# Archive for February, 2020

## ELL’s and Math as a Language

When working with Ell learners, you should always have a content goal and a language goal (Echavarria, Vogt & Short, 2000). You want to always think about the ways in which you are exposing the students to the vocabulary over time.

- Content Goal

The content goal is the math that students are working on. This should be written in an* I can* or *I am learning to* statement on the task.

- Language Goal

When working with ELL’s, (however I would argue that this is a good practice when working with all learners), teachers should have a variety of strategies to make the language accessible to the students. Language frames are part of the tools used to scaffold access to the words and phrases. So, things like “I am proving my thinking by…” should be put on a sentence frame for students to use. Another example is “I have _________ *more than * __________. I have __________ *less than* __________.

The issues of * linguistic complexity *(readability, syntax and complex vocabulary) and word problems have long been studied (Martiniello, 2008). Martiniello looked at how the linguistic complexity interferes with Ell’s comprehension of word problems. The NRC (2000 p.20) points out that “A test [of proficiency in a content area] cannot provide valid information about a student’s knowledge or skills if a language barrier prevents the students from demonstrating what they know and can do” (cited in Martiniello).

Happy Mathing,

Dr. Nicki

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## Word Problems are a Distinct Genre

Several researchers have argued that math texts are a distinct genre and that students have to learn how to unpack that type of genre (Winograd and Higgins 1994/1995; Kang & Pham, 1995; Irujo, 2007). Spanos (1993) discusses how even though they are called “story problems” they lack the traditional storytelling devices. We have to help students to understand the genre. We should teach it, building on what we already know about teaching genres.

Students can get so bogged down in the language of the problem that there is a “suspension of sensemaking (Verschaffel, Greer, & de Corte, 2000)..” Sometimes students are victims of bad word problems that not realistic but “styled representations of hypothetical experiences (Lave, 1992).”

I also think we have to approach word problem presentation in a different way. I am very excited about the possibilities of 3-act tasks, numberless word problems, 3 read problems and picture prompt word problems.

Happy Mathing,

Dr. Nicki

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## Function Matters or Unpacking the skills!

We ask students to do a lot of different things in math, including *reading* the word problem, *writing* the answer, *illustrating* the answer, *showing *their thinking, *using* their math words, *proving *the answer with different strategies, *giving *an explanation and *sharing* their thinking. These all require different types of talking and organizing of thoughts. We have to be very explicit about what we are asking students to do and then teach them how to do these different things.

When of I think of all the types of things we ask students to do, I think about Larry Bell’s 12 power words. See some resources below. We ask our students to do so many things and they are all different. How do you teach your students these interdisciplinary skills in your classroom? Do your students know the difference between compare and contrast? Can they tell you the difference between analyzing the problem and summarizing the problem. I find that many students struggle with this and that we need to take more time to explicitly work with these concepts.

http://www.caywood.org/lms/index.php/homepage/teacher-extensions/104-12-powerful-words

Happy Mathing,

Dr. Nicki

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## Wording Matters

Researchers have resoundingly found that **language matters when it comes to understanding and solving word problems.** *Many researchers have found that rewording the text of word problems so that students understand the problem and that they reflect the problem structure greatly improves problem-solving success* (De Corte, Verschaffel, and De Win (1985) and De Corte and Verschaffel (1987)).

Wording matters. Hudson (1983) posed this problem to some children: “There are 5 birds and 3 worms. How many more birds are there than worms?” Many of the children could not solve the problem. However, when the problem was reworded, “How many birds won’t get a worm?” many of the students could solve the problem.

Riley et al. (1983) says that **rewording helps students to understand the problem and when students understand the problem they can solve it**. Cummins (1991) pointed out that “the data seem to indicate that the knowledge [to solve problems] is there, but is simply is not accessed when problems are worded in certain ways (p. 267).” She argues that **students who fail do so because they are “missing” or “have” inadequate mappings of verbal expressions to part-whole structures**. She maintains that **“rewording enhances performance.”**

Happy Mathing,

Dr. Nicki

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