California Removes Memorizing Multiplication Tables - A Detailed Analysis

A deeper dive into the California Math Framework's attempt to re-write the state's curriculum standards

Introduction

In our March 5, 2024 commentary article (also archived on this website here) we pointed out that California’s new math framework, a document which according to the California Department of Education is supposed to “offer guidance for implementing content standards,”  has removed mention that students are expected to memorize their multiplication tables. This is striking because California’s math content standards state that by the end of third grade students are expected to be able to:

“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.” 

However, when the 2023 framework quotes this standard, it omits the second sentence. The second sentence of the standard stating, “By the end of Grade 3, know from memory all products of two one-digit numbers,” is absent. Not once in its 1,000 pages does the 2023 framework state or mention that students should “know from memory all products of two one-digit numbers.” This raises the question: If a document that is expected to “offer guidance for implementing content standards” has effectively changed a standard in a significant way, how will this lead to successfully “implementing content standards?” 

Through a detailed comparison of the 2023 framework to the previous 2013 framework and the recommendations of nationally convened expert panels on math instruction, several points are demonstrated:  1) Memorizing the multiplication tables has transformed from being an emphasized skill in the 2013 framework and these expert panels to being deliberately removed and unmentioned in the 2023 framework, 2) the 2023 framework redefines the meaning of student fluency to avoid students memorizing their multiplication tables, contradicting the recommendations of the 2013 framework and these expert panels, and 3) the 2023 framework fails in implementing content standards, as the 2013 framework clearly stands out in comparison with its clear and specific guidance.

What is a framework? 

The official definition of a framework from the California Department of Education (CDE) site is: 

“Curriculum frameworks offer guidance for implementing content standards. Frameworks describe the curriculum and instruction necessary to help students achieve proficiency, and they specify the design of instructional materials and professional development. Further, they provide guidelines and selected research-based approaches for implementing instruction to ensure optimal benefits for all students.”

The content standards mentioned in the framework definition above are the California Common Core State Standards: Mathematics (CA CCSSM) approved by the State Board of Education in 2010. These describe the math content students are expected to learn and were vetted through an extensive approval process. Frameworks themselves are revised every seven years or so.

In addition to offering guidance on how to teach these standards, the framework offers guidance on many aspects involved in communicating the standards to students. It offers guidance on curriculum, instruction, instructional materials, professional development, and more. It offers guidance on implementing content standards. The framework is state approved guidance offered to teachers, districts, and textbook publishers affecting the teaching of math to California’s nearly 6 million pre-college public school students.

State curriculum frameworks are not granted the authority to change the standards. Frameworks are not granted the authority to choose which standards to teach and which ones not to teach. The purpose of a framework is not to allow its authors a chance to circumvent the standards based on their own opinions. The purpose of a framework is to “offer guidance for implementing content standards.”

Two points to understand about the new 2023 framework, which was adopted in July 2023 with the final version made publicly available in October 2023, are: 1) it is the framework that has changed – the standards have not; 2) the framework is not a mandate. Districts that conclude its guidance is not evidence-based and does not lead to effective student learning, do not have to adopt its guidance. However, because the framework affects curriculum and professional development, even these districts will struggle to remain completely immune from its effects.

The new 2023 California Mathematics Framework

Much of the discussion concerning the new 2023 California Math Framework has focused on its harmful effects on middle school and high school education. In particular, two major areas of concern that have been spotlighted are: 1) its guidance which hinders prepared and motivated students from moving ahead in their math learning; and 2) its guidance to replace the essential foundational course Algebra II with courses the authors call “data science,” but which contain so little math that they were recently deemed instead to be “more akin to data literacy courses” by a committee of UC professors. Multiple open letters signed by members of the Science, Technology, Engineering and Math (STEM) community, by academic staff at 4-year colleges and universities in California, by industry leaders in the field of Artificial Intelligence , and by California STEM professionals have addressed these issues in detail. In response to replacing Algebra II with “data science,” the University of California Board of Admissions and Relations with Schools (BOARS) makes it crystal clear that Algebra II is a necessary course for college preparedness in their Area C Workgroup Phase One Report and Recommendations.

Although most of these open letters were written in response to earlier drafts of the framework, which caused the final version of the framework to soften its stance, the concerns raised by these letters remain applicable to the adopted version of the framework. The concerns are by no means resolved.

The framework’s harmful guidance for elementary school math education has also been critiqued, but this topic has gone under the radar in comparison. The purpose of this discussion is to shed more light on this crucial issue. Since students are learning their foundational skills and number sense in elementary school, which is required for high school math and beyond, the framework’s guidance for the elementary grades may present even greater harm than its guidance for middle and high schools.

That the 2023 framework was adopted unanimously despite significant public opposition indicates an unwillingness by those involved in its creation to critically listen. Over and above the open letters previously mentioned, the submitted public comment for the third field review, which is essentially the final adopted version, was 3 to 1 against it. This framework is not at all what the public wanted.

Is memorizing the multiplication tables important for students?

The short answer is a resounding, “yes.” Nationally convened expert panels assessing requirements for high school math readiness, in particular Algebra, say memorizing the multiplication tables is important. Both the National Mathematics Advisory Panel (NMAP), established via presidential executive order, and the federal Institute of Education Sciences (IES) discuss in detail the importance of students achieving this skill. 

In its 2008 Final Report, when describing how to best prepare students for Algebra, the NMAP states:

1. “Computational facility requires the automatic recall of addition and related subtraction facts, and of multiplication and related division facts.”

2. “Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing … the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts…”

Similarly, the IES, after an extensive literature review, states:

“Quickly retrieving basic arithmetic facts (addition, subtraction, multiplication, and division) is not easy for students who experience difficulties in mathematics. Without such retrieval, students will struggle to follow their teachers’ explanations of new mathematical ideas. Automatic retrieval gives students more mental energy to understand relatively complex mathematical tasks and execute multi step mathematical procedures. Thus, building automatic fact retrieval in students is one (of many) important goals of intervention.”

Automatic fact retrieval is emphasized because it enables student success in K-8. Students progress from multiplication, to division, fractions, percentages, and exponents, eventually arriving at algebra. Each step is facilitated by having multiplication tables memorized. Common mathematical tasks like simplifying fractions, comparing fractions, factoring numbers and equations, finding common denominators, and working with exponents can be straightforward for a student with their multiplication tables memorized, but time-consuming stumbling blocks for one without.

Memorizing multiplication tables is more than just being about the ease of doing math, it is important because a person can actively think and concentrate on only so many things at once. Cognitive scientists call this “working memory.” Working memory is very limited and easily overloaded. Researchers discuss that a person can “process about four items in working memory at a time.”

Cognitive Load Theory describes the role limited working memory plays in student learning. Essentially, when solving multi-step problems requiring deduction, if a student’s working memory is occupied calculating simple math facts, that student will be at a considerable disadvantage compared to a student who can readily retrieve these facts from long-term memory. These latter students have freed up their working memory to concentrate on problem solving or following teacher’s lectures, while students without their multiplication tables memorized may be “stopped cold.”

The question around the importance and relevance of memorizing multiplication tables is not “does one need to memorize the multiplication tables to survive in this world?”, or “why bother memorizing them when phones can calculate tips and computer programs can do taxes?”, or “why is it necessary to memorize them for students not pursuing a STEM career?” The question is how to best position a student for success in high school math and beyond. If memorizing multiplication tables demonstrably benefits students, it should be required.

Students pursuing STEM careers should not have to strategize about basic arithmetic, like calculating 7 x 9, in upper-division college courses while their peers forge ahead with advanced topics like magnetism. Having to rely on calculators or phones for basic calculations like this would significantly slow students down and place an unnecessary burden on their working memory. 

Some argue that automaticity with basic math facts is unnecessary for students not pursuing STEM fields. However, third-grade students are unlikely to know their future career interests, so all educational doors should remain open. The safest approach is to prepare every student for potential STEM careers at this stage. If memorizing multiplication tables is part of this preparation, it should be given its due focus. A key purpose of K-8 education is to position students for success in high school, college, and beyond, which may include a career in a STEM field.

The designers of California’s state math standards understood all of the above, making memorizing the multiplication tables by the end of third grade unequivocal. This is stated in CA CCSSM standard 3.OA.7.

California Common Core State Standard Mathematics (CA CCSSM) – standard 3.OA.7

CA CCSSM grade 3, Operations and Algebraic Thinking, number 7 (3.OA.7) is:

The second sentence of the standard 3.OA.7 clearly states that students should “By the end of Grade 3, know from memory all products of two one-digit numbers.” Acquiring this skill is placed at the end of third grade because in fourth grade students work with products of two-digit numbers and fractions.

Comparing guidance on implementing standard 3.OA.7 in the 2013 framework to the 2023 framework

A detailed comparison of the 2013 framework to the 2023 framework shows how memorizing the multiplication tables changes from being a ubiquitous theme emphasized in the third-grade section of the 2013 framework to being deliberately removed and completely absent in the 2023 framework. 

2013 Framework

Below is an abbreviated guide through the grade three chapter of the 2013 framework showing the many excerpts where “By the end of Grade 3, know from memory all products of two one-digit numbers” is explicitly stated, mentioned, or discussed. This phrase is highlighted in the excerpts shown below and demonstrates in the framework’s own words the emphasis it gives to this skill. The 2013 framework presents its guidance for implementing the content standards students are expected to learn in third grade, which includes memorizing the multiplication tables, in its third-grade chapter. 

A link to the complete PDF file of the 2013 framework is available in the Resources section of the SaveMath.net website so the framework does not need to be opened chapter by chapter as it does on the California Department of Education (CDE) site.

The third-grade chapter starts with a section in the introduction titled “Critical Areas of Instruction.”

The 2013 framework then writes out the standard in its entirety, verbatim:

The framework denotes this standard with an upward pointing “triangle” symbol, as defined below. This means the standard is part of a “Major cluster” of standards, meaning the standard is emphasized. 

The 2013 framework then continues with a section devoted to teaching strategies. Noteworthy is that the strategies are a means to an end, and not the end itself, with the end being that the student achieves standard 3.OA.7, which is that they have memorized their multiplication tables.

The 2013 framework concludes this section on multiplication with:

It wraps up the grade 3 section with an “Essential Learning for the Next Grade” section:

And:

Finally, in the summary at the end of the chapter the standard is written explicitly yet again:

In summary, the 2013 framework makes it crystal clear that students are expected to memorize their multiplication tables by the end of third grade, and that this is important.

It is further noteworthy that the framework has a section focused on assisting students with memory difficulties, which could affect their ability to learn standard 3.OA.7. Some of this section is shown below:

2023 framework

In stark contrast, when the 2023 framework quotes standard 3.OA.7, it removes the second sentence which explicitly states, “By the end of grade 3, know from memory all products of two one-digit numbers.” This significantly changes the standard. The 2023 framework does this in two places:

In chapter 3,

And in Chapter 6,

Moreover, nowhere in the 2023 framework does it state that students should memorize their multiplication tables. All the explicit discussions about memorizing the multiplication tables that the 2013 framework presented in its grade three chapter in its Critical Areas of Instruction section, achieving standard 3.OA.7 discussion, Essential Learning for the Next Grade section, and in its concluding and summary sections, are absent from the 2023 framework. Even the section on helping students with memory difficulties is absent. In fact, the 2023 framework does not even have a third-grade section. It just groups all grades K-5 in one chapter called “Chapter 6—Mathematics: Investigating and Connecting, Transitional Kindergarten through Grade Five.” These are all striking differences between the 2013 and the 2023 frameworks.

As an aside, some have claimed that the grouping of content standards in the 2023 framework by a range of grades — called a “grade band” — as opposed to grade by grade, is a transformative innovation. Making it an acceptable practice to allow the content expected to be learned grade by grade, to instead be left to any time arbitrarily during a 6-year period, has the dangerous consequence of not ensuring it gets mastered.

Although the framework does not openly say that students should not memorize their multiplication tables (of course it cannot do this even if it wanted to because that would be obviously contrary to the standard), it accomplishes this message in three ways:

1. When the 2023 Framework mentions memorization, these sentences usually include phrases disparaging it like “unproductive beliefs”, “facts devoid of meaning”, “low cognitive demand”, “arbitrary laws”, “not ‘blind’ memorization of number facts”, “lower-level demands”, “little conceptual development”, “arbitrary rules out of thin air”, “least effective way”, “meaningless formulas”, “deemphasizing”, “’tricks’ and short-lived rules”, “unproductive notions”, etc. 
   
   Is the product 7 x 9 = 63 a “fact devoid of meaning?” Is memorizing the multiplication tables an “unproductive belief” and something of “low cognitive demand” that results in “little conceptual development?” The 2023 framework appears to believe the answer to these questions is “yes.”
   

2. The framework argues that timed testing, something often interwoven with enabling student multiplication fact memorization, causes math anxiety. It claims in chapter 12:

Researchers have examined a similar claim to the one made in the framework in detail, which stated that “for about one-third of students, the onset of timed testing is the beginning of math anxiety”, and concluded it is not evidence-based. 

Brian Conrad, Stanford Mathematics Professor and Director of Undergraduate Studies in Math, has extensively reviewed the Framework in his published public comments. Of the Framework claim shown above relating timed tests to math anxiety he concludes in his comments on the final adopted version “none of the cited references support the key claim made about timed tests causing math anxiety, so this entire paragraph must be removed,” adding “the passage is ideology in search of citations.” The framework writers ignored this, keeping the paragraph.

The framework ignores what is currently the best understanding of the literature, which concludes timed activities are beneficial. The framework also ignores the recommendations of the Institute of Education Sciences (IES), which concludes in its section on “Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades” to “regularly include timed activities as one way to build students’ fluency in mathematics.” The IES states in its What Works Clearinghouse (WWC) recommendations:

“Timed activity can engage students by providing feedback in real time, including goals for improvement, and steadily increasing item difficulty. Timed activities can be structured similarly during intervention, regardless of whether the focus is on automaticity with basic arithmetic facts or building fluency in other mathematical subtasks. 

The WWC and the expert panel assigned a strong level of evidence to this recommendation based on 27 studies of the effectiveness of activities to support automatic retrieval of basic facts and fluid performance of other tasks involved in solving complex problems.”

It places timed activities as one of its six “strong” recommendations:

In fact, Jo Boaler, one of the five framework authors and in whose work the statement relating timed tests to math anxiety originated (see citation misrepresentation instance A-24 and A-25 here), has admitted that the reference cited in the framework (Engle), which was also cited in her work, does not support the claim. In her own work, she replaced this reference with a different one, which has also been shown to not support the claim. 

Therefore, this framework recommendation that timed tests “have been found to prompt mathematics anxiety” is completely unsupported and is not evidence-based.

3. The framework demotes memorization from its inclusion as a standard in a Major cluster, as was guided in the 2013 framework, to something else.
   
   For example, in chapter 2 of the 2023 framework:

And in chapter 3:

Whatever citations the framework is using to justify this demotion, they are clearly in conflict with the evidence-based recommendations of both the NMAP’s final report and the IES, which emphasize the importance of student automaticity with math facts.

The framework is over 1,000 pages long. Not including the second sentence that completes standard 3.OA.7 that states “By the end of grade 3, know from memory all products of two one-digit numbers” is thus not related to space constraint issues. In fact, the paragraphs where the framework removed this sentence from the standard (shown earlier) can readily be seen to just repeat the content of each other. The framework writers felt it necessary to repeat this content, but in neither case include the second sentence of standard 3.OA.7. The vastly different guidance given for implementing standard 3.OA.7, observed when comparing the 2023 framework to the 2013 framework, leads to the conclusion that the 2023 framework’s omission of this second sentence is a deliberate choice by the framework writers. 

Perhaps this is not surprising once it is realized that the framework’s most influential author, Jo Boaler, is an educator who previously wrote, “I never memorized my times tables… It’s never held me back.” Her repudiation of memorizing the times tables is well known. It is further noteworthy that Boaler inveighs against the course Algebra II, the course BOARS made clear is foundational for college readiness, as an “an awful course!” She says this not with the intention of improving the course, but with the intention of replacing it with the data literacy courses mentioned earlier. In fact, in a meeting discussing writing the framework, she stated that making the math course pathway culminating in Algebra II “just as vibrant, and interesting, and illustrated” as a pathway culminating in these data literacy courses, would send the wrong message to kids. Her opinions have seeped into public policy through her co-authorship of the framework.

All that is left standing of the extensive discussion devoted to memorizing the multiplication tables given in 2013 framework, left standing like the last Truffula Tree in the Lorax after all else has been cut down, is the following statement in the 2023 framework:

This statement is an intentional re-writing of the following 2013 Framework statement:

The 2023 framework has changed the “know from memory” of the 2013 framework, and standard 3.OA.7, to “establish… in their memory.” This introduction of language not used in the standard opens a Pandora’s box for interpreting the standard, introducing fundamental ambiguity. For example, the Oxford Dictionary definition of establish is “set up (an organization, system, or set of rules) on a firm or permanent basis.” Changing to establish shows the framework’s intent is that it is a set of rules that are in the student’s memory, and not the actual memorized products. This is not what the standard calls for. This subtle but significant change illustrates the 2023 framework’s refusal to say that students should “know from memory” anything. After having suppressed mention of the standard in two places, this new language appears a deliberate attempt to obfuscate know from memory from the standard. This is a second example of the 2023 framework attempting to change the standard. 

In the 2023 framework, the strategies to find products (e.g. I can find 7 x 8 by knowing 7 x 10 = 70 and then counting back by 7 twice to eventually arrive at the answer of 56) are the end themselves, and not a means to an end as they are in the 2013 framework.  Thus, the 2023 framework assiduously avoids guiding students to memorize their multiplication tables. Students do not know from memory as in the 2013 framework, but it is the strategies or set of rules which “can help” establish in their memory all products of two one-digit numbers that the students know. This means that when a student encounters the need to know a math fact, the student does not instantaneously recall from memory the fact, rather they use a strategy to calculate the fact. Meanwhile, students with their math facts memorized are steps ahead in the problem leaving the student without their math facts memorized behind, or the teacher has moved on in the discussion leaving the student confused because they missed what the teacher said while they were strategizing about the product.

Moreover, there is a great difference between the phrase “can help” and the statement “expected to know.” The phrase “can help” is all the 2023 framework offers after all mention that students should memorize their multiplication tables is omitted. Saying that something “can help”, if it is left at that, removes the expectation that students are ever “expected to know.”

Table comparing the use of the word memorization in the 2013 and 2023 frameworks

The table below summarizes the differences between the 2013 and 2023 frameworks on memorization. Of the 26 times the 2013 framework uses a word directly related to memorization, 15 of those times are explicitly related to the specific parts of standard 3.OA.7 or standard 2.OA.2, that specifically direct memorization. These standards state, “By the end of grade 3, know from memory all products of two one-digit numbers,” and “By the end of Grade 2, know from memory all sums of two one-digit numbers,” respectively. The 2023 framework does not mention memory in these contexts.

Of the 32 times a word associated with memorization is mentioned in the 2023 framework, 26 times those sentences come with phrases disparaging memorization. In contrast, the 2013 framework does not disparage memorization.

Comparing direct usage of words associated with “memory” between the 2013 and the 2023 California Math Frameworks (CMF):

Fluency redefined

Fluency in language implies an ability to instantaneously recall words and phrases such that the language can be spoken or written easily and accurately. Analogously, fluency in mathematics should imply the ability to instantaneously recall math facts such that certain math tasks can be performed easily and accurately. 

What follows is a comparison of the definition of fluency between the 2013 and 2023 frameworks, as well as how the term fluency is used by the NMAP and the IES. The 2013 framework, NMAP, and IES all use a definition of fluency involving the automatic recall of math facts, while the 2023 framework redefines fluency, so it does not.

NMAP Final Report

The use of the word fluency in the NMAP’s final report includes automatic recall of multiplication facts as shown in this excerpt from the report below: 

The IES’s recommendations

Two excerpts from the IES’s recommendations emphasizing automatic recall of multiplication facts were already shown. They were from its section titled “Regularly include timed activities as one way to build students’ fluency in mathematics.” Below is one further excerpt from their discussion describing why:

2013 framework

The 2013 framework defines fluency in its glossary, with key phrases highlighted:

A summary of the 2013 framework’s guidance on fluency is below. This is followed by excerpts from the framework showing this guidance in the framework’s owns words. 

1. The 2013 framework states a relationship between fluency and speed, “the word fluent is used in the standards to mean ‘reasonably fast and accurate’” and possessing the ability to “use certain facts and procedures with enough facility that using such knowledge does not slow down or derail the problem solver as he or she works on more complex problems.”

2. Students are expected to know “single-digit products and sums from memory.”

3. “By the end of grade three, students also know all products of two one-digit numbers from memory (3.OA.7).”

4. “…In grade three… reaching fluency… represents a major portion of students’ work.”

5. Much of this is clearly laid out in a chapter devoted to grade three.

2023 framework

The 2023 framework’s definition of fluency from its glossary is one sentence:

The 2023 framework redefines the term fluency to not include memorizing multiplication tables, but instead students are to use “strategies.” It presents this guidance in several ways:

1. Speed is not part of fluency – “avoid any temptation to conflate fluency and speed.”

2. Knowing from memory some facts might be used, but there is no statement that students are expected to “By the end of Grade 3, know from memory all products of two one-digit numbers” and that Standard 3.OA.7 is successfully learned.

3. Instead of memorization, the use of “strategies” appears to be the method students are to use when working with math facts.

4. There is no third-grade section, instead K-5 are grouped as one.

5. Instead of “By the end of Grade 3, know from memory all products of two one-digit numbers” the framework indicates that acquiring fluency “begins in third grade and development continues in grades four and five.”

The 2023 framework’s discussion of “fluency” was shown earlier. Instead of memorizing the multiplication tables, and achieving the standard 3.OA.7, the framework is guiding that students should use “strategies” to determine math fact products. For example, instead of memorizing that 4 x 6 = 24, the student might “know” that 2 x 6 = 12, then they are to double it to determine that the product 4 x 6 = 24. Even here, the framework makes it unclear what it means by “know.” Is it “know from memory?”

These might be strategies a third-grade student might use as they are memorizing their multiplication tables, but using these strategies for the rest of their mathematical career would be detrimental to the student’s success. Continuing to rely on strategies like these for all products in the later grades could “slow down or derail the problem solver,” needlessly occupying limited working memory needed for problem solving and following teachers’ lectures. 

Since the 2023 framework does not present its guidance for implementing content standards grade by grade, as the 2013 framework did, but instead appears to group all learning in elementary school in one chapter, it is unclear when the students attain its definition of fluency. While the 2013 framework makes it clear that students are expected to “By the end of Grade 3, know from memory all products of two one-digit numbers”, as stated in the standard, the 2023 framework states:

The 2023 framework does not make it clear what it specifically means by this. However, instead of “By the end of Grade 3…” acquiring the 2023 framework’s definition of fluency only “begins” in third grade and “development continues in grades four and five.” Since fluency is only developed, with no skill ever specifically attained, it is unclear if students are ever expected to fully achieve even the 2023 framework’s definition of fluency.  The memorization goals explicitly stated in standard 3.OA.7 appear unachieved in the 2023 framework.

Finally, in contrast to the 2013 framework, which discusses fluency in terms of “reasonably fast and accurate,” the 2023 framework removes speed from fluency stating in chapter 6:

The authors of the framework are well aware and very proud of their redefinition of fluency, celebrating that the framework creates “a new definition of fluency - neither number sense nor ‘fluency’ are about speed, they are about flexibility.” If it takes a student one minute to determine the product of 6 x 8, is that satisfactory as long as the student is “flexible?”

Shown below is a table summarizing the key differences between the 2013 and 2023 frameworks regarding their definitions of the term “fluency.”

Discussion and conclusion

The 2023 framework has removed the key sentence “By the end of Grade 3, know from memory all products of two one-digit numbers” from the standard 3.OA.7. This is a significant omission which significantly changes the standard. Therefore, the Framework has, de facto, changed the standard. There is nothing written in the CDE’s definition of a framework that indicates framework writers are granted the authority to do this. The framework writers took a significant liberty doing this, which the CDE has enabled by voting unanimously to adopt the framework despite significant public disapproval.

Students should clearly understand what memorization is. However, at some point, once multiplication is understood, the student moves on and commits math facts to memory, consistent with the state’s math standards and the recommendations of the NMAP and the IES. Thus, a student is prepared for more advanced material and more involved problem solving. If not, just imagine a student working in their high school Algebra I or Algebra II class, spending time calculating simple products like 6 x 8 every time they come up. Problem solving would grind to a halt.

Although the 2023 framework’s egregious guidance offered for implementing one content standard has been described in detail here, there are many standards the 2023 framework has similarly transformed. For example, try to find in the 2023 framework the part of the second-grade standard 2.OA.2 which clearly states, “By end of Grade 2, know from memory all sums of two one-digit numbers.” You can’t because it is not there.

It could be thought that since the standards have not changed and memorizing the multiplication tables is a clear directive of standard 3.OA.7, then it is not significant that the framework removes this part of the standard. However, if the document that California looks to for “guidance for implementing content standards,” removes a significant part of a standard and changes its wording, as the 2023 framework does, without informing the reader it has done this, what ensures that the standard will be successfully communicated to, and learned by, the student?

This is especially a concern when this standard is considered by nationally convened expert panels, and the previous framework, to be a standard requiring major emphasis. Furthermore, if a framework is engaged in this practice of manipulating the standards, would this be considered a dereliction of its duty? It is said that “Instead of organizing curricula and instruction around individual standards, the framework outlines ‘big ideas in mathematics.’” This is fraught with peril because the “big ideas” are ill-defined, leaving to chance what math content is covered in the classroom. 

The Framework’s solution to students struggling to learn the standards appears to be to simply cease teaching them. Students relying completely on public schools for education will not be taught essential skills listed in the standards, while students with greater resources can learn these skills elsewhere. This will worsen the achievement test disparities that are painfully apparent in standardized test scores.

The framework claims, “equity—of access and opportunity—is essential and influences all aspects of this document.” By not teaching students skills fundamental to their success, students may both lose access to STEM career pathways, and lose the opportunities to be successful in these pathways. Therefore, the framework has fundamentally failed even in its own stated mission.

The 2023 framework presents non-evidence-based guidance that conflicts with the evidence-based recommendations for elementary school education from nationally convened expert panels. The framework changes the standards, misleading the reader as to what the standards state, meaning that it offers unsound guidance for implementing content standards. Districts should not adopt the framework’s harmful recommendations and instead turn to sound guidance from sources like the NMAP and the IES.