The End is Here :)

I've come to the end of my Literacy book - what I thought would be a fast read (< 100 pages) has taken me a week to read. Of course, taking the time to annotate the book (my AVID buddies would be SO proud of me), blogging about what I've earned, and of course spending LOTS of time on twitter learning about a multitude of things have slowed me down a bit. And while I can easily burn through a lengthy novel in a day or two, professional literature just doesn't flow at that same level :) However, I am eager to move on to my other books (especially those about assessment & Standards Based Grading), so I'm trying to get this one finished up. As such, this post will not be as lengthy as the previous posts (which is probably a good thing!)


Make a Picture! Make a Picture! Make a Picture!
Chapter 4 was about Graphic Representations in the math classroom. While this chapter was an enjoyable read, with several vignettes, I really didn't learn much. Of course, I am a VERY visual learner, so maybe I already knew this chapter's information from experience.

The main theme of this chapter was that student drawings allowed us to catch a glimpse of student thinking processes, which can be extremely helpful for students who cannot fully explain verbally where their confusion lies. Through the power of a diagram, teachers may find that what makes sense to our more mature thought processes does not make sense to our students based on their prior knowledge. One example in this chapter was about quadrupling a recipe that called for 1 1/4 cups of flour. Without prior knowledge of how "cups" relate, the student answered that they needed 8 total cups of flour in the new recipe - 4 big ones and 4 small ones. I'm not much of a cook, and as a kid, I rarely spent time watching my parents cook, so I could have easily had this same misconception when I was younger. As teachers, we have to be careful that we don't assume that students have prior knowledge about everyday things and having the students draw a picture can help us pinpoint these problems.

As math teachers, we often tell our students (particulary with a "word problem") to draw a picture. Using graphics helps with teacher assessment, but more importantly it allows students to make connections between the words and the concepts. For visual and hands-on learners, making a picture may be vital to the learning process because it forces them to slow down and process. For me personally, I am not auditory at all - I struggle in traditional classrooms, in meetings, listening to NPR, because I have to focus so much on what is being said that I can't keep up. :)

Talk it up!
The last literacy strategy of the book is discourse, which is what Chapter 5 is devoted to. This strategy comes easier to me in Stats than in Algebra, mainly due to the nature of the course. Even so, I still came away with some useful jewels of knowledge.

One of the first statements in this chapter says that "discussion and argumentation improve conceptual understanding." Personally, that statement shows itself to me all of the time via my twitter PLN. For example, this morning, I tweeted a question about standards based grading, which lead to a lengthy conversation with several colleagues, a few new blogs to read, and in the end, way more questions than I had started with. This discourse with my peers truly improved my understanding of SBG and allowed me to put the puzzle pieces together in my head of how to implement SBG in the classroom. The free-flowing idea stream that came out of today's discussion was simply amazing, although in the classroom, I could definitely see where this "non-controlled" environment could stress some teachers out. I had no idea where my question would lead me and in the classroom, that can be a scary thought (especially depending on your clientele!)

I have always tried to keep my classroom open for discussion, often asking students "why" in order to get them to explain their thinking. However, I may change that. One teacher that is used as an example in this book uses the word "More?" as a way to keep kids talking about an idea and appending previous student comments. I like that idea because it opens up the discussion to more than just an explanation - it could be any comment about the idea at hand.

The other big idea that I got from this chapter that will impact my classroom is this: "Rich, deep, and argumentative discussions occur when students display their work and present their strategies". I really need to have students tackling more application-rich problems and presenting their findings to the class. Of course, while I know that I need to do it and I really think I would enjoy doing it, I have no earthy idea of where to start, so obviously some research will be required there. I'll get back to you on that :)

A couple of other tidbits I got from this chapter:
- Don't rush to save kids too quickly. Often they will discover and correct errors on their own as they think and explain their reasoning.
- Have students share their methods, esp non-traditional, as it help everyone grow mathematically (I had this happen this year as a student noticed a pattern w/ perpendicular slopes when the equations were written in standard form - love when kids come up with their own algorithms!)
- Don't have kids just memorize vocabulary - they need to process the concept before the vocab word makes any sense to them
- Graphic organizers are great tools, but in order for students to truly expand learning w/ these tools, they need to discuss and share with others in order to clarify thinking

The big ideas...
Overall, I really enjoyed this book. I came away with a lot of ideas on integrating reading, writing, graphical representations, and discussion in my classroom. I know that not all of those ideas will make it into my classroom this year, but that's part of the purpose of this blog - to act as my "holding place" for my "mindful mediation" :) Having these thoughts written down here will help me throughout the years as I reflect back on previous ideas and things I want to change. Now I get to dig through my treasure trove of books from last week to find my next mind-bending adventure....