastery at home. This hides needed academic tracking at home and allows educators to believe that either their differentiated instruction works or that their ideas of natural learning work. I had many teachers tell me that “kids will learn when they are ready.”

    Our state’s supplier of the Common Core test specifically says (maybe they took it out now) that it’s not a STEM level of preparation. It starts in Kindergarten and has one slope to no remediation for a College Algebra course. This means (at best) that the goal is Algebra 1 as a freshman in high school. The College Board is now pushing “Pre-AP” classes in 9th grade that include a proper Algebra I class that emphasizes skills. Then they claim that it’s possible to pack in four additional math classes in three years! Only in their dreams. They let K-8 off the hook and then expect students to magically shift up to a much higher slope to AP Calculus as a senior. It’s quite incredible. Ed dreamland of K-8 hits the reality of the real world AP/IB classes pushing downwards. As I’ve said many times before, I got to calculus in high school with absolutely no help from my parents, but my son (and his STEM friends) all got help at home and with tutors. This is a simple project. Ask us parents of all of the high school STEM-ready students what we had to do at home for K-8. It’s a simple questionnaire.

    High school AP/IB math teachers know that Common Core math in K-8 is not good enough. Parents in our town fought back to replace CMP with proper Glencoe math textbooks in 7th and 8th grades so that kids are ready for Geometry as a freshman in high school. However, the schools still use Everyday math in K-6 and that requires mastery help at home or with tutors to get into the Pre-Algebra class in 7th grade. If you don’t do this, then the probability of getting into any STEM field is greatly reduced. It’s all over by 7th grade.

    Not acknowledging the slow Common Core path and not offering a fast track in math in K-6 is educational incompetence. Ask us STEM parents. It’s not difficult.

    Low expectations. That is real social injustice.

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  4. So how do Ed-school pedagogues explain how they handle Differentiated Instruction in a world where teaching techniques beyond grade level are taboo? How do they explain away accelerated in-class groups? Generally, they have avoided the word acceleration and used enrichment, because I guess they think that it’s not the same thing. How do you allow advanced students to get ahead without calling it acceleration? If enrichment is not getting ahead of others in some way (understanding?), then what is it? But what is either acceleration or enrichment when there is grade-level tracking of content and skills? Do they accelerate and then do nothing at the end of the school year? How much enrichment is worthless when cross-grade-level acceleration is needed, especially when Common Core lowers the slope to a NON-STEM level?

    They increase the spread of student abilities and willingness in K-6 with Full Inclusion, but then do nothing about it? Many even resist the option of allowing a proper Algebra I in 8th grade. This goes against decades of common practice and success. However with Full Inclusion in K-6, they really need to offer different academic options for acceleration. They want to age-track all kids in one classroom, but that creates separate groups (tables?) for the advanced kids. The other kids know what’s going on. This is no surprise. Why are those tables filled with kids from affluent families – something that educators don’t want to see? It’s because those parents provide the missing facts and skills at home – things that many other kids could easily handle.

    Why are high schools allowed to offer different levels of classes for same-age students? What’s different in K-6, especially with Full Inclusion increasing the academic range? Why do they resist the traditional split of students in math and foreign language in 7th and 8th grades? How do they expect freshmen to move directly into Geometry or a foreign language level II class? Are low slope K-6 students now so steeped in understanding that they can immediately accelerate to a higher AP slope and handle Geometry, Algebra II, Pre-Calc, and Calculus in 3 years? This is hard enough in 4 years for those who have done well in Algebra I in 8th grade.

    This is not as if delayed Algebra I has been tested out as a success. On the contrary, studies have shown that those who don’t get to Algebra I in 8th grade rarely get into STEM programs in college, let alone AP Calculus in high school. So schools forced more kids into Algebra I in 8th grade without fixing their math education in K-7 and then are surprised at the poor results. Now, apparently, they think that Algebra I in 8th grade is not good for anyone. This is just incredible and we STEM parents just shake our heads in disbelief and do the work at home and with tutors. The high school AP/IB track math teachers just keep a low profile and their mouths shut. Reality goes on without the K-8 Ed-school pedagogues.

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