The Common Core State Standards (CC) provide guidelines for how to teach mathematics for understanding by focusing on students’ mathematical reasoning and sense making. Here I will only summarize four emphases provided by the CC to describe how mathematics instruction for ELs needs to begin by following CC guidelines and taking these four areas of emphasis seriously.
Emphasis #1 Balancing conceptual understanding and procedural fluency
Instruction should a) balance student activities that address both important conceptual and procedural knowledge related to a mathematical topic and b) connect the two types of knowledge.
Emphasis #2 Maintaining high cognitive demand
Instruction should a) use high-cognitive-demand math tasks and b) maintain the rigor of mathematical tasks throughout lessons and units.
Emphasis #3 Developing beliefs
Instruction should support students in developing beliefs that mathematics is sensible, worthwhile, and doable.
Emphasis #4 Engaging students in mathematical practices
Instruction should provide opportunities for students to engage in eight different mathematical practices: 1) Make sense of problems and persevere in solving them, 2) reason abstractly and quantitatively, 3) construct viable arguments and critique the reasoning of others, 4) model with mathematics, 5) use appropriate tools strategically, 6) attend to precision, 7) look for and make use of structure, and 8) look for and express regularity in repeated reasoning.
Source: Mathematics, the Common Core, and Language by Judit Moschkovich