Chapter 5: "Planning, Teaching, and Assessing CLD Students"
Whether you work in a rural Pennsylvania school or an urban California school, you will more than likely teach culturally and linguistically diverse (CLD) students. CLD students are commonly referred to as English language learners. It is important to remember that some students may move from a differing culture, although they still speak English. For instance, you may have a student move from the United Kingdom. So, I will be referring to nonnative students as culturally and linguistically diverse. If you are teaching CLD students, you may believe that they only need specialized instruction for specific literacy concepts. It is a common misconception that mathematical concepts, and the strategies used to solve them, are universal across cultures. However, this is far from the truth! Conceptual knowledge, such as addition, is universal across cultures. Yet, problem-solving strategies, such as skip-counting, and symbols, such as the dollar sign, are culturally bound (Van de Walle, Karp, Lovin, & Bay-Williams, 2014). It is important that teachers understand these cultural differences, so they can properly support their CLD students’ mathematical success. I have found three instructional methods that are perfect for differentiating problems and scaffolding problem-solving strategies.
- Limit the Linguistic Load: Oftentimes, CLD students have the ability to solve the mathematical component of a problem, but the wording of it confuses them. Their ability to successfully solve the problem is impeded, because they are overwhelmed by words they do not understand. If you have students who are simultaneously acquiring English and learning our mathematical system, it is beneficial to limit the linguistic load of problems. To limit the linguistic load, teachers remove all of the unnecessary words and replace the necessary words with words that the CLD students understand. They can simplify sentence structures and shorten the length of problems, as well. This allows the students to correctly comprehend the problem and solely focus on the mathematical component. If they are solely focusing on the mathematical component, teachers can better assess their true understanding of the concept (Van de Walle et al., 2014).
- Honor Use of Native Language: Let your CLD students use their native language! According to Van de Walle et al. (2014), “Valuing students’ native language is one of the ways you value their cultural heritage. In a mathematics classroom, students can communicate in their native language while continuing their English language development” (p. 62). It is possible for CLD students to strengthen their mathematical skills, although they still have limited English proficiency. It is important that their mathematical reasoning is affirmed, despite their inability to fully communicate in English. If they are allowed to communicate with a mixture of their native language and English, they intrinsically feel valued as members of the class. Consequently, they will continue to work hard and contribute to the classroom discussions.
- Create Meaningful Context: Van de Walle et al. (2014) stated, “Both researchers and teachers have found that telling stories about their own lives, or asking students to tell stories, makes the mathematics relevant to students and can raise student achievement” (p. 60). It is important for all students, especially CLD students, that they personally connect to the mathematical concepts. If students understand how the concepts relate to real-world situations, they will be more interested in the learning process. If they are more interested in the learning process, they will put forth more effort and successfully grasp the concepts. Creating instructional methods and practice problems that are rooted in meaningful context is extremely beneficial. However, a context that is meaningful to native students may not be meaningful to nonnative students. That is important to remember. Teachers should integrate different aspects of their students’ native cultures into their instructional methods and practice problems (Van de Walle et al., 2014). For instance, write a word problem that incorporate a few of their native words or tell a mathematical story that takes place in their native country. The possibilities for meaningful context are endless, so be creative!
"5 Strategies for Scaffolding Math Discourse with ELLs"
According to Banse, Palacios, Merritt, and Rimm-Kaufman (2016), “Discourse [student communication of mathematical ideas with peers] can be difficult to implement, especially in classrooms with students who are learning English in addition to mathematics” (p. 101). We want students to communicate their problem-solving strategies with peers, so they strengthen their ability to construct viable arguments and critique other individuals’ reasoning. We want them to practice using mathematical terms, so they are eventually comfortable using them in their everyday vocabularies. For CLD students, concurrently acquiring English and learning how to properly communicate with mathematical terms can be overwhelming. They may know how to solve the problems. They just cannot verbalize the process, during classroom discourse. Luckily, there are specific strategies that teachers can implement to enhance their CLD students’ discourse success! I am going to share two of my favorite strategies with you.
- Model Mathematical Vocabulary: CLD students need explicit instruction of mathematical terms, such as skip-counting and quarter. As I discussed previously, mathematical terms are culturally bound. Students may understand the concept, but not be comfortable using the English word that describes it. However, research suggests that teachers should pair their explicit instruction with personal usage of the terms. Banse et al. (2016) stated, “When students, particularly ELLS, are exposed to mathematical vocabulary use in their teacher’s language use, they may be more likely to include mathematical vocabulary in their own responses as the year progresses” (p. 106). CLD students benefit from hearing their teachers use mathematical terms in a meaningful context. Essentially, they are modeling the proper way to naturally use the terms in collaborative discourse. If CLD students are provided with understandable models, they are more comfortable communicating in similar ways.
- Scaffold Responses with Revoicing: Oftentimes, a CLD student will participate in the classroom discourse. He will sum up the courage to communicate his problem-solving strategy. However, his response may lack precise mathematical terms or confuse the other students. When this situation occurs, it is important that the teacher does not respond with nitpicky criticisms. Instead, she should revoice the response. Banse et al. (2016) stated, “Revoicing offers teachers a method of capitalizing on ELLs’ mathematical contributions and adapting those contributions as necessary, so that the essential idea becomes mathematically accurate and correctly articulated” (p. 105). Teachers can revoice a response by repeating it back to the whole class, which ensures that everybody clearly understands what was explained. They can elaborate the response, which models mathematical thinking and expands the student’s reasoning. Or, they can reformulate, which rephrases the response with the precise mathematical terms (Banse et al., 2016). If a teacher repeats, elaborates, or reformulates, she is still praising the correct parts of a CLD student's response and making him feel proud of his hard work. Yet, she is implicitly strengthening his mathematical reasoning with precise terms. He will feel that his contribution was valued, which will make him more willing to contribute at other times!
Classroom Activity: Differentiated Money Problems
By then end of second-grade, Common Core State Standard (2010) 2.MD.C.8 expects students to solve word problems involving dollar bills, quarters, dimes, nickels, and pennies. They should use the money symbol and cent symbol correctly, as well. In the above video, I explain how to differentiate word problems that involve coin values for culturally and linguistically diverse students. I provide an example of a limited linguistic load and a meaningful context, which allows students to focus on the mathematical component. When CLD students can focus on the mathematical component, they are more likely to successfully solve the problem.
Independent Practice: Skip Counting
According to the Common Core State Standard (2010) 2.NBT.A.2, by the end of second-grade, students should count within 1,000 and skip-count by 5s, 10s, and 100s. Your CLD students may need extra support with this counting strategy, because it is culturally bound. Some of your students may have transferred from a school that never explicitly taught skip-counting, so they struggle to correctly apply it. This online game is the perfect independent practice to strengthen your CLD students' skip-counting skills! As shown in the picture above, the game has a limited linguistic load. It has short, specific directions and questions. Additionally, each problem is accompanied by graphics of everyday objects, which CLD students will be able to recognize. They can count each individual object, until they feel comfortable mentally skip-counting. If they answer correctly, the game instantaneously praises the students. However, if they answer incorrectly, they are provided with instantaneous written and visual explanations. Click on "Independent Practice" to access this awesome resource!