While at the TESOL convention last week, I learned of a well-attended presentation titled “Taking on Mathematics: How the CCSS can work for ELLs.” The interactive, manipulative-based workshop focused on engaging ELLs in mathematics while highlighting key areas of the Common Core standards. The presenters were Anita Bright from Portland State University as well as Angela Vargas and Dulce Nash, two Dual Language Elementary Teachers who work with Dr. Bright.
The presenters explored the language of mathematics and practiced making mathematics content visible and concrete. When thinking about how popular this session was, I decided to turn my attention to focus on teaching the CCSS for Mathematics to ELLs.
In this post, I’ll describe the shifts of the CCSS for Mathematics, share Dr. Bright’s analysis of what the new standards will mean for ELLs, provide Dr. Judit Moschkovich’s recommendations for connecting mathematical content to language, and share some resources on the CCSS for Mathematics. This post will be the first part of two blogs on teaching the CCSS for Mathematics to ELLs. Next week I’ll highlight two new books that focus on the academic language of mathematics for ELLs.
Shifts of the CCSS for Mathematics
While I could probably describe the three shifts of the English Language Arts CCSS in my sleep, I am admittedly not as well-versed in the shifts of the Mathematics CCSS. According to Achieve the Core, the three the shifts of the CCSS for Mathematics are:
1. Focus strongly where the Standards focus
Implication: The mathematics standards place more emphasis on depth instead of breadth, focusing deeply on the major work of each grade. In this way, students can gain strong foundations, conceptual understanding, procedural skill and fluency and be able to apply the math they know to solve problems in the math classroom and beyond.
The priorities in support of conceptual understanding and fluency in Grades K-8 are:
K–2: Addition and subtraction concepts, skills, and problem solving
3–5: Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6: Ratios and proportional relationships; early expressions and equations
7: Ratios and proportional relationships; arithmetic of rational numbers
8: Linear algebra
In high school, the content of the standards is organized by domains such as Algebra and Geometry that progress over grades.
2. Coherence: Think across grades, and link to major topics within grades
Implication: The standards are designed so that teachers connect learning across grades and students will build new understanding onto mathematical foundations they build over the years. Additional or supporting topics actually serve to strengthen the grade level focus.
3. Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.
Implication: The standards call for conceptual understanding of key concepts such as place value and ratios. To that end, teachers must support students’ ability to access these concepts from multiple perspectives with the end goal being that students see math as more than a set of discrete procedures. In addition, the standards require speed and accuracy when performing calculations. Finally, students will need to use math flexibly for applications. Teachers will need to provide opportunities for students to apply math in context. In particular, teachers who work with students in content areas outside of math (such as science) must ensure that students use math to access their content.
What the CCSS for Mathematics Mean for ELLs
Dr. Bright eloquently describes how the new standards will impact ELLs below. She writes:
In the past, much of our work as mathematics educators of English learners has focused on supporting our students in decoding the information presented in mathematical contexts—like word problems. The need for this is not going away, but rather, is being augmented by the new verbs included in the CCSS. With the advent of the CCSS and the central positioning of the Standards for Mathematical Practice, asking students to learn how to select the right answer is no longer enough. The verbs in the CCSS push us to prepare students to “make sense of”; to reason; to construct; to model. These are no longer icing-on-the-cake or special skills reserved for the gifted or most fleet; rather, these are obligatory actions we need to prepare all of our students to undertake, including those learning English. At root, the primary shift with the CCSS in mathematics is the new and unflinching emphasis on answering the question, “Why?”
So what’s new and different about the CCSS in mathematics is that in addition to this same urgency in learning to decode the often convoluted language of mathematics, our students are now increasingly being asked to encode in very specific ways – that is, to explain, justify and defend their thinking using mathematically accurate language. Emphases are being gradually shifted away from multiple-choice assessments to evaluate student learning, and are moving instead to performance-based assessments that require students to use illustrations, numbers and words to articulate their thinking. Equipping our students to confidently engage in this will require us to think creatively about how best to scaffold and support their learning. We’ll need to provide multiple opportunities for them to examine strong models, make multiple attempts, and engage in self-evaluation.
Although we may flinch at the added layers of complexity this adds to our work as mathematics educators of English learners, it’s important that we realize that the CCSS reflect the shifts in our world at large, and emphasize the growing need to communicate with clarity and specificity. Supporting our students in meeting these standards will, at root, serve them very, very well as they move beyond our K-12 settings and into their lives beyond school. It’s not that our English learners “have to” meet these new standards; rather, they GET to meet them.
Recommendations for Connecting Mathematical Content to Language
In keeping with the changes Dr. Bright described, Dr. Judit Moschkovich, Professor of Mathematics Education in the Education Department at the University of California, Santa Cruz, and contributor to Stanford University’s Understanding Language project, outlines five recommendations for teachers to connect mathematical content to language:
- Focus on students’ mathematical reasoning, not accuracy in using language.
- Shift to a focus on mathematical discourse practices, move away from simplified views of language.
- Recognize and support students to engage with the complexity of language in math classrooms.
- Treat everyday language and experiences as resources, not as obstacles.
- Uncover the mathematics in what students say and do.
Resources on Teaching Math to ELLs
Several resources have been created to help teachers effectively teach the CCSS for Mathematics, and many focus on special considerations for teaching the standards to ELLs. I will highlight some selected resources below.
- Common Core FlipBooks: The Kansas Association of Teachers of Mathematics has Common Core “FlipBooks” that contain a compilation of research, “unpacked” standards from many states, instructional strategies and examples for each standard at each grade level. They are designed to show connections to the Standards of Mathematical Practices for the content standards and to share detailed information at each level.
- Mathematics, the Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the Common Core: This paper, written by Judit Moschkovich and commissioned for the Understanding Language project, outlines recommendations for developing mathematics instruction for ELLs that is aligned to the CCSS. You can also access a video by Dr. Moschkovich here.
- Parent Roadmaps to the Common Core Standards – Mathematics: The Council of the Great City Schools’ parent roadmaps in mathematics provide guidance to parents about what their children will be learning and how they can support that learning in grades K-8. Also available in Spanish.
- Sentence frames: Mathematics content sentence frames for grades K-5 can be found here.
- Springing to Life – How Greater Educational Equality Could Grow from the Common Core Mathematics Standards: This article written by William Schmidt and Nathan Burroughs appears in the Spring 2013 edition of the American Federation of Teachers’ American Educator magazine. The authors analyze how a state’s math standards shape students’ opportunities for academic achievement and what the CCSS mean for student equity.
- Student rubric: This rubric by Exemplars is written in student-friendly language for students to self-assess or peer-evaluate. Each of the 5 categories on this rubric generally maps onto the CCSS Standards for Mathematical Practice.
- Tips for ELL Math Instruction: These articles from Colorín Colorado highlight math strategies for ELLs, as well as additional tips for incorporating academic language and vocabulary instruction into the classroom.
- TODOS: Mathematics for ALL: The mission of TODOS is to advocate for an equitable and high quality mathematics education for all, in particular Hispanic/Latino students. The professional association offers multiple sources of information to its members such as publications, conferences, and networking opportunities.
- TESOL International Association: Dr. Anita Bright has written an article on the Mathematics CCSS in TESOL Connections that can be found here. She will offer an academy titled Implications and Applications of the Common Core State Standards in Mathematics for Effectively Teaching K–12 English Learners in Baltimore, MD in June 2013.
What has your experience been like with the CCSS for Mathematics standards (or your own state’s mathematics standards) so far? Are you seeing them implemented with ELLs in your district yet? What do you think would help your math colleagues in their work with ELLs? We’d love to hear from you!