Algebraic Literacy

More than ever, I need the guidance of the Math Twitter Blogosphere. 

Background: I got a fellowship from Heinemann to do some action research on a topic of my choosing over the next two years. I am trying to wrap my head around a big, complicated topic and I’d love anyone’s input. There’s something I want to research, and I don’t know what it’s called, so I’m calling it algebraic literacy.

Here’s what I mean: When we ask students to read a passage in language arts class, we certainly expect them to be able to read each word in a given sentence. But we also expect them to be able to summarize the content of the sentence as a whole. Moreover, we hope that they can mentally break the sentence into its phrases and clauses, knowing which noun is being modified by that adjective, or which clauses are independent or dependent. These skills are a significant part of our students’ growing levels of literacy.

But in math class, we have a less refined understanding of algebraic literacy. Let me give you a context and a matching expression so we have something concrete to discuss:

Ava has a job at a restaurant that pays her a wage of w dollars per hour. One day, Ava's boss informs her that she is getting a $0.50 raise on her wage. That night, Ava works for 7 hours and also earns $43 in tips.

Here’s the expression:

7(w + 0.50) + 43

Kids can read the expression above on a number of levels. At a baseline, one could read the expression phonetically. Lots of my kids can do this. They can say “seven times w plus point five plus forty three.” 

On another level, kids can read it word-by-word and also understand its mathematical structure for purposes of evaluating the expression. Meaning, a student could substitute in a given value for w and evaluate using the correct steps.

On yet another level, kids can read the expression and understand how it represents the context of Ava’s job. On this level, kids could identify that the entire expression represents Ava’s total wages. Beyond that, kids could match specific pieces of the expression with their corresponding parts of the context. For example, if asked “Find the part of the expression that represents Ava’s new wage” students could identify “w + 0.50” as that element.

This is the level of algebraic literacy I want to focus on. Kids have a REALLY hard time generating expressions from a given context, and I think it’s because we focus too much on the phonics of algebra and not enough on comprehension. 

So that’s what I want to study. But I need to answer a lot of questions first. Questions such as:

1) I am calling this “algebraic literacy” but I am sure that other people have researched it and called it by other names. Where is this prior research and what are people calling it?

2) How do kids attain higher levels of literacy in English, and to what extent is that trajectory transferrable to algebraic expressions and equations?

3) What tasks, activities and structures would be most useful for helping me understand my students’ current levels of algebraic literacy? Which structures would most facilitate their growth in this area?

4) There’s another level of literacy that I can’t quite wrap my head around. It’s the literacy around the idea of equivalence. I want kids to know which sorts of algebraic manipulations maintain equivalence and which affect the meaning of the expression or equation being manipulated.

As an analogy, think of the sentence “Tom and Joey gave Denise an apple"

A language arts teacher would want kids to understand that switching Tom and Joey in the sentence preserves the meaning, whereas switching Tom and Denise in the sentence changes something fundamental about the problem.

In the same way, taking the expression 14 - 6 + 5, I want kids to know why we can switch this to 14 + 5 - 6, but not to 6 - 14 + 5


There’s a lot going on in this post. Let me know in the comments - what resources does this make you think of?