20150216 3 Structures for Literacy in Mathematics
Literacy is a life skill often relegated to English class. In mathematics, we need to create opportunities for learners to practice and develop their literary skills.
Mathematical texts tend to be very dense. That is, the text is rich in academic language which describes conceptual or procedural knowledge that is difficult for learners to access.
Giving learners the opportunity to access, decode, interpret, and understand mathematical texts prepares them to be self-directed, self-motivated learners. Literacy is difficult to teach, so here are three ways you may incorporate literacy into mathematics.
Number One: Anticipation Guide
The anticipation guide is a way to get learners thinking about their own knowledge and provides access to the text in a non-threatening way. For example, this article from the Mathematics Teacher (Vol 8, No 7) magazine provides an example of the how and why to use an anticipation guide in mathematics instruction.
Personally, I like to have about five questions, which I like to write addressing learners’ misunderstandings. Below is an example of an anticipation guide for an article I wrote for Edutopia:
Notice that some of the statements are untrue and vary in level of difficulty. In a math text, I like to write my anticipation guides where there are misconceptions or surprising ideas that may appear in the text. For example, the California Frameworks (2013) 8th-grade edition on page 382 has the following discussion
One of my T/F statements on the anticipation guide would be 1. Directly proportional quantities give the most difficult approach to understanding slope. 2. The constant of proportionality is also known as the location where the line crosses the y-axis. 3. The connection between direct variation problems and linear equations is linear equations may be translated up/down. 4. Developing your understanding of direct variation problems makes understanding linear equations easier. 5. Linear equations (and direct variation) problems have no connection to the real world.
You may be thinking, “This all sounds good, but where/how do we fit this in too?”
For me, I make space for anticipation guides in three ways in a lesson:
- I use the “Before” column as a warm-up as I go about the business of class setup. Once the warm-up time is done, I give learners the opportunity to read the text and finish the “After” column.
- Next, the students turn and talk with their partners, and then we have a whole class discussion. The discussions provide me with a formative assessment of what students know/don’t know about the topic which I can address in a myriad of ways.
- Later in the unit, students create anticipation guides for the next class, next period, or future students. The student-created anticipations guides are another assessment tool to see what my student authors understood and what they (my student authors) thought was challenging.
*Pro Tip – The anticipation guide is the only one of the three that requires you to do a little work ahead of time.
Number Two: Frayer Model
The Frayer Model is an organizational structure for learners to access academic vocabulary.
While I am a fan of templates, I prefer students to be able to make their own Frayer Models on the fly. Building practice through repetitions with the various templates gives students a common understanding. Here are a few examples:
A Classroom Example
For learners to make their own, they need a blank sheet of paper and then they can fold their paper “hamburger” and “hotdog” style to create four even-sized squares. Students write the word in the middle. They can also turn it over to write another word. This is one of my favorite tools to use in the classroom because of the variable activities that I have my learners interact with text with this. As a classic example, I may pull four academic words from a lesson or unit and give direct instruction on these. Then I give learners the opportunity to create their own assigning pairs for two words and another pair with another two words. Each student is responsible for their word, they create their Frayer model, they share their model with their pod, and they must choose one of the four to be the model of a word they want to present. Then each member of the group will go to other groups with their best representation, they must describe the other representations and then detail why they think this is the best one. That same learner will then hear similar stories three times, and they will return to their original group to share out. The next day there are four posters in my room, each area laminated square meter of instructional gold. Learners will see some partially filled out squares from the day before, as pairs, they have a few minutes to fill out the remaining squares however they see fit and return to their seats (this is the warm-up). Within five minutes they should have 20 answers ready for me, the result of which is like a “quiz.” This same routine is also used with classification schemes and detailing steps to various problem types, and now with multiple representations.
Number Three: SQRQCQ
The learner interacts with a dense text through the strategy sequence SQRQCQ. The sequence is Survey, Question, Read, Question, Compute, Question, where each questioning type adds a different layer of exploration. While I was originally introduced to this wonderful strategy from Teaching Reading in Mathematics (TRIM) (2nd Edition), I have utilized the work of Amy Bernhard and made this template for my students.
SQRQCQ – Math Strategies (weebly.com)
When I employ this strategy, it is usually with a particularly dense and rich text or challenging word problem I want the learners to interact with. My facilitations start with each learner receiving the text in print or digital medium so students can annotate the text. The students are given 1-2 minutes to survey the text and record their thoughts in the corresponding box of the graphic organizer. Students then discuss with their partners and go through the questions in the Question phase.
On the next pass, I give about three minutes to read and encourage learners to annotate the text, write down thoughts, and details, or perform necessary computations. Learners then share what they highlighted, details, or what computations they made with a peer. Pairs share out with the whole class and I record these details like the first pass.
On our final pass, we learners make calculations, incorporate final details, and write a sentence describing why they believe their solution is correct. The process is a dance between student conversations and moving the process going forward. The slow burn mentioned above occurs when we are able to chunk the pieces so we may do the SQ, RQ, and CQ over three different sessions, each about 10-15 minutes long.
The last thing we do is talk about how our thinking changed with each pass, what became clearer, and how our understanding grew with the processing and multiple approaches to the text, all of which is brought out by asking the learners about how our thinking changed over the analysis.
Conclusion
Three structures that provide a natural way to incorporate literacy into your lessons without much additional preparation. Driven by the learners, the interactions and engagement are more meaningful than purely direct instruction. I hope you enjoyed this discussion and you will find some ways to incorporate these (or any other) structures into your lessons to increase learners’ literacy. If you do have any success with literacy in mathematics or if you have additional suggestions, please share I am always interested in learning new or seeing that wish is already known in new ways. Please enjoy making your learners’ thinking visible.
Resources
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