According to CDE data, less than 40% of CA students met the achievement standards in math in 2018-19. Even more alarming, in post-covid testing, math scores of average 8^th graders were at the 5^th grade level in Spring of 2021 (link). So what is the 2022 Second Field Review (SFR) draft framework doing to ensure more students reach math proficiency? Are they giving teachers suggestions and resources to make math content standards more accessible to students? Quite the opposite. The SFR draft framework is replacing the Math content standards with so called “big ideas” and “content connections”. They also hope to replace the standardized assessments that test mastery of the math content standards. Why are they doing this? One motivation may be that if the focus on math content standards and the standardized testing of those standards is removed, then there will be no way to measure how badly California students are failing at mathematics!

Math content standards list the specific learning outcomes for each grade level, K-8 and then for each course in High School. The current CA math content standards, the California Common Core State Standards for Mathematics (CA CCSSM), were carefully examined, reviewed, and adopted by the State Board of Education in 2013. (LINK) For example, a grade 3 math content standard states that students will “fluently multiply and divide within 100.” Thus, math content standards make it clear to teachers what their students are expected to learn and when they should learn it so that they become proficient. Moreover, explicit math content standards also let parents know what their children should be learning in each course and in each grade level.

Content standards, and measuring attainment towards those standards via standardized assessment, are essential to ensure equitable math instruction. They set forth expected learning for all students. As the SFR draft framework accurately notes, “The California Common Core State Standards for Mathematics (CA CCSSM) describe mathematics learning objectives for California” (Ch. 8, Line 34). Yet, in the actual text of the SFR draft framework, it suggests teachers and (textbook) publishers avoid the process of organizing around the detailed math content standards:

“This framework reflects a revised approach, advocating that publishers and teachers avoid organizing around the detailed content standards , and instead organize around the most important mathematical ideas—" big ideas” (Ch. 1, Lines 437-440).

The SFR draft framework further explains,

“Instruction is organized and designed in the spirit of investigating the “Big Ideas” of mathematics and connecting content and mathematical practices within and across grade levels” (Ch. 6, Lines 1255-1257)

Note that “big ideas” are NOT content standards, as is detailed below. Showing their true colors of failing to emphasize and uphold the math content standards, the SFR draft framework goes on to say,

“As discussed in Chapters 1 and 2, the Standards for Mathematical Practice (SMPs), Content Connections (CCs), and Drivers of Investigation (DIs) combine to create an effective lesson design model.” (Ch. 7, Lines 91-93)

Note that “Standards for Mathematical Practice” are NOT content standards, but instead are habits of thinking; e.g. “Make sense of problems and persevere in solving them”. There are 8 standards for mathematical practice, (SMPs) which are identical in each grade K-12; these were included in the 2013 Framework as well. Rather than emphasizing the math content standards, the SMPs are what are highly emphasized in the SFR draft framework. The math content standards seem to be missing in action from the SFR draft framework, with little specificity on which content standards will be learned when. The standards for mathematical practice are not a substitute for the math content standards, but are to be emphasized WHILE focusing on math content standards. Where are the math content standards in all of this writing? They have been REPLACED by “Big Ideas”, in some kind of end around that came to be during the midst of school closures with the Covid-19 pandemic.

‘Big Ideas’

The authors of the SFR draft framework are replacing the math content standards with their “big ideas”. They write,

“This document presents a “big idea” approach to mathematics to support teachers and students in making consistent, productive use of the mathematical practices and recognizing the connections among mathematics topics.” (Ch. 6, Lines 557-559)

Are “big ideas” bad things to focus on? For sure, not in and of themselves, but they can NOT replace the content standards, as it’s the content standards that give explicit detail of what needs to be mastered in each course. The SFR draft framework states,

“As students explore and investigate with the Big Ideas, they will likely encounter many different content standards and note the connections between them.” (Ch. 6, Lines 1064-1066)

Are we okay with students “likely encountering” content standards? Don’t we want to make sure students DO ‘encounter’ content standards? What will happen in subsequent math courses when topics come up dependent upon knowledge of content standards which students did not end up ‘encountering’?

So what are these “Big ideas” that the SFR draft framework plans to replace the content standards with and where did they come from? The SFR draft framework tells us,

“The state of California set out the most important mathematical content and practices by highlighting a collection of big ideas in mathematics, transitional kindergarten through grade ten, in the Digital Learning and Standards Initiative (CDE, 2021).” (Ch. 8, Lines 137-139)

The Digital Learning Integration and Standards Guidance was a document created in relation to the school closures as a result of Covid-19, in response to Senate Bill 98, which “called for the development of draft distance learning curriculum and instructional guidance for mathematics, English language arts, and English language development to be adopted by the State Board of Education by May 31, 2021.” (Link). However, CA public schools are no longer conducting classes via distance learning, and schools are no longer closed. Were educators made aware that these new Digital Learning “standards” were intended to replace the math content standards in place in California since 2013? Of course not!!! This document was the work of one of the authors of the SFR draft framework (Jo Boaler) and her colleague. Much of the SFR draft framework comes directly from this “digital learning guidance” that came about under the radar as most people assumed the “Digital Learning and Standards” developed during remote and hybrid instruction was specifically for the purpose of providing suggestions during the pandemic. In reality, this “Digital Learning Integration and Standards Guidance” became Jo Boaler’s way of replacing the math content standards. While a bit less explicit in the SFR draft framework, Jo Boaler’s disapproval of the math content standards is clear in her writings. In her article entitled, “The derailing impact of content standards–an equity focused district held back by narrow mathematics”, we read, "While these achievements are impressive, we found that the work of the teachers and district leaders was undermined by the nature of the mathematics set out in the Common Core State high school standards." In Jo Boaler’s opinion, clearly the “math standards” get in the way of learning math. In case that first example was not clear enough, she concludes her paper saying, “We end this paper with a call for a revision of the Common Core Mathematics Standards (LaMar, T., Leshin, M., & Boaler, J. (2020).” HOW CAN ONE OF THE PRIMARY AUTHORS OF THE SFR DRAFT FRAMEWORK (WHICH HAS THE PRIMARY TASK TO SUPPORT THE IMPLEMENTATION OF THE CONTENT STANDARDS) BE SOMEONE WHO THINKS THE STANDARDS “UNDERMINE” THE LEARNING OF MATH? If Jo Boaler wants to “revise the Common Core Mathematics Standards”, then she should begin work on that through proper channels rather than try to remove and replace them on her own in the SFR draft framework!

What’s even worse is that these “big ideas” that were “set out by the state of California” (i.e., Jo Boaler) are not even the definitive “big ideas” to teach; in fact, the SFR draft framework tells us these are just one “variation” of big ideas. As the SFR draft framework states,

“However, it should be noted that there are many interpretations of big ideas in mathematics, and those presented in those figures are one variation . As noted in Chapter 2, providing mathematics teachers with adequate release time to collaborate with colleagues and engage in discussions around their vision of big ideas at their grade level or in a course can enable them to create rich, deep tasks that invite students to explore and grapple with those big ideas.” (Ch. 7, Lines 204-209)

So what exactly will your child learn in each grade if “big ideas” are taught rather than the explicit grade level math content standards? Apparently it depends upon how much ‘release time’ your district allocates to its math teachers, so that they may decide on “their” big ideas or on which “variation”of big ideas your district or school chooses.

How specific are these “big ideas”? One big idea from Grade 4 is “Connected Problem Solving”. (Ch. 6, Line 1332). A Grade 6 big idea is “Model the World”. (Ch. 7, Line 161) Yes, the three words “Model the World” are the entire “big idea”; in fact most every “big idea” is a three to five word phrase. Compare that level of specificity (“Model the World”) to a current grade 6 math content standard: “Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x, and are all non-negative rational numbers.” You can quickly see the difference between the adopted math content standards and the SFR draft framework’s “big ideas”: there is a level of detail and specificity in the explicit math content standard which let educators and parents know EXACTLY what students must learn in each grade/course, versus the vague, non-specific, ill-defined ‘big idea’, where “Model the World” could mean just about anything.

Below is an example of the “big ideas” for grade 2 from the SFR draft framework. This is the specific information about what is projected to be taught according to the SFR draft framework. Can you tell specifically what your children will actually be learning? From this diagram, can a teacher figure out what specifically they are supposed to teach? (Ch. 6, Line 1091)

‘Big Ideas’ and the 4 “Content Connections”

In line with what the authors of the math content standards (adopted by the State Board of Education in CA in 2013) wrote, the 2013 framework authors clearly told teachers which content standards were “major” and which were considered “additional” or “supporting” standards. As not all math content standards are equally important (e.g. understanding the place value system is much more important than naming shapes), being told what is “major” allows teachers to focus more time on these standards to ensure mastery by all students. This, in effect, let teachers know what was most essential to the future success of each student. The list of “major” standards was delineated intentionally, making sure students are prepared for the subsequent grade levels.

The SBAC (the standardized state assessment exam California students take) is designed to align with the focus on the “major” math content standards when assessing student math achievement levels. One would assume that these new “big ideas” in the SFR draft framework would center around and focus on the “major” content standards as well. They do not.

Instead, the “big ideas” of the SFR draft framework are centered around 4 “Content Connections,” which are the same across all grade levels and courses: CC 1) Communicating Stories with Data; CC 2) Exploring Changing Quantities; CC 3) Taking Wholes Apart; Putting Wholes Together; and CC 4) Discovering Shape and Space. As far as we know, these Content Connections are new, and did not exist prior to the SFR draft framework, but have recently been created by the SFR draft framework authors. We read,

“The Content Connections (initially presented in Chapter 1) are big ideas which span TK–12 in this framework.” (Ch. 3, Lines 150-151)

The authors expand further upon this, writing,

“This framework identifies three Drivers of Investigation (DIs), which provide the “why” of learning mathematics, to pair with four categories of Content Connections (CCs), which provide the “how and what” mathematics (CA CCSSM) is to be learned in an activity.” (Ch. 1, Lines 447-450)

How do these 4 Content connections, described as providing the “How” and “What” of teaching in every course, align with the “major standards”? Very poorly!!! The “major (content) standards”, which are specific to each course, generally include the topics of place value, operations on whole numbers, fractions and decimals, and content around the learning of algebra and functions. The “major standards” do NOT focus on Geometry or Data; however, the ‘‘Content connections” now make Data and Geometry 50% of the math content in all courses, K-12, as they are two of the four Content Connections (CC 1- Communicating Stories with Data and CC 4- Discovering Shape and Space). Students will no longer be directed to focus on the most essential math content, the “major standards,” which have been clearly defined by the State, per the 2013 Math Curriculum Framework. If our students are no longer focusing on the most essential topics in mathematics, how will that affect our future STEM (Science, Technology, Engineering and Mathematics) workforce?

Consider this simple question- if you have ever played card games, what do you call the red cards that are not hearts? Did you say “diamonds”? That’s what nearly everyone calls them; e.g. the queen of diamonds. And yet, a “diamond” is NOT actually the name of that shape on the card - it is actually either a rhombus or a parallelogram. So you’ve been using incorrect geometry your whole life; how has that affected your ability to succeed in life? It has not! While geometric shapes might be interesting to investigate and discuss, geometry itself is NOT considered part of the “major standards”; however, if you never understood how to add or subtract or what a fraction was (all “major” standards), you would have struggled greatly. In grades K-2, for example, “major” standards, as defined in the CA-CCSSM, generally include counting and cardinality, place value, and addition and subtraction of whole numbers. In grades 3-5, in addition to those that are “major” for K-2, “major standards” also include all work with fractions and decimals as well as multiplication and division. By grades 6-8, the “major” standards include the topics of ratio and proportion (including percent), algebraic expressions and equations and linear functions. With the exception of volume in grade 5, Geometry is never part of any “major standards” as it is not an essential math building block, or integral to the math required to be prepared for the next grade level. In much the same way, the data standards in K-8 are also not considered “major” in and of themselves; though, the skills needed to interpret and apply the data are essential and “major” (e.g. addition, subtraction, fitting a function to the data, etc). The authors of the SFR draft framework suggest that teachers and students devote 50% of their time to non-”major” topics, those which do not lead to nor are required for future success. There was significant and accurate research done in the writing of the 2013 math content standards and in accurately describing which were “major” vs “minor” standards. And yet, rather than focus on how to help all students learn and master the “major” content standards, the SFR draft framework seeks to replace them with ambiguously defined “big ideas” and “Core Connections”. Will children likely have more fun with this new focus? Yes! Will they learn and be able to have a chance at a STEM career? No! Without the necessary foundation in the “major” standards, such as multiplication or solving linear equations, students will not be able to progress and understand high school or college math, or the sciences that rely on that level of mathematics, such as chemistry, physics, engineering, biology, computer science, economics, psychology and even data science.

In case you have not seen the SFR draft framework, below is the graphic showing what it projects children will learn in grades K-12 (Ch. 1, Line 458). Notice there are few specifics and there is no mention of math content standards. The standards of mathematical practices are included, but not the math content standards. Looking at this graphic in detail, it’s impossible to understand what specific content students will learn and when. Rather, this appears more like a child’s board game where anything could be learned at any point with no specific focus or explicitly required math content learning for each grade.

The hidden agenda behind removing focus on the standards

There seem to be two obvious reasons, in our view, why the authors of the SFR draft framework would seek to remove the focus on the math content standards and instead replace them with a focus on what they call “big ideas”:

1) a lack of explicit standards removes accountability, making it harder to measure what’s being taught — so all students can be construed as “succeeding”, even if they are not;

2) the SFR draft framework aims for students to have “meaningful math experiences”, something easier to ‘achieve’, rather than aiming for students to achieve at math by mastering the math content.

Reason #1: If we don’t focus on math content standards and assess those standards, no one will be able to tell that students are not learning!!

Currently, we know that the average grade 8 student in CA is at a grade 5 academic level in math BECAUSE we have standardized tests (link) that measure expected math content learning by grade level. Without this type of assessment, we would not be aware of the gaping holes in students’ mathematics learning, and the issues that need to be addressed. Just as advocates have sought to eliminate the SAT for college admittance (source), so the authors of the SFR draft framework want to change assessment in CA K-12 public schools. The SFR draft framework calls the change in K-12 grading and assessment “mastery based grading”. Rather than having a standardized exam assessing mastery of content standards, they suggest

“Assessments should match the focus on big ideas” (Ch. 12, Line 99).

In terms of “grading”, the SFR draft framework suggests,

“Advice on Grading: Many teachers have to grade students, as it is a requirement of their school district or their administrators. Ideally, teachers are asked to provide grades only at the end of a course—not during the course, when students need information on ways to learn, which should be given through formative assessment. The following list compiles advice on ways to grade fairly and to continue communicating positive growth messages through assessment.

1. Always allow students to resubmit any work or test for a higher grade—this is the ultimate growth mindset message, communicating to students that you care about learning, not just performance.
   
   

2. Share grades with school administrators but not with the students if used during a course. If your school requires grades before the end of a course, this does not mean that you must give them to students. Instead, give students verbal or diagnostic written feedback on ways to improve.
   
   

3. Use multidimensional grading. If you believe in the breadth of mathematics and value multidimensional mathematics in the classroom, use mathematics work rather than test performance—recording, for example, whether students ask questions, reason and justify, challenge or contribute to other’s thinking.
   
   

4. Do not use a 100-point scale, this is mathematically egregious (see Boaler, 2016). Instead use a 4-point scale: A=4, B=3, C=2, D=1F=0
   
   

5. Do not include early assignments from math class in the end-of-class grade. When teachers do this, they are essentially grading students on their work from a previous class. Grades should include only work and assignments from the point in the class when students are working on what is learned in the class.
   
   

6. Do not include homework, if given, as any part of grading. Homework is one of the most inequitable practices in education; its inclusion in grading adds stress to students and increases the chances of inequitable outcomes.”

Extract from Mathematical Mindsets, Boaler, 2016 (Ch. 12, Lines 729-756)

The ‘Advice on Grading’ suggestions above bring some questions to mind:

What does it mean to grade “fairly” and “communicate positive growth messages throughout assessment”? How is it beneficial to the student to NOT have their grades be shared with them such that they do not know how they are doing until it is too late? What is wrong with a 100 point scale? How is a 100 point scale ‘mathematically egregious’? What does ‘multidimensional grading’ mean – does it mean to grade some students in the same class on a different rubric or scale? If so, could bias enter into grading? Where does learning the math content standards for that grade fit into ‘multidimensional grading’? According to the ‘multidimensional’ grading example given above, can students who ask questions or challenge others’ thinking get A’s, even if they do not know how to actually do the math? What evidence does the SFR draft framework have that these grading suggestions lead to improved math achievement — or even that these suggestions lead to more equitable math achievement?

In our view, all of this changing focus on assessment serves to cover-up the fact that students are no longer mastering math content standards, just as this article (link reveals 8^th grade CA students have only mastered math at the 5^th grade level. Suggesting assessing K-12 students based on vague and ill defined ‘big ideas’, rather than using standardized assessments based on mastery of math content standards moves away from objective, merit based assessment, which truly is the most equitable means of assessment.

Reason #2: Rather than focus on standards, the focus is on “experiences”

As the authors of the SFR draft framework write,

“The framework no longer needs to provide as much expansion on the individual standards; rather, curriculum designers and California educators need guidance for creating mathematics experiences that provide access to the coherent body of understanding and strategies of the discipline. (Ch. 1, Lines 427-431)”.

We read that

“Students need to experience the “wonder, joy, and beauty of mathematics.” ( Ch. 7, Line 70)

What are these “experiences” that allow students to master math? One example for grade 7 (Ch. 7, Lines 522-631) begins by stating,

“In this example, students observed flocks of crows and seagulls hovering over the lunch area by the cafeteria around nutrition and lunch times. During a campus-wide survey and mapping activity, students observed large amounts of trash and food waste. They wanted to study the effects of this waste on the health of students and teachers as well as the local and regional natural systems and local community.” (Ch. 7, Lines 529-533)

The vignette continues,

“Working in small groups, students generated several questions, ultimately settling on three to reflect the fact that students/grades eat lunch at different times: Do students in different grades produce the same amounts and types of food waste and “trash”? Do students in different grades deal with food waste and “trash” in the same way? Are there different numbers of birds in the lunch area when different grade-level students are eating?” (Ch. 7, Lines 574-579)

The classroom experience ends with,

“They determined that students in different grades discarded their food waste and “trash” in different ways. They were also able to determine whether larger numbers of birds visited the lunch area when different grade-level students were eating.” (Ch. 7, Lines 588-590)

“The findings from their investigation resulted in many other wonderings from the students, for example, how the food waste and trash might be affecting students and people living near the school; the plants and animals on and near the campus; local water quality; the town’s litter prevention program?” (Ch. 7, Lines 591-594)

While this vignette described above might be perceived as an engaging experience for some, keep in mind this is for a grade 7 math class, and it’s very hard to see significant MATH learning anywhere close to grade 7 math content standards. The SFR draft framework is full of “vignettes” (stories of what could happen in an ideal math classroom), almost none of which help students understand and master significant mathematics (e.g. Ch. 7, Lines 446-509 or Ch. 8, Lines 1100-1213). To be clear, math can and should be engaging and relevant, but NOT at the EXPENSE of mastering crucial math content standards.

So why does the SFR draft framework suggest deemphasizing the math content standards? Why are the authors replacing the focus on math content standards with ill defined “big ideas” and “content connections?” The California Dept. of Education says the purpose of a curriculum framework is to “...provide guidance to educators, parents, and publishers, to support implementing California content standards.” The purpose of a curriculum framework is to ‘support implementing the content standards’, not replace them, or move away from them. Students still need to master the math content standards to achieve at math. With less than 40% of CA students proficient at math, this is not the time to “move on” from math content standards to their replacement — vague ‘big ideas.’ The authors of the SFR draft framework write,

“The framework’s role is to guide implementation of the CA CCSSM, not to simply restate or explicate its standards (learning goals). Thus, the framework is written from the perspective of instruction (both instructional materials and enacted instruction). This requires careful consideration of many issues in addition to learning goals: motivation, coherence, students’ and teachers’ cultural and linguistic assets, access and equity, context, sustainability, and many more. (Ch. 8, Lines 65-70).”

Apparently, standards based instruction takes a back seat with all these other things to consider!

Summary

Having explicit content standards and using standardized means to measure attainment of those standards is the best way to ensure equity in learning and to be confident students actually know the math needed for college and career. Without a focus on math content standards, students will not be learning the same content within each course, as each classroom will focus on different topics. There will be no way to know what math content is actually covered or learned in each course. Removing and replacing standards based math instruction with vague and ill defined concepts like ‘big ideas’ and ‘content connections,’ will be a disaster, leading to lower math proficiency and increased inequity. While many students may like math class more, that does not mean they will end up proficient at math, and our future workforce will lack necessary mathematics mastery to compete in the world arena.