Maker Learning Cycles are designed to ...

From Zwiers, J., Dieckmann, J., Rutherford-Quach, S., Daro, V., Skarin, R., Weiss, S., & Malamut, J. (2017). Principles for the Design of Mathematics Curricula:

Promoting Language and Content Development. Retrieved from Stanford University, UL/SCALE 

website: Supporting ELLs in Mathematics | Understanding Language

1. SUPPORT SENSE-MAKING

Scaffold tasks and amplify language so students can make their own meaning.

Students do not need to understand a language completely before they can start making sense of academic content and negotiate meaning in that language. Language learners of all levels can and should engage with grade-level content that is appropriately scaffolded. Students need multiple opportunities to talk about their mathematical thinking, negotiate meaning with others, and collaboratively solve problems with targeted guidance from the teacher (Cazden, 2001; Moschkovich, 2013). In addition, teachers can foster students’ sense-making by amplifying rather than simplifying, or watering down, their own use of disciplinary language.

Teachers should make language more “considerate” to students by amplifying (Walqui & van Lier, 2010) rather than simplifying speech or text. Simplifying includes avoiding the use of challenging texts or speech. Amplifying means anticipating where students might need support in understanding concepts or mathematical terms, and providing multiple ways to access those concepts and terms. For example, organizing information in a clear and coherent way, providing visuals or manipulatives, modeling problem-solving, engaging in think-alouds, creating analogies or context, and layering meaning are all ways to amplify teacher language so that students are supported in taking an active role in their own sense-making of mathematical relationships, processes, concepts and terms.

Several routines can be used to Support Sense-Making. In particular, MLR2 - Collect and Display, MLR6 – Three Reads, and MLR8 – Discussion Supports

2. OPTIMIZE OUTPUT

Strengthen the opportunities and supports for helping students to describe clearly their mathematical thinking to others, orally, visually, and in writing. 

Linguistic output is the language that students use to communicate their ideas to others. Output can come in various forms, such as oral, written, visual, etc. and refers to all forms of student linguistic expressions except those that include significant back-and- forth negotiation of ideas. (That type of conversational language is addressed in the third principle.)

Students need repeated, strategic, iterative and supported opportunities to articulate complex mathematical ideas into words, sentences, and paragraphs (Mondada, 2004). They need spiraled practice in (a) making their ideas stronger with more robust reasoning and examples, and (b) making their ideas clearer with more precise language and visuals. They need to make claims, justify claims with evidence, make conjectures, communicate their reasoning, critique the reasoning of others, and engage in other mathematical practices. Increasing the quality and quantity of opportunities to describe mathematical reasoning also will allow teachers to frequently formatively assess students’ content learning and language use so that teachers can provide feedback and differentiate instruction more effectively.

Several routines can be used to Optimize Output. In particular, MLR1 – Stronger and Clearer, MLR3 – Critique, Correct, and Clarify, MLR4 – Info Gap, MLR5 – Co-craft Questions and Problems, and MLR7 – Compare and Connect.

3. CULTIVATE CONVERSATION

Strengthen the opportunities and supports for constructive mathematical conversations (pairs, groups, and whole class).

Conversations are back-and-forth interactions with multiple turns that build up ideas about math. Conversations act as scaffolds for students developing mathematical language because they provide opportunities to simultaneously make meaning and communicate that meaning (Mercer & Howe, 2012; Zwiers, 2011). They also allow students to hear how other students express their understandings. When students have a reason or purpose to talk and listen to each other, interactive communication is more authentic. For example, when there is an “information gap,” in which students need or want to share their thoughts (which are not the same), students have a reason or purpose in talking and listening to each other.

During effective discussions, students pose and answer questions, clarify what is being asked and what is happening in a problem, build common understandings, and share experiences relevant to the topic. As mentioned in Principle 2, learners must be supported in their use of language, including within conversations, to make claims, justify claims with evidence, make conjectures, communicate reasoning, critique the reasoning of others, and engage in other mathematical practices – and above all, to make mistakes. Meaningful conversations depend on the teacher using lessons and activities as opportunities to build a classroom culture that motivates and values efforts to communicate.

Many routines can be used to Cultivate Conversation. In particular, MLR1 – Stronger and Clearer, MLR3 – Critique, Correct, and Clarify, MLR4 – Info Gap, MLR5 – Co-craft Questions and Problems, MLR7 – Compare and Connect, and MLR8 – Discussion Supports.

4. MAXIMIZE META-AWARENESS

Strengthen the ”meta-” connections and distinctions between mathematical ideas, reasoning, and language.

Language is a tool that not only allows students to communicate their math understanding to others, but also to organize their own experience, ideas, and learning for themselves. Meta-awareness is consciously thinking about one's own thought processes or language use. Meta-awareness develops when students and teachers engage in classroom activities or discussions that bring explicit attention to what students need to do to improve communication and/or reasoning about mathematical concepts. When students are using language in ways that are purposeful and meaningful for themselves, in their efforts to understand – and be understood by – each other, they are motivated to attend to ways in which language can be both clarified and clarifying (Mondada, 2004).

Meta-awareness in students is strengthened when, for example, teachers ask students to explain to each other the strategies they brought to bear to solve a challenging multi-step problem. They might be asked, “How does yesterday’s method connect with the method we are learning today?,” or, “What ideas are still confusing to you?” These questions are metacognitive because they help students to reflect on their own and others’ learning of the content. Students can also reflect on their expanding use of language; for example, by comparing the differences between how an idea is expressed in their native language and in English. Or by comparing the language they used to clarify a particularly challenging mathematics concept with the language used by their peers in a similar situation. This is called metalinguistic because students reflect on English as a language, their own growing use of that language, as well as on particular ways ideas are communicated in mathematics. Students learning English benefit from being aware of how language choices are related to the purpose of the task and the intended audience, especially if an oral or written report is required. Both the metacognitive and the metalinguistic are powerful tools to help students self-regulate their academic learning and language acquisition.