Week 6: Disciplinary Literacy - Mathematics

Summary

Video:

Students are able to understand the texts in one class, but not another, which is why focusing on disciplinary literacy is so important. Teachers and students have to navigate all the time, so navigating types of texts and navigating among disciplines is crucial to students' functioning and success. There is interaction among disciplines, between students and teachers, between school knowledge and out-of-school knowledge, etc., so navigation is a literacy skill itself. I is important to note that navigating is not just for advanced students; in fact, it creates greater access to educational opportunities for all students, and it may be particularly beneficial to disenfranchised students. Navigating disciplines supports both students' understanding of interdisciplinary thinking and of concepts in each field. Navigating also supports metacognitive awareness, according to the video. This skill relates to literacy because authentic literacy is an active aspect of learning, which navigating supports. Navigating helps students have more agency in their textual exploration of concepts within a discipline. Teachers must teach literacy skills and strategies and field-specific literacy practices before students can understand navigating. Teachers can teach navigating by focusing on these strategies: expose all students to texts, engage students in disciplinary language, elicit domain-specific knowledge and practices, examine specific aspects of the disciplinary language, and evaluate why/when/how those texts and skills are important. One way to scaffold struggling readers while using these strategies is to give those readers smaller texts with similar tasks like questioning, summarizing, and synthesizing. Another important note is that the disciplines are social in terms of making and communicating claims, as well as evaluating those that others have made. Teachers should focus on these areas within an interactive setting, which also helps scaffold students' understanding. This interactive nature should include reading with students, rather than requiring them to think about the text independently and without models.

H & S-T:

One characteristic of mathematical language is that it incorporates symbolic and visual language into the oral and written language to which students are accustomed in other disciplines. Students are also required to have “the ability to identify the technical meanings of everyday terms,” in addition to the technical vocabulary of mathematics (192). One principle for helping students tackle these difficulties is to have them explore new concepts while using their prior knowledge as a reference point. With that principle, teachers should limit their “initial concern for the precision of [students] verbal expression,” so teachers can later model how to use mathematical language to express those concepts, which is the second principle suggested by the chapter (197). The third principle is to give students the opportunity to practice new mathematical vocabulary and linguistic patterns “in conjunction with mathematics language that was already familiar to them” (197-198). Another important principle is to provide students feedback on their verbal and written use of mathematical language in order to hone their precision of language use. The final principle discussed in the chapter asks students to “assume expert identities” and write for an external audience (203).

J & S:

One important thing to remember about literacy support in mathematics is that the ultimate goal is to help students understand mathematics, not just to read well in general. Literacy is important for achieving this goal, but it is also important to note that "the difficulty in reading many mathematics-related texts may not be facility with print, but facility with the underlying mathematical ideas" (175). Some educators do argue, however, that while literacy for literacy's sake is not valuable, increasing text exposure can result in "an increase of their literacy development" and "an increase in their content knowledge," which creates a cyclical relationship between literacy and content knowledge (176). While traditional texts in math classes may have their place, authentic mathematical activities require that "the textbook becomes a secondary source... for mathematical knowledge and understanding" (179). Because of this complicated relationship between traditional texts and mathematical learning, this chapter redefines "text" to "include all objects created or interpreted for the purpose of constructing, sharing, and negotiating meaning"--a perspective that frames the mathematical classroom as a very text-based environment (182). The chapter continued with an approach to designing mathematics instruction with a literacy-based focus. The first suggested step is to "identify the texts that are to be read and written," with the broadened definition of "text" discussed above" (185). Then teachers should identify "the specific ways that texts are to be read and written," since the texts are so varied and multimodal (185). Finally, teachers should plan instruction to make "explicit the texts and literacies" to be used to support students' learning of mathematical processes (186). The chapter concludes with examples of exemplary mathematics instruction and tips for creating collaborations between teachers and literacy coaches, such as learning from the expertise of the teacher and focusing on a shared purpose.

Response

Video:

I find it fascinating that students could understand one subject's texts well while struggling in another area, but I suppose it really does reflect the different literacy skills that each field requires. It does also reflect my experiences in school; I understood English texts the best, and history was also fairly accessible to me, but I often struggled when reading science and mathematics texts.

Navigating in general is a life skill, and I think teaching it in relation to navigating the disciplines might be the key to helping students who struggle. They need to learn explicitly how to navigate the differences among texts, disciplines, and even those among different environments, jobs, etc. Adaptability and flexibility that comes from navigating skills is an important life skill that is applicable in any situation, literary or not.

I think it is definitely important to expose students to all types of texts at all ages, especially if we are not expecting expertise early on. We think of elementary as the stage of "learning to read" and secondary as the stage of "reading to learn," but I think early exposure to a wide variety of disciplinary texts might help bridge that gap more easily as students transition into secondary school.

I really like the section on "talking to the text." I love that it helps students think about the context of the text, as well as the purpose for reading the texts. It's also focusing on how to relate the texts to each other, as well as evaluating the text. I feel like the way this is broken down, it tackles almost the entirety of Bloom's Taxonomy, and I think that approaching close reading that way helps scaffold deep thinking even for students who struggle with reading.

H & S-T:

The second principle discussed in this chapter “involves being able to explain/define [the concept] using mathematics language” (196). I had a great math teacher in high school, but I really wish that he had not only modeled the language for us, but also asked us to use it in our speech and writing. That was something I always struggled with, even though I eventually picked up on the language. I was very good at math, so I think it would definitely help students who struggle with math because of linguistic issues.

I really like the last principle in this chapter. It’s something you would definitely do after having the students work thoroughly with a concept and the related language, and I’ve done something similar that really helped me see how well students understood the language and ideas. I like the idea of doing that as a sort of late-in-the-game formative assessment.

J & S:

I think this chapter makes a good point about the purpose of disciplinary literacy instruction. I think it's very easy to forget that while general literacy strategies are important, the ultimate goal should be "to develop disciplinary expertise" (174). The chapter brought up instances in which teachers incorporate texts into the classroom just for the sake of incorporating "texts," and it detracted from students' understanding of mathematics. I think that's why it's so important to think about what "literacy" and "text" really mean within each discipline.

I reached a point in this chapter where the author was emphasizing the importance of understanding mathematical ideas when reading mathematical texts. I wondered whether having a strong literacy focus in math classes is actually that important, if the lack of text comprehension often results from not understanding the concepts. However, as I kept reading, I do think it is important to support students' literacy with the symbolic aspects of math texts, as well as the expanded definition of "texts" that the chapter provides. Students are regularly creating and interpreting artifacts and communication, and that is something that might require teacher support.

Questions

• If you’re seeing some trends among your students in terms of misuse of technical vocabulary, what’s an activity you could do with them to hone their language use after you’ve given them feedback?
• If you have students produce writing from an “expert identity,” as discussed in H & S-T chapter 11, how would you address a student who is still struggling with concepts and terms even after having worked with them for quite some time? 
• If there is a mathematics class in which the structure of the class usually follows a framework of lecture followed by individual practice (as many math classes do), would you say that there are any texts being read and written in that class, with the broadened sense of the word "text" as discussed in chapter 7? It's just something I'm curious about.
• What's your favorite tool to teach disciplinary language that the video discusses?