3 Design Shifts Content Developers Can Make to Meet California’s New Math Framework

The Opportunity the California Math Framework Represents

High quality instructional materials play a vital role in learning outcomes. This means that content developers are an integral piece of the educational puzzle. Yet, a recent ELSF national survey showed that 60% of surveyed math teachers in California report that their primary math materials include little to no guidance on how to support English Learners. That may soon change in California, especially after the implementation of the newly adopted Mathematics Framework.

With this new framework, California has taken up the clarion call to close the learning opportunity gaps in math. The framwork’s  assets-based focus positions all students as drivers of their own math learning.  Arbiters like EdReports have come a long way in articulating quality as it relates to standards-alignment. The framework takes it one step further by clearly outlining additional equitable design features critical to EL student success, such as cultural and linguistic responsiveness. If implemented well, this framework can have a cascading effect on improving the 20% gap in proficiency between ELs and Non-ELs, and ultimately on math engagement and outcomes for the over 2 million multilingual students in California.  

Curriculum Design Changes and the Framework’s Assets-based Approach for Multilingual Learners

Instructional materials will likely need to include a few fundamental design shifts in order to meet the recommendations and criteria laid out in the California Mathematics Framework. Below, we outline a few of these shifts. While not comprehensive, they represent an important starting point for designers of quality curriculum. With standards-alignment as a foundation, these shifts serve as a roadmap for where the field is heading in regards to cultural and linguistic responsiveness.  These design shifts are framed here as “from-to” to highlight changes in conceptualizations of language development and culturally sustaining education.1

Three Integral Curriculum Design Shifts

Design Shift Feature From this… Expanding to this…
1) Specific strategies to develop language skills needed Generic language development strategies Language development objectives explicitly tied to the mathematical learning objectives
2) Formative assessment using multiple methods Formative Assessment of mathematical content Formative assessment of content understandings and practices as well as the language used to express them
3) Include strategies that are consistent with CA ELD Standards Application of ELD standards that doesn’t directly link to the mathematics learning of the unit Application of ELD standards that provide meaningful opportunities to use the mathematics language associated with the core content

Key Design Shift 1:

“Specific strategies to support students in developing the language skills needed to meet the mathematical learning and language objectives that are explicitly and clearly associated with instruction and assessment.”

(Chapter 13, Category 5: Instructional Planning and Support).

From this:

Historically, curricular materials have focused on generic language strategies such as graphic organizers and “think-pair-share” interaction structures that are not related to the specific math lesson. Or if they do focus on mathematics, the supports are primarily for math vocabulary development, terms and definitions. While these may be useful in a general sense, the framework is calling for a more integrated approach to language, math practices and math content.

Expanding to this:

What could this look like in instructional materials? Here are two practical examples:

  • In an  elementary lesson on fractions, instructional materials could provide a variety of examples of written mathematical explanations for how to compare fractions with unlike denominators, so that these examples could serve as math language models for the class to analyze, and adapt, and ultimately construct their own explanations that share the same features as the example explanation but said in their own words. Note that the strategy of using language models is directly tied to the mathematical content and language.
  • In a middle school unit on proportional reasoning, students could be given language frames/structures to build up mathematical justifications to analyze and determine if a pattern of ordered pairs is directly proportional, inversely proportional, or neither. Note again that the strategy of a language frame is not an add-on to the lesson, but rather a means to deep thinking and clarify students’ communication about proportional relationships.

We see that explanation and justification are mathematical practices AND language practices simultaneously. They are both cognitive and linguistic accomplishments.  

Key Design Shift 2:

“Student and teacher materials include formative assessments to provide multiple methods to assess student understanding to inform instruction, such as graphic organizers, student observation, student interviews, journals and learning logs, mathematics portfolios, self- and peer evaluations, tests and quizzes, self-reflection, and performance tasks”

(Chapter 13, Category 3: Assessment).

From this:

Although formative assessment has become largely recognized as effective teaching practice, it has focused exclusively on content, and not the related assessment of students' disciplinary language through which they communicate their understanding of math content. Formative assessment practices gathered through exit tickets, student journals, or class observation checklists have tended to focus on whether students are making progress on the mathematical knowledge and skills, but not on specific linguistic forms that characterize mathematical displays of understanding.

Expanding to this:

Since we know that math content, math practices and math language are interrelated, formative assessments will need to be expanded to capture not only what students understand, but also how they express their understanding, as part of a mathematical community. The CA framework lays out a rich array of data sources (student interviews, portfolios, performance assessments, etc), but in order for them to be useful and actionable for teachers, instructional materials will need to provide guidance in the following areas:

  • How to analyze these formative data from a math language development perspective such as “listen fors” or specific criteria to understand if and how students are progressing toward the key language learning objectives across time
  • Based on that analysis, what are the specific implications for supporting students' math language development toward the identified language goals of the unit or lesson?  

Key Design Shift 3:

“Teacher materials include strategies for students who are English learners that are consistent with the California English Language Development Standards: Kindergarten Through Grade 12 adopted under EC Section 60811”

(Chapter 13, Category 4: Access and Equity).

From this:

The California English Language Development (ELD) Standards is a rich and complex document, representing the most current research and best practices in language development. Yet most mathematics specialists and curriculum developers often struggle to productively link or integrate the ELD standards in ways that deepen the mathematics of a unit or lesson for English learners. In recent years, we have seen some important steps in this direction, for example, when content developers include guidance for how different instructional supports might be needed from students of varying language proficiency levels within the same class. Materials that include this feature are signaling to teachers to pay attention to where English learners are in their English language development. Again, steps in the right direction.

Expanding to this:

One of the questions we get asked in our work with math content developers is how to identify key language demands and how to formulate language objectives at the lesson and unit level. (Sometimes the language objective is integrated with the content learning goals, and sometimes it stands apart for emphasis.) The CA ELD provides a useful framework for identifying opportunities to develop language in Part 1: Interacting in Meaningful Ways. (see below)

*Excerpt from California English Language Development Standards, pg. 14

Using this framework, math content developers and specialists can begin to see the ways that language is woven into every phase of a lesson, not just vocabulary. Language goals and objectives can be drawn from how lessons expect students to interact with one another, how students interact with written and spoken texts, and what students are asked to produce as evidence of their learning. This framework shines a light on how language is used in different ways as students learn mathematics.

Of course, there is a lot more to unpack in the CA ELD standards, but this example is meant to serve as a practical way for content developers to begin mapping out the language demands and language opportunities within their materials. We invite writing teams to choose a sample lesson and apply this framework. This exercise will generate lots of ideas for language learning objectives and goals.

Quality implementation of the math framework by all stakeholders is the next step in the process. For content developers, ensuring that mathematics materials robustly reflect the shifts outlined above will demonstrate commitment to that imperative.  If you’re ready for a more robust analysis of your curriculum, these California-specific Criteria–created  by ELSF in partnership with EdReports and UnboundEd (formerly Pivot Learning) to support framework-aligned curriculum adoptions in the state--are for those seeking to ensure they are designing materials responsive to culturally and linguistically diverse learners. ELSF’s Fall Institute is another great opportunity to learn how to identify the opportunities for language development in math lessons and units and to build in responsive design features.

Jack is Senior Advisor, Mathematics at ELSF. He advises on reviews of math curricular materials to support language development. Jack currently also has an academic appointment as the Director of Research at youcubed at Stanford University, documenting the effectiveness of youcubed’s learning opportunities including Jo Boaler’s online courses in mathematical mindset and other youcubed research-based practices and materials. Prior to joining youcubed, Jack was the associate director for curriculum at the Stanford Center for Assessment, Learning, and Equity (SCALE), where he led the math team in performance assessment development. As a scholar of teaching, Jack’s additional research interest is in the area of “language for mathematical purposes”, especially for English learners. Jack received his doctorate in mathematics education at Stanford GSE in 2009, co-advised by Jo Boaler and Linda Darling-Hammond. For the past 16 years, Jack has served as an instructor in the Stanford Teacher Education Program (STEP), Jack continues to consult across the country and internationally in China, Brazil, and Chile in the areas of math education and teacher learning.

Renae Skarin has almost 30 years of experience working with English learner and minoritized populations through research, advocacy, and program development and implementation with educators nationwide and abroad. She currently serves as the Senior Advisor for Content at the English Learners Success Forum (ELSF) where she leads its research efforts to identify strategies and develop resources for improving education policies and practices with regard to high quality instructional materials for multilingual learners. Before joining ELSF she served as an associate researcher at Understanding Language at Stanford University. She received her M.A. in Second Language Studies at the University of Hawaii at Manoa, and did Doctoral studies in Educational Linguistics at Stanford University.


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