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This is the third in a series of articles on Disciplinary Literacy (DL).  This month’s disciplinary focus is mathematics.

Authentic learning in the mathematics classroom is enhanced when students have opportunities to engage in literacy processes and strategies specific to that discipline (Shanahan & Shanahan, 2012). As pointed out in our December newsletter, teachers can support students in “doing” mathematics by applying three guiding principles: designing disciplinary inquiry and tasks, selecting appropriate disciplinary texts, and scaffolding disciplinary practices. This edition of Insights will highlight how this can be done in a middle school mathematics classroom.

Designing Disciplinary Inquiry and Tasks
When applying this principle to the teaching of mathematics, it is critical that we remember to provide the students with the purpose for the lesson, the reason to investigate the task, and opportunities for application. To highlight how this might be done, we will consider the below problem (Haltiwanger, Horton, & Lance, 2014).

The Problem: Building a Pen for Browser
Your dog Browser, needs a pen to run and play in. You purchase 200 feet of fence, which you will use to build a rectangular pen. Because there is already a long fence at the back of the yard, you need to fence in only three sides.
 
Imagine that as students enter the classroom, images of dogs are displayed, along with the text describing this situation. To begin the discussion, we might ask our students if they have dogs and, if they do, what types of dogs they own. Doing this helps students prepare for investigating this problem; it helps make the mathematics they are about to engage in meaningful. To ensure a productive conversation, we must also design a set of questions that are relevant and important to investigate in mathematics. A sample of potential disciplinary questions are provided below.
  • Explore possible dimensions for Browser’s pen by drawing pictures to represent your thinking. What can be the minimum width for the pen? What will this do to the length?
  • What can be the maximum width for the pen? What will this do to the length?
  • Develop a table that shows all possible whole-number widths and lengths.
  • What do you think the graph of the widths and lengths would look like? Use an appropriate technological tool (Desmos, GeoGebra, Google Sheets, etc.) to graph this relationship.
  • What does our graph tell us about our original sketches of Browser’s pen?
  • What might be the largest area for Browser’s pen? Use technology to find all possible areas for Browser’s pen.
  • What happens to the area as the width and length continue to increase? Why do you think this is so?
  • What do you think the graph of the area and width of Brower’s pen would look like? Use technology to explore the relationship between the two dimensions graphically.
  • Investigate the possible areas more. What is happening to the area values? How does this relate to the graph of the area and the width of the pen?
  • If the width of the pen is considered x, what would the length of the area of the pen be?
Selecting Appropriate Disciplinary Texts
According to Draper and colleagues (2010), a text is “any representational resource or object that people intentionally imbue with meaning, in the way they either create or attend to the object, to achieve a particular purpose.” In the mathematics classroom, then, appropriate texts can consist of tables, graphs, proofs, technological displays, and manipulatives; these can either be student-generated or other-generated. As long as the student is able to assign meaning to these objects, the objects then count as a “text” in mathematics.
           
Returning to the problem, Building a Pen for Browser, we can understand that in planning, students would be required to make use of multimodal texts, texts that are composed of words, symbols, functions, drawing, tables, and graphs. For example, when asking students to connect the graphical representation of the possible lengths and widths to their original drawings, we are in essence asking the students to make use of student-generated (their original drawings, part a) and technology-generated (part d) texts. Here, it is critical that student use of text are discipline-specific. In this case, the student references mathematics specific texts that help them make connections between multiple representations of Brower’s pen.

Scaffolding Disciplinary Practice
Scaffolding learning in mathematics depends, in part, on the design of the tasks. When an inquiry task is designed, it is critical that the task is framed to pique student interest, to challenge and perturb, but with appropriate scaffolds in place. In this instance, once the original problem is presented to students, prompts can be provided (one at a time) so that students first gain a sense of what the problem is asking (drawing pictures) prior to digging-in to the mathematics. When scaffolded appropriately, students can explore mathematics more deeply. For instance, when a group of 7th grade students was presented with this problem, they ultimately investigated the first and second order differences and realized that the first order differences of a linear function was the slope of that function. Without scaffolding, the students would not have necessarily arrived at this level of mathematical understanding.

Scaffolding disciplinary practices also requires that we pay attention to the ways in which students interact with and create texts. In this case, we must take time to have a whole class discussion about the texts (drawings) that students create in part a; understanding here is critical to forward movement. It is also important to allow students time to engage with each other, discuss and compare their graphical representations, and connect their understanding of these graphs to their original drawings. Allowing students to interact with texts in this way, either student- or other-generated, is at the crux of becoming an independent, self-sufficient learner of mathematics.
 
Leigh Haltiwanger is the Interim Executive Director, Field & Clinical Partnerships & Outreach at Clemson University
Resources
Broomhead, P., Jensen, A. P., Nokes, J. D., Siebert, D. (2010). (Re)Imagining Content-Area Literacy Instruction. R. J. Draper (Ed.). New York, NY: Teachers College Press.

Haltiwanger, L., Horton, R. M., Lance, B. (2014). Using technology to build a pen for Browser.  Mathematics Teaching in the Middle School, 20(1), 46-50.

Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy. Harvard Educational Review78(1), 40-59.

Community STEM Events

Visit STEM Linx to learn about more STEM events and opportunities around the state.
Charleston STEM Festival and Storm the Citadel
Saturday, February 11, 2017, 10am-3pm
Brittlebank Park, Charleston SC


Join us for a full-day of hands-on activities, live performances, interactive demonstrations, and family-oriented STEM entertainment.  Don't miss this opportunity to "do" and learn about STEM!
This School's Got STEM Video Contest
February 20th  - March 5th 2017

Win $500 for you and $500 for your school!  Submit a 3-5 minute video showing off your coolest STEM project.  Show us the WOW in STEM!
Fluor Engineering Challenge
SC 4-H Engineering Challenge, sponsored by EnlightenSC
Saturday, March 25, 2017
Orangeburg-Calhoun Technical College


An opportunity for students ages 9-19 to learn, have fun, demonstrate the science, technology, engineering, and math skills, and compete for individual and team honors. A STEM Fair will be set up during the event to provide hands-on STEM activities for participants and their families.  More info.
iMAGINE Upstate STEAM Fest
Saturday, April 1, 2017, 11am - 5pm
Downtown Greenville, SC

Come experience the FREE STEAM festival that transforms the streets of downtown Greenville into a world filled with electric cars, high speed drone races, 3D printers, virtual reality, and robots. Check out our website to find out more about this family-friendly event! To become and exhibitor at the festival, fill out the online registration form by January 31, 2017! Non-profit organizations and k-12 schools can host an exhibit for free!
Field trips at Clemson University Life Sciences Outreach Center

The Clemson University Life Sciences Outreach Center offers laboratory field trips in modern genetics and biotechnology to school groups in our labs on the beautiful Clemson campus. Students will use modern technology to generate and analyze results and to learn key concepts. Students will also be introduced to relevant career pathways. View a list of labs and for information on bringing CULSOC labs to your school.

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