6th to 8th Grade - Multilingual Learner Supports

The instructional materials reviewed for Grade 6-8 of Kiddom® v.360 partially meet the criteria of providing support for Multilingual Learners’ (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 Grade 6, Unit 5, Arithmetic in Base Ten, Lesson 11, Activity 11.2, students make sense of the process of long division by studying an annotated example before applying their new learning to independently find quotients of long division problems (6.NS.2). First, students work in partners to analyze how a fictional student named Lin solved a long division problem. A written description of how Lin found the quotient is provided: "Lin arranged the numbers for vertical calculations. Her plan was to divide each digit of 657 into 3 groups, starting with the 6 hundreds. .... ” The materials support MLLs with the language demands of analyzing Lin’s work with a suggestion in a note titled Supporting Multilingual Learners: the use of Mathematical Language Routine (MLR) 8 Discussion Supports, which states, “Invite students to repeat their explanations for Lin’s steps using mathematical language: ‘Can you say that again, using the terms ‘place value,’ ‘ones place,’ and ‘tenths place’?’.” Then, students move independently to the next question in which they apply their understanding of the process of long division in three new problems. The Activity Synthesis directs teachers to display the three new problems and to select a student to explain the steps for at least one of the long division problems. There is no connection drawn for teachers between the suggested use of MLR8 to explain Lin’s steps and the independently completed problems and the Activity Synthesis. Therefore, the activity lacks consistent language supports for the productive language demands of explaining the process of long division. The materials do not provide consistent language supports during explanation and justification tasks, which are necessary for MLLs to express procedural understanding using academic language.

In Grade 8, Unit 7, Exponents and Scientific Notation, Lesson 4, Activity 4.3, students answer a series of questions designed to extend exponent rules to discover why it makes sense to define 10^0 as 1 (8.EE.1). The activity begins with students working independently to respond in writing to Student Task Statements such as, “Write 10^12⋅10^0 as a single power of 10. Explain or show your reasoning.” After students work independently, they engage in partner and then whole-group discourse to review the answers and explanations. Through this work, there are no language supports present for the productive language demands of explaining mathematical reasoning. Then, language supports appear in the facilitation of the Activity Synthesis, which suggests the use of MLR3 Critique, Correct, Clarify, where teachers are directed to give students the opportunity to improve a sample written mathematical statement. Specifically, students are discussing how to fix common conceptual errors and how to add details to improve ambiguous language. This practice supports students with the language needed to make sense of the procedural skill of exponent rules, as called for in the standards. However, because the language supports appear only during the Activity Synthesis, this activity lacks consistent language supports to provide for the full and complete participation by MLL students. 

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 is called for in the standards. Without consistent language supports, MLLs may have limited opportunities to fully demonstrate procedural understanding or engage in discussions requiring explanation and justification.

The instructional materials reviewed for Grade 6-8 of Kiddom IM® v.360 partially meet the criteria of providing support for Multilingual Learners’ (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. 

In Grade 6, Unit 2, Introducing Ratios, Lesson 15, Activity 15.3, students work in small groups to use tape diagrams to represent and reason about part-part whole ratios and solve non-routine, real-world word problems (6.RP.3). The activity begins with a whole-class discussion in which students are introduced to the idea of using “parts” in recipes: “Draw students’ attention to a ratio that uses ‘parts’ as its unit. Ask students what they think ‘one part’ means or amounts to, and how situations expressed in terms of ‘parts’ could be diagrammed. Make sure they understand that ‘parts’ do not represent specific amounts, that the value of ‘one part’ can vary but the size of all parts is equal, and that a tape diagram can be used to show these parts.” The materials do not include additional language supports to help MLLs comprehend the concept of using “parts” in recipes, creating a barrier in the point of entry into the task for MLLs. Then, students work in small groups to solve three word problems using tape diagrams. A note titled Supporting Multilingual Learners suggests the use of the Mathematical Language Routine (MLR) 2 Collect and Display, which directs teachers to circulate, listen for, and display language that supports students’ use of the concept of ratios that use “parts” for their units, such as, “one part of ____ represents …” The note encourages teachers to invite students to use the language from the display as needed, updating it throughout the lesson, to support MLLs in using precise mathematical language during partner discussions. In the Activity Synthesis, the teacher facilitates a whole-class discussion on the way in which tape diagrams are used to represent the quantities in the problems. The Activity Synthesis does not include guidance for addressing the listening and speaking language demands of participating in the whole-class discussion. Therefore, this activity does not provide consistent language supports at the task entry point as well as the language demands of speaking and listening while MLLs grapple with, make sense of, and solve application problems. 

In Grade 8, Unit 8, Pythagorean Theorem and Irrational Numbers, Lesson 11, Activity 11.2, students work in partners to solve a routine, real-world word problem involving the Pythagorean Theorem (8.G.7). The activity starts with the teacher reading the word problem aloud, inviting a class discussion to make sense of the word problem; a note titled Supporting Multilingual Learners suggests the use of MLR6 Three Reads to further support MLLs with making sense of the problem. The last read in MLR6 suggests the teacher asks a question aimed at providing students with an entry point into the task: “What are some ways we might get started on this?” Then, students work with partners to solve the word problem and justify their reasoning in writing. The activity lacks suggestions to support the productive language demands of partner discussions and justifying reasoning in writing. The activity concludes with the teacher facilitating a whole-class discussion in the Activity Synthesis, inviting 1-2 students to share their solutions and justifications. The materials do not provide suggestions for language supports for MLLs to participate fully in the whole-class discussion. In summary, this activity does not consistently provide language supports for all four domains of language: reading, writing, speaking, and listening. The lesson’s absence of consistent language supports limits MLLs’ access for grappling with routine, real-world application problems, limiting their full and complete participation in tasks. 

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 multiple representations, such as number lines, arrays, and symbolic equations, and lesson structures that move from independent exploration to partner discussion and group synthesis, promoting reflection and connection-making. However, these opportunities often do not consistently include language supports for MLLs to participate in the full depth of application-based learning at critical moments, such as the launch of new tasks or during partner synthesis in discussions and through writing.

The instructional materials reviewed for Grades 6-8 of Kiddom IM® v.360 partially meet the criteria of providing support for Multilingual Learners’ (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 are the Instructional Routines. Specifically, the Course Overview, 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).” 

As described in the report for 1d.MLL, the materials consistently employ Mathematical Language Routines [MLRs] by Stanford University UL/SCALE. The specific MLRs that directly support MP2 are as follows:

• MLR4 Information Gap: In a group, each student has different parts of a mathematical situation, and they piece together that information orally or visually to bridge the gap between the parameters of the situation. They ask questions to solve a mathematical problem. Through this questioning, students are clarifying the meaning of the  numbers and symbols in the mathematical situation.

• MLR6 Three Reads: Students are guided to read a problem three separate times with three separate purposes, with quick discussions between each read. In the second read, students are guided to consider quantities and units involved in the problem.

• MLR7 Compare and Connect: Students identify, compare, and contrast their own understandings with other students’ mathematical approaches, representations, concepts, examples, and language. These discussions help students make sense of the relationships between representations and the problem to solve.

• MLR8 Discussion Supports: Teachers provide a variety of support to foster inclusive whole-class discussions, which at times focuses on making sense of representations and symbols. 

Specifically, in Grade 6, Unit 5, Arithmetic in Base Ten, Lesson 12, Activity 2, students use long division to divide whole numbers whose quotient is not a whole number, which is a new complexity for students. The activity begins with a partner and then a whole-class discussion analyzing a worked example. The materials encourage the teacher to ask students questions that aim to support abstract reasoning by drawing connections between what’s happening symbolically in the worked example with place value understanding, such as, “What value does the 4 in the quotient represent? How do you know?” The lesson does not provide language support for MLLs to participate fully in this crucial whole-class discussion. Next, students complete five long division problems either with partners or individually. The materials do not provide language supports to help MLLs to apply the understandings from the whole-class discussion to new and novel long division problems, and this pattern of limited language support for MP2-related reasoning tasks appears across multiple lessons.

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 and MLRs, the materials lack language supports at point-of-use within problems in which students are asked to reason abstractly and quantitatively.

The instructional materials reviewed for Grades 6-8 of Kiddom IM® v.360 partially meet the criteria of providing support for Multilingual Learners’ (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 Supporting Multilingual Learners. An example of a feature embedded within the lesson facilitation are the Instructional Routines. Specifically, the Course Overview, Standards for Mathematical Practice states, “Some instructional routines are generally associated with certain MPs. For example… 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).”

As described in the report for 1d.MLL, the materials consistency employ Mathematical Language Routines [MLRs] by Stanford University UL/SCALE. The specific MLRs that directly support MP4 are:

• MLR4 Information Gap: In a group, each student has different parts of a mathematical situation, and they work together to piece together that information orally or visually to bridge the gap between the parameters of the situation and a question to solve a mathematical problem. Through this questioning, students are breaking down the modeling process, identifying important information in the problem. 

• MLR7 Compare and Connect: Students identify, compare, and contrast their own understandings with other students’ mathematical approaches, representations, concepts, examples, and language. Through this discussion, students are modeling the situation with representations and describing what they do with the models. 

• MLR8 Discussion Supports: Teachers provide a variety of supports to foster inclusive whole-class discussions, which at times provides sentence frames to support students with describing what to do with mathematical models. 

Expanding on the sentence frames occasionally provided in MLR8 Discussion Supports, the Course Overview, Advancing Mathematical Language and Access for Multilingual 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 Overview 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 point-of-use. 

In Grade 6, Unit 3, Unit Rates and Percentages, Lesson 17, students work independently and in partners to apply prior concepts and skills from the past three units to estimate and calculate various quantities in a home improvement context. Students must make reasonable assumptions (e.g., about paint coverage or rounding costs) and use prior knowledge from multiple units to make sense of an open-ended, real-world scenario, which reflects the iterative nature of modeling described in MP4. Activity 1 begins with whole-group discussion meant to activate or build prior knowledge around the context of painting the walls of a room, which is used throughout this culminating lesson for this unit. This activity supports MLLs with anticipating both the language needed to engage with the context of the lesson as well as predicting the types of mathematical models students might need to engage with to calculate the cost of painting a room. Activity 17.2 provides specific details about the room to be painted, and a note titled Supporting Multilingual Learners suggests the use of MLR6 Three Reads in which MLLs are supported in reading the printed details. The note suggests that the teacher guides MLLs to read the details about the room three separate times with three separate purposes with quick discussions between each read. Then, the rest of Activity 2, and Activity 3 engage students in structured partner and whole-group discourse to calculate the total area of walls that need to be painted and then apply their understanding of rates and percentages to determine the amount of paint needed. These tasks exemplify mathematical modeling (MP4) as students must interpret a real-world context, decide what quantities and operations are needed, represent the problem mathematically (e.g., through area calculations and proportional reasoning), and interpret their results to determine quantities such as surface area and paint cost. The materials do not provide consistent language support for MLLs to participate fully in the structured small-group and whole-class discourse in which they model with mathematics.

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 during partner and whole-class discourse in which students are asked to model with mathematics.

The instructional materials reviewed for Grades 6-8 of Kiddom IM® v.360 partially meet the criteria of providing support for Multilingual Learners’ (MLLs’) full and complete participation in the intentional development of MP5: Choose appropriate tools strategically.

As described in the report for 1d.MLL, the materials consistently employ Mathematical Language Routines [MLRs] by Stanford University UL/SCALE. The specific MLRs that directly support MP5 are:

• MLR7 Compare and Connect: Students identify, compare, and contrast their own understandings with other students’ mathematical approaches, representations, concepts, examples, and language. Through this discussion, students are choosing appropriate tools or strategies and recognizing the pros and cons of each tool. 

• MLR8 Discussion Supports: Teachers provide a variety of supports to foster inclusive whole-class discussions, which at times focuses on describing how to use various tools.

Specifically, in Grade 6, Unit 2, Introducing Ratios, Lesson 16, Activity 2, students work independently and in small groups to choose an appropriate tool (double number line, table, or tape diagram) to solve ratio word problems. This activity supports MP5 as students are prompted to select from among multiple mathematical tools—double number line, table, or tape diagram—based on the structure of the problem and their own reasoning. The materials direct teachers to facilitate MLR6 Three Reads to support comprehension of the ratio word problems. The Launch of the activity states, “Arrange students in groups of 3–4. Use Three Reads to support reading comprehension and sense-making about this problem… In the first read, students read the problem with the goal of comprehending the situation... In the second read, students analyze the mathematical structure of the story by naming quantities... In the third read, students brainstorm possible starting points for answering the questions.” The materials direct teachers to provide sentence frames for students to discuss possible solution strategies after the third read, such as, “To find the number of tickets for chaperones (or students), I can start by… ” Then, students independently complete a ratio word problem using one of three partially completed representations. In the Activity Synthesis, the teacher arranges students in groups of 3, where a group includes one student who used each representation. Then, small groups compare and contrast the three representations. Students engage in structured comparison of the tools, evaluating the advantages and limitations of each. This culminates in a written reflection in which they justify their preferred representation, a key behavior associated with MP5. The lesson does not provide language supports to aid MLLs in discussing in groups of 3, fully participating in the whole-group discourse, or writing to explain which representation is their preferred representation. In summary, lessons inconsistently apply language support for MLLs to engage with choosing appropriate tools strategically. Without language scaffolds, MLLs may struggle to fully participate in the analytical discourse and reflective writing that MP5 requires.

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 Grades 6-8 of Kiddom IM® v.360 partially meet the criteria of providing support for Multilingual Learners’ (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 are the Instructional Routines. Specifically, the Course Overview, 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.”

As described in the report for 1d.MLL, the materials consistency employ Mathematical Language Routines [MLRs] by Stanford University UL/SCALE. The specific MLRs that directly support MP8 are as follows:

• MLR7 Compare and Connect: Students identify, compare, and contrast their own understandings with other students’ mathematical approaches, representations, concepts, examples, and language. Through this discussion, students notice repeated calculations or evaluate the reasonableness of answers.

• MLR8 Discussion Supports: Teachers provide a variety of supports to foster inclusive whole-class discussions, which at times provides sentence frames to support students with describing a general formula or algorithm.

Expanding on the sentence frames occasionally provided in MLR8 Discussion Supports, the Course Overview, Advancing Mathematical Language and Access for Multilingual 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 Overview 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. 

For example, in Grade 6, Unit 1, Area and Surface Area, Lesson 9, Activity 2, students work independently and in small groups to generalize a process for finding the area of a triangle, justifying why this process can be abstracted into a formula. In Activity 9.1, students examine written statements about bases and heights of triangles, determining whether the statements are true or false. The teacher gives students two to three minutes of independent work time before discussing their responses with a partner. The Activity Synthesis directs teachers to facilitate a whole-class discussion, inviting students to explain how they know each statement is true or false. The activity does not provide language supports to aid MLLs with comprehending the written statements or participating in the partner and whole-class discussion. Activity 2 invites students to build on prior understandings from the previous lesson to determine the areas of triangles on graph paper. Students work first independently and then in small groups to determine and record areas, with access to a geometry toolkit and tracing paper. The activity lacks language support for the listening and speaking demands of working in small groups. The Activity Synthesis directs the teacher to facilitate whole-class discourse using questions designed to generalize a process for finding the area of a triangle by asking questions like, “Can you explain why this expression is true for any triangle?” A note titled Supporting Multilingual Learners suggests the use of MLR8 Discussion Supports in which the teacher provides MLLs with the opportunity to orally rehearse with a partner their explanation for why the algorithm works for finding the area of any triangle before they share it with the whole class. In summary, the materials provide inconsistently applied language support to help MLLs with generalizing and looking for repeated reasoning. 

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 Grades 6-8 of Kiddom IM® v.360 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 Overview, Advancing Mathematical Language and Access for Multilingual 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 the 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 1d.MLL, the Course Overview, Advancing Mathematical Language and Access for Multilingual 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. The Course Overview, Scope and Sequence outlines the progression of the mathematical content, the disciplinary language usage, and new terminology in each unit for each course. There is no discernible progression of disciplinary language within this information, as noted in the 1.2.MLL-2 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 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 Overview, 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 three 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 invites 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 Grades 6-8 of Kiddom IM® v.360 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 some lessons, 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. When lessons contain language goals, 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. The language goals do not incorporate the language structures and vocabulary used in conjunction with the listed language function, and they are not always measurable or specific enough for teachers to be able to formatively assess language usage and development. 

Specifically, in Grade 6, Unit 3, Unit Rates and Percentages, Lesson 1 the Learning Goals are, “Compare (orally) the relative size of different units of measure for one attribute, that is, length, volume, and weight or mass. Comprehend the approximate size of 1 “inch,” “foot,” “yard,” “mile,” “millimeter,” “centimeter,” “meter,” “kilometer,” “ounce,” “pound,” “ton,” “gram,” “kilogram,” “cup,” “quart,” “gallon,” “milliliter,” and “liter.” Identify which unit is closest to the length, volume, weight, or mass of a given object, and explain (orally) the reasoning.” These language goals clearly focus on the language domain of speaking which is associated with two language functions: compare and explain. These language domains and functions are embedded throughout the lesson with teacher prompts such as, "How close are these estimates to each other?" In Activity 1.2, students use prior knowledge from Grade 4 to sort units of measure into which attributes it measures (length, volume, or weight) while working in structured groups of 2-4.  In a note titled Supporting Multilingual Learners, MLR2 Collect and Display is suggested. The teacher is directed to collect language that students use to describe their understanding of units, such as, “... how long..” and “...how much can fit into…” This suggestion is a support for the language function of describing, which is not listed in the language goals, but could build towards the language function of comparing. This example demonstrates what designers want students to do with language to reach the content goals. The language goals themselves lack clear performance measures; students are asked to compare units and explain their reasoning, but there is no guidance for assessing the quality, specificity, or complexity of the language used.

Not all lessons contain language goals. For example, in Grade 7, Unit 6, Expressions, Equations, and Inequalities, Lesson 12, the Learning Goal is, “Solve word problems leading to equations of the form  px+q=r or p(x+q)=r.” This Learning Goal does not contain a language domain, language structures, or vocabulary. 

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 Grades 6-8 of Kiddom IM® v.360 partially meet the criteria of providing teacher guidance to support Multilingual Learners (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.

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 (see the reports for 2e.MLL-2l.MLL). The Course Overview,  Advancing Mathematical Language and Access for Multilingual Learners guides 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… Use the suggested MLRs and language strategies, as appropriate, to provide students with access to an activity, without reducing the mathematical demands of the task… Decide which optional MLRs to use and when to use them, based on students’ individual needs.” The materials do not provide teacher guidance for how to “decide which optional MLR to use” nor to “adapt and incorporate” the suggested MLRs “as appropriate.” Without this guidance, materials do not facilitate understanding in teachers new to working with MLLs, nor do they support deepening the understanding of MLL experts. Therefore, the teacher guidance around implementing MLRs is not inclusive of all levels of teachers’ understanding in instructing MLLs.

The Course Overview, Scope and Sequence provides a list of new mathematical terminology per unit, which allows teachers to anticipate language demands. It states, “The table shows lessons where new terminology is first introduced in this course, including when students are expected to understand the word or phrase receptively and when students are expected to produce the word or phrase in their own speaking or writing. Terms that appear bolded are in the Glossary. Teachers should continue to support students’ use of a new term in the lessons that follow where it was first introduced.” The Scope and Sequence does not provide teacher guidance as to what to observe for and how to respond to the language demands associated with MLLs learning new mathematical terminology. 

In Grade 6, Unit 7, Rational Numbers, Lesson 1, students extend their understanding of the number system from positive numbers to negative numbers by exploring real-world contexts. One of the Learning Goals is as follows, “Interpret positive and negative numbers that represent temperature or elevation, and understand the convention of what ‘below zero’ typically means in each of these contexts.” Before Activity 3 begins, the materials suggest the use of MLR 5 Co-Craft Questions in a note titled Supporting Multilingual Learners. It states, “Keep books or devices closed. Display only the table of elevations from the Task Statement, without revealing the questions, and ask students to record possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, ‘What do these questions have in common? How are they different?’ Reveal the intended questions for this task and invite additional connections.” The Instructional Routines section of the lesson provides guidance around how teachers can anticipate the language demands of the activity, stating, “Through this routine, students use conversation skills to generate, choose (argue for the best one), and improve questions and situations, as well as develop meta-awareness of the language in mathematical questions and problems.” The lesson does not provide guidance for teachers to observe student language development in regards to MLLs’ disciplinary language usage outlined in the Learning Goal of interpreting positive and negative numbers that represent elevation. 

A similar example is found in Grade 7 Unit 4, Proportional Relationships and Percentages, Lesson 4, where students apply the distributive property to write algebraic expressions for real-world situations where one quantity is described in relation to another quantity. One of the Learning Goals for this lesson is, “Coordinate tables, equations, tape diagrams, and verbal descriptions that represent a relationship involving adding or subtracting a fraction of the initial value.” Interspersed throughout the lesson, the materials suggest the use of three different MLRs in notes titled Supporting Multilingual Learners: MLR2 Collect and Display, MLR8 Discussion Supports, and MLR7 Compare and Connect (located in the optional Activity 4.4). In Activity 2, MLR2 Collect and Display suggests that the teacher listen for, collect, and display the language students use to describe the relationship between initial distance and total distance walked. The materials do not provide teacher guidance about how teachers can provide feedback about MLLs’ usage of the language from the display. Additionally, the materials do not provide teacher guidance to connect this suggested language support with the disciplinary language usage outlined in one of the Learning Goals of coordinating tables, equations, and verbal descriptions that represent a mathematical relationship. In Activity 3, MLR8 Discussion Supports suggests that the teacher display sentence frames such as, “I noticed ____, so I matched…” to support MLLs in explaining their reasoning to their partner. The lesson does not provide additional teacher guidance around how teachers can anticipate possible language demands, such as what teachers can look for or listen for as MLLs engage in partner discourse.

The instructional materials reviewed for Grade 6-8 of Kiddom IM® v.360 partially meet the criteria of guiding teachers on how to match students with language supports, progressing along a continuum. The materials provide three strategies that guide teachers on how to match students with language supports, progressing along a continuum. The materials do not guide teachers on how to be responsive to students’ current language development in relation to the content. 

In the Course Overview, Advancing Mathematical Language and Access for English Learners, the materials outline the language supports and instructional approaches to support Multilingual Learners (MLLs), stating “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 foster language-rich environments in which there is space for all students to participate” (see report for 3e.MLL). 

Similar evidence is found in lesson-level materials. The materials include language supports such as Mathematical Language Routines (MLRs) and student-facing glossary definitions. These supports are not differentiated by students’ language proficiency levels and do not guide teachers in adjusting scaffolds over time based on language growth.

Additionally, in the Course Overview, Advancing Mathematical Language and Access for Multilingual Learners, the materials contain a document titled 6-8 Spanish Cognate Toolkit. This Toolkit outlines how incorporating instruction on English-Spanish cognates can support translanguaging and metalinguistic transfer for MLLs whose home language is Spanish, stating, “For ELLs, cognates act as a bridge between their native language skills and new academic vocabulary, facilitating quicker comprehension of challenging concepts.” The Toolkit features three sections: an overview of the research and background of cognate instruction, three strategies to teach English-Spanish cognates, and a list of cognates for each grade. Each of the three strategies to teach English-Spanish cognates includes a strategy description, an outline of what teachers will do, and an outline of what students will do, broken down by WIDA levels 1-5. These descriptions of what students will do based on WIDA levels outline language supports at varying language proficiency levels. Therefore, these three strategies guide teachers on how to match students with language supports, progressing along a continuum. The materials do not reference these strategies in any other location; the onus is on the teacher to identify when to implement one of the strategies, which would add time to lesson facilitation. The strategies do not guide teachers on how to be responsive to students’ current language development in relation to the content. Additionally, the Toolkit centers English-Spanish cognates with no guidance for identifying and supporting cognates in other home languages.

The instructional materials reviewed for Grade 6-8 of Kiddom IM® v.360 partially meet the criteria of providing guidance to encourage teachers to draw upon student home language to facilitate learning. The materials offer translated resources, but include minimal guidance for teachers to leverage Multilingual Learners’ (MLLs’) home language in math learning. Additionally, the materials lack teacher-facing guidance at point-of-use within lessons on how to integrate MLLs' home languages into classroom instruction. 

As found in the reports for 3.1.MLL-3 and 3e.MLL, the Course Overview section titled Advancing Mathematical Language and Access for Multilingual Learners includes a resource called the 6-8 Spanish Cognate Toolkit, designed to support teachers working with MLLs whose home language is Spanish. This Toolkit outlines how incorporating instruction on English-Spanish cognates can support translanguaging and metalinguistic transfer for MLLs whose home language is Spanish. The Toolkit features three strategies to teach English-Spanish cognates and a list of cognates for each grade. 

• Strategy 1: Follow the Leader instructs teachers to model the identification and analysis of cognates using visual aids, anchor charts, and guided questioning. It explicitly teaches the concept of cognates and demonstrates how to distinguish true, false, and partial cognates.

• Strategy 2: 1 Thumb, 2 Thumbs is an interactive classroom practice that engages students in self-assessing their ability to recognize and use cognates in context. Teachers reinforce learning through ongoing discussion and visual tracking of vocabulary.

• Strategy 3: My Own Dictionary supports independent vocabulary development by having students document and categorize cognates in a structured note-taking system that they can reference throughout the unit.

Each strategy includes teacher actions, differentiated expectations for students at English Language Proficiency levels 1–5, and suggested materials to support implementation. While these strategies are well designed, they are not embedded throughout lessons in a way that ensures consistent use by all teachers;  the onus is on the teacher to identify when to implement one of the strategies, which would add time to lesson facilitation. Additionally, the toolkit applies exclusively to MLLs whose home language is Spanish. There are no parallel strategies or models offered for students who speak other home languages. Therefore, the materials provide very minimal guidance for teachers to leverage MLLs’ home language in math learning, and it is limited to MLLs whose home language is Spanish.