The Final Four: Detailed Reviews

by Sugi Sorensen
April 13, 2026

The La Cañada Unified School District (LCUSD) is nearing the final step in its K-8 elementary math instructional material adoption process for the 2025-26 school year. The parent review period of the final four curricula is nearing an end — the review window is open from March 26 to April 27, 2026 with district parents invited to come look at and provide feedback on the sample publisher materials at the LCUSD District Office. As a reminder, the final four candidate curricula as selected by the district are:

• California Math Expressions (Heinemann)
• enVision+ (Savvas Learning)
• Eureka Math² (Great Minds)
• Math In Focus: Singapore Math by Marshall Cavendish (Houghton Mifflin Harcourt)

The all-teacher LCUSD Math Adoption Committee will meet for the last time this school year on Tuesday, April 28th to make its final recommendation to pilot two of the final four curricular programs next school year (i.e. 2026-27.) The committee’s recommendation will then be taken to the LCUSD Governing Board for official approval at their meeting in early May or June.

La Cañada Math Parents leadership spent multiple days reviewing the above four curricula at the District office on Friday, March 27 and Friday, April 3rd, 2026. This report provides a detailed assessment beyond the information in our preliminary analysis conducted in February.

Summary Overview

We provide first a summary overview of the four curricula with overall letter grades assigned from A to F:

Grade	Curriculum & Summary
A-	Math In Focus (HMH): Singapore Math — the gold standard of explicit, teacher-led instruction used in one of the world’s top-performing countries as measured by international benchmarks (e.g. TIMSS, PISA.) Follows a clear Concrete → Pictorial → Abstract (CPA) sequence: kids manipulate objects first, then pictures, then numbers/symbols/equations — in that order, as research recommends. Emphasizes mastery before moving on. Fewer topics per grade, covered in greater depth. Already used by LCUSD in grades 6–8. Selecting it for K–5 gives students a seamless, coherent K-8 math education. High volume of practice problems in print workbooks — exactly what the Hanover survey said parents and teachers want. Consideration: Ask yourself why LCUSD is ditching Everyday Mathematics in grades K-5 yet keeping Math In Focus for grades 6-8.
C+	enVision+ (Savvas Learning): Student Edition workbooks do include concept explanations and some examples — better than Eureka Math² in this respect, and usable as a student reference. However, the teacher’s edition prescribes that all lessons start with a class-wide Explore and Share activity where kids engage in productive struggle and attempt to solve an open-ended question before explicit instruction proceeds in the next step called Visual Learning. This front-loads cognitive demand before students have the prerequisite knowledge — the opposite of what research recommends. Guided practice sections are too short. Practice volume does not match Math In Focus, which had more worked examples, fewer distracting asides, and more problems per topic in direct comparison. The Differentiation Library Teacher’s Guide is almost entirely a catalog of project-based learning (PBL) projects. PBL is grossly time inefficient relative to the amount of math students actually encounter and practice. No enrichment or challenge track for advanced students — differentiation resources cover intervention only. Math In Focus includes challenge extension components; enVision+ does not. Choosing enVision+ recreates the constructivist-vs-explicit mismatch at the K–5 / 6–8 interface that LCUSD is trying to fix.
C-	Eureka Math2 (Great Minds): Logistical overload: each grade has six modules, and each module ships two separate student consumable books — a Learn book and an Apply book. That is up to 12 student booklets per child per year. Neither the Learn nor the Apply book contains concept explanations or worked examples. All instructional content lives in the teacher’s edition only — so students have no reference material to review at home. The teacher’s edition is scripted to the 5-minute mark, instructing teachers to coordinate across all 12 component books per grade. This level of complexity is a practical barrier to consistent implementation. Prescribes sub-optimal instructional methods including mandatory partner practice segments. Practice sets are not long enough to build the fluency that research requires. A student who misses class or needs to review a concept has no self-contained resource to turn to — a significant gap for independent learning and parent support at home.
D	California Math Expressions (Heinemann): Student Activity Books are not terrible in isolation, but the teacher’s guide directs fully inquiry-oriented implementation — the instructional quality of the curriculum depends entirely on whether the teacher follows it. Severe logistical burden: teachers are required to cut out and physically prepare custom manipulatives and props for lessons as part of the standard lesson workflow. This is not a minor ask — it is a recurring preparation tax on teacher time. Lesson activities are project-based learning in orientation, which is time-inefficient and mathematically thin relative to the time invested. Weakest research base of the four finalists. The combination of inquiry-oriented design, logistical complexity, and thin evidence makes this the least defensible choice for LCUSD.

The above summary is available as a 1-page printable PDF that parents can take to the District office when reviewing the final four.

Detailed Reviews:

LCUSD uses the 2013 edition of Math In Focus (MiF) in grade 6 for all district elementary schools, as well as in the lower pathway Math 7 and Math 8 courses in the middle school. LCUSD uses the 2020 edition of MiF for its accelerated Math 7/8 Advanced course in the upper pathway in 7th grade. LCUSD is considering the 2020 edition of Math In Focus for adoption in grades K though 5 for the current math adoption process.

The MiF program consists of the following components:

• Student Edition – Two consumable printed paperback textbooks/workbooks per student per year – volume A for first semester and volume B for second semester. The student editions contain explanations for every math concept taught, scaffolded worked examples with step-by-step explanations, and guided and independent practice for each chapter, as well as chapter reviews and cumulative reviews. Each chapter also ends with a performance task that allow students to demonstrate their knowledge and understanding of concepts taught in that chapter.
• Teacher Edition – Two large, wire-bound printed manuals per grade – volume A for first semester material and volume B for second semester. Contains point-of-use instructional support for the teacher when teaching topics, questioning techniques, background information, a skills trace, model problems, and a planning guide.
• Supplemental Student Components – MiF also include an Extra Practice and Homework book from which the teacher can assign additional problem sets for each chapter and section, Fact Fluency books for grades K-5 and course 1 (i.e. 6th grade), downloadable Reteach activities that the teacher can assign for extra support for students struggling to understand on-target topics, and a similar printable Enrichment resource matched with each grade-chapter-section for reach problems.
• Supplemental Teacher Resources – Downloadable and editable Lesson Plans; pre-made and editable Class Presentations that teachers can use during classroom instruction; manipulative kits and activity cards for younger grades; a very thorough Assessment Guide Teacher Edition that includes summative assessments for chapter, unit (i.e. 2 or 3 chapter), mid-course and end-of-course for grades 3 through 8 along with answer keys; pre-written school-to-home connections family letters for each chapter to help parents understand what is being taught to their student in class; online benchmark assessments, quick checks, and extra online independent practice assignments.
• Online Resources – The student online portal provides an eBook version of the Student Edition, Learn Videos to explain complex mathematical concepts, mini-games that the teacher can assign, as well as virtual manipulatives. The teacher’s Ed digital platform also has an eBook version of the Teacher Edition, a Teacher’s Corner to support teachers with a library of learning and background and other learning resources, and editable assessments. HMH has also added special teacher supports for the first year of implementation including a Professional Learning Guide and Transition Guides for districts transitioning from less rigorous curricula like LCUSD would be doing, and Scope-and-Sequence guides for all grades. MiF also includes Waggle, an online student activity guide that includes independent practice that can either be automatically assigned based on student formative assessment results or that the teacher can assign. Unfortunately, Waggle was not accessible from the sample student login that was made available at the parent review from the QR Code provided.

Analysis

MiF is an Americanized version of Singapore Math, and uses a traditional math instructional approach that relies upon explicit instruction as opposed to student-centered inquiry learning (a.k.a. constructivism.)¹ It uses a mastery model where students are expected to master concepts before moving on to new topics. Fewer topics are covered at a greater level of depth per grade, and the math questions posed, particularly on MiF tests, are much more rigorous than almost all American math curricula in common use.

MiF also uses the concrete-pictorial-abstract (CPA) progression to build strong foundations, emphasizing standard algorithms, visual models (e.g. bar diagrams), and sequential topic development. Topics are introduced earlier and with more focus on connections (e.g. linking fractions directly to decimals through division.) MiF places a premium on developing procedural fluency and achieves this in many cases by introducing arithmetic operations one or two grades earlier than prescribed in the California math standards.

These design principles are readily evident in the sample MiF materials on display at the LCUSD district office, particularly when compared to the other three finalists under consideration. Not apparent to parents reviewing the sample MiF materials on view is the rigor of the MiF tests due to the fact that the Assessment Guide Teacher Edition books were not made available to parents. However, having taught MiF to district 5th through 7th graders for 11 years at JEI Learning and then Math Pod, I can attest to the significantly more challenging rigor of MiF assessments, at least in the course 1 through 3 middle school program, particularly the mid-course and end-of-course assessments (i.e. final exams.) It is possible the K-5 MiF assessments are less rigorous than the course 1 through 3 assessments given we haven’t seen the K-5 assessments.

MiF scored higher than the other three finalists in three of the most important areas of the rubric I developed in my capacity as Director of Policy and co-founder of the Institute for Mathematic Instruction (IMI) for this adoption that the district declined to use when offered:

• Content Rigor and Depth in the area of Mathematical Content – This criterion is missing altogether from Hanover Research’s High-Quality Instructional Materials rubric.
• Instructional Examples and Practice Opportunities in the area of Instructional Design. These criteria are partially covered in Hanover’s rubric as indicator P3-4 – Provides clear and sufficient number of teaching examples.
• Procedural Fluency Development in the area of Practice, Fluency and Application. This criterion is also on the Hanover rubric as indicator P1-2 – Opportunities for students to practice math fact fluency and math skills to promote automaticity.

MiF offered clear step-by-step instructions for concept explanations, scaffolded worked examples, and far more practice opportunities than the other three.

MiF was not given a full ‘A’ grade because it is not as good as two other Singapore Math curricula that were available for consideration – Singapore Math: Primary Mathematics and Dimensions Math, which as with the IMI rubric were suggested to LCUSD staff, but ignored or rejected for consideration. In addition, the 2013 edition of MiF sequences some topics sub-optimally compared to other versions of Singapore Math, and sometimes presents multiple methods to solve particular types of arithmetic problems when more time mastering the standard algorithms would be a better use of time.

enVision+ California Mathematics is Savvas Learning’s upgrade to their earlier enVision curriculum, aligned to the 2023 California Mathematics Framework (CMF). Savvas touts their upgraded product as “an elementary math curriculum that develops deep math connections and lasting understanding through student investigations and experiences that focus on the why, what, and how of mathematics.”²

The Program Guide provided to LCUSD claims that enVision+ California Mathematics “puts students at the heart of learning, helping them feel confident and capable as they explore math concepts.” The new enVision+ leans heavily into alignment with the new 2023 CMF. The Program Guide emphasizes the new curriculum’s commitment to “teaching the Big Ideas”, discovery-oriented activities focused on the CMF’s Drivers of Investigation (the Why), Standards for Mathematical Practice (the How), and its Content Connections (the What):

enVision+’s other refocusing on the 2023 CMF includes trying to make math more personally relevant to students through what they call “Living in Math” and an instructional activity they call Math Walks. Here is how it is described in the Program Guide, “Living in Math: Drive student investigation, connect to students’ lived experiences, and spark topic Big Ideas questions with Math Walks – Place-Based Learning, Real-World Context, Notice/Wonder Observations, STEAM-to-Math Connection.” Each topic in enVision+ begins with a Math Walk video meant to inspire students and help them see the relevance of mathematics to their daily lives, or in the equity language of the CMF, their “lived experiences.”

Another design change driven by the 2023 CMF is enVision+’s focus on building Data Literacy. Savvas says enVision+ “drives learning with a problem-based structure that promotes active participation, builds content connection, enhances data literacy, and instills transferable enduring skills.”

Savvas adopts wholesale the most problematic pedagogical practices pushed in the 2023 CMF such as productive struggle, growth mindset through their “Build G.R.I.T. (Growth Mindset, Resilience, Self-Efficacy, and Time Management)” activities, the elevation of student engagement over building student mathematical understanding, the infusion of environmental principles and concepts when it should be teaching mathematics,³ Universal Design for Learning (UDL), and the focus on equitable instruction over mathematics as exemplified in the otherwise ambitious Program Overview document:

The 2026 upgrades to enVision change some of the names of activities (e.g. “Solve and Share” has been renamed “Explore and Share” in enVision+), but remains structurally the same as the older program – a problem-based learning curriculum with real-world performance tasks and visual instruction. enVision+ puts student exploration first, before the teacher explains concepts, which inverts Haring & Eaton’s Instructional Hierarchy.

Analysis

For all the alluring new AI tools, online digital resources, adaptive assessment and differentiation tools, and integration with student information systems like Aeries and Learning Management Systems like Google Classroom and Canvas, enVision+ at its core uses an investigation-first approach to math instruction, using Let’s Investigate lessons to “engage students in open-ended, real-world tasks that spark curiosity and build a conceptual foundation.”⁴

Strengths

In spite of its inquiry orientation, enVision+ has much to like when compared to California Math Expressions and Eureka². The Student Editions, in spite of the weaknesses noted below, are usable and contain the principal elements of a good direct instruction textbook – the content is mostly logically sequenced though many subjects are taught a year or two later than MiF, there are explanatory sections for each math concept taught, some worked examples, and independent practice opportunities for students.

Where enVision+ really excels compared to the other top three is in its online resources. Parents can glean all that this entails in the Digital Walkthrough Grades K-5 book available in the sample materials in the District office. The teacher program dashboard is particularly impressive, at least as described in the Savvas marketing brochure. Since the sample login provided to LCUSD parents allows access only to the student dashboard – Realize – we were not able to evaluate the numerous new digital teacher features. We remain somewhat skeptical that the actual usability meets the printed marketing hype as the online student components once accessed were much less impressive than described in the Digital Walkthrough guide.

Speaking of Savvas’ teacher-view Program Dashboard, if it competently implements all of the components shown in the printed marketing brochure, then it offers teachers links to eText versions of both Student and Teacher Editions, course assessments and performance tasks, the CCSS-M standards and how they align to enVision+ lessons, lesson planning resources like pre-made projectable presentations, background resources about topics taught in lessons, a student management system that includes student practice and assessment results, and their new AI-driven component called Savvas Studio.

Also intriguing from a teacher’s perspective in the Savvas Studio is the individual student-level reports and performance analysis by CCSS-M standard, class aggregate performance data on the same assignment, and the ability to provide tailored practice and targeted differentiation to either individual students or student groups. However, the devil is in the details and without the ability to try these features for ourselves, we were unable to ascertain if they are useful.

Weaknesses

Unfortunately, the rewriting of enVision+ to align with the 2023 CMF has effectively nullified whatever merits the previous enVision program contained. This is nowhere more evident than in the Differentiation Library Teacher’s Guide, which is on display in the LCUSD district office. When we first were told about the differentiation guide in the Program Guide, we were intrigued by the promise that enVision+’s differentiation library would “provide a comprehensive variety of differentiation resources to support topic and lesson concepts.” Instead the Differentiation Guide is a catalog of time-consuming group and individual student activities of dubious value that contain very little actual mathematics.

The Differentiation Guide supposedly “honors student choice and autonomy” through activities called Pick a Project that Savvas insists “allow students to connect math to their interests, fostering engagement and motivation.”

However, looking at the Pick a Project activities in the Differentiation Guide, it presents instead a plethora of low- to medium-quality project based learning (PBL) activities that are logistically difficult if not impossible for a classroom teacher to plan and implement given how much time would be required, resources (not provided by Savvas) gathered and organized, and run if implemented as directed. For example, the following Pick a Project from the Grade 5 Topic 3 (multi-digit multiplication) allows students to pick from four different “rich projects”, each of which requires substantial prep time from the teacher:

While some of the activities, particularly the fluency games, in the Differentiation Guide resource book are interesting and might enhance learning, most are merely time-consuming PBL activities that teachers would never be able to incorporate into their daily lesson plans, particularly if teachers had to prepare multiple activities to “honor student choice.”

Another major weakness of enVision+ in the grades we examined are the Student Editions. Two major deficiencies surface. First, new concepts are not sequenced logically and concepts are not explained in sufficient detail for a student to be able to understand the concept without teacher guidance. Second, there are not enough worked examples nor enough practice to solidify concepts taught.

A third but less concerning problem of all lessons examined is the poor instructional design of the Student Edition pages. There is an over abundance of distracting photographs, cartoon drawings with bubble callouts, and QR codes linking to online digital activities. Consider the layout of a 5th grade lesson (3-1) on multiplying multi-digit whole numbers. The lesson starts out with a Big Idea investigative question called Explore and Share:

The above is literally a textbook case of what is known in Cognitive Load Theory as extraneous cognitive load. Note the distracting, large pictures on the left that have nothing to do with the investigative question on the right-hand page. The pictures are actually referring to the Pick a Project activities in the Differentiation Guide. Notice also the cartoon girl in the bottom right who again is talking about a concept (i.e. “use appropriate tools” – one of the CCSS-M’s Standards for Mathematical Practice) that is secondary to the topic being taught.

According to Cognitive Load Theory, extraneous cognitive load is the load on working memory (limited to 4 or 5 elements of novel information) secondary to the target learning topic. Any design feature caused by poor instructional design that forces the learner to process information irrelevant to the target schema is consuming capacity that could otherwise be devoted to learning.

With regard to the more salient design weaknesses of the enVision+ Student Editions, when a concept is introduced, the topics are not sequenced logically in several of the lessons we analyzed. For example, sticking with the 5th grade chapter 3 on multiplying multi-digit whole numbers, the standard algorithm for multiplication is not introduced until lesson 3-3, and is the fifth method introduced. Before the standard algorithm is explicitly shown, enVision+ first invites students to come up with their own methods, then suggests using pattern recognition using knowledge of place-value relationship in lesson 3-1 that they call model with math, then suggests students estimate products in lesson 3-2, then in lesson 3-3 introduces the partial products method and then an area model as “one way to record multiplication,” then finally as the fifth method teaches the standard algorithm. Even more concerning, the last three methods are all taught in one lesson over the span of just two pages!

Even then, when enVision+ gets to the heart of multiplying multi-digit whole numbers by a one-digit number, they do a mediocre job listing the steps and show only two worked examples. When they get to independent practice, they have just 16 practice problems (and only 10 in the Additional Practice supplemental book), though to its credit the problems are properly scaffolded in complexity.

When examining how the other three finalist curricula teach multi-digit multiplication, Math In Focus is vastly superior. Aside from the fact that MiF teaches the concept starting in grade 3 and continues in grade 4, the 4th grade treatment in chapter 2 on “Multiplying by a 1-Digit or 2-Digit Number”, MiF is much more concise and precise in its mathematical explanations, breaks each worked examples into more explanatory steps, has more worked examples (6 vs 2 in enVision+), and far more practice problems (14 for 1-digit multiplier, another 17 for 2-digit multiplier in just the Student Edition), and has fewer distractions than enVision+.

Similar to enVision+’s lower rigor and instructional deficiencies in its Student Edition compared to Math In Focus’ Student Editions, enVision+’s assessments are just as concerning. When we examined the enVision+ Assessment Sourcebook that contains all of the diagnostic, formative, and summative assessments, the assessments were deemed non-rigorous. For example, the grade 5 topic 3 assessment on multi-digit multiplication contained just 12 questions over two pages, and six performance tasks over two more pages.

The cumulative/benchmark assessment for grade 5 covering topics 1 through 3 had 30 questions, which seems appropriate, until you realize a third of the questions (i.e. 9 of 30) were multiple choice. Compared to Math In Focus, enVision+’s assessment items were far less rigorous.

These criticisms are based on sampling a handful of topics in two different grades, and their impact when used by LCUSD teachers is ultimately unknown. This limitation reinforces the importance of piloting actual materials in the classroom next school year.

Program Overview

Eureka Math² California is Great Minds update to its earlier Eureka Math curriculum upgraded to align with the 2023 California Mathematics Framework. Great Minds describes the new version as “bringing the California Framework to Life” on its top-level program description web page. This design goal, unfortunately, made Eureka Math worse than its progenitor. Great Minds appears to have succumbed to the false promises of the 2023 CMF. Emphasized in the new edition are equitable access, teaching toward social justice, student-centered learning, building conceptual understanding, integrating more Data Science into its activities, and teaching Big Ideas:

The Eureka² program components include:

• Two different student edition consumable books – a Learn student workbook, an Apply book meant to be kept at home that provides additional practice for home along with family activities that can reinforce concepts learned at school. Each grade is thematically organized into six modules, two per trimester, which means that each student must be given 12 books per school year!
• For teachers, the Teach book is effectively the Teacher Edition. Explanations of math concepts being taught are contained only in the Teach book, a disqualifying shortcoming in our estimation.
• Manipulative Kits that contain physical classroom materials to help develop student mathematical understanding. The kits contain items like color tiles, dice, beads, blocks, ten frames, deci-disks, printed cards and counters, geometric solids, and traditional math tools like rulers and protractors.
• Data Talks worksheets, observational assessment recording sheets (OARS) for teachers, and assessments.
• Online digital curriculum materials including teacher-oriented resources like implementation guides, scope and sequence documents, assessments from exit tickets to summative and diagnostics assessments; and student-oriented digital resources like background context videos and digital manipulatives, and online games.

Analysis

To its credit, Great Minds explains that their instructional approach philosophy with Eureka² is not inquiry-oriented. They instead claim to blend three instructional approaches: student-centered learning, cognitively guided instruction (CGI), and explicit & systematic instruction.

To its detriment, we were severely disappointed with Eureka² once we reviewed the printed sample materials given how positively it is described by teachers who use it and by normally reliable curriculum review sources.

Fatal Flaws

Eureka Math² suffers from two fundamental flaws that we believe disqualifies it from further consideration.

First, Eureka²’s student-facing materials — the Learn workbook and the Apply supplemental resource — contain no expository prose, no worked examples, no annotated sample problems, and no guided practice models with accompanying explanations. Every element of direct instruction: the conceptual framing, the procedural demonstration, the teacher-guided worked examples, resides exclusively in the Teach book, which is a teacher-facing resource. Students never hold it. Parents never see it. Once the lesson ends, the instructional content vanishes from the student’s world entirely.

The Family Math letters home to parents in the Apply book give a high-level description of concepts being taught that week, but not step-by-step instructions for students so it is questionable how helpful the one-page Family Math topic overviews would be to families if they had to re-teach the concept taught that day in the classroom, much less make up instruction missed due to a student absence.

What Explicit Direct Instruction Actually Requires

The LCUSD Math Vision Statement that staff and the math selection committee created to guide its current elementary math curriculum adoption contains the following non-negotiable pillar, “Using both explicit direct instruction and activities that allow students to apply their math learning to real-world problems, we can inspire our students to explore math concepts with confidence and curiosity.”⁵

Explicit direct instruction has a well-defined architecture. Rosenshine’s Principles of Instruction⁶, drawn from decades of observational research on effective teaching, identify several non-negotiable components: clear presentation of new material in small steps, the provision of models and worked examples, guided practice with feedback before independent practice, and the ability to re-engage with that instruction as needed.

The key phrase is re-engage with that instruction as needed. Rosenshine was describing what effective teachers do in the classroom. But the instructional design literature has always recognized that the student-facing materials must carry the same load when the teacher is not present. This is precisely why high-quality instructional materials (HQIM) math curricula like Singapore Math (including MiF) invest heavily in the design of the student book as a primary instructional document, not merely a practice repository.

Cognitive Load Theory provides the explanation. Novice learners — which is what every student is at the beginning of each new unit, regardless of overall ability — cannot construct a schema for new material through practice problems alone. They need worked examples that allow them to study the expert’s process before attempting the procedure independently. Worked examples reduce extraneous cognitive load by providing an external representation of the solution path, freeing working memory for the critical act of schema construction. Stripping worked examples from the student book and reserving them for the teacher-only guide does not eliminate this cognitive need. It simply ensures it goes unmet for any student working without a teacher in the room.

Haring and Eaton’s Instructional Hierarchy makes the sequencing requirement explicit. Students must achieve acquisition — correct initial performance — before entering the fluency stage where repetitive practice becomes productive. Practice problems administered to a student still at the pre-acquisition stage produce practice of errors, not consolidation of correct performance. Eureka²’s Learn and Apply books are pure fluency- and application-stage materials. They presuppose that acquisition has already occurred in the classroom under teacher direction. The moment that presupposition fails — a missed class, a moment of inattention, a concept that did not click during the lesson — the student has no resource to return to and re-acquire the concept. The books become unusable through no fault of the student.

The Advanced Student Barrier to Advancement

The second category of student harmed by this instructional design flaw are mathematically capable students who are ready to work ahead.

Good mathematics textbooks have always served a dual function. They are the vehicle for classroom instruction, and they are the resource for independent inquiry. The student who has mastered this week’s material and wants to explore next week’s, the student who is curious about where the current procedures are heading, the student who simply works faster than the class pace — all of them can, in a well-designed textbook curriculum, open the book to a future chapter, read the exposition, study the worked examples, and begin building understanding independently.

This is not a marginal use case. In a district like LCUSD where 84% of all students are at the top math performance level (i.e. Standard Exceeded on the CAASPP, though the descriptor was recently changed to Advanced), it is one of the primary mechanisms by which mathematically precocious students develop and sustain their interest in the subject.

In Eureka² this pathway is closed by design. The Learn workbook for the next unit contains only practice problems and metacognitive prompts (i.e. the Self-Reflection questions.) Without the explanations and worked examples from the Teach book — to which the student has no access — those problems are not productive challenge; they are a wall. The curriculum has, in effect, made independent mathematical exploration impossible by design. Every act of self-directed learning beyond the current lesson requires a teacher intermediary.

This is particularly striking given that one of the stated virtues of structured, content-rich curricula is that they support students who learn at different speeds — a priority that LCUSD’s own Hanover-administered survey identified as the single greatest area needing improvement (43% of respondents). A curriculum that confines all instructional exposition to a teacher-only document structurally cannot support students who learn faster than the class pace through independent engagement with the materials. It cannot support them because the materials they have access to contain no instruction.

The Second Fatal Flaw: Teacher Overload

Eureka’s second fatal design flaw is instructional design – the teacher editions (i.e. called Teach) are insanely long, too detailed, and overly scripted. The choice to break up the student editions into twelve modules, with two student books per module, means that teachers are taxed with the added logistical burden of regularly handing out and collecting student Learn and Apply books. The Teach books, while containing useful background mathematical information intended for the teacher, actually recommend lessons scripted to the 5-minute level of detail. And it prompts teachers to assign elements from the super abundance of printed and digital resources, and switch quickly between multiple instructional methods – direct instruction at the whiteboard or from an overhead projection, choral response, mini-whiteboards, partner practice, independent practice in the Learn workbook, and homework assigned from the Apply student book.

Compounding this logistical nightmare for teachers is the demand on preparation time prior to teaching a day’s lesson. Teachers are frequently directed to cut out manipulatives or props used in the hands-on classroom activities.

To appreciate the excess of demand placed on a teacher of Eureka², consider the following lesson from the 5th grade on the aforementioned topic of multi-digit division of whole numbers. The single lesson spans 21 pages in the Teach manual. It should be noted that there are an additional 15 pages of background explanation and context the teacher is expected to read and understand prior to preparing the lesson, and another half dozen pages of manipulatives that need to be reproduced, cut out, and handed out to students:

Note how the Agenda on page 27 scripts lesson activities to the 5-minute level. And the “Organize and Count Bills to Compare” class-wide activity in the Learn sub-activity requires making copies of the bills on pages 48 & 49 and cutting them out into bills that the students can use and exchange. In total, there are about 40 pages from the Teach guide covering one 45-minute lesson. This level of teacher preparation is excessive to say the least, and it was the first lesson we sampled in our analysis.

It should be noted that the 5th grade sample materials were missing from Heinemann’s California Math Expressions display in the District office when we examined the materials, so we could not complete our methodology of comparing how each of the four finalists taught the same topic – multi-digit multiplication of whole numbers.

Program Components

Like the other three finalist curricula, Math Expressions has core print instructional resources for students and teachers, and supplemental downloadable printable materials:

• Student Activity Book – The student textbook comes in two volumes and is a paperback consumable workbook that contains student lessons including family letters that are presumably supposed to be torn out and handed to mom or dad, vocabulary flashcards that are meant to be torn out of the workbook and cut into cards that can be studied at home, as well as the unit lessons with partial summaries of concepts presumably taught in class by the teacher, but no worked examples.
• Teacher Edition – The teacher editions come in multiple volumes per grade and like the other three finalists are spiral bound. The introductory section to each teacher’s edition repeats the same overview of the program’s larger design philosophy – student-centered inquiry-based approach to learning mathematics. They then discuss Math Expressions’ five core structures: Building Concepts (i.e. build conceptual understanding based on students’ prior knowledge), Math Talk (i.e. students in small groups try to figure out how to solve questions carefully posed by the teacher), Student Leaders basically recruits students with better understanding than their classmates to assist the teacher in teaching other students, Quick Practice (i.e. short activities at the start of lessons to recall prior knowledge), and Helping Community (i.e. students and the teacher acting as a peer and not the expert instructor engage in community discussions about how to solve math.) The Teacher Edition then delves deeper into its inquiry-oriented instructional philosophy and approaches. Only then does it get into specific teacher guidance in teaching each lesson within a unit. The teacher lesson pages are vastly less detailed and lengthy than Eureka²’s. Math Expressions units are 8-15 pages in length, less than half Eureka²’s, which is a good thing.
• Digital Supplemental Resources include the following components that teachers can access from the Teacher Dashboard, download, and print out:
  • Assessment Guide
  • Homework and Remembering
  • Practice, Reteach and Challenge differentiation book
  • Teacher Resource Book
  • Activity Center Guide
  • Response-To-Intervention (RTI) Tier 3 supplement
• Student Dashboard – The QR Code provided to parents at the District office allows parents to access the online Student Dashboard on Heinmann’s website. Logging into the demo student account reveals three components: a dashboard with access to eBook versions of the Student Activity Books, as well as an Assignments tab that presumably allows students to access teacher-assigned digital assignments (there were no activities assigned) after clicking on the Assignments tab, and a Scores tab that theoretically allows students to see scores on completed assignments that the teacher has entered into Heinemann’s student information system. The Dashboard tab also allows students to access Matific, Heinemann’s online math practice game platform. More on that later.
• Teacher Dashboard – Since parents were not given access to the teacher-facing online digital components, we can only make reasoned guesses about its components from the Program Description print guide. Teachers gain access to Heinemann Flight, a “easy-to-access platform with interactive tools to provide educators with what they need to create dynamic learning experiences that foster deep understanding and accelerate progress.” The screenshots in the brochure and sparse accompanying prose reveal the following additional teacher-accessible digital support components:
  • iTools – Digital Math Manipulatives
  • Math Library – Access to the Student Activity eBooks, and Math Readers, whatever those are as they were not described elsewhere.
  • Reporting Dashboard – A student classroom management system that allows teachers to assign math activities and Matific games to individual students, a place to enter student homework and assessment scores, an Assessment Report to see class aggregate and individual student scores on formative and summative assessments, and a Standards Report that presumably shows where individual students meet or don’t meet state standards based on diagnostic assessment results. The results from the student classroom management system can be used to assign targeted fluency activities, provide RTI/MTSS re-teach activities and tailor Matific game activities assigned to individual students.

Analysis

After reading the Program Overview guide and the voluminous introductory section to each Teacher Edition, which all heavily emphasize the program’s inquiry-oriented design and approach, we were pleasantly surprised by the relatively good instructional design and usefulness of the Student Activity books, especially when compared to the vastly underwhelming and inferior Learn and Apply student books in Eureka². They’re actually quite solid in comparison to deficiencies in the student books from both enVision+ and Eureka².

However, the Math Expressions Student Editions also contain serious deficiencies when evaluating their content versus Rosenshine’s Principles of Instruction, notably the lack of detailed steps in explaining new concepts, the lack of sufficient models and total lack of worked examples. Where Math Expressions eclipses enVision+ and Eureka² is in number of practice problems, and review of previously taught topics particularly at the end of each chapter.

In addition, in its Program Overview guide Heinemann vastly oversells the Matific game platform:

Having spent a significant amount of time on the Matific game platform, it is a far cry from Heinemann’s hyperbole in the Program Overview brochure. The brochure implies that Matific is a personalized learning tool that enables (student) “adaptive agency” and “targeted practice.” It hilariously says that every Matific “game-based activity is an assessment that adapts personalized learning paths based on each student’s pace and progress to ensure they receive the appropriate level of challenge an support.” Instead the Matific games were overly-produced middle-of-the road video games embedding minimal math content that spent more money on transition animations and cute character development than on the math content embedded within.

Final Thoughts on California Math Expressions

A curriculum review that confined itself to the Student Edition of Heinemann’s Math Expressions might reach a charitable verdict — C or C+. The student-facing materials contain recognizable mathematical content and ample practice problems that are, at least on their surface, defensible. But a curriculum is not just its content—it includes its prescribed pedagogy. And the Teacher’s Edition makes the curriculum’s inquiry-oriented constructivist pedagogy impossible to ignore or misinterpret.

Heinemann’s own introductory pages lay it out with unusual candor: this is an inquiry-first, student-centered, Math Talk–organized program whose entire lesson architecture is built on a foundation that cognitive science has repeatedly discredited. What the Student Edition offers in content, the Teacher Edition systematically undermines in delivery:

Math Expression’s organizing framework is called the ‘Inquiry Learning Path,’ and it consists of three explicit phases. Phase 1 – labeled “Elicit Student Methods: explore and grow understanding”– is the entry point for every new topic. Before any instruction occurs, students are asked to share ideas about what they already know, discuss different approaches, and collaboratively explore solution methods. This is hard core student-centered discovery learning.

Phase 2 – “Discuss Research-Based Mathematically Desirable and Accessible Methods” – then has students begin “forming conceptual networks” through further discussion and tool use, during which “methods are analyzed empowering students to become problem solvers.” Only in Phase 3 – “Formal Math Methods: fluent use of knowledge” – do students finally reach the practice stage for gaining fluency with mathematical procedures, and even then, the text notes that “students are able to gain fluency with mathematical methods of problem solving,” leaving open which method: the Teacher Edition explicitly says students “become faster and more efficient with their chosen method.” Standard algorithms, in other words, are one option among several that students may or may not adopt. The sample lesson examined in Grade 4 – 1-1 Place Value to One Million – spends all of its length on inefficient methods, dot arrays with lines and place value drawings. The standard algorithms are delayed until much later.

Anyone familiar with Haring and Eaton’s Instructional Hierarchy will immediately recognize what has happened here: the sequence has been inverted, with consequences that cascade through every lesson in the program. The Instructional Hierarchy identifies four stages of skill development – Acquisition, Fluency, Generalization, and Adaptation – that must be traversed in order. A student in the Acquisition phase is encountering a skill for the first time. The appropriate instructional method is explicit teacher modeling, clear demonstration of the correct procedure, and immediate corrective feedback. A student who has not yet acquired a skill cannot be meaningfully asked to achieve fluency with it, and a student without fluency cannot generalize reliably across problem contexts. The sequence is not arbitrary – it reflects the cognitive reality that automaticity must precede application, and application must precede transfer.

Math Expressions places students in Phase 1 exploration – a task that presupposes generalization-level capability – before acquisition has occurred. Students are asked to share and compare solution methods for content they have not yet been taught. The inevitable result is that Phase 1 surfaces whatever prior knowledge, partial understanding, and misconceptions students happen to bring to the lesson, then invites collaborative discussion that can just as easily reinforce error as correct it. The teacher’s prescribed role in Phase 1 is not to instruct but to elicit — a facilitative stance that is precisely wrong at the acquisition stage of learning.

The program’s violations of Rosenshine’s Principles of Instruction are equally systematic. The “Inquiry Learning Path” architecture Math Expression uses structurally excludes the most critical of these. There is no prescribed daily review sequence before Phase 1 elicitation begins. There is no teacher-led modeling prior to student exploration. Modeling, when it appears at all, is categorized as one of the “responsive means of assistance” a teacher may deploy during Math Talk discussions, listed alongside “engage and involve,” “manage,” and “connect.” Small steps with explicit instruction at each step are replaced by open-ended collaborative inquiry. The result is that students who have not mastered prerequisite content are deposited into Phase 1 exploration with no corrective floor under them, because the teacher’s role is to “orchestrate collaborative instructional conversations” rather than to detect and address gaps in prior learning. The high success rate that Rosenshine identifies as both a predictor and a product of effective instruction is structurally unavailable in a Phase 1 environment. Students cannot succeed at tasks that require knowledge they have not yet acquired.

The Teacher Edition does contain some gestures toward effective practice. Phase 3 includes fluency work, “remembering pages” provide some distributed practice, and formative assessment tools are described. But these elements are downstream of a fatally flawed entry architecture, and their presence does not rehabilitate the program’s core structure. A distributed practice routine added at the end of a lesson whose acquisition phase was replaced with student inquiry and conjectures is not remediation, it is practice of whatever each student happened to take away from the inquiry session, which may or may not bear any resemblance to correct mathematical procedure.

The infusion of the 2023 CMF principles makes the situation worse. The Teacher Edition explicitly states that the “Math Talk Community supports all of the California Mathematics Framework practice standards,” and the program’s investigation-centered approach to real-world problems, its emphasis on student self-regulation and self-reflection, and its framing of the teacher as a facilitator of student sense-making rather than a transmitter of mathematical knowledge all align tightly with the 2023 CMF’s constructivist commitments.

For a district that has already acknowledged Everyday Mathematics was a mistake – a curriculum that committed precisely these pedagogical errors for over a decade – adopting California Math Expressions would not be a correction. It would be pedagogical malpractice of a new form. The student-facing pages would look different; the lesson architecture would not. For that reason alone, California Math Expressions does not warrant further consideration in this adoption process.

Conclusion

LCUSD having reached the current stage in its elementary math adoption process must now hope that its Elementary Math Selection Committee makes a wise decision at its April 28th meeting when it will decide which two curricula to eliminate from the above final four. In our view, this should be an easy decision as Math In Focus stands clearly above the other three in achieving the district’s stated objectives for the adoption. The more difficult decision is which curriculum survives to the piloting phase next school year. Based on our analysis, enVision+ is the more defensible pilot partner for Math In Focus, though neither its constructivist implementation architecture nor its weak assessments make it an acceptable long-term choice.

It should be mentioned that piloting of finalist materials in the classroom is critical to surface implementation issues that escape notice when merely reviewing limited sample materials provided by the publisher in this phase of the selection process. The district’s past pilots have been abbreviated to the point of being inconclusive. A proper pilot — with defined evaluation criteria, pre- and post-assessment performance comparison between treatment and control groups, and systematic teacher feedback — is not optional at this stage; it is the minimum standard a district that has acknowledged a decade-long curriculum mistake owes its students and families.

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1. See the section on “Constructivism versus Explicit Instruction Explained” in my article Math Survey Results Shared: Mostly Aligned, Some Not So Much for an explanation of the differences between constructivist and explicit instruction curricula. ↩︎
2. Quoted from Savvas’s top-level web page for the enVision+ Mathematics K-5 elementary math curriculum: https://www.savvas.com/solutions/mathematics/core-programs/envision-mathematics-grades-k-5 ↩︎
3. On the enVision+ California Mathematics product description page, Savvas touts how enVision+ incorporates the Environmental Principles and Concepts (EP&Cs) developed by the California Environmental Protection Agency as required by California Education Code 51227.3 to be incorporated in a framework whenever it is revised. The enVision+ Program Guide also talks about a new Environmental Principles & Concepts Handbook, that “provides tips and ideas on how to infuse principles and concepts into activities and discussions during the entire year.” ↩︎
4. Page 10 of the enVision+ California Mathematics Program Guide. ↩︎
5. The LCUSD Math Vision Statement was first unveiled in final form by Jim Cartnal in slide 16 from his presentation slides at the second elementary math adoption parent information meeting on January 28, 2026, a full accounting of which is documented by LCMP in this article. The vision statement is also included in the introduction to Hanover HQIM rubric. ↩︎
6. Rosenshine, B., “Principles of Instruction: Research-Based Strategies That All Teachers Should Know.” (2012), American Educator , Spring 2012. ↩︎