Reflection 4: Textbooks v. Literally (ha!) Anything Else

The Daniels and Zemelman chapters this week were all about putting textbooks in their place. And you know what? I agree. Textbooks are fantastic reference books when you need some quick, basic facts or a general knowledge of a topic; but they're hardly engaging, deep explorations of important ideas. For me, the math book is where I send my students if they ask for a step-by-step algorithmic solution for a problem type or for extra practice problems to drill and kill. It's not what I'm going to use for primary instruction, especially in light of the graphic layout of our current Geometry textbook. "Browser windows" clog up the page and cutesy CGI people pop out of nowhere; it's difficult to establish a flow for reading. Speaking of flow, all the talk of 'narrative' nonfiction made me think of my History of Math textbook; there were some sections written in that style, and I might find them useful in my Geometry courses to give some history and reason to geometric theorems as constructions (as opposed to a rule to be memorized). I also had an interesting discussion after I read these chapters about how these textbook failings don't seem to apply to college texts nearly as often. Why? Because college texts (outside of gen ed courses, usually) are generally written by an expert with a focus in that particular field, and address only that specific topic rather than trying to explain a whole brand of study at once. These texts are written by people who 'discover' the knowledge, not middlemen in the exchange of information.

Reflection 3: Reading Strategies and Textbooks, Oh My!

Chapter 5 of Daniels and Zemelman was chock full o' reading strategies. I myself really liked the fact that the strategies were grouped by time of deployment; not all struggling or reluctant readers have difficulty during the same part of the reading process. I know I could definitely use some of the 'before reading' strategies with my geometry class -- the students can read the passages competently and tell me what was in them, if they bother to read the passages. But they have no motivation to do so from the outset,and thus don't read; or, when they do, we haven't discussed any prior knowledge to which students can connect this new information. It seems like the students view texts in that course as disconnected and dull. I can pick and choose strategies according to the needs of my students. Chapter 6 talks about the dreaded textbook and how we as educators can compensate for its shortcomings. One of the strategies discussed is that of essentially writing your own textbook for your course. I've had some professors who've done this, with varying degrees of success. I know my mentor teacher is doing a version of this right now, also with mixed results. While it's good to pare down and dig deeper into more essential topics of a subject, you're relying on the judgement of one individual to make the distinction between these topics and those that are superfluous. Also, this instructor may not be a stellar instructional writer, or more likely, a great layout designer. My mentor is using bits and pieces of other texts to build his own Frankentext with which to teach; and while we cover everything we need to, the formatting is often wacky and it's difficult to determine which ideas are the most important. In short, we lack text features!

Web Source Review 1: TI-nspire CAS

TI-nspire CAS is an app that mirrors the functionality of the new TI-nspire calculators. It is available at in the iTunes store for a hefty $29.99, though your school can negotiate a license so the app is free of charge to students and faculty. (Tough luck, Android crowd; but as Apple has cornered the education tech market at the moment...) The nspire app lets you do calculations on a 'scratchpad' screen, much like you would on a traditional TI-89 calculator. It's capable of detailed color graphs for functions, making spreadsheets and lists for statistical analysis, and constructing interactive geometric figures. It uses a file structure similar to that of a computer, so one can create a file with section 1 problems in it, and then a separate document for each problem that contains a calculation scratchpad, function graphs, statistical analysis, etc. to encompass all the various representations of that problem. These files can be saved, so navigating between problems doesn't mean you have to lose all your work. The app is, honestly, notoriously difficult to use at first, but with practice, it has incredible utility for fluidly navigating different representations of problems, which is something I know my students need to see and practice more often. As well, the TI website has interactive lessons and simulations that you can download. Students can do things like drag to alter a function and see how it changes the equation in real time.

Reflection 2: Content Specific Reading Skills and Text Sets

This week's readings in Tovani had us consider how exactly literacy is used in content areas besides English, and what skills are relevant in different content areas. Reading a math text is different than reading a short story is different than reading an article from a science journal, and all require specific literacy skills to be read meaningfully. The book talks at length about how we as teachers are expert readers in our content areas and fluidly and automatically use our content-specific skills to make sense of a text -- but our students are not (yet) expert readers in this area. They don't know to employ these skills that we use without recognizing it. It is crucial that we, as good readers of content-area text, slow down our thinking and strategy use so that students can see how good readers handle particular types of text. I can think of two ways this is particularly relevant to math: first, math has its own terse variety of English; second, math textbooks often have a particular structure that is sometimes difficult for students to follow. Math uses English in a very compact way, where modifiers drastically change the meaning of a noun, but yet no redundancies are built in. (Consider the example "If A and B are finite sets, |A| is greater than or equal to |B|, and f is a function f:A->B, then the function f is surjective," and "If A and B are finite sets, |A| is greater than or equal to |B|, and f is a function f:A->B, then there exists a surjective function f." The first is false, the second true; and the the key difference is "the" or "a" -- the definite versus indefinite articles.) Modeling precise reading and interpretation of mathematical properties is a crucial aspect of my pedagogy because it is not a skill present in other disciplines. I would have to explicitly discuss the meanings of 'the' and 'a' in a literary sense in the previous example, and talk about the mathematical implications thereof. Math also requires a particular heuristic for problem solving. I had a discussion recently with some other teachers in my school's math department about how much I hated KWL charts (sorry Sterg), which sparked a conversation about using them in other subject areas or as framework for a lesson. As it turns out, we found a modified KWL chart online that is perfect for scaffolding word problems for students. (I'm sure I'm not the only one who's seen the panic-give up response to word problems in students.) The structure aspect of math texts is particularly interesting for me at this moment because in one of the classes I'm co-teaching, we use presentations made from various book and website clippings for direct instruction. Students are allowed to use these presentations as resources on their mini-quizzes, but I've had several quizzes turned in blank because students can't seem to find the relevant material in their presentation notes. Now that I've considered how important structure (even just on a graphic/layout level) is to the understanding of a mathematical text, this may be attributable to inconsistent structures among our sources and a lack of strategies in my students for recognizing different structures in math text.

Reflection 1: The 30 Million Word Gap, SREs, and the Value of Culture

The Hart and Risley article in essence says that children in higher SES environments have experience with around 30 million more words than students from families on welfare by age 4. This gap in experience continues to widen as children age, and is predictive of the achievement of students. To me, its worth noting the constraints of the study; as it was a longitudinal study, they needed families that had long-term residence in the area and families that did not mind having researchers come in to observe household interactions every month. This automatically excludes transient families and families where various illegal activities may be taking place (who clearly won’t want to be observed) -- families who arguably offer less support for exploratory and linguistic experiences for their children. This means that the gap may be larger than that found in the Hart and Risley study, and that the ratio of positive to negative comments made to children may also be skewed. The Fitzgerald and Graves article explains how scaffolded reading experiences can help, in particular, English language learners and how some of these experiences can be implemented. The goal here is that English language learners don't have to sacrifice content-area learning in exchange for reading skills, nor are they sacrificing learning English skills for content mastery in their native language. The article also talks about how language is a medium for cultural understanding; that learning a new language and syntax means also learning a new cultural outlook. In a twisted sense, one could almost look at families in poverty having their own distinctive culture and language, as evidenced by the Hart and Risley study; and thus we come perilously close to a discussion about the relative worth of cultures in these two articles. I think it would also be interesting to see if the type of gap seen here would be found again in a sister study of children in Mexico, France, China -- anywhere else with a public school system.