I teach math at a small Catholic school in California. I teach 7th grade math and 8th grade algebra. For those who have read my latest book, you know that I use a 1962 version of Dolciani’s “Modern Algebra” as my textbook. The students like the simplicity of its presentation, and so do the parents. I have had parents tell me they like the book, and one in particular said that it is how she learned algebra, and it allows her to help her daughter. She thanked me, and said “I can’t stand that Common Core stuff.”
The Common Core stuff that irks parents are the alternative “strategies” that replace the standard algorithms. One of these is for multidigit addition/subtraction; another is for multiplication and division. As I’ve documented before, these strategies (such as ‘making tens’) are nothing new. Traditional textbooks of the past have taught them, but they were introduced after students mastered the standard algorithms. The standard algorithms served as the “main dish” in the dinner party known as math. The alternatives were “side dishes” and the two were distinguishable. Now they are not; it is one big mess, with students sometimes thinking that they have to use a particular strategy for particular problems.
Therefore it is of interest to hear William McCallum’s view of this aspect of Common Core. He was one of the two lead writers of the Common Core math standards. When I wrote an article that was published in the online Atlantic about Common Core, I pointed out that the standard algorithm for multi-digit addition and subtraction did not appear until 4th grade. Until then, teachers and students were saddled with “strategies” which included pictures and inefficient methods in the name of “understanding”. The view of reformers is that teaching standard algorithms first eclipses the conceptual underpinning of why the algorithms work as they do—this in spite of the pictorial explanations that appeared in early textbooks from the 60’s, 50’s and earlier that provided such explanation.
McCallum commented on my Atlantic article and disagreed with me that the standard algorithms were delayed. I provided him evidence until he finally stated that the Common Core standards do not prohibit the teaching of the standard algorithms prior to the grade in which they appear. Specifically his comment was:
“The standards (1) do not say that conceptual understanding must come first, and (2) also say explicitly on page 5 that ‘These Standards do not dictate curriculum or teaching methods. For example, just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time.”
This was news to me, and apparently news that was buried in the material accompanying the standards, despite McCallum’s belief that it was made clear. In particular, a guidance document for publishers, which came out in tandem with the Common Core standards, advises publishers not to test students on standard algorithms prior to the grade in which they appear in the standards. I guess it’s OK to teach the standard algorithms earlier, but just not to ensure that students know them.
There are few “Common Core aligned” textbooks that address the standard algorithms prior to the grades in which they appear in the Common Core standards, so apparently McCallum’s word has not really made the rounds. There is one exception and that’s the Common Core editions of Singapore Math. They do teach the standard algorithms earlier. They also test the students on them, which has cost them a penalty by the company EdReports which rates textbooks in terms of the degree to which they are aligned with Common Core. Singapore Math’s Common Core edition is considered by EdReports to not be aligned.
Since people mistakenly believe that alignment with Common Core implies effectiveness, EdReports’ rating of Singapore’s books may have cost the company some sales.
The Standards continue to be interpreted in accordance with math reform ideology. And although McCallum in his remarks to me in the comment section of the Atlantic article stated that “the phrases ‘critical thinking’ and ‘collaborative learning’ do not occur anywhere in the standards and that the standards “neither dictate nor forbid any particular style of pedagogy”, the die has been cast for the lower grades (K-6).
In the world of Common Core, alignment equals effectiveness, and book publishers happily comply with the guidelines they have been given. In my opinion, as well as others, it would have been helpful if McCallum’s statements to me could have been made more public than in the comment section of an Atlantic article. It also would be helpful if publishers are not punished by outfits such as EdReports for ensuring that students know standard algorithms prior to the grade in which they appear in Common Core.