K-2nd Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades K–2 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide some strategies for MLLs’ participation in grade-level problems, but they do not apply these supports consistently across units and sessions.  Also, they are often not tailored to the specific language demands of individual sessions.

The materials provide authentic, real-world contexts that engage students in solving meaningful, language-rich mathematical tasks and encourage them to share their thinking orally and through drawings or models. The materials provide language supports for MLLs’ participation in grade-level problems at two levels: in notes titled, MLL in the sessions and in Work Place guides, and embedded in session facilitation. In the resource titled, Supporting Language Development with Discussion Structures & Routines, the materials describe how math routines and discussion structures embedded in session facilitation support MLLs in using the language needed to participate in grade-level problems. It states, “Math routines and discussion structures are part of students’ everyday experience in the Bridges classroom. Bridges supports multilingual learners in developing the language skills and vocabulary needed to explain and justify their thinking, respond to the thinking of classmates, discover and describe patterns, and make conjectures and generalizations… These practices have been shown to support language development and deepen mathematical understanding.” Then, the resource lists the following discussion structures and math routines embedded within sessions, along with a description of the routine and why it is useful:

• Discussion structures: Think-Pair-Share, Noticing & Wondering, Open Strategy Sharing, Gallery Walk, Compare & Connect, What’s Best & Why?, Math Forums

• Math Routines: Choral Counting, Quick Images, Dot Talks, Would You Rather?, Same & Different, Which One Doesn’t Belong?, Guess My Rule, What Comes Next?, I Have, You Need, Number Talks, Number Strings, Problem Posing

While math routines and discussion structures provide support for MLLs by providing predictable, language-rich structures, the materials do not include educational teacher guidance to fully and completely support MLLs with accessing the mathematical content discussed in each math routine and discussion structure. 

In addition, the introduction to each grade level in the Teacher Edition contains two sections that outline how the materials support MLLs with participation in grade-level problems. The Community of Learners section outlines considerations for successfully developing a community of learners, including suggestions that support MLLs’ full and complete participation such as, “Encourage active engagement from all students. The Think-Pair-Share routine allows students to process ideas individually and rehearse their explanation with a partner before engaging in whole-group discussion.” The Language Supports section provides an explanation of the instructional approaches of the program for MLLs, including general recommendations to support math language development (see the report for 3e.MLL for details). These general recommendations are periodically found in MLL notes at point-of-use within session facilitation and Work Place guides. These notes are repetitive in nature, typically falling into one of these general recommendations: flexibly pairing MLLs to leverage home language usage, encouraging multimodal expression, providing clarifying questions and sentence frames and starters, and referencing the ABCs of Math Talk poster and the Word Resource Cards. The Work Place guides feature similar recommendations for each Work Place game, leaning more heavily on sentence frames and starters that are specific to the game. The teacher guidance for supporting students with authentically using the sentence frames and starters is brief and generic, suggesting that the teacher print the sentence frames and starters and make them available while students play the Work Place games. Across the MLL notes in both the session facilitation and the Work Place guides, the materials infrequently reference the ABCs of Math Talk poster and frequently reference the Word Resource Cards. This does not support MLLs’ full and complete participation. Within sessions, the MLL notes are found infrequently, and often remain general in nature and not specific to the task, which limits their impact on MLLs’ ability to access grade-level problems. Additionally, the placement of the MLL notes within sessions often does not correspond with the section of the session that directly addresses grade-level standards.

As a result, the linguistic access points that MLLs need with grade-level problems, such as intentional scaffolds for productive and receptive language, suggestions for structured academic discourse, amplification of language (such as explicit attention to morphology), and support for language functions, are inconsistently applied. MLLs may successfully play the Work Place games or complete the Problems & Investigations tasks, but the materials do not consistently provide language scaffolds to support MLLs’ ability to use and develop precise mathematical language within grade-level problems.

The instructional materials reviewed for Grades K–2 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ conceptual understanding of key mathematical concepts. The materials consistently engage students in reasoning about mathematics through structured oral interactions and the use of concrete and visual representations, which promotes conceptual understanding. However, while these experiences create natural opportunities to use and develop language, the materials do not provide systematic, embedded supports to ensure that MLLs develop reading, writing, and academic English in a deliberate way.

Across the grade band, the materials provide students with the opportunity to find relationships within and between concrete representations, visual representations, and various abstract written strategies. The sessions’ instructional design fosters multimodal ways of building conceptual understanding alongside rich oral discourse. For example, in Kindergarten, Unit 8, Computing & Measuring with Frogs and Bugs, Module 1, Session 1, Problems & Investigations, students listen to a subtraction problem situation and spin a double spinner to determine how many bugs are present and how many bugs to catch (K.OA.1). They create different visual representations and connect the visuals to an equation and a number rack. They reason about the difference aloud, debating how many bugs remain, and justify strategies using the number rack, such as, “I pushed back 2 on the top and 1 on the bottom to show 6.” Teachers model the use of mathematical terms like minus and subtract while allowing informal phrases such as take away, guiding students toward more formal language. Through the whole-class discussion, students connect oral discussion with visual representation and equations. These tasks provide MLLs with authentic opportunities to use language to build conceptual understanding around subtraction problem situations.

Although the sessions engage MLLs in rich oral discourse, they do not provide the type of sustained opportunities for the intentional development of all four domains of language, specifically reading and writing. Written tasks are generally limited to drawing or labeling. Additionally, the materials do not provide explicit language scaffolds that enable MLLs to internalize academic English independently. The material’s attention to morphology (e.g., teen versus -ty), syntax (word order in equations), or etymology is incidental rather than intentionally developed. Without these intentional language supports, the success of MLLs depends heavily on teacher facilitation and the incidental repetition of vocabulary during conversation. Visuals and manipulatives provide powerful visual entry points and work to build conceptual understanding, but without intentional language supports, MLLs may struggle to connect these concrete and pictorial representations to abstract symbols and numbers and precise mathematical language.

In summary, the materials promote conceptual understanding by engaging students in mathematical reasoning through oral interactions and concrete and visual representations, but they lack systematic language supports for MLLs.

The instructional materials reviewed for Grades K–2 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ procedural skill and fluency. Sessions provide frequent opportunities for students to build procedural fluency through aspects of the instructional design that invite oral explanation and partner discourse around procedural fluency, like Warm-Ups, Number Corners, and practice problems. While these experiences promote accurate and efficient computation, the materials do not systematically embed linguistic supports needed to ensure that MLLs develop academic English while mastering procedures.

Throughout the grade band, students encounter carefully sequenced tasks that emphasize flexible strategies and efficient procedures alongside rich oral discourse. For example, in Kindergarten Unit 8, Computing & Measuring with Frogs & Bugs, Module 1, Session 3, students participate in the Same & Different routine during the Warm-Up. The teacher reads two subtraction stories aloud, and students observe the images, Think-Pair-Share how the problems are alike and different, and explain their reasoning.  The materials state, “They both have 3 pennies for the answer…one subtracts 2 pennies and the other subtracts 3.” Teachers emphasize efficiency in procedural skills by restating student ideas and highlighting the language of subtraction. The Same & Different routine supports listening and speaking while reinforcing procedural understanding of subtraction (K.OA.5). Similar routines appear across units as students chorally count, share strategies for doubles or combinations of ten, and record solutions in their student books.

While aspects of the instructional design focusing on procedural skills and fluency give MLLs repeated chances to use language, the materials do not intentionally develop language around communicating how and why an algorithm works. Manipulatives such as coins, number racks, and ten-frames provide strong visual anchors to support procedural skills. But, without intentional language support around using these tools to calculate accurately, efficiently, and with flexibility, MLLs will manipulate the materials without fully connecting them to precise mathematical terminology. Without this intentional connection, students must rely on teacher questioning and incidental repetition to intentionally develop the academic language associated with independently demonstrating procedural skills. As a result, MLLs may develop procedural fluency yet lack the structured language practice needed to express their strategies independently.

In summary, the materials support the development of procedural skills and fluency by engaging students in rich oral discourse, but they lack systematic language supports for MLLs.

The instructional materials reviewed for Grades K–2 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ ability to apply mathematics in real-world and mathematical contexts. Across units, students encounter authentic application tasks that require them to read short word problems, write numerical solutions, and justify their reasoning using diagrams and equations. These activities promote mathematical reasoning and the transfer of skills to new contexts, but the materials do not systematically provide the language supports needed to ensure that MLLs can access and express the embedded language demands.

Across the grades, the materials engage students regularly in applying mathematics in routine and non-routine contexts, including single- and multi-step problems. These applications provide repeated opportunities for students to demonstrate their ability to transfer and apply mathematical concepts and skills. The sessions’ instructional design fosters multimodal ways of solving application problems alongside rich oral discourse. For example, in Grade 2, Unit 7, Measurement, Fractions & Multidigit Computation, Module 1, Session 5, Problems & Investigations, students learn the Work Place game Measure & Compare Centimeters which focuses on measuring lengths in centimeters and determining the difference between two lengths (2.MD.5). Students Think-Pair-Share to brainstorm and then create their own object cards and measure classroom items. They work with partners to calculate differences in length using a self-selected strategy and record results on a class chart. During this student-to-student discourse, MLLs use language as they choose their solution strategy. The materials prompt the teacher to, “ask students to share their strategies with the class. Look for opportunities to record students’ thinking on the record sheet using equations and open number lines.” The task provides ample opportunity for MLLs to use language as it blends reading (game instructions and object labels), writing (recording measurements and differences), speaking (sharing strategies and observations), and listening (following peer and teacher explanations). 

While these experiences provide rich opportunities for MLLs to use all four language modalities, the materials do not embed the language supports necessary for MLLs to fully access the linguistic demands of solving routine and non-routine application problems. Specifically, the materials lack systematic language development of the reading, writing, speaking, and listening demands within application tasks when students are asked to use language to self-select a solution strategy, write equations, and justify solutions. Visuals and manipulatives such as object cards, measuring tapes, and record sheets offer MLLs multimodal entry points to the task but are not paired with explicit linguistic supports for MLLs to develop academic language. Without intentional language development around the language needed to solve application problems, MLLs’ success relies largely on teacher facilitation and the chance repetition of vocabulary in discourse.

In summary, while the materials  engage students in authentic application of mathematical concepts, but they lack systematic language supports for MLLs.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP1: Make sense of problems and persevere in solving them. While the materials provide supports for MLLs engaging in MP1, they do not consistently ensure MLLs’ full and complete participation.

Across Grades K-2, students engage in open-ended tasks that support key components of MP1 by prompting them to make sense of mathematical situations, develop and revise strategies, and persevere through challenges. Embedded in the session facilitation, the teacher guidance provides MLLs with multiple entry points to engage with MP1 multimodally through storytelling, partner discussions, physical movement, and mathematical recording. In Grade 2, the ABCs of Math Talk poster provides sample questions and sentence frames organized into language functions such as add, connect, and clarify. The sample questions and sentence frames support interdisciplinary language connections since they are generic in nature. For example, under the language function clarify, the following questions and sentence frames are listed: 

• “Why did you use that strategy?”

• “How did you get that answer?”

• “When you said ____ did you mean ___?”

• “I would like to know why…” 

The materials reference the ABCs of Math Talk poster within session facilitation, most frequently in the teacher guidance for the Math Forums. The sample questions and sentence frames for the language functions add, connect, and clarify could support MLLs’ use and development of language around making sense of problems. However, the materials present the ABCs of Math Talk poster as supporting the Math Teaching Practice of facilitating meaningful mathematical discourse, and not as explicitly supporting MLLs’ full and complete participation in making sense of problems. The onus is on the teacher to intentionally integrate the ABCs of Math Talk as a language support for MLLs to engage in MP1. 

Additionally, language supports to ensure MLLs’ full and complete participation in engaging with MP1 are inconsistently applied in Sessions, Work Places, and Number Corners. The materials do not consistently include explicit language scaffolds to support MLLs with understanding the information in a problem or to determine if their answer makes sense, which would strengthen MLLs’ ability to engage in MP1. Furthermore, the lack of targeted strategies to sustain MLLs’ engagement means that some MLLs may struggle to persevere in problem solving without heavy teacher guidance. For example:

• In Grade 2, Unit 8, Measurement, Data & Multidigit Computation with Marble Rolls, Module 2, Session 1, Problems & Investigations, students engage with an open-ended task that challenges them to design a system capable of moving a marble without direct pushing. Using everyday classroom materials, they brainstorm ideas and predictions before working with partners to construct, test, and revise marble runs made from tubes, tape, blocks, and other supplies. There is a lack of language supports for MLLs to participate fully with their partners, and there are a lack of scaffolds for MLLs to use and develop the language functions:  brainstorm, predict, and revise. Throughout the process, students encounter obstacles, use a variety of solution strategies, monitor their progress through adjusting their designs, and incorporate measurement tools to determine the distance the marble travels. They consolidate their learning by sharing observations through a whole-class discussion and illustration. The materials do not provide language supports for MLLs’ full and complete participation in the whole-class discussion in which they reflect on the problem solving process and determine if their design makes sense. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, as many sessions and Number Corners do not have specific language support or have inconsistent guidance on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP1. MLLs are supported to enter and engage in problem solving, but they are not consistently scaffolded to sustain their perseverance or to use language that supports sense-making and evaluation. These missed opportunities prevent the materials from fully developing the iterative and reflective aspects of MP1 for MLLs.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP2: Reason abstractly and quantitatively. While the sessions’ instructional design offers meaningful opportunities for MLLs to engage in reasoning, the supports are not consistent or comprehensive to ensure full participation for all MLLs.

The sessions’ instructional design provides multiple supports that partially serve MLLs in reasoning abstractly and quantitatively. The materials employ representations moving from concrete to representational to abstract, giving MLLs accessible entry points into the mathematical task and support MLLs with making sense of abstract symbols. For example:

• In Grade 1, Unit 3, Adding, Subtracting, Counting & Comparing, Module 1, Session 1, Problems & Investigations, students observe a picture of a traditional Cherokee game played with butter beans and pose problems about it. Next, the teacher draws connections between the real-world situation to introduce a similar game, Drop the Beans. Students drop seven double-sided beans and count how many land red side up and how many land white side up. They record the combinations on a graph displaying expressions of the combinations to seven. A note titled MLL states, “As you teach the game, use gestures and repetition to tie the words spill, count, and beans to the action of spilling beans and counting them. Many students can access this game in their home language. You can also write a sentence frame on the board to provide language support: You have ____ red beans showing, so you have ____ white beans under your hand.’” This note contains three separate language support suggestions to scaffold MLLs’ engagement in MP2. The first two suggestions of supporting specific terms used in the gameplay and connecting to home language may allow MLLs to participate equitably in the game. The suggestion for teachers to display a sentence frame on the board supports MLLs’ ability to understand the meaning of the numbers and symbols within the expressions on the graph, which supports MLLs’ engagement with MP2.

However, the materials stop short of ensuring full participation for all MLLs; they lack explicit language scaffolds for the language demands associated with representing situations symbolically or explaining what the numbers and symbols mean in solution strategies. For example:

• In Grade 2, Unit 4, Measurement, Module 3, Session 4, Problems & Investigations, students engage deeply with MP2, as they share their solution to a task from a previous session and respond to strategies of their classmates. The materials direct teachers to facilitate a structured strategy-share routine where partners present their solutions to the class, justify their thinking through drawings, equations, and verbal explanations, and listen to and restate the strategies of their peers. After each strategy is shared, the materials present question stems to prompt student discussions, such as, “Can you tell us more about ____?” and “Why did you decide to ____?” While the structured strategy, share and the question stems may support MLLs with equitable participation, the materials lack language supports for MLLs to produce the language functions of justify and restate. Additionally, the structured strategy, share and the question stems, do not support MLLs with engaging in MP2, specifically with representing situations symbolically or explaining what the numbers and symbols mean in each solution strategy.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not intentional in supporting MLLs with the language demands of engaging in MP2. MLLs have opportunities to reason quantitatively and symbolically, but they are not supported to use language that helps them justify strategies, restate peers’ reasoning, or explain the meaning of symbols. These missed opportunities prevent the materials from fully developing the decontextualizing, contextualizing, and interpreting aspects of MP2 for MLLs.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP3: Construct viable arguments and critique the reasoning of others. While sessions include entry points and structures that invite MLLs into mathematical argumentation, the supports are not consistent or comprehensive to ensure full and sustained participation for all MLLs. 

As described in the report for 2g, students participate in tasks that support key components of MP3 by constructing mathematical arguments, analyzing errors, justifying their thinking with multiple representations, engaging with and evaluating others’ reasoning through questions, and making and testing conjectures while solving problems. In Grade 2, the ABCs of Math Talk poster provides sample questions and sentence frames organized into language functions such as add, build, connect, and challenge. The sample questions and sentence frames support interdisciplinary language connections since they are generic in nature. For example, under the language function challenge, the following questions and sentence frames are listed that support students critiquing each other:

• “Why did you… ?”

• “I respectfully disagree because… ”

• “A more efficient strategy might be… ”

The materials reference the ABCs of Math Talk poster within session facilitation, most frequently in the teacher guidance for the Math Forums. The sample questions and sentence frames for the language functions add, connect, and clarify could support MLLs’ use and development of language around constructing viable arguments and critiquing the reasoning of others. However, the materials present the ABCs of Math Talk poster as supporting the Math Teaching Practice of facilitating meaningful mathematical discourse and not as explicitly supporting MLLs’ full and complete participation in constructing arguments and critiquing others. The onus is on the teacher to intentionally integrate the ABCs of Math Talk as a language support for MLLs to engage in MP3. 

Additionally, language supports to ensure MLLs’ full and complete participation in engaging with MP3 are inconsistently applied in Sessions, Work Places, and Number Corners. The materials do not consistently include explicit language scaffolds to support MLLs with constructing viable arguments and critiquing the reasoning of others. For example:

• In Grade 2, Unit 5, Place Value to 1,000,  Module 4, Session 1, Problems & Investigations, students engage in MP3 by building, sharing, and debating their ideas about growing patterns with Unifix cubes. They recall patterns from prior lessons and everyday life, then they recreate a sequence of cube trains (1, 3, 5, 7) to determine if it represents a pattern. Through partner and whole-class discussions, students construct arguments about how the sequence grows and critique the reasoning of others by comparing different perspectives (e.g., whether a pattern must repeat or can grow indefinitely). Some aspects of the session’s instructional design support MLLs, such as working with manipulatives, using visual displays, and engaging in structured partner talk before whole-class sharing. However, while these supports give MLLs entry into the task, they are not consistently strong enough to help students construct clear mathematical arguments or provide the language scaffolds needed to fully participate in critiquing the reasoning of others. As a result, opportunities to access MP3 are present but not consistently supported for MLLs’ full and complete participation.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not intentional in supporting MLLs with the language demands of constructing arguments and critiquing the reasoning of others.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP4: Model with mathematics. While sessions include entry points and structures that invite MLLs into mathematical modeling, the supports are not consistent or comprehensive enough to ensure full and sustained participation for all MLLs. 

Across Grades K-2, students engage in tasks that support MP4 by reasoning with quantities, representing situations symbolically, and interpreting numbers and symbols in context to connect real-world scenarios with mathematical representations. Session features such as visuals, manipulatives, and contextual stories create conditions where MLLs can begin to model situations with representations and connect different representations for the same problem. However, the materials do not consistently provide the explicit language supports necessary for MLLs’ full participation in MP4, specifically in regards to making decisions about the most effective model, evaluating whether their model makes sense, or revising it. For example:

• MLLs are not fully supported in participating in Grade 1, Unit 4, Leapfrogs on the Number Line, Module 1, Session 3, where students engage with MP4 as they use a contextual story about Nevaeh and a frog to model addition and subtraction on the number line. The teacher introduces the number line through a relatable context and a toy frog, helping students connect hops to counted intervals. Students act out the frog’s movements, write matching equations, and later use student book pages to represent hops with two colors and create both addition and subtraction equations, reinforcing the idea that the operations are inverses. These concrete and visual supports partially allow MLLs to access the mathematical modeling by connecting multimodal instruction and a story context with manipulatives to abstract equations. However, the lesson lacks more robust and targeted language scaffolds that would support MLLs with the language demands of mathematical modeling, such as identifying the important information in the problem, using math they know to solve new problems, and checking to see if their answer makes sense and change the model when necessary.

• In contrast, MLLs are supported in Grade 2, Unit 1, Sorting & Graphing, Module 1, Session 4, where students sort a class collection of objects to create a Venn diagram and then co-construct a picture graph as a whole class. After generating comparison statements about the picture graph, each student transfers the information to a bar graph and makes their own comparisons. The materials direct teachers to display the Word Resource Cards for sum, difference, greater than, and less than and to encourage students to use the terms in their comparison statements, which supports MLLs’ application of those terms in context. In a whole-class discussion, the teacher is directed to connect the comparison statements to the mathematical symbols for greater than, less than, and equal to. A note titled, MLL states, “Write the following sentence frames on the board to support students’ work:

  • The number of ____ is (greater than/less than) the number of ____.

  • The sum of ____ and ___ is ____.

  • The difference between the number of ____ and ____ is ____.”

With these provided scaffolds (model a story context with multiple representations and to describe what they do with the models), this program provides MLLs with full participation in MP4 in this session.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not consistent in supporting MLLs with the language demands of modeling with mathematics.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP6: Attend to precision. The materials provide support for MLLs full and complete participation in MP6 sometimes, but those supports are not employed consistently throughout the program.

As described in the core report for 2j, the materials support precise language by modeling accurate mathematical language so that students can understand and apply precise definitions. The Word Resource Cards help students attend to the precision of mathematical language with cards printed with a nonlinguistic model of the word and a definition on the back. However, there is limited teacher guidance around supporting MLLs to formulate clear explanations utilizing the Word Resource Cards or providing feedback to students on the accurate use of mathematical language. Therefore, language supports are inconsistently applied for MLLs to engage in MP6 in Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in Grade 2, Unit 2, Setting Foundations for Place Value & Measurement, Module 1, Session 3, Problems & Investigations, where students work with a partner to estimate, count, and compare beans to practice working with numbers within 100. The materials direct teachers to prompt students to explain how many cups are needed to hold 50 beans. Students then complete a structured student book page by counting their beans by 10s and 1s and determining how many more or fewer they have than 50.   Then they combine their collection with their partner’s to determine how many more or fewer they have than 100. Through this activity, students engage in precise counting, use benchmarks like 10s and 100s, and explain their strategies clearly in this problem. The materials provide no language support for any aspect of the activity. Specifically, the materials lack in language supports for MLLs’ use of precise language to describe their thinking, their receptive language needs of listening to their partner explain, and their reading needs of the student workbook page.

• In contrast, MLLs are fully supported in Grade 1, Unit 4, Leapfrogs on the Number Line, Module 3, Session 2, where students are building fluency with their addition and subtraction facts in a game setting. The game directions tell students to draw a card. The session facilitation contains a note titled MLL which states, “Be precise when using a word that has different meanings. For example, the word draw can mean to sketch or, as in this case, to take a card. Be sure to clarify your meaning with synonyms or demonstrate drawing a card as you say ‘Draw a card’.” This language support amplifies the English language and draws MLLs’ attention to making sense of homonyms, which supports using precise language. 

In summary, MLLs engage in tasks with opportunities to attend to precision, but the materials do not consistently provide language supports that help students articulate precise explanations, interpret peer reasoning, or refine their use of mathematical language. These missed opportunities prevent MLLs from fully developing the habits of precise communication expected in MP6.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP7: Look for and make use of structure. While MLL specific language supports are available in some sessions where students are engaging in MP7, their purpose is not intentionally to scaffold the language demands associated with looking for and explaining structure to make generalizations.

Across Grades K-2, students engage in tasks that highlight MP7 by recognizing patterns, identifying structure, and breaking down complex problems. Sessions encourage comparing strategies, justifying reasoning, and reflecting on how structure supports deeper understanding through teacher-facilitated discussion. Language supports for MLLs to engage fully and completely in MP7 are inconsistently applied within Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in participating in Kindergarten, Unit 2, Numbers to 10, Module 4, Session 2, where students assemble quilt blocks they made in the previous session into a classroom quilt, and share observations about the shapes and patterns that emerge. As the class is co-constructing the quilt, students Think-Pair-Share to predict and extend the pattern, and the teacher is directed to facilitate whole-class discussion using prompts like, “What would come next? How do you know?” There are no language supports for MLLs to fully engage in the class discussion, or to support the language demands of predicting the next sequence in the pattern. As more blocks are added, students engage in a Think-Pair-Share, then a whole-class discussion, to identify and describe the structure of the quilt, noting repeated elements and spatial relationships. There is a lack of language supports to ensure MLLs’ full participation in the student-to-student and whole-class discourse, including no language support for MLLs to engage with the language function describe. 

• In contrast, MLLs are partially supported in Kindergarten, Unit 7, Measurement & Teen Numbers, Module 2, Session 3, Problems & Investigations, which begins with students engaging in a Think-Pair-Share around how many dots they see on a double ten frame, and how they saw the dots. The teacher is directed to invite students to listen carefully to their partners, and during the whole-class discussion, the teacher prompts students to rephrase what their partners said. There are no language supports provided for students to rephrase their partner’s reasoning, or for MLLs to engage fully in the whole-class discussion. The session continues with students playing the partner game, Double Top Draw, in which they make use of structure by counting and comparing quantities from 10 to 20 represented on double ten frames. Students then spin a spinner with the terms greater than and less than as the two options and then compare their quantities with their partner. The materials lack language supports for the meaning of the timers greater than and less than, and of the language demands of reading those terms. The session facilitation continues as it states, “Emphasize that when students determine how many dots are on a card, they should use what they know about the structure of teen numbers to count them. Mention that students should refer back to points made in the student discussion during the warm-up as needed.” There are no language supports provided for the language demands of using the structure of teen numbers to explain reasoning, nor are there language supports for MLLs to remember and refer back to the summary points made in the Warm-Up. The session facilitation for the game concludes with a note titled, MLL that provides one option for language supports, stating, “Model the use of a sentence frame: ____ dots is greater than/less than ____ dots.” This language support helps MLLs look for and explain the structure within mathematical representations.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, as many sessions and Number Corners do not have specific language supports on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP7. MLLs engage in tasks with opportunities to look for and make use of structure, but the materials provide limited or no scaffolds to help students articulate generalizations, justify reasoning, or describe patterns precisely. These missed opportunities prevent MLLs from fully developing the habits of identifying and explaining structure as expected in MP7.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP8: Look for and express regularity in repeated reasoning. The materials provide supports for MLLs engaging in MP8 primarily through notes titled, MLL, but those notes are inconsistently applied throughout the program.

Throughout Grades K-2, the materials provide opportunities for students to use and develop language when looking for and expressing regularity in repeated reasoning through Work Place math stations that include partner games and the Number Corners bulletin display that incorporates whole group discussion. Language supports are inconsistently applied for MLLs to engage in MP8 in Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in participating in Kindergarten, Unit 3, Bikes & Bugs: Double, Add & Subtract, Module 2, Session 3. In Problems & Investigations, students use number racks to model the growing groups and recognize patterns in the addition of one bead at a time. The materials direct the teacher to record equations for each added bead, facilitating a class discussion using the prompts, “What do you notice? What do you wonder?” Through this class discussion students recognize repeated structure, which helps them generalize the idea of adding 1 and lays the groundwork for understanding number patterns. While MLLs may have deep understanding of concepts being presented through the demonstration, the materials lack language support for MLLs to make generalizations focused on the repeated patterns, and to participate fully in the class discussion. 

• In contrast, MLLs are supported in Grade 1, Unit 5, Figure the Facts with Penguins, Module 1, Session 2.  Problems & Investigations introduces Work Place game 5A Spin to Win Bingo, which invites students to make sense of problems, recognize patterns, and develop efficient, mathematically sound strategies through repeatedly adding 9 and 10 to a randomly generated number. The introduction to the game in the session facilitation states, “Explain your strategies on your turn, and invite students to do the same.” In the Work Place guide, a note titled, Multilingual Learners provides language support for MLLs to explain their strategies, stating, “Write the following on the board: addend, spun, strategy, made a 10, pretended the 9 was a 10. Encourage students to explain how they found the sum using these words and phrases. Suggest partnerships that allow students to play in the language they are most comfortable speaking or that provide support in mathematical discourse, interaction, language development, or understanding the game’s rules.” These language supports encourage MLLs to develop language around explaining their multimodal engagement with generalizing through pattern recognition. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program.   Many sessions and Number Corners do not have specific language support or have limited guidance on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP8. MLLs engage in tasks with opportunities to look for and express regularity in repeated reasoning, but the scaffolds provided are limited or absent, leaving students without consistent support to notice repeated calculations, make generalizations to create or explain an algorithm, and evaluate the reasonableness of answers. These missed opportunities prevent MLLs from fully developing the habits of generalization as expected in MP8.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations of intentionally developing language in ways valued by disciplinary practices over time, across lessons, units, and throughout the course. 

The first page of the introduction to each grade level outlines the guiding principles of The Math Learning Center, including the interdependence of content and language, stating, “Bridges teachers… promote discourse, draw out student thinking, and embed assessment in their instruction through deliberate noticing and purposeful questioning.” The materials show partial evidence of supporting students with this interdependence and intentional development of disciplinary language. 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 content rather than explicitly advancing disciplinary language development over time, as noted in the reports for 2a.MLL-2c.MLL. The materials lack a longitudinal plan for developing language as a disciplinary practice beyond moments embedded within mathematical content. As noted in the report for 2j.MLL, the materials partially meet the expectations for supporting precision of mathematical language over time.

For example, the Overview for Grade 2, Unit 5, Place Value to 1,000, Module 3 outlines the mathematical content of the module, highlighting the following language functions of the module: build, describe, compare, and order. It states, “This module helps students develop an understanding of place value with 3-digit numbers. As students build, describe, compare, and order numbers, they make connections among money value pieces, base ten number pieces, standard form, and expanded form. They also use number paths and number lines as visual models to support skip-counting patterns.” The Summary of each Session in the Module lists vocabulary of the session, including terms like decimal point, expanded form, ones, tens, and hundreds. Throughout the module, there are periodic language supports for the mathematical vocabulary, but inconsistent language supports for the language functions listed in the Overview. 

Specifically, in Session 1, Problems & Investigations, students work as a class to first estimate, and then reason about the number of pennies in a large jar. Students compare their first estimates with the actual number of pennies it takes to fill half the jar using the Instructional Routine Think-Pair-Share. The materials state, “Ask students to think-pair-share new estimates and explain their thinking.” While students are invited to use everyday language during this opening activity, there are no additional language supports suggested to support MLLs with using comparative language and explaining their thinking within the Think-Pair-Share. As the Session progresses, students continue to describe and compare numbers shown in various representations. There are no language supports suggested to support MLLs with bridging from everyday language to using more mathematically precise vocabulary related to place value, such as ones, tens, or hundreds. As the Session concludes, students move to Work Places where they have the option to engage in partner games using vocabulary related to comparing numbers shown in various representations. The Work Place Guides contain language supports in notes titled Multilingual learners. Specifically, in one of the Work Places for this Module, 5A Close to 25 Cents, the Multilingual learners note contains three suggestions for language support. One of them states, “To help students recall coin names and values, post a penny piece, a nickel piece, and a dime piece where they can easily be seen. Label the pieces with the names and values of the coins.” This note that supports MLLs’ use of specific mathematical vocabulary is present in the Work Place Guide; no language supports for mathematical vocabulary are present within the Session itself, disciplinary language development is inconsistent within the Session.

As the Sessions in Module 3 progress, the materials contain similar patterns of inconsistent disciplinary language development. The summary for Session 2 states, “The session opens with students visualizing what 1,000 might look like and then working in small groups to represent the number 1,000 using base ten number pieces. Other activities in this session include ordering 3-digit numbers, finding 10 more or 10 less than a number, and finding 100 more or 100 less than a number.” Students continue to compare and describe numbers in Session 2, using mathematical vocabulary related to place value, such as expanded form, ones, tens, hundreds, and thousands. The Problems & Investigations section of the Session does not contain any Instructional Routines or notes titled Multilingual learners, and the Work Places contain language supports as described in Session 1. 

Continuing on to Session 3, Problems & Investigations directs the teacher to engage the whole class in a multimodal learning activity where students work in groups to make a line of tens place value blocks to represent the number 1,000. Students then work to place specific numbers on the number path, comparing and describing numbers using mathematical vocabulary related to place value. Similar to Session 2, the Problems & Investigations section of this Session does not contain language supports for mathematical vocabulary or for the functional language of building, describing, or comparing. 

Overall, the materials provide some, but not consistent, support for the ongoing use and development of disciplinary language across Sessions and Modules. Support for functional language development and mathematical vocabulary development lacks a clear progression. While Sessions encourage the use of everyday language, they do not offer explicit guidance for teachers to bridge from everyday language to more mathematically precise vocabulary.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations that materials provide explanations of the instructional approaches of the program for MLLs and the identification of research-based strategies. The materials explain the instructional approaches of the program for MLLs through general recommendations. The materials provide a cited list of literature and research that influenced the design of Bridges in Mathematics but do not include explanations of how the literature base is used in the instructional approaches of the program for MLLs.

The Introduction to each grade level provides an explanation of the instructional approaches of the program for MLLs. Before listing general recommendations, the materials state, “Bridges Teachers Guides include specific support suggestions to assist teachers with providing access and opportunity for all students, including multilingual learners (MLLs).” The materials then list the following recommendations:

• “Flexibly pair multilingual learners with peers who demonstrate a range of language skills to allow flexible use of language and to support sensemaking. While MLLs should sometimes be paired with other MLLs, it is not appropriate to always pair MLLs together.

• Allow students to work and collaborate in the language they are most comfortable speaking. Provide support in understanding the content, participating in mathematical discourse, and interacting with peers.

• Give students multiple opportunities to share their ideas in different ways, including orally, in writing, and through gestures, drawings, and the use of models. Provide time for students to rehearse an explanation first with the teacher, a partner, or small group before sharing out. When students present orally, allow them to use visual representations to accompany and explain their work.

• Ask clarifying questions to probe student ideas. Productive questions include:

  • ‘How did you find ______? Can you show me how you found ________?’

  • ‘How did you use this tool to _________? Can you show me?’

  • 'What did you do first? What did you do next?’

  • ‘I see you drew/wrote _____________. Can you tell me about that part?’

• Provide sentence frames to support students in expressing ideas during Work Places and other instructional activities. Consider writing sentence frames on the board or posting them somewhere visible to students during math forums (grades 3–5), strategy shares, and whole-class math games to support language and facilitate the sharing of ideas.

• Use the Word Resource Cards or Math Vocabulary app to provide visual support for vocabulary development. Show students the Word Resource Card and provide opportunities for them to discuss and share their prior knowledge related to the word or phrase. Unpack the vocabulary in the session using visuals and examples to clarify meaning for students. Ask students, ‘Can you restate that using (insert specific vocabulary word)?’ to support the use of the vocabulary used in the session.

• Pair visual supports and gestures with language whenever possible. Visuals and gestures not only support MLLs but all learners with varying language needs. Visuals help to clarify students’ understanding of the content as well as shared directions.”

The above recommendations frame the material’s MLL approach, which aligns broadly with best practices for language development. However, the recommendations are framed generically for “…all students, including MLLs…” which does not outline the explicit purpose of ensuring MLLs are able to meet the standards by using language to perform disciplinary practices. Furthermore, while the recommendations reflect widely accepted practices, there are no direct citations between these recommendations and specific research-based frameworks or findings. 

The Bridges Educator Site includes a document entitled Literature Base for Bridges in Mathematics Third Edition (extended), which lists citations of “influential works in mathematics education.” This introduction to this document states, “… these works influenced the design of Bridges in Mathematics Third Edition.” This document references several established sources in language development for MLLs, including:Bresser et al. (2009), Chval et al. (2021), Hill & Flynn (2006), and the Multilingual Learning Toolkit developed by the American Institute for Research.While the materials identify their literature base of influential works, this document does not reference these citations in the instructional approach for MLLs located in the Introduction to each grade level. The materials do not indicate how the strategies from these sources were selected, adapted, or systematically embedded throughout the curriculum for the explicit purpose of ensuring MLLs are able to meet the standards by using language to do disciplinary practices.

The instructional materials reviewed for Grade K-2 of Bridges in Mathematics partially meet expectations for providing guidance to encourage teachers to draw upon student home language to facilitate learning. The materials offer Spanish translated resources, but they lack specific teacher-facing guidance on how to integrate MLLs’ home languages into daily classroom instruction. The materials partially provide guidance to teachers on how to draw upon MLLs’ home language as a resource for learning, but this guidance is inconsistent and lacks specificity connected to MLLs learning grade-level mathematics content.

The materials present multilingualism as an asset in learning grade-level mathematics. The Guiding Principles section of the Introduction to each grade level states, “Bridges teachers… both in and out of the classroom, honor and build upon students’ cultural resources, knowledge bases, languages, and prior experiences with mathematics.” The Language Support section of the Introduction to each grade level lists general recommendations for language supports for MLLs, including, “Allow students to work and collaborate in the language they are most comfortable speaking. Provide support in understanding the content, participating in mathematical discourse, and interacting with peers.” While the materials present multilingualism as an asset, the recommendations to leverage home language usage are not comprehensive, because they do not include specific teacher guidance on using home language to support MLLs in learning grade-level mathematics content.

Similar evidence is found periodically at point-of-use within sessions and Work Place Guides. For example, in Grade 1, Unit 2, Module 1, Session 2, the Work Place Guide for Domino Top Draw provides the following teacher guidance: “Suggest partnerships that allow students to play in the language they are most comfortable speaking or that provide support in mathematical discourse, interaction, language development, or understanding the game’s rules.” This teacher guidance is found infrequently within sessions and Work Place Guides and is not consistently focused on supporting MLLs in learning grade-level mathematics content.

Additionally, the materials do not include guidance on how to garner information that will aid in learning, including the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic or everyday English.