Language Objectives Just Appeared in My Math Textbook. Now What?

December 2024

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What Are Language Objectives?

While content objectives explain what students will learn in a lesson, language objectives clarify how they will reach that goal. They create a language-rich environment to help all learners acquire and use language to communicate mathematical concepts and other ideas. 

Consider the following examples:

Note how the language objective identifies how students will use language to make sense of content and/or what language they will need to show understanding of the content. They pinpoint opportunities for language in action within each lesson. In a math classroom, language objectives can help students learn and use the language they need to participate in discussions, solve problems, and explain their reasoning. 

CPM language objectives are specific and measurable, connecting language skills with content objectives. They are often structured using Jose Medina’s 4+1 model, incorporating a domain, a verb focused on either how to say something (a form) or the reason for saying something (a function), connections to the content, a specified interaction, and sometimes a meta-linguistic connection tailored to the specific classrooms’ needs. That is a lot! Let’s step back. 

Why Are Language Objectives Important in Math Class?

Language objectives play a crucial role in supporting learners in accessing and understanding mathematical content. 

Language objectives help all learners, not just those who do not speak the same language as the teacher or those struggling with academic English, by clarifying how language is used in math. They clearly explain to students what they are supposed to do with math content and how to access it. They support learners, including multilingual learners, by valuing the variety of languages spoken in the classroom and amplifying the variety of ways students might express and connect ideas. 

Language objectives are important for several reasons: 

  • Language objectives make learning more equitable and inclusive. They acknowledge and value the different languages students draw from and create opportunities for them to use their full linguistic repertoires. Some have argued that language and cultural objectives are THE most important tools in culturally responsive pedagogy because so many students benefit from them. 
  • Language objectives help students understand content more deeply. By focusing on a lesson’s specific language demands, they bridge the gap between content knowledge and language proficiency. 

Language objectives are particularly important in math instruction for several reasons: 

Language objectives promote explicit instruction on the language students need to access and succeed in mathematics. 

  • Clarity: Language objectives help clarify what language students are expected to use in the lesson, making learning expectations clear for both students and teachers. 
  • Support: Language objectives help teachers identify potential language barriers and resources and plan appropriate touchpoints and supports, such as visuals, sentence frames, graphic organizers, translation tools, and cross-language connections. This can enable learners to access the content and participate more fully in the lesson. 
  • Academic Language Development: Language objectives provide opportunities for students to practice and develop the language skills they need for long-term success in math. This includes vocabulary, language functions, and language skills. 
  • Assessment: Language objectives can help teachers assess students’ understanding of the content and their language proficiency. This information can inform future instruction. 

Mathematics is, and ought to be, accessible to people in all languages. Norwegians do not outscore Americans on international assessments because they have superior English skills, and Euclid had no mastery over the difference between “you’re” and “your,” no opinion about the pronunciation of “ask” as /ask/ or /aks/. Language objectives help students identify the language tools they need to engage with and communicate mathematical ideas, regardless of who they are working with. Students can successfully master language objectives by drawing on a variety of linguistic resources. But every time a student hears that they said something wrong, their willingness to contribute gets squashed, so note that language objectives do not demand students say anything “the one true way.” 

How Can Teachers Use Language Objectives in Math?

Inspiring Connections and Core Connections 3rd Edition courses now include student-facing language objectives at the top of each lesson. Here are some ways teachers can use language objectives to improve math instruction: 

  • Identify Language Demands: When planning a lesson, carefully consider what language students might use and what gaps they might have that could interfere with the tasks and content objective. 
  • Incorporate Language Supports: Plan for and provide language supports that help students meet the language objectives. This might include visuals, sentence frames, graphic organizers, STTSs, language routines, prompts in multiple languages, translation technology, strategic partnerships, and pre-planned cross-linguistic connections. 
  • Amplify, Don’t Simplify: Try to identify opportunities to amplify, rather than simplify, the languaging students need to meet the objective. Cognates and homonyms are great places to start! 
  • Present Objectives to Students: Language objectives should be shared with students at the beginning of the lesson and reviewed at the end. This helps students understand the purpose of the lesson and track their progress. It also helps them see their contributions to the mathematical community beyond “answer-getting.”
  • Assess Student Progress: Teachers should assess students’ progress toward meeting the language objectives. This can be done through observation, student work, interaction, or formal assessments. 

Let’s consider a hypothetical example, such as, “Speak: I can explain the steps to solving an equation with teammates.” What language demands come with this goal? What language might you need?

Students will need to explain their thinking. How might students do that? They might show their steps with algebra tiles, double-number lines, tape diagrams, etc, so provide visuals to represent the steps in solving equations. They will definitely need to “say their becauses,” so remind them that explaining means saying why something works rather than just showing that it does. 

Students might need precise mathematical terms such as “variable,” “equation,” and “solution” to clearly communicate their ideas. A multilingual word bank might be helpful.

Students will need to clarify meaning with teammates. I recently observed a class working on a task from Inspiring Connections 3. Students had a list of criteria and were asked to write equations to match the criteria. The conversations students had were golden: Does an “equation” have to have an x in it? Is the “solution” the number that goes in for x or the number on the right side of the equal sign? Does 2(x + 1) = 12 get solved in two “steps” or three? Encourage these discussions and have students share their key points with neighboring teams or the whole class as you wrap up the lesson. By digging deeper into their language, students develop deeper content knowledge. This effect is compounded (not divided!) when the class can pull from multiple languages, so amplify what you hear from multilingual learners, too!

You will need to describe steps in sequence, so you might provide sentence frames such as: 

  • First, I noticed _____, so I _____. 
  • Then I _____ because _____. 
  • Finally, I _____ because _____.

By planning for language objectives, teachers can make math content more accessible to all students, particularly students still acquiring the language of access. Let us know how you are using them! 

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
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  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.