It Will Widen the Achievement Gap

Item 4 of 6

Summary in Brief:

Math content standards set out the expectations for what math all students should learn in each grade level/course. Holding students to these high expectations, to meet and master the content standards, while providing support to help all students reach these expectations, is the only way to ensure that students make progress towards learning and mastering math itself. California has begun to make progress for all groups towards meeting proficiency; however, rather than continue to hold all students to these high expectations and supporting them to succeed, the authors of the Second Field Review Draft Framework (SFR draft framework) seemingly assume that students are NOT capable of mastering the math content standards. The SFR draft framework seeks to replace the math content standards with vague and ill defined “big ideas”, asking teachers to teach “authentic tasks” about which students “wonder” and “pose problems” about, instead of the content standards. Allowing the content of math class to be subjective and dependent upon what students “wonder” about marks a clear move AWAY from the focus on math content standards and the expectation that all students can and should meet them. Without the common expectations for all students (the math content standards), classrooms and students within classrooms across the state can and will be learning different math topics at varying levels of difficulty; thus, the implementation of the SFR draft framework will lead to increased inequity in math.

NEXT: It Will Fail Our STEM Students


It Will Widen the Achievement Gap

In the K-12 school system every student — regardless of race, creed, wealth or color — can and should be academically successful.

Yet, California does have wide achievement gaps in mathematics. How can we best ensure that ALL California students achieve in mathematics?

  1. We need common required, clear, and objective outcomes for all students to achieve in math;

  2. We need a standardized and objective means by which to measure progress towards those outcomes; and

  3. We need to use the data that measures student progress towards the required outcomes to provide support to students who have yet to meet them.

Fortunately, we have those shared, common, clear and objective outcomes already: the math content standards! We also have the standardized common means to measure progress towards mastery of the content standards: the SBAC (the exam all CA grades 3-8 & 11 students take in math each Spring). What educators are still working on is how to best support students who have yet to reach proficiency in mastering the math content standards. It is expressly this, the best means by which to support ALL students to master the math content standards, that should be the focus of a CA Math Framework. Unfortunately, the SFR draft framework seemingly believes not all students are capable of learning the math content standards; as such, rather than focus on means to support students of all backgrounds to be successful in mastering the math content standards, the SFR draft framework proposes to remove the focus on standards based math. In doing so, the SFR draft framework is both lowering the required outcomes for all students, and creating situations across California where there are no “common” required outcomes, as students in different classrooms will no longer be focused on the explicit and detailed math content standards. This will not only harm all our students (as the decision about what topics to cover will be up to teachers and students), but it will also lead to increased achievement gaps in math.

Background on the Achievement Gap
In California, less than 40% of students are proficient in mathematics. An even more dismal feature of math proficiency is observed when it is analyzed as a function of race and socioeconomic status. Black, Latino and poor students still lag dramatically behind Asian American, white, and wealthier students of all races. Source. One encouraging feature of the data is that CA math test scores have been slowly improving for all student groups. However, the achievement gap between Latino and White and Asian-American students, while not widening, remains large and hasn’t decreased. The math achievement gap between Black and White and Asian-American students has widened, however. Link

In addition to achievement gaps between students of different races, there is also a significant gap between low income students and their higher-income peers. See graphic below.

The essential role of math content standards to ensure equity for all
If we want to narrow the achievement gap, we need to ensure all students have access to the teaching and assessment of the same rigorous content standards. We can not leave the decision of what topics to teach up to chance or teacher discretion; if we let the selection of math topics be subjective, disparities in what students are taught will emerge. This could lead to students with perceived abilities being given higher level material and others perceived to be less likely to achieve being given remedial work.

Such was the case before 1997 when California did not have standards based math instruction (link). Once California had standards and accountability (STAR testing) tied to the standards, the burden of deciding what to teach students was no longer placed on a teacher. No longer would teachers decide a group of students needed to spend the entire year learning material years below grade level. Having explicit and objective math content standards, coupled with standardized assessments tied to those standards, put both students and teachers in a better place. As a state, California has been making progress towards ALL student groups increasing their math achievement.

Rather than continue to improve the teaching and the learning of the content standards, the SFR draft framework proposes that CA math education should regress back to the time before implementation of standards based instruction and assessment. The SFR draft framework says teachers should be “Teaching from Big Ideas, not individual standards” (Ch. 10, Line 246) and use “mastery-based assessment at the “big idea” level” (Ch. 10, Line 1167-68) (rather than assessing based on the detailed math content standards).

What are these “big ideas” the SFR draft framework suggests should replace the math content standards? ”. As the SFR draft framework writes, so I think it fits better down here . . .

“Big ideas in math are central to the learning of mathematics, link numerous math understandings into a coherent whole, and provide focal points for students’ investigations.” (Ch. 13, Lines 506-508)

“Big ideas” sound like a great idea, but the SFR draft framework’s list of ‘big ideas’ are so vague and general, that it’s possible that no two students in different classrooms across CA will learn the same thing. For example, a current grade 6 math content standard reads, “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.” In contrast, a grade 6 “big idea” reads, “Model the World” (Ch. 7, Line 157). 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. 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. In addition to the SFR draft framework listing vague and ill-defined “big ideas” instead of specific math content standards as the focus for each course, the SFR draft framework itself notes that these “big ideas” are only one “variation” of “big ideas” such that each grade level team can use release time to decide on “their” big ideas.

“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, Line 204-209)

(See “It removes standards based instruction” for more detailed information about “big ideas” and how the SFR draft framework is trying to replace the math content standards with them).

In addition to changing to a focus on “big ideas” versus focusing on math content standards, the SFR draft framework also suggests teachers focus on tasks about which students “actually wonder” in lieu of specific math content standards. (Ch. 1, Lines 573-574) The SFR draft framework authors want teachers and students to focus on “math experiences” and things that “elicit wondering” (Ch. 6, Lines 1287-88). The authors 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“ (Ch. 1, Line 427-431).

There is naturally a variance between math classrooms and the specific experiences students receive in math education; however, having explicit, detailed math content standards gives clear guidance to all teachers and helps maintain consistency, reliability, and accountability both within districts and across the state for the math content that will be learned in each grade level and course. If, instead of standards-based instruction, teachers focus on ill-defined “big ideas” and only things about which students “actually wonder”, classes will all learn very different math content; therefore, there is no way to ensure equitable math teaching and learning among different math classrooms if this SFR draft framework is adopted and implemented.

What will a focus on ‘mathematics experiences’ instead of explicit, objective math content standards lead to? In our view, it will lead to massive inequities and a greater number of students who are “illiterate” in math. The removal of a focus on standards based education coupled with a focus on math about which students “actually wonder” and which is “authentic” (Ch. 1, Line 573) is akin to the situation in Reading Instruction in the 1980s, which led to less literate students in the 1990s. Source

When the focus on phonics (the building blocks of reading) was removed, reading scores suffered. In much the same way, removing the focus on standards-based mathematics, specifically removing any requirement for procedural fluency, will take us to the same place — with significant portions of our population illiterate in math. While there is much debate about the approach to teaching reading, “The best argument for phonics is that no one is harmed by it and a large subset of students is helped by receiving explicit phonics instruction from kindergarten through second grade.” Link
Many experts claim we need a “balanced” approach to reading (link). In math, the 2013 CA math framework REQUIRED balanced math instruction: “rigor requires that conceptual understanding, procedural skill and fluency, and application be approached with equal intensity.” (CA CCSSM, 2013) Balanced mathematics instruction means equal time is devoted to procedural learning (algorithms & facts), conceptual learning (understanding), and problem solving (application). While it can be good to allow students to focus on math about which students “actually wonder”, this can NOT be at the EXPENSE of a focus on mastering foundational math content standards and procedures. The 2013 CA math framework had “required fluencies” for each grade K-8; e.g. “Add and Subtract within 10” by the end of grade 1. These required fluencies ensured mastery of specific procedures to ensure students could succeed in future courses; without these key fluencies, math becomes over laborious and students struggle to keep up and learn anything new as their peers who have mastered these procedures are significantly quicker and more confident. These “required fluencies” are eliminated in the SFR draft framework, revealing the authors true intention that no standard be a required fluency. A lack of fluency in grades K-8 will surely harm all students, but especially those students who don’t have outside support to help develop these key foundational fluencies. In this way, the achievement gap will increase.

Gaps will widen based upon what the proposed 2022 framework describes should happen in classrooms.
What will students be learning in K-12 classrooms that follow the SFR draft framework? To be clear, the learning is not focused on the 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, Line 437-440).

Instead of standards-based education, we read that

“students can make sense of the world (DI1) by exploring changing quantities (CC2) through classroom discussions wherein students have opportunities to construct viable arguments and critique the reasoning of others (SMP.3)” (Ch. 1, Line 473-476).

This sounds interesting, but exactly what MATH is being learned? We go on to read,

“Within each Content Connection, students’ experiences should first emerge out of exploration or problems that incorporate student problem-posing” (Ch. 8, Line 496-497).

So math class will learn whatever students pose problems about? Sounds fun, but will it lead to math achievement, mastery of content standards, and a narrowing of the math achievement gap? After all, the SFR draft framework claims its primary goal is “equity”.

“Equity influences all aspects of this document.” (Ch. 1, Line 239)

If ‘student problem-posing’ takes primacy, won’t each classroom potentially pose different math problems due to different sets of students? Will the problems posed be anywhere near grade level standards? And what if students don’t pose the questions that lead them to learn the math content standards, and thus the math needed to power our world? How will our students be prepared for college and especially any career in STEM? In a classroom example we read,

“After the question has been raised (hopefully by students)” (Ch. 8, Line 514-515).

Are we now just “hoping” that students ask about things essential for them to learn to build a solid math foundation? What if students don’t ‘pose’ those questions? Do they then simply not learn the material?

The SFR draft framework goes on to say,

“Mathematics is never developed in order to answer questions about which the explorer is not curious; and learning mathematics is not much different“ (Ch. 8, Line 699-700).

So the “content” of math, according to the SFR draft framework, will be whatever problems kids are curious about, and ‘pose’ questions about. How does allowing students to choose the math content close the math achievement gap?

The SFR draft framework gives us dozens of examples of what ideal classroom teaching and learning would look like. As you read some of these examples of the SFR draft framework’s guidance, consider whether and how the different classroom experiences and the diminished access to the content standards will provide anywhere near equitable learning for students across CA.

The SFR draft framework says:

“In grades one and two, many teachers introduce terms like vertex, edge, and face.” (Ch. 6, Line 922-923)

What if your child does not have one of the “many” teachers? Will those students just not learn about those terms?

In one vignette, we read about a high school Math 1 or Algebra I class studying Whale Hunting (Ch. 8, Line 1106-1213).

“Lesson Context: In the 1970s the stock (or number) of bowhead whales in the Bering Sea was calculated to be as low as 600–2000 whales, mostly due to heavy commercial whaling. This was, of course, mightily concerning to environmentalists and thus the International Whaling Commission completely halted permissions to hunt whales hoping to restore the population. Commercial whaling had long been a known issue, and it was already restricted, but this really hurt native populations that hunt bowhead whales for subsistence. Note that this provides a good opportunity for discussing and reinforcing California Environmental Principle I, “The continuation and health of individual human lives and of human communities and societies depend on the health of the natural systems that provide essential goods and ecosystem services.”

After reading about why indeginous people hunt whales, the vignette continues.

“Task: The tribe has assembled a committee of tribal scientists and community members, along with outside scientific and economic advisors, to make a recommendation to the International Whaling Commission. The proposal will specify how many whales the Inupiat and Siberian Yupik people will hunt this year as part of the Aboriginal Subsistence Whaling management plan, while making sure the whale population continues its growing trend. As a member of the committee, it is your task to help create the proposal.

The task as presented is deliberately very open-ended. Different student teams will consider many different factors (beyond Inupiat and Siberian Yupik hunting) that might affect the committee’s recommendations and about which they might wonder—such as changing mortality rates due to shrinking ice cover, ship collision mortality, age structure of the population, etc.”.

While this may be an engaging task for some students, one must ask what math students are LEARNING as they do this (and also wonder, is this math class or science class). For sure students are learning research skills, reading skills, group work skills, and about the history of whale hunting, but math- who knows. It definitely does not come close to the level of math a high school student in Algebra I or Integrated Math I should learn according to the content standards. The vignette continues to describe what one group (of about 10-15 students) did, including using “Wolfram Algebra” (which is something freshmen don’t use or know about as it’s not part of a typical Algebra I or Integrated Math 1 course), and writing equations and doing a variety of math, all on their own. If you’ve ever worked in a group of 10-15 people, you know the reality is that only a select few students will be doing all of this work and those who are uninterested or who have not already mastered the standards will be watching others do the work. How does this arrangement help all students learn and master the content standards?

A second vignette (Ch. 8, Line 1238-1247) describes the engaging task of creating a drone light show (for Math III or Algebra II).

“Students are instructed to work together in three groups to design a solution to the problem. All three groups start out by reading the task and discuss the task. They are then given access to the video, which includes closed captioning, and then prompted to conduct a search for photos and clip art of Ferris wheels as a type of moving light system. Some groups want to watch the video several more times to be sure they understand. From experience, they know that this is not the kind of problem that allows them to find the answer in the back of the textbook. This kind of a problem can be approached in a variety of ways, and the challenge of the openness of the problem is thrilling! This flexibility aligns with the UDL principle - Provide multiple means of engagement by optimizing individual choice and autonomy.”

First question to consider- the vignette calls for three groups to design a solution. Most high school math classes have about 36 students in the class. How well does a group of 12 (⅓ of a class) work? Apparently in this vision of ideal teaching, it works perfectly as “with every group member contributing to the brainstorm, students quickly start sketching as a way to visualize solution paths” (Ch. 8, Line 1253-1254).

Ask yourself, from your own experience, how realistic is it that “every group member” will contribute? Then, magically, each group begins doing all types and different levels of math. One group uses “polar coordinates” to program this. That sounds great, but polar coordinates are NOT INTRODUCED until pre-calculus, so how does ⅓ of the class in Algebra II or Math III magically know how to use them?

What we read in nearly all the vignettes in the SFR draft framework are examples of engaging tasks that are vaguely connected to math; yet they assume that all or some students have already mastered all the math content needed and can magically work in large groups to create questions, research, and use math to answer the questions. What will happen in reality is that those students who are already proficient at math (generally by outside tutoring or support), and motivated by the task will do all the work, while those who struggle in math or are not motivated, will sit by and watch, rather than learn how to do the math. Thus the math achievement gaps will widen.

In the SFR draft framework math proficiency seems to magically occur

The 2013 framework and authors of the common core content standards for math called for balanced instruction, meaning equal time devoted to procedural learning (algorithms/ facts), conceptual learning (understanding) and problem solving (application). This balance, along with a requirement and focus on content standards, gave all students a chance to succeed in math. On the contrary, the SFR draft framework has almost completely removed any reference to procedural (algorithms/ facts) or conceptual learning (understanding); rather, everything is problem solving (application). What’s the problem with that you might wonder? Without guided teacher instruction and support, most students will NOT learn concepts and procedures (or will have to find outside means to get this learning). It is true that some students often see patterns and discover things on their own, and it is true that students who get tutoring will learn the concepts and procedures, but what about the rest of the students? Consider a few examples from the SFR draft framework:

In a high school Math II (likely sophomores in high school) classroom, a teacher named Ms. G has noticed her students have struggled with “motivation” for the topic she’s presenting. (Ch. 3, Line 1808)

So what task does she give her class to motivate them? She asks them (Ch. 3, Line 1820),

“Without checking on a calculator, is 186 divisible by three? Before they begin, she asks for a reminder of what “divisible” means. One student observes that “you can divide into it”. Another student questions this, as “you can divide any number by another number, it just keeps going.” The class eventually arrives at a reasonable definition of divisible as “b is divisible by c if you can divide b by c without any leftover remainder.” (Ch. 3, Lines 1820-1825).

First, what class of ‘unmotivated’ sophomores is engaged by the task (186 ÷ 3) and second, comes up with a definition using “b” and “c”? Continually, the SFR draft framework describes things that are NOT realistic or which only happen with a few students (thus increasing gaps as a few “get it” and the rest do not). The vignette continues,

“Ms. G pauses for an aside here to have the students graph g(x) = (x-1)(x+2). As they quickly see the link between root locations on the x-axis and factors of g(x), they then are able to recognize that setting each factor equal to zero and solving gives a root.” (Ch. 3, Lines 1864-1866)

Again, ask yourself how many students would “quickly see the link” and “recognize” the connection between solving and roots. The reality is only a few would just “quickly” see this and the rest will be watching and falling further behind.

One more example from the SFR draft framework:

“Students might notice during a mathematical discussion that interior angle sums regularly increase in relation to the number of sides in a polygon and use this repeated reasoning to conjecture a rule for the sum of interior angles in any polygon.” (Ch. 4, Lines 833-835)

Who “might” notice this? Which students? The struggling student, or the advanced student who will continue to advance while the rest of the class is left watching and not comprehending?

In addition to vignettes in which the authors magically assume students quickly see and understand everything, the SFR draft framework gives the readers other examples of unrealistic situations where math is “magically” learned. In Chapter 4 (Line 447) we read a vignette from a “grades 5-8 class”. Really? Since when do teachers have a grade 5-8 classroom? How would 5th- 8th grade students all be learning together at widely differing levels — and equitably? The SFR draft framework authors tell us,

“This can be achieved through teachers allowing students to work through courses at different paces, illustrated by the “personalized by teachers” vignette below, or with the support of computerized systems, as illustrated in the ‘personalized learning’ vignette in chapter 2” (Ch. 9, Lines 364-367).

What happens in this “personalized learning”? The SFR draft framework tells us students “sit in groups and work on the course materials.” (Ch. 9, Line 381). Anyone who has ever been in or volunteered in a classroom knows this is not realistic or sound instruction to just have students “sit in groups and work on course material”. If students can learn without a teacher, what’s the role of the teacher? Also, would struggling learners be the ones most likely to advance themselves by working at their own pace on their own, or will the option to “work through courses at different paces” likely increase the achievement gap?


Students with means will use tutors and outside support to ensure success, leading to even greater inequity based upon SES (Socio-Economic Status).
As discussed above, by replacing the focus on math content standards to a focus on “mathematics experiences” and problems students “wonder about”, achievement gaps will widen as each classroom will focus upon whatever math students and teachers decide. But beyond how the lack of focus on standards will likely lead to greater inequity, the SFR draft framework itself suggests that students might need supplemental resources and tutoring to achieve mathematical proficiency:

“It may be fruitful to consider how the pathway to pre-calculus or calculus and other advanced mathematics courses may be made more efficient in high school, and how students might get access to supplemental coursework ” (Ch. 9, Lines 226-230).

“Systematic use of tutoring could reduce the felt need for lower-track classes that derail students from STEM careers at early grades.” (Ch. 9, Lines 456-457).

Given that the SFR draft framework suggests moving away from math content standards being explicitly taught in K-12 classrooms, and that only some students happen to “quickly see” and notice things, it follows that the rest of the students will need supplemental coursework or tutoring to succeed. But who can afford tutors and supplemental classes? Those with economic means, who, by the way, are typically already ahead on the good side of the achievement gap. It is true that many students may be able to access free tutoring at school or attend summer school, but WHY should students have to give up time outside of the school day to learn the content standards they should have been taught DURING the school day? And what about the reality that many socioeconomically disadvantaged students may have to care for younger siblings and/or work jobs after school? Will these students never learn the material? Why do students need to get tutoring or supplemental classes to learn content standards they should have been taught inside of the public school classroom?

Why should public school students need tutoring to have a chance at math success? In reading what the authors of the SFR draft framework say, it can be easy to see why many will need this tutoring:

“It is worth pointing out here that although it is tempting to provide lists of steps (e.g., simplify both sides of the equation, do the same operation to both sides, isolate the variable using operations, etc.), lists of steps should only be provided when generated by students themselves in describing their steps on particular problems, lest students trade active reasoning from intrinsic properties to a reliance upon rote procedural skills (Reys and Reys, 1998).” (Ch. 3, Lines 1664-1669)

So if students don’t generate the “list of steps” themselves, needed to solve an equation, then what? Since they will not be provided those steps, they will just fall further behind while their more prepared public school peers advance, or those peers with means will just go to a tutor who will provide them with the list of steps.

Throughout the text of the SFR draft framework, we read of students who “must” have certain skills to succeed at math.

“Many of the properties that students use in solving these types of equations are reliant upon a well-developed number sense. In other words, in order to solve equations involving unknowns that are rational numbers, students must rely upon their understanding of rational numbers themselves, at times .” (Ch. 3, Line 1651-1654)

The question is, when, where, and how did they get those skills if their math classes focus only on “authentic tasks” about which students in their particular classroom actually “wondered” about? Consider, for example, Line 1898 of chapter 3,

“The arithmetic skills students have used prior form the basis of their ability to understand operations involving complex numbers.”

But then we also read,

“Rather than insisting on mastery of prior content—especially computational speed and recall—the goal should be access to the content of the current investigation.” (Ch. 7, Line 374-376).

So teachers can’t insist on mastery of the (earlier) skills that are needed to access the content of the current (later) investigation? What if students haven’t mastered those earlier skills? How are they supposed to get them? What will the process be for students to master those earlier skills? Outside supplemental work? Tutoring? Where does that leave students who do not have the means to get extra needed math support? The answer continues to be that disadvantaged students in classrooms and districts which implement this SFR draft framework will continue to fall further behind their peers who either attend a district that does not adopt this SFR draft framework (and who do teach the math content standards), or who get tutoring and outside support.

A lack of focus on standards based assessment will HIDE the inequity.

The primary way we know that the achievement gaps exist is through the use of standardized testing, and yet there is a major push to remove this. If we don’t focus on content standards and assess students on mastery of those standards, no one will be able to tell that students are not learning!! Perhaps that’s the goal?

As the recent push has been to eliminate the SAT for college admittance, so the authors of the SFR draft framework want to change assessment. They call the change they propose for grading and assessment “mastery based grading”. Rather than using a standardized exam to assess mastery of content standards, they suggest

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

As the “big ideas” are vague and ill-defined, and, as the SFR draft framework writes “there are many interpretations” of them (Ch. 7, Line 204) , the assessment of them will also necessarily be ill-defined.

In terms of “grades’, the authors of the SFR draft framework suggest the following:

“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=1, F=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)

These suggestions raise quite a few questions: 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. The SFR draft framework suggests removing merit based assessment, which truly is the most equitable means of assessing students, and the means by which we know if achievement gaps exist, so teachers can then focus on supporting students to close those gaps.

Summary:

Clear math content standards, consistently taught, coupled with supports for struggling students, applied in every math classroom, and backed by assessments that gauge student progress towards mastery of the same — is the only way to level the playing field and reduce achievement gaps. Holding students to high expectations — to master those math content standards – is the only way to ensure that students make progress towards learning and mastering math itself. California has begun to make this progress for some groups, but rather than continue to hold all students to high expectations (standards) and support them to succeed on those, the authors of the SFR draft framework seemingly assume that students are NOT capable of learning the standards, replacing them with “big ideas”, asking teachers to teach “authentic tasks” about which students “wonder” and “pose problems” about. Vague ‘big ideas,’ ‘mathematics experiences,’ and untested and unclear concepts like ‘content connections,’ and ‘multidimensional mathematics,’ are no substitute for learning and practicing rigorous, well defined, long known and long established math content standards and math procedures that lead to math mastery. Pairing vague ‘big ideas’ with classrooms where each group decides what to investigate will lead to increased achievement gaps, as those with resources and means will excel in school through outside support (both in terms of tutoring and supplemental classes) and those without means will not. The SFR draft framework will lead to significantly greater inequities in the math classroom.