A Closer Look at the Six Finalist Curricula: Claims versus Reality

by Sugi Sorensen
February 10, 2026

Introduction

In our coverage of the second elementary math adoption parent meeting on January 28, 2026, we noted that La Cañada Unified School District (LCUSD) presented six finalist curricula for the K–5 math adoption. We also noted that several claims made about these curricula during the presentation deserved closer scrutiny. This article provides that scrutiny.

Before we begin, some important context. The district’s math adoption process has improved significantly since it began. The Elementary Math Adoption Committee received Science of Math training from Dr. Robin Codding in December 2025, and by all accounts this training has genuinely shifted thinking on the committee. Committee members and administrators have acknowledged the superiority of explicit instruction over constructivist approaches for novice learners. The district has questioned the California Math Framework’s (CMF) advice. Associate Superintendent Jim Cartnal has publicly stated that the Science of Math training made him “think differently about some of the policies coming from the State of California.” The committee’s revised Math Vision Statement now emphasizes “explicit direct instruction” and “procedural fluency.” These are meaningful steps in the right direction, and the district deserves credit for taking them.

The concern is that the new thinking has not yet transferred to the actual curriculum selections. The committee’s stated principles now point clearly toward explicit instruction, CPA alignment¹, and preparation for Math In Focus in grades 6–8. But when we examine what the six finalist curricula actually are – not what Cartnal said about them at the 01/28/26 meeting, but what their own publishers and developers say about them – we find that only two of the six are consistent with those principles. The other four range from marginally compatible to fundamentally opposed to what the district says it wants.

This is not a criticism of the committee’s intentions. At the November 5, 2025 first parent meeting, Cartnal promised that a “high-quality” instructional materials rubric would be developed after the LCUSD Math Priorities Survey had been conducted and analyzed, and only then used to down-select materials from all those available. In practice, the committee attended LACOE’s publishers fair at the Arboretum in Arcadia in December — and narrowed the field to six finalists — before that rubric had been developed.

This is also a call to align the curriculum selections with the committee’s own evolving understanding of effective math instruction. The Science of Math training opened a door. Now the committee needs to walk through it.

A Framework for Evaluating Curricula: The Instructional Hierarchy

Before examining each curriculum, it is worth understanding a research framework that should guide how we evaluate any K–5 math program: Haring and Eaton’s Instructional Hierarchy (1978). This framework, which has been validated by decades of subsequent research and is central to the Science of Math literature², describes four stages through which learners progress when acquiring any new skill:

• Acquisition: The student is first learning a new concept or procedure. At this stage, instruction should be explicit and teacher-led. The teacher models, demonstrates, and guides. Errors are corrected immediately. This is the “I do, we do” phase of gradual release mentioned by Cartnal at the 01/28/26 meeting as a non-negotiable result from the LCUSD Math Priorities Survey.³
• Fluency: The student can perform the skill correctly but needs to build speed and automaticity. At this stage, students need structured, repeated practice with feedback. Timed drills, fact practice, and systematic review are appropriate. This is the “you do” phase of gradual release.
• Generalization: The student can perform the skill accurately and fluently, and is now ready to apply it in varied contexts. At this stage – and only at this stage – open-ended problems, novel applications, and transfer tasks become appropriate.
• Adaptation: The student can modify learned skills to solve novel problems. This is where genuine mathematical reasoning and creative problem-solving emerge – but only after the prior three stages have been mastered.

The Instructional Hierarchy has a critical implication for curriculum evaluation: the type of instruction a curriculum provides must match the stage of learning. A curriculum that asks students to “discover” or “explore” concepts they have not yet been explicitly taught is providing generalization-stage activities to acquisition-stage learners. This is pedagogically backwards. It is the equivalent of asking someone to compose an essay in French before they have learned French vocabulary and grammar. Research consistently shows that failing to follow the proper sequence laid out in the Instructional Hierarchy increases cognitive load, produces frustration rather than understanding, and widens rather than narrows achievement gaps.⁴

With this framework in mind, the key question for each finalist curriculum becomes: Does this program provide explicit, teacher-led instruction during the acquisition stage, then build fluency through structured practice, before moving to open-ended application? Or does it ask students to engage in “productive struggle” with concepts before they have been taught them? The answer tells you whether a curriculum is compatible with the Science of Math – and with Math In Focus’s approach in grades 6–8.

At a Glance: Claims versus Reality

Here is a summary of the claims made by Cartnal at the January 28th meeting and what the publishers’ own materials actually say:

Math In Focus (Marshall Cavendish/HMH): Claim: “Obviously a very strong contender” for K–5 extension. Reality: Accurate. Math In Focus is the gold-standard Singapore Math adaptation for the U.S. market. CPA-aligned, explicit instruction, mastery-based. It is the logical choice for K–5 coherence with grades 6–8.

Eureka Math² (Great Minds): Claim: CPA-aligned. Reality: Partially accurate. The original Eureka Math was designed as a reverse-engineered Singapore curriculum with genuine CPA architecture: number-as-unit emphasis, bar model usage, concrete-pictorial-abstract progression. Eureka Math² retains that mathematical core but has layered on progressive pedagogical language (equity, discourse, “positive math identity.”) The mathematical content progression has legitimate CPA bones. Whether the classroom delivery still aligns with explicit instruction requires careful evaluation.

California Math Expressions (Heinemann/HMH): Claim: CPA-oriented; rooted in East Asian math practices; would prepare students for Math In Focus. Reality: False on all counts. The publisher’s own materials describe it as an “inquiry-based,” “reform-oriented,” “student-powered” curriculum. See detailed analysis below.

enVision+ (Savvas): Claim: CPA-oriented. Reality: Inaccurate. Savvas’ own materials describe it as a “problem-based learning” curriculum with “student-centered activities.” See detailed analysis below.

Into Math (HMH): Claim: A “California-ized version of Math In Focus” with “Singaporean concepts at its heart.” Reality: Inaccurate. Built from the ground up around the California Mathematics Framework, not Singapore Math. See detailed analysis below.

Amplify Desmos CA Math (Amplify): Claim: Not CPA-aligned, but included because teachers like Amplify’s DIBELS platform. Reality: Correct that it is not CPA-aligned. What was not disclosed is that it is built on Illustrative Mathematics, one of the most controversial inquiry-based curricula in the country, currently under fire in New York City. See detailed analysis below.

1. Amplify Desmos CA Math: Built on Illustrative Mathematics

Amplify Desmos CA Math is built on Illustrative Mathematics (IM), a curriculum created by Bill McCallum, a lead author of the Common Core math standards. IM is designed around a philosophy that inverts the gradual release model: students grapple with problems before the teacher provides instruction. IM’s own CEO has described its method as one that “flips the ‘I do, we do, you do’ model on its head.” In terms of the Instructional Hierarchy, this means providing generalization- and adaptation-stage tasks to students who are still in the acquisition stage – exactly the mismatch that research warns against.

Amplify’s own materials confirm this orientation. The program describes itself as offering “student-centered instruction” where students “figure out how math works instead of simply memorizing formulas and tricks.” Its caregiver materials explicitly tell parents that “student-centered instruction may look different from the way you learned math.”

The NYC Cautionary Tale

LCUSD parents should be aware of what has happened in New York City, where Illustrative Mathematics was mandated across the city’s public schools as part of a $34 million initiative called “NYC Solves.” The rollout has been deeply troubled:

• In a south Queens district that piloted Illustrative Math, Algebra I Regents pass rates dropped from 59% to 45% in a single year, as reported by the district’s own superintendent.⁵
• City-wide, the Algebra I Regents exam pass rate fell from 56.2% to 46.8%, a staggering one-year drop of 9.4%.⁶
• NYC’s own instructional guide acknowledged that topics including unit conversions, polynomial equations, and sequences are “not sufficiently covered” by Illustrative Math.
• The United Federation of Teachers formally pushed back, with union president Michael Mulgrew citing “the curriculum’s lack of remediation for students below grade level” and “unrealistic expectations about how quickly teachers should move through lessons.”⁷
• As recently as January 2026, NYC’s new Schools Chancellor announced changes to the program, acknowledging the need to ensure students “have a grasp of the basics, including multiplication and division.”⁸

A Philadelphia evaluation study reached similar conclusions: educators reported difficulty with pacing and differentiation. One principal observed: “Sometimes, continually doing productive struggle all the time is not always the answer.”⁹

The DIBELS Brand-Halo Problem

The rationale for including the Amplify Desmos CA Math curriculum – that teachers are familiar with Amplify’s DIBELS assessment platform for ELA – rests on a misunderstanding of who actually created DIBELS and what Amplify’s role is.

DIBELS was not developed by Amplify. It was developed by researchers at the University of Oregon’s Center on Teaching and Learning (CTL), beginning in the late 1980s. The first DIBELS measures were created as part of Dr. Ruth Kaminski’s doctoral thesis in 1992 under Dr. Roland Good. The University of Oregon retains intellectual ownership of DIBELS to this day, continues to conduct the underlying research, publishes updates to the assessment, and makes the paper-and-pencil testing materials available for free download from its website. DIBELS is excellent because it is grounded in decades of rigorous university research on the Science of Reading – measuring discrete, specific sub-skills like phonemic awareness, phonics, fluency, and comprehension.

Amplify’s connection to DIBELS is as a technology delivery vendor, not as a research partner. Amplify began as Wireless Generation, a company that built mCLASS – a digital platform for administering and scoring DIBELS on handheld devices. News Corp acquired Wireless Generation for $360 million in 2010, renamed it Amplify in 2012, invested roughly $1 billion, wrote most of it down, and sold the company to its own executives in 2015. More recently, the University of Oregon transferred management of the DIBELS Data System to Amplify, making Amplify the exclusive licensed digital provider of DIBELS 8th Edition through mCLASS. But the research credibility belongs to the University of Oregon, not to Amplify. Amplify is the delivery app; UO is the science.

Then, in a completely separate transaction in May 2022, Amplify acquired the Desmos curriculum – a math teaching platform built on Illustrative Mathematics. The Desmos graphing calculator was spun off as an independent public benefit corporation; what Amplify kept was the inquiry-based math curriculum.

So when LCUSD teachers say “we like Amplify’s DIBELS,” what they actually like is the University of Oregon’s assessment, delivered through Amplify’s software. The brand-halo reasoning involves a double category error: first, attributing UO’s research credibility to Amplify (the delivery vendor); and second, extending that misattributed credibility to Amplify’s completely unrelated acquisition of an Illustrative Mathematics-based math curriculum. The University of Oregon’s DIBELS team and the Illustrative Mathematics developers share no intellectual lineage, no common research tradition, and no pedagogical philosophy. They happen to sit under the same corporate umbrella because Amplify bought both – one as a technology platform deal, the other as a curriculum acquisition. Choosing a math curriculum on this basis is like buying a Toyota Camry because you like the Bose Audio system in a Lexus sedan.

Instructional Hierarchy assessment: Amplify Desmos CA Math provides generalization-stage activities (open-ended exploration, group problem-solving) to acquisition-stage learners. This is a fundamental mismatch. Not compatible with the district’s stated commitment to explicit instruction and gradual release.

2. California Math Expressions: Inquiry-Based, Not CPA

California Math Expressions was described at the 01/28/26 meeting by Cartnal as “really, really strong work, rooted in the close analysis of East Asian country high schools” and as CPA-aligned. These claims are contradicted by the program’s own publisher, developer, and marketing materials.

What Heinemann Actually Says

Heinemann’s own press release for the newest edition (June 2025) describes it as offering “the same research-proven, inquiry-based approach to math instruction.” The publisher calls it a “student-powered math curriculum” and describes Dr. Karen Fuson’s research as exploring “how students build on and use conceptual supports for a balanced inquiry path to mastery.”

The Evidence for ESSA evaluation describes Math Expressions K–2 as “a reform-oriented curriculum that balances teaching of efficient procedures with promoting natural solution methods”¹⁰ — language HMH itself highlighted in its own 2019 press release.

The program’s five core structures – “Math Talk, Building Concepts, Quick Practice, Helping Community, and Student Leaders” – are the organizational touchstones of student-centered, constructivist instruction. The program invites students to “choose their own path to the answers” and emphasizes that “students just don’t learn math; they experience it.” Fuson says in a video on the California Math Expression’s main web page, “Students start by inventing their own methods, but then move to better strategic methods that are introduced, taught and supported, and then move to practice and fluency.” This is an inversion of Haring and Eaton’s Instructional Hierarchy.

The East Asian Claim

Dr. Fuson’s faculty page notes that her program is “based on research in the NRC reports and on aspects of international math programs.” The word “aspects” is doing a lot of work in that sentence. The primary intellectual foundation of Math Expressions is the National Research Council’s Adding It Up and Dr. Fuson’s NSF-funded Children’s Math Worlds project – not the curricula of Singapore, Japan, or any other East Asian country.

What makes East Asian math education effective – explicit instruction, systematic practice, high expectations for procedural fluency, carefully sequenced scope and sequence, teacher-led CPA progression – is largely the opposite of what Math Expressions emphasizes. Dr. Fuson studied how children naturally develop mathematical understanding; Singapore Math prescribes a carefully engineered instructional sequence. Those are different design philosophies. Referencing East Asian research is not the same as building an East Asian-style curriculum.

Not a Bridge to Math In Focus

Math In Focus uses a structured, explicit instructional model where the teacher leads students through carefully designed problem types in a controlled CPA sequence. Math Expressions uses “Math Talk communities” where students develop and share their own solution strategies in a “Helping Community.” A student raised on Math Expressions’ approach would arrive in 6th grade with a fundamentally different mathematical preparation than what Math In Focus expects. This is not a bridge to Singapore Math – it is a different road.

A Pattern Parents Should Recognize

LCUSD parents may recall that Math Expressions is published by Heinemann – the same publisher behind the Fountas & Pinnell “balanced literacy” materials that the district abandoned after recognizing they were built on scientifically unsound premises.¹¹ The district retrained its teachers in the Science of Reading and adopted evidence-based instruction instead. Heinemann’s literacy products were grounded in the same “student-centered,” “inquiry-based” philosophical DNA that undergirds Math Expressions. The district learned in literacy that these labels can sometimes mean “we don’t explicitly teach children the things they need to know.” It would be worth reflecting carefully before repeating that experience in mathematics with a product from the same publisher.

Instructional Hierarchy assessment: Math Expressions blends acquisition-stage and generalization-stage activities from the outset, asking students to “choose their own path” and participate in “Math Talk” communities before mastering foundational procedures. This inverts the research-supported sequence. Math Expressions is clearly not compatible with the district’s stated commitment to explicit instruction.

3. enVision+: Problem-Based Learning, Not CPA

enVision+ was claimed by Cartnal to be among the curricula characterized as CPA-aligned. Savvas’ own materials tell a different story.

Savvas explicitly describes enVision+ as featuring “problem-based learning, performance tasks, and visual instruction.” Its CEO describes a curriculum that “engages students with hands-on, problem-based learning.” The instructional model is built around a two-step design: Problem-Based Learning followed by Visual Learning. In the first step, students are “given time to struggle to make connections to the mathematical ideas” and “can choose to represent their thinking and learning in a variety of ways.”

The newest edition introduces three lesson types – “Let’s Investigate,” “Let’s Build,” and “Let’s Model” – with “high-interest, student-centered activities that engage learners in real-world, meaningful math.”

Nathaniel Hansford, an educator and author of The Scientific Principles of Teaching who conducts independent, evidence-based curriculum reviews at Teaching By Science (Pedagogy Non Grata), clearly calls out enVision’s inversion of the Instructional Hierarchy in his review of the program:

“The enVision program uses a three part math lesson; however, their lesson format is quite different from the often promoted ‘I do, we do, you do’. Instead, the first step has students try to solve a complex situational math problem, often involving virtual manipulatives, the second step gives students explicit explanations of concepts and procedures coupled with visual diagrams. The third step provides students with an assessment which allows the AI to then offer the student additional instruction based on the students conceptual deficits. …

Firstly, it has students complete the most challenging part of their lesson first. While providing the explanation how to do this second. This means that students will often not have the prerequisite skills to effectively complete the first part of the lesson. The first part of the lesson is based on application skills; however, as application skills are a synthesis of conceptual, procedural, and computational skills, it makes far more sense to me to put this work at the end of a lesson or unit, not the beginning.”¹² 

The CPA progression in contrast is a structured, teacher-led sequence where the teacher introduces a concept with concrete manipulatives, transitions to pictorial representations, and moves to abstract notation in a deliberate, controlled arc. enVision+’s model reverses this: students explore a problem first, choose their own representations, engage in “productive struggle,” and then the teacher synthesizes. That is constructivist pedagogy with visual supports, not Singapore-style CPA.

Does enVision+ include bar models? Yes – as one tool among many, alongside number lines, area models, arrays, and ten-frames. But in Singapore Math, bar models are used systematically across problem types as the critical bridge between concrete and abstract. In enVision+, they appear episodically. A student who masters Singapore-style bar modeling has a powerful, general-purpose problem-solving tool. A student who encounters bar models occasionally among many other representations may never develop that same depth.

Instructional Hierarchy assessment: enVision+’s lesson structure – student exploration first, teacher synthesis second – places generalization-stage demands on acquisition-stage learners, the inverse of the gradual release model the district’s own survey identified as a “non-negotiable feature.”

4. Into Math: A California Framework Product, Not a Singapore Math Product

The characterization of HMH’s Into Math by Cartnal as a “California-ized version of Math In Focus” with “Singaporean concepts at its heart” is the claim that most needs correction, because it could directly mislead the committee’s final decision.

What HMH Actually Says

HMH’s own press release announcing the California SBE’s approval of Into Math California in November 2025 describes it as “a comprehensive, research-based math program built specifically to align with the California Mathematics Framework.” The product page describes “discourse-rich instruction, hands-on learning, and robust multilingual supports,” built around “the Framework’s Big Ideas and Drivers of Investigation.” It emphasizes “inquiry-based tasks, multimodal learning tools, and language-rich routines that promote active participation, reasoning, and collaboration.”

Nowhere in HMH’s marketing of Into Math California – not on its product page, not in its press releases, not in its promotional materials – does the company describe it as based on Math In Focus or Singapore Math. And for good reason: it isn’t.

Where the Claim May Have Came From

In a conversation on February 7, 2026, I asked Cartnal directly what the basis was for his “California-ized Math In Focus” characterization of Into Math. His answer: HMH sales representatives at the publishers’ fair on December 12, 2025 at the Arboretum in Arcadia said so.

This is understandable but concerning. LCUSD’s team arrived at the publishers’ fair having already decided to retain Math In Focus in grades 6–8, and having communicated that they were looking for a K–5 curriculum to better prepare students for that transition. HMH’s sales representatives – whose job is to sell Into Math – probably told the LCUSD team what any good salesperson would: that their product is exactly what the customer is looking for.

This is not nefarious, rather a standard sales tactic. But it is why curriculum decisions should never be based on publisher sales pitches. The economics are straightforward and worth understanding: HMH sells both Math In Focus and Into Math, but they are very different business propositions. Math In Focus is Marshall Cavendish’s intellectual property, distributed by HMH under a licensing arrangement — meaning HMH must share revenue with Marshall Cavendish on every sale, and a district only buys new textbooks once every 7–8 years. Into Math, by contrast, is wholly owned HMH IP, and a district that subscribes to the Into Math platform with HMH’s Performance Suite pays annual digital subscription fees — all of which flow to HMH. As Cartnal himself noted at the January 28th meeting, “Printing one of these and selling it one time in a 7–8 year period is a very different business proposition than annual digital subscription fees.” That observation perfectly describes the economic incentive for HMH’s sales team to steer a district from their licensed Math In Focus product toward their wholly owned, higher-margin Into Math platform.

Two Different Products From the Same Company

The fact that HMH publishes both programs does not make them similar. HMH is the exclusive U.S. distributor of Math In Focus under a licensing partnership with Marshall Cavendish Education, a subsidiary of Singapore’s Times Publishing Limited. Marshall Cavendish retains ownership of both the Math In Focus brand and its intellectual property — HMH did not acquire Marshall Cavendish or its curriculum. Math In Focus was developed in Singapore by Marshall Cavendish Education as the U.S. adaptation of My Pals Are Here! Maths, Singapore’s most widely used primary math series, and is tailored for U.S. classrooms through a collaboration between Singaporean authors and American math educators.¹³ Into Math, by contrast, was developed domestically by HMH, built from the ground up around U.S. reform-era standards and, in its California edition, specifically around the California Mathematics Framework’s Big Ideas and Drivers of Investigation.

Math In Focus uses explicit, teacher-led instruction following a CPA progression. Into Math California uses “inquiry-based tasks” and “discourse-rich instruction.” They are different products with different origins, different design philosophies, and different instructional models that happen to share a parent company.

Instructional Hierarchy assessment: Into Math California is designed around the California Mathematics Framework – the same framework the district’s own leadership has publicly questioned following Science of Math training. Its “inquiry-based tasks” and “discourse-rich” approach place significant emphasis on exploration and discussion before mastery, misaligning with the acquisition–fluency–generalization sequence.

The Two Legitimate Contenders on the List

Of the six finalist curricula, two have legitimate claims to CPA alignment and pedagogical coherence with Math In Focus in grades 6-8.

Math In Focus K–5 is the most logical choice if the goal is pedagogical continuity. It is the same program the district’s own teachers praise in grades 6–8, adapted for younger students. Same CPA progression, same bar model methodology, same explicit instructional model. It eliminates the K–5/6–8 pedagogical discontinuity at its source.

Eureka Math² has genuine CPA architectural DNA from the original Eureka Math, which was designed as a reverse-engineered Singapore curriculum. The mathematical content progression – emphasis on number as a unit, systematic bar model usage, concrete-pictorial-abstract sequencing – is legitimate. The concern is that the newer edition has layered progressive pedagogical framing over this mathematical core. Careful evaluation using a rigorous rubric and diligent classroom piloting, as Cartnal has repeatedly promised, would be needed to determine whether the classroom delivery still aligns with explicit instruction and gradual release.

The Question That Wasn’t Asked: What About Off-List Curricula?

The district’s search has been confined to curricula on the CDE’s state-approved lists from 2014 and November 2025. This is understandable – it is the default path, it’s what most other districts being advised by County Offices of Education are (lazily) doing, and it is simpler. But it may not be the best path for LCUSD.

California Education Code §60210 explicitly authorizes local educational agencies to adopt instructional materials that are not on the state-approved list, provided the materials are aligned with state academic content standards (CCSS-M) and comply with the state’s social content requirements (Education Code §§60040–60045). The only additional procedural requirement is that a majority of the reviewers in the adoption process must be classroom teachers assigned to the relevant subject and grade level – a requirement the district’s Math Adoption Committee already meets.

LCUSD is already keenly aware of CEC § 60210 because Everyday Mathematics does not appear on any state adopted curriculum lists and during the contentious LCUSD adoption in 2016 I asked Cartnal’s predecessor, Anaïs Wenn, how it validated that Everyday Mathematics met CEC § 60210’s requirement that it minimally met the CCSS-M academic content standards. In a staggering display of chutzpah, Wenn produced a memo written by Everyday Mathematics’ publisher McGraw-Hill.

Why does this matter? Because if the district’s top priority is preparing K–5 students for Math In Focus in grades 6–8 as it proclaimed at the January 28th meeting, the most aligned curricula in the country are not on either state list. They are the other Singapore Math programs published for the U.S. market:

• Primary Mathematics (Singapore Math, Inc./Marshall Cavendish): This is the curriculum that put Singapore Math on the map in the United States. The original 1998 U.S. Edition is nearly identical to the curriculum used in Singapore when Singapore rose to the top of international student assessments. A completely rewritten 2022 Edition, led by Dr. Kho Tek Hong (one of the original Singapore curriculum architects), has been updated with a Readiness–Engagement–Mastery instructional design while preserving the CPA approach, bar modeling, and mastery-based scope and sequence. Primary Mathematics has a direct lineage connection to Math In Focus – both originated from the same Singaporean curriculum tradition, both were published in Singapore by the same publisher, and both were adapted for U.S. classrooms by related teams.
• Dimensions Math (Singapore Math Inc.): A newer program for PK–8 than the 1998 Primary Mathematics based on the methods and scope and sequence of Primary Mathematics, but designed from the start for U.S. teachers and students. It retains all key Singapore Math features – CPA progression, number bonds, bar modeling, mastery-based sequencing – with clearer lesson presentations and more robust teacher support. An independent comparison by Hillsdale College’s K–12 program concluded that Dimensions Math “maintained or improved upon” the critical elements of Primary Mathematics while making Singapore’s techniques more accessible to American teachers.¹⁴ Critically, Dimensions Math extends through 8th grade, meaning it could provide complete K–8 coherence – even more continuity than pairing a K–5 program with Math In Focus 6–8.

Both Primary Mathematics and Dimensions Math offer Common Core-aligned editions, satisfying the §60210 content standards requirement. A properly designed rubric that weighted preparation for Math In Focus 6–8 as its primary criterion would likely rank these programs above Eureka Math² – and certainly above the four inquiry-based finalists – because they share the same pedagogical DNA, the same CPA methodology, and in some cases the same developmental lineage as Math In Focus itself.

Other off-list programs worth consideration by a committee genuinely committed to explicit instruction and procedural fluency include JUMP Math (a structured, teacher-led program with strong evidence of effectiveness for struggling learners), Connecting Math Concepts (a Direct Instruction program from the Engelmann tradition with rigorous scope and sequence), and Beast Academy (Art of Problem Solving’s elementary program, which combines rigorous content with an engaging format). Each of these operates outside the reform-math mainstream and offers instructional approaches far more consistent with the Science of Math and the Instructional Hierarchy than most of the state-approved options.

None of this requires the district to abandon its current process. It requires only that the committee acknowledge that the state’s approved lists were curated using criteria – particularly alignment with the 2023 California Mathematics Framework – that the committee’s own Science of Math training has called into question. If the framework’s advice is suspect, then a list built around that framework’s criteria may not contain the best options. CEC §60210 exists precisely for situations like this.

Conclusion

The district has done important work over the past several months. The Science of Math training, the decision to retain Math In Focus in grades 6-8, the LCUSD Math Priorities Survey – these all point in the same direction: toward explicit instruction, procedural fluency, CPA methodology, and coherent K-8 sequencing. The committee’s principles are sound.

The gap is between those principles and the curriculum selections. Four of the six finalists are inquiry-based or self-described “balanced” programs that lean inquiry, whose own publishers describe them in terms that directly contradict the committee’s stated priorities. And the search has been confined to state-approved lists that were curated using the very framework the committee has learned to question, while excluding off-list Singapore Math programs that would provide the strongest possible alignment to Math In Focus in grades 6–8.

The evaluation rubric that is being developed by Hanover Research offers an opportunity to course-correct. A rubric informed by the Instructional Hierarchy would ask: Does this curriculum provide explicit, teacher-led instruction during acquisition? Does it build fluency through structured practice before moving to application? Does it use CPA progressions systematically, or merely decoratively? Does its scope and sequence prepare students for Math In Focus’s expectations in 6th grade? These questions would naturally filter the field – and might also reveal that the best candidates aren’t on the current short list at all.

LCUSD spent a decade with a K–5 math curriculum that was pedagogically misaligned with its 6–8 program. The whole point of this adoption is to fix that. The committee has the knowledge, the training, and the community support to get this right. The question is whether the process will be allowed to catch up with the committee’s own learning.

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1. CPA stands for concrete-pictorial-abstract, also sometimes called concrete-representational-abstract (or CRA). CPA is a research-backed instructional sequence in which students learn a concept in three progressive stages. First, they work with physical objects they can touch and manipulate (the concrete stage): beads, base-10 blocks, or fraction tiles. Next, they transition to two-dimensional visual depictions of those same ideas (the pictorial or representational stage): drawings, diagrams, number lines, bar models, or arrays. Finally, they move to conventional mathematical notation — numerals, symbols, and equations (the abstract stage): for example, writing 4 × 4 = 16. CPA is a hallmark of Singapore Math–style curricula like Math In Focus. ↩︎
2. See How teachers can make learning happen, https://www.thescienceofmath.com/how-teachers-can-make-learning-happen ↩︎
3. Cartnal said, “Across every measure, the gradual release approach emerges as a non-negotiable feature for the next LCUSD K–8 math program” when summarizing the quick results from the math priorities survey. See our report from the Second Elementary Math Adoption Parent Meeting – January 2026. ↩︎
4. See Ashman, G., Kalyuga, S., & Sweller, J., “Problem-solving or Explicit Instruction: Which Should Go First When Element Interactivity Is High?” Educational Psychology Review, 32(1), 229–247 (2020); Carlson, R. A., Lundy, D. H., & Schneider, W., “Strategy Guidance and Memory Aiding in Learning a Problem-Solving Skill.” Human Factors, 34(2) (1992), 129–145; and Kapur, M., “Productive Failure in Learning Math.” Cognitive Science, 38(5) (2014), 1008–1022. ↩︎
5. “NYC Algebra Regents scores tank amid new ‘disaster’ math curriculum,” New York Post, Nov.23, 2024. ↩︎
6. Ibid. ↩︎
7. https://www.uft.org/news/nyc-solves-policy-updates-address-our-concerns ↩︎
8. Jessica Gould, “New NYC schools chancellor plans changes to controversial math curriculum,” Gothamist, January 14, 2026. ↩︎
9. Sarah Schwartz, “New York City’s New Curriculum Gets Caught in the Math Wars,” EdWeek, Feb. 07, 2025. ↩︎
10. Evidence for Every Student Succeeds Act Math Expressions web page. Center for Research and Reform in Education, Johns Hopkins University. ↩︎
11. See my December essay, “Pseudoscience as a Basis for Reading Instruction,” Cryptomeric Thoughts, (2022). ↩︎
12. Nathaniel Hansford, enVision Math review, Teaching by Science (Pedagogy non Grata), (2022). ↩︎
13. Cassandra Turner, “Primary Mathematics vs Math In Focus,” Singapore Math Source,(2026) . ↩︎
14. Nicholis Wagner, “Dimensions Math Improvements On Primary Math,” Hillsdale College, (2019). ↩︎