High School - Multilingual Learner Supports

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in intentional opportunities for students to develop procedural skills and fluencies. The materials partially provide embedded opportunities for MLLs to engage in developing procedural fluency through well-structured tasks and routines. They lack consistent and explicit language supports necessary for MLLs to fully and completely participate in all phases of procedural learning, particularly in explanation, justification, and synthesis.

In Algebra 2, Unit 2, Polynomial Functions, Lesson 3, students identify key features of a wide variety of polynomial graphs and connect them to the structure of their corresponding expressions (A-SSE.2). In Activity 3.1, students engage in the Instructional Routine Which Three Go Together, where students use familiar terms such as term, constant, and exponent when they compare and contrast four expressions. The materials direct the teacher to provide one minute of quiet think time followed by time to share responses within a small group, providing oral rehearsal for MLLs before they are asked to participate in whole-class discourse. In their discussions, the materials direct students to use precise language to describe their choices, and in the whole-class discussion in the Activity Synthesis, the materials direct teachers to record and display students’ responses for all to see. Additionally, teachers press for precision with questions such as, "What do you mean by...?" and "Can you say that in another way?” and through prompting students to explain the meaning of any statistical terminology they use. Students use and apply the same precise language through a collaborative Card Sort in Activity 3.2. The Activity Narrative alerts the teacher to have students “focus on the structure of the expressions” when working with a partner to match polynomial graph cards with equation cards. During the Card Sort, the materials direct teachers to "highlight the use of terms like constant term, degree, increasing, decreasing, linear, and quadratic" as students describe features more precisely. The materials do not provide linguistic supports for MLLs to “focus on the structure of the expressions” using precise language, nor to negotiate matching choices with their partner. In the Activity Synthesis, the teacher facilitates a whole-class discussion in which groups justify how they matched their cards, explaining which matches were the most difficult and describing when they needed to make adjustments. The materials do not provide linguistic scaffolds for MLLs to fully and completely participate in this synthesis.

The materials partially meet the criteria for this indicator because the lessons’ instructional design includes Warm-Ups, one to three instructional Activities, Lesson Syntheses, and Cool-Downs, which are designed to give students repeated access to procedural skills and fluency. However, these aspects of the instructional design often do not consistently include built-in supports for MLLs who may need productive language supports for speaking or writing their thinking in English, specifically where procedural skills and fluency are called for in the standards. Without consistent language support, MLLs may have limited opportunities to fully demonstrate procedural understanding or engage in discussions requiring explanation and justification. 

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications. The materials partially provide supports that allow MLLs to engage in applying mathematical concepts and skills in routine and non-routine tasks, as well as partner and whole-class discourse focusing on mathematical reasoning. These supports are not consistently provided or available at the point of entry, which results in inconsistent opportunities for MLLs to fully participate across all lessons. 

MLLs are supported in Algebra 1, Unit 3, Two-Variable Statistics, Lesson 6, Activity 6.2, where students engage in problem solving around a non-routine application problem that introduces the concept of residuals. This activity uses data from a video in a previous lesson about the relationship between the number and weight of oranges in a box, which is then organized into a table, and students use technology tools on the platform to plot a line of best fit (N-Q.3). As students apply the new concept of a residual to a scatter plot, the materials provide linguistic scaffold Math Language Routine [MLR] 2: Collect and Display to help them focus on key vocabulary to interpret and explain what specific points, intercepts, and slopes represent in relation to the context. Teachers are directed to "collect the language students use to describe how to calculate residuals" and "what positive and negative residuals mean," displaying phrases such as “difference between actual data and estimates” and “linear estimate is close to actual data.” This routine creates a shared reference that captures developing mathematical language, empowering MLLs to amplify their language in order to explain their reasoning using precise terminology while reinforcing their conceptual understanding.

However, not all the lessons in the materials provide linguistic supports for MLLs to use and develop language around solving application problems. For example, in Geometry, Unit 5, Solid Geometry, Lesson 7, Activity 7.2, students engage in problem solving around a routine application problem that demonstrates the complex mathematical relationship between volume and scale factor (N-Q.1). However, the materials fail to provide the linguistic supports necessary for MLLs to articulate their findings. The activity requires students to explain non-linear rates of change and compare competing mathematical models, yet it lacks linguistic supports for these high-level, content-dependent explanations. Additionally, the Activity Synthesis directs the teacher to facilitate a whole-class discussion to “draw conclusions from the graph about the relationship between volume and scale factor,” yet the materials do not provide a linguistic entry point for MLLs to share their conceptual insights, creating a disconnect between the mathematical complexity of the task and the support provided for academic communication. 

The materials partially meet the criteria for this indicator because in every lesson, students engage with routine and non-routine application problems through: tasks that promote the use of known facts to build new understanding, the incorporation of multimodal representations, such as video, tables, and graphs, and lesson structures that move from independent exploration to partner discussion and group synthesis, promoting reflection and connection-making. However, these opportunities do not consistently include language supports for MLLs to participate in the full depth of application-based learning at critical moments, such as explaining their reasoning and describing relationships between variables, or compare a new function with a familiar function.

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in the intentional development of MP2: Reason abstractly and quantitatively.

In every unit, the materials provide opportunities for students to use and develop language when reasoning abstractly and quantitatively through whole-group and student-to-student discourse. The materials provide these opportunities through features embedded within the lesson facilitation or as a suggested support in notes titled Access for English Language Learners. An example of a feature embedded within the lesson facilitation is Instructional Routines. Specifically, the Course Guide, 3. What’s in an IM Lesson, describes how the Instructional Routine Card Sort supports MP2. Card Sort states, “A card-sorting task gives students opportunities to analyze representations, statements, and structures closely, and make connections (MP2 and MP7).” While there are other Instructional Routines and MLRs that support the language needed to engage in MP2, Card Sort is the only routine the materials identify as supporting MP2. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP2.

Specifically, in Algebra 1, Unit 6, Introduction to Exponential Functions, Lesson 8, Activity 8.2, students reason abstractly and decontextualize when they use variables to represent one real-world quantity as a function of another. In the Activity Synthesis, the materials direct teachers to facilitate a whole-class discussion guiding students to think quantitatively using questions such as, “Can the independent variable be something like 1.5, a number that is not a whole number? Is there an area that is associated with 1.5 days?” The materials guide teachers to “attend explicitly to language that students learned in the prior unit on functions.” In a note titled Access for English Learners, Math Language Routine 2: Collect and Display directs the teacher to capture and display student-generated language such as independent/dependent variable and input/output value. This scaffold helps MLLs contextualize the abstract variables by providing a bridge between the mathematical symbols and their real-world referents. 

However, the strategies and supports for MLLs to fully and completely participate in reasoning abstractly and quantitatively are not reflected in other lessons. For example, in the same unit, Lesson 4, Activity 4.2, students reason abstractly and quantitatively when they decide how to scale axes to represent the exponential decay of the problem scenario in the graph. The materials do not provide language supports for MLLs to connect the idea of the growth factor between 0 and 1 causing the function to decrease, nor does it provide linguistic scaffolds for MLLs to explain the relationship between the problem scenario and the mathematical representation of the graph.

The materials partially meet the criteria for this indicator because while the materials embed opportunities for students to engage with MP2 through the use of specific Instructional Routines, the materials lack consistent language supports at point-of-use within problems in which students are asked to reason abstractly and quantitatively.

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in the intentional development of MP4: Model with mathematics.

In every unit, the materials provide opportunities for students to use and develop language when modeling with mathematics through whole-group and student-to-student discourse. The materials provide these opportunities through features embedded within the lesson facilitation or as a suggested support in notes titled Access for English Language Learners. An example of a feature embedded within the lesson facilitation is Instructional Routines. Specifically, the Course Guide, 3. What’s in an IM Lesson states, “Poll the Class is used to register an initial response or an estimate, most often in the Launch of an activity or to kick off a discussion… going on record with an estimate makes students want to know if they are right, and increases investment in the outcome. If coming up with an estimate is daunting for students, ask them for a guess that they are sure is too low or too high. Putting some boundaries on possible outcomes of a problem is an important skill for mathematical modeling (MP4).” While there are other Instructional Routines and MLRs that support the language needed to engage in MP4, Poll the Class is the only routine the materials identify as supporting MP4. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP4.

The Course Guide, 4. Advancing Mathematical Language and Access for English Learners contains a table with sample sentence frames and sentence starters for nine language functions. Two of the language functions are directly related to MP4: represent and interpret. Example sentence frames include:

• Represent: “_____ represents _____.” / “Another way to show ____ is…”

• Interpret: “We are trying to…” / “It looks like _____ represents…” 

These sentence frames support interdisciplinary language connections since they are generic in nature. This section of the Course Guide states, “The table shows examples of generic sentence frames that can support common disciplinary language functions across a variety of content topics. Some of the lessons in these materials include suggestions of additional sentence frames that could support the specific content and language functions of that lesson.” The materials do not reference these sentence frames within lessons at the point of use. 

Additionally, the materials include a component called Mathematical Modeling Prompts to “choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.” It provides a list of targeted questions that teachers can use to elicit specific mathematical language. These questions act as prompts for students to define and describe their thinking. The Course Guide, 7. Key Structures in This Course describes the mathematical modeling prompts, providing teacher guidance around when to use the prompts and how to prepare for and conduct the mathematical modeling prompts, including ideas for how to set up a conducive environment for students to engage in mathematical modeling. Included in this section of the Course Guide are a series of questions teachers can ask if students need guidance with a specific part of the modeling cycle, such as, “What quantities are important? Which quantities change and which quantities stay the same? (identify variables)” and “What pictures, diagrams, graphs, or equations might help people understand the relationships between the quantities? (formulate)” Beyond these teacher prompts, the materials do not provide linguistic scaffolds for MLLs to fully and completely participate in the mathematical modeling prompts.

Within lessons, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely engage in modeling with mathematics. For example, MLLs are not fully supported in participating in Algebra 1, Unit 2, Linear Equations and Systems, Lesson 9, Activity 9.2, where students model with mathematics when they use spreadsheet technology to create mathematical models, test them, and solve problems. While the Launch encourages oral rehearsal in small groups before students share with the whole class, overall the Activity lacks specific language support for MLLs to fully and completely engage in the language of mathematical models, which hinders MLLs’ participation in the mathematical modeling process. Specifically, the Activity features the real-world scenario of shipping cargo in which MLLs need to understand and use context-specific language such as automobile manufacturer and weight constraint. Yet, the materials do not provide language supports for MLLs to understand the relationship between these terms and the variables. Furthermore, this Activity directs students to work in small groups, and the Activity Synthesis directs the teacher to facilitate a whole-class discussion. The materials do not provide language supports for MLLs’ full participation in the small group and whole-class discourse.

In contrast, MLLs are supported in Lesson 1, Activity 1.2 of that same unit, where students model with mathematics by considering relevant variables, making assumptions and estimates, performing calculations, and refining their thinking throughout the modeling process. The Launch invites teachers to activate or build prior knowledge around the real-world scenario of planning a party, providing MLLs with initial access to the task by previewing the contextual language they will use within the lesson. Within the small group work time, the materials prompt teachers to ask students to identify "quantities that might change," which guides them to distinguish between fixed values and variables before they are required to write an equation. The Activity Synthesis supports MLLs with engaging in this concept through the use of Mathematical Language Routine [MLR] 7: Compare and Connect; by prompting a discussion on how different groups represented values that "remain fixed" compared to those that "change," the materials support MLLs in articulating the reasoning of their models. This intentional focus on the meaning of the variables ensures that the transition to abstraction is a discursive and meaningful process rather than a purely procedural one. 

The materials partially meet the criteria for this indicator because while the materials embed opportunities for students to engage with MP4 through the use of specific Instructional Routines and MLRs, the materials lack language supports consistently throughout the units in the activities in which students are asked to model with mathematics.

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in the intentional development of MP5: Choose appropriate tools strategically.

In every unit, the materials provide opportunities for students to use and develop language when using appropriate tools strategically through whole-group and student-to-student discourse. The materials provide these opportunities through features embedded within the lesson facilitation or as a suggested support in notes titled Access for English Language Learners. An example of a feature embedded within the lesson facilitation is Instructional Routines. While there are Instructional Routines that support the language needed to engage in MP5, the materials did not identify any routines as supporting MP5. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP5.

Specifically, in Geometry, Unit 2, Congruence, Lesson 1, Activity 1.3, students identify corresponding parts of congruent triangles using self-selected methods of representing triangles, choosing tools of either physical sketches or the platform's digital geometry tools. Students follow the Student Task Statements to construct triangles using the tools of their choosing, identify corresponding triangle parts, and make and justify conjectures about the corresponding parts. The materials do not provide linguistic scaffolds for MLLs to choose between either physical sketches or the platform’s digital geometry tools. The materials support MLLs’ participation in the task through Math Language Routine [MLR] 7: Compare and Connect in the Activity Synthesis. MLR7 supports MLLs with making and justifying conjectures about the corresponding parts of their two triangles in problem #5 by inviting the teacher to facilitate a class discussion to compare, contrast, and connect different student approaches with sentence frames like, “What did the approaches have in common? How were they different?” Additionally, a note titled Access for English Language Learners suggests that the teacher facilitate MLR8: Discussion Supports where students turn to a partner to restate what they heard using precise mathematical language. The use of MLRs 7 and 8 support MLLs’ participation in the task, but the lesson fails to provide the linguistic scaffolding necessary for MLLs to engage in a strategic decision-making process around tool choice.

The materials partially meet the criteria for this indicator because while the materials embed opportunities for students to engage with MP5 through the use of specific MLRs, the materials lack language supports during partner and whole-class discourse in which students are asked to choose appropriate tools strategically.

The instructional materials reviewed for Kendall Hunt IM v.360 AGA partially meet the criteria of providing support for MLLs’ full and complete participation in the intentional development of MP8: Look for and express regularity in repeated reasoning.

In every unit, the materials provide opportunities for students to use and develop language when looking for and expressing regularity in repeated reasoning through whole-group and student-to-student discourse. The materials provide these opportunities through features embedded within the lesson facilitation or as a suggested support in notes titled Access for English Language Learners. An example of a feature embedded within the lesson facilitation is Instructional Routines. Specifically, the Course Guide, 9. Standards for Mathematical Practice, describes how the Instructional Routine Math Talk supports MP8. Math Talk states, “The Math Talk routine offers opportunities to look for and make use of structure (MP7) and look for and express regularity in repeated reasoning (MP8) as students explain the strategies they use and apply strategies as they develop fluency.” While there are other Instructional Routines that support the language needed to engage in MP8, Math Talk is the only routine the materials identify as supporting MP8. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP8.

The Course Guide, 4. Advancing Mathematical Language and Access for English Learners contains a table with sample sentence frames and sentence starters for nine language functions. The language function of generalizing is directly related to MP8, and the materials provide sentence frames to support this language function such as, “Is it always true that…?” and “____ will always _____ because…” These sentence frames support interdisciplinary language connections since they are generic in nature. This section of the Course Guide states, “The table shows examples of generic sentence frames that can support common disciplinary language functions across a variety of content topics. Some of the lessons in these materials include suggestions of additional sentence frames that could support the specific content and language functions of that lesson.” The materials only mention these sentence frames in this section of the Course Guide. The materials do not reference these sentence frames within the lessons at point-of-use, limiting their potential utility during instruction. 

In Algebra 1, Unit 7, Introduction to Quadratic Functions, Lesson 2, students look for and express regularity in repeated reasoning as they analyze visual patterns using a table and generalize the relationships with variable expressions. MLLs are not supported to fully and completely participate in Activity 2.2, where students reason repeatedly about the number of dots at different steps of a quadratic pattern either visually (with actual dots), numerically (with values in tables), or in a graph. The materials do not provide linguistic supports for MLLs to explain patterns, look for general methods, or describe the structural changes in mathematical representations between the steps. Similarly, in Activity 2.3, students reason repeatedly, extend a pattern, write a general expression describing it, and explain how they know if a value is growing linearly or exponentially. While both activities require the complex language function explain, the available support is limited to a single instance of Math Language Routine 8: Discussion Supports at the end of Activity 2.3. This MLR supports MLLs’ participation in the Activity Synthesis by inviting students to restate what they heard using precise mathematical language with a partner. However, the materials fail to include any linguistic scaffolds to support MLLs with the actual language production of the required explanations. Consequently, MLLs are left without the necessary linguistic tools to bridge the gap between noticing a pattern and formally expressing its regularity. Additionally, though the Course Guide identifies Math Talk as supporting the language needed to engage with MP8, the materials do not feature the Math Talk routine in the entirety of Unit 2, where MP8 is practiced. 

The materials partially meet the criteria for this indicator because while the materials embed opportunities for students to engage with MP8 through the use of specific Instructional Routines and MLRs, the materials lack language supports during partner and whole-class discourse in which students are asked to look for and express regularity in repeated reasoning. 

The instructional materials reviewed for Kendall Hunt IM v. 360 AGA partially meet the criteria of intentionally developing language in ways valued by disciplinary practices over time, across lessons, units, and throughout the course. 

The Course Guide, 4. Advancing Mathematical Language and Access for English Learners outlines the interdependence of content, language, and practices. It states, “Adapted with permission from work done by Understanding Language at Stanford University. For the original paper, Principles for the Design of Mathematics Curricula: Promoting Language and Content Development, please visit https://ul.stanford.edu/resource/principles-design-mathematics-curricula. In a problem-based mathematics classroom, sense-making and language are interwoven. Mathematics classrooms are language-rich—and therefore language-demanding—learning environments for every student. The linguistic demands of doing mathematics include reading, writing, speaking, listening, conversing, and representing (Aguirre & Bunch, 2012). Students are expected to say or write mathematical explanations, state assumptions, make conjectures, construct mathematical arguments, and listen and respond to the ideas of others. In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English, in their development of language, this curriculum includes instruction devoted to advancing language development alongside mathematics learning, and fostering language-rich environments in which there is space for all students to participate.” As noted in the report for 1b.MLL, the Course Guide, 4. Advancing Mathematical Language and Access for English Learners outlines how the lesson design centers the unique language needs of MLLs by embedding Stanford University’s four design principles: Support Sense-Making, Optimize Output, Cultivate Conversation, and Maximize Meta-Awareness. This lesson design is rooted in multimodal instruction, which creates accessible entry points and structured opportunities for disciplinary language usage alongside mathematics learning. 

The materials show partial evidence of intentional disciplinary language development aligned to mathematical content and practices. Disciplinary language development consists of functional language development alongside mathematical vocabulary development. In the materials, functional language development is inconsistent and often serves students’ understanding of the mathematical practices rather than explicitly advancing disciplinary language development over time, as noted in the reports for 2e.MLL-2l.MLL. There is no discernible progression of disciplinary language within this information, as noted in the 1.1.MLL-4 report. Instead, it appears that parallel language functions are practiced over time, and the depth of language usage does not exhibit a progression. As noted in the report for 2j.MLL, the materials fully support the development of mathematical vocabulary over time.

The materials do not provide a formal plan for teachers to bridge between students’ informal and everyday ways of communicating and more precise mathematical ways of communicating. However, the materials encourage students to use informal and everyday ways of communicating, and the lesson design supports teachers in connecting students’ informal language with more precise mathematical language. Specifically, in the Course Guide, 3. What’s in an IM Lesson, the materials describe the problem-based lesson design, which begins with a Warm-Up, then engages students with one to four instructional activities, and ends with a Lesson Synthesis and Cool-Down. This lesson design supports students’ use of informal and everyday ways of communicating within Warm-Ups that feature Mathematical Language Routines or Instructional Routines like Notice and Wonder, which invite students to use everyday language to describe what they notice and wonder about a mathematical situation. Within the lesson, Activities encourage disciplinary language usage within partner, small-group, and whole-group discourse. Lessons close with a Lesson Synthesis, which provides an opportunity for students to summarize mathematical learning by either listening to or orally practicing precise language usage. Therefore, the materials support students in connecting informal with more formal language usage, but the materials do not provide a plan for teachers to bridge the two. 

Overall, the materials provide some, but not comprehensive, support for the ongoing development of disciplinary language. While they promote language-rich classrooms and consistently build mathematical vocabulary, support for functional language development is inconsistent and lacks clear progression. The lesson design encourages the use of informal language and provides opportunities to transition to more precise mathematical language, but it does not offer explicit guidance for teachers to bridge the two.

The instructional materials reviewed for Kendall Hunt IM v. 360 AGA partially meet the criteria of including language goals/objectives at the lesson level that are clear, measurable, and support language development in service of content learning. 

The materials provide language and content goals that are one in the same, called Learning Goals. In approximately half of the lessons in each course, the Learning Goals include references to language use or development, partially fulfilling the purpose of a language goal, even though the materials do not explicitly name them as language goals. Due to this design, not all of the language goals are clear or measurable, especially in relation to language. For example, the Learning Goals of Geometry, Unit 5, Solid Geometry, Lesson 2 are, “Generate multiple cross-sections of three-dimensional figures. Identify the three-dimensional shape resulting from combining a set of cross-sections.” These Learning Goals do not function as language goals because they do not contain information on the language demands of the lesson, specifically language domains and language forms used to support the language functions within the Learning Goals. 

When lessons’ Learning Goals contain information on the language development and usage within the lessons, they are tied directly to the content goals and are clearly focused on at least one domain of language (reading, writing, speaking, or listening) and at least one language function. In these cases, where the Learning Goals function as language goals, they do not consistently incorporate the language structures and vocabulary used in conjunction with the listed language function, and therefore are not always measurable or specific. For example, in Algebra 2, Unit 5, Exponential Functions and Equations, Lesson 1, the Learning Goals are, “Compare and contrast (orally) exponential growth and decay. Determine values of simple exponential functions in context.” The first Learning Goal functions as a language goal because it is clear, tied directly to mathematics content of the lesson, and it lists language functions (compare and contrast) and a language domain (orally). It does not contain information about the language forms used to support the language functions compare and contrast within the lesson.

These examples explicitly demonstrate that while the materials include lesson-level Learning Goals that describe the language-rich mathematical tasks, they partially meet the expectation that goals are clear, measurable, and supported with explicit scaffolds for language structure and form. 

The instructional materials reviewed for Kendall Hunt IM v. 360 AGA partially meet the criteria of providing teacher guidance to support MLLs and to utilize the strategies, supports, and/or accommodations found. The materials partially provide useful suggestions for language supports, outlined in the Course Guide and at point-of-use within lessons. However, the materials do not provide teacher guidance on how to consistently anticipate and respond to potential language demands, challenges, and opportunities in a lesson along the progression of language acquisition.

The Course Guide, 8. Scope and Sequence does not fully support teachers of various stages of language acquisition in anticipating potential language demands, particularly for MLLs who enter high school at different points in their language acquisition or with different formal educational backgrounds. A portion of the AGA curriculum is built upon the assumption of prior U.S. middle school experience. Evidence from the Scope and Sequence includes:

• Algebra 1, Unit 1: “These concepts are revisited... because the first half of the unit mostly revisits material from middle school.”

• Algebra 1, Unit 2: “The unit builds on learning from middle school when students used variables to write equations.”

• Algebra 1, Unit 4: “The unit builds on concepts from middle school when students write and solve inequalities.”

• Geometry, Unit 1: “In grade 8, students determined the angle-preserving and length-preserving properties... Students have also previously studied the angle properties.”

For MLLs who did not yet learn the prerequisite content in English, this “revisit” is actually their first encounter with complex mathematical terminology in English (e.g., interquartile range, standard deviation, or transversals). The materials do not provide comprehensive guidance for teachers to identify these linguistic demands or observe whether and how MLLs can use the necessary mathematical terminology and where further support is needed. Without these observe and respond guidance, teachers cannot effectively anticipate the language demands of each lesson.

Furthermore, in every unit, the materials describe language supports, such as Stanford UL/SCALE’s Mathematical Language Routines (MLRs), in teacher guidance embedded within lesson facilitation or as a suggested support in notes titled Access for English Language Learners. The Course Guide, 4. Advancing Mathematical Language and Access for English Learners instructs teachers to, “adapt and incorporate these flexible MLRs across the lessons in each unit to support students at all stages of language development in improving their use of English and disciplinary language.” However, the materials do not provide specific guidance for how to “decide which optional MLR to use” nor how to “adapt and incorporate” them effectively for specific lesson content. 

This lack of specific teacher guidance fails to facilitate understanding in teachers new to working with MLLs and does not support the refinement of knowledge for MLL experts. For instance, in Geometry, Unit 1, Constructions and Rigid Transformations, Lesson 1, Activity 1.3, the materials suggest MLR1: Stronger and Clearer Each Time, telling teachers to ask students what makes a good explanation, using radius instead of it. While this provides a general focus on using precise language, the lesson facilitation lacks sample responses or guided questions that demonstrate how students should integrate that specific vocabulary into their writing.

Similarly, in Lesson 2, Activity 2.1 of the same unit, the MLR8: Discussion Supports suggest displaying general sentence frames like, “First, I _____ because . . . .” While helpful, these frames are not tailored to the specific geometric needs of the lesson. A more comprehensive support would provide lesson-specific frames such as, “I noticed _____ and _____ are equal/congruent,” which would allow MLLs to focus on the mathematical content rather than the linguistic construction of the sentence. Because the guidance remains generic rather than lesson-specific, the materials are not inclusive of all levels of teacher understanding.

In summary, while the materials provide a framework for MLL support, the teacher guidance is often too general to address the specific language demands of high school mathematics. The materials fail to offer detailed strategies for anticipating and responding to student needs along the progression of language acquisition, particularly for students missing the foundational U.S. middle school context.