Disciplinary Literacy in Action: Mathematics Problem-Solving through Collaborative Inquiry

Teaching

By: Lindsey Douglas, English teacher at Gettys Middle School.

Literacy is often wrongly associated with only the humanities, namely English Language Arts and Social Studies. However, as contemporary studies suggest, disciplinary literacy is a necessary educational shift to meet the demands of the twenty-first century student as they participate in literacies of varied subjects (Lent & Voigt, 2019). The heart of disciplinary literacy is an accurate understanding of how content knowledge is constructed and how literacy (reading, writing, viewing, reasoning, and communicating) supports the knowledge of the respective content (Lent & Voigt, 2019).

For that reason, I teamed up with an experienced, award-winning math educator who is considered an expert in her field. We collaborated and co-taught a lesson, with each teacher valuing the other’s expertise. While the text in Math may look different than texts in my English Language Arts class, we define a text as anything a student can see, interpret, and assign meaning.

Introducing the Lesson

Our first text of the lesson was an image. The images used in the lesson were found on reasonandwonder.com. We introduced the lesson with visual literacy in which students “read” the image to interpret, evaluate, and understand the meaning. We posed two questions for the students to prompt their thinking: What do I notice and What do I wonder? The students first worked independently. Before students began reading the text, we discussed what it means to both “notice” and “wonder.” The classes acknowledged that the skill of “noticing” is what we call observing, and that of “wonder” is to inference. Like Lent suggests, “we want students to know how to interrogate texts rather than simply read them” (Lent, 2015, p.109).

Academic discourse is a critical cornerstone of a Math Disciplinary Literacy classroom. Following the image was both a small group discussion and class discussion of the students’ discoveries. However, before discussing their findings, the Math teacher reestablished group norms.

The group norms of this classroom include:

No one is done until everyone is done
You have the right to ask anybody in your group help
No talking outside your group
No naked numbers
Remember to play your role
Put the question in your answer
Say your “becauses”
Listen to others’ ideas
Take turns
Be Respectful
Confusion is a part of learning
You have the duty to give help to anybody who asks
Disagree with ideas, not people
Helping is not the same as giving answers

Many of the group norms reiterate the marriage between content and literacy such as “say your because” and “put the question in your answer.”

After the small groups discussed their answers, the teacher jotted down their responses on the board. The conversation with the whole class continued until a student finally responded with “The phone is charging!” From that response, the teacher shifted to the second sentence starter posed to students, “I Wonder…”, in which the students start sharing inferences based on the image. Eventually, a student says, “What time will the phone be charged?”

Solving the Problem

Once students land on this essential question, the lesson then shifts to the “second act” where students attempt to solve the problem. The Math teacher then asks the students to make a “too low, too high, and just right” guess at what time the phone will be charged if it is 5% at 9:02. Asking students to estimate a too high, too low, and just right answer is critical thinking and at the heart of student’s mathematical practice standards. (SCCCR.MP 1-7). In just one sentence, a too high, too low, and just right guess allows students to use reasoning and analysis to create a path to problem solving. After students shared some guesses, the teacher shared three more images, revealing the next three stages of charging.

The teacher then told the class: “Now we are going to represent data. Four representations of math are words, tables, graphs, and equations. Please remember to answer your questions in the form of a sentence.” She also reminded students of one of the group norms: say your becauses. For the math teacher, it is important that students represent Math in all four representations every lesson. This representation of data reiterates the importance of students developing a deeper mathematical knowledge. The students first represented math through words, so they moved onto representing it in a chart.

Before they began developing their charts, the teacher and the class worked together to define their variables for this situation (x=minutes of charging since 9:02; y=battery percentage).

X	Y
0 8 12 24	5 14 19 33

After creating the chart, the teacher asked, “using the data in your table, can you determine the type of relationship between these two variables?” The class consensus was that it is a positive relationship and appears nearly linear.

The teacher then told the class, “For now, let’s assume it is nearly linear. If this is true, could we use the data to write an equation to use for prediction when the phone will be fully charged?”

Y = 1.17x + 4.88

100 = 1.17x + 4.88

X ≈ 81.3

Therefore, they determined the phone will be charged approximately 81 minutes after 9:02, or 10:23. After they solve the equation, the teacher then revealed the answer to show the students by slowly showing the progression over time.

The slow reveal built suspense, and ultimately curiosity from the students. As Lent states, “The process of wondering, formulating questions, and thinking through concepts while respecting multiple viewpoints is as much the goal as certitude about a concept” (Lent & Voigt, 2019, p 111). If Math is the aspirin, then teachers must create the headache. Not a migraine, but a “cognitive conflict” or a “disequilibrium” (Meyer, 2015). This headache is created through the processes of wondering, questions, and thinking. And at just the right time, with just the right amount of curiosity and inquiry, the aspirin is given to the students in a sigh of relief (and frustration!).

At this point, the class has represented math in three different ways: words, charts, and equations. The last representation is a graph. After the final reveal, the teacher says to the class, “What happened? We assumed that it would continue charging at the same rate. But as we start charging batteries, it actually gets slower. It starts slowing down.”

The Importance of Disciplinary Literacy and Collaboration

While there may be hesitation for educators to pedagogically shift towards a disciplinary literacy approach to instruction, collaboration and co-teaching narrows the gap. Disciplinary Literacy is not merely reading and writing across the content, but rather placing literacy within the discipline itself. Lent explains, “…While practice is still important, the emphasis has shifted from only teaching the principles of math to helping students develop a deeper mathematical knowledge– and such instruction often includes collaboration” (p 155). I am thankful for Math teachers who take transformative action about the way in which they think about their content. I am thankful for a school where disciplinary literacy is a school-wide initiative. But most of all, I am thankful for literacy itself and its rightful place in all disciplines across all curriculums.

References:

Lent, R. C. (2016). This Is Disciplinary Literacy: Reading Writing, Thinking, and Doing… Content Area by Content Area. Corwin.

Lent, R. C. & Voigt, M. M. (2019). Disciplinary Literacy In Action: How to Create and Sustain a School-wide Culture of Deep Reading, Writing, and Thinking. Corwin.

Meyer, Dan. 2015, 17, June).If Math Is The Aspirin, Then How Do You Create The Headache? Dy/dan. https://blog.mrmeyer.com/2015/if-math-is-the-aspirin-then-how-do-you-create-the-headache/

About the Author

Lindsey Douglas is a Clemson University graduate in English Literature, Secondary Education, and a Masters in Literacy K-12. Lindsey is a third year English teacher and is the 8th grade English Department Head at Gettys Middle School. She is passionate about disciplinary literacy and helping teachers embed literacy practices into their content. She also coaches volleyball and enjoys spending time outdoors, and reading.

About the Collaborator

Ashley Weaver is a National Board Certified Teacher and math nerd with 13 years of experience teaching middle schoolers. She teaches with the belief that all students can learn math and achieve at high levels and hopes to instill a love for learning in her students. When she isn’t teaching or learning about teaching, she enjoys reading and spending time with her husband and daughter.

When Teaching Music and Teaching Literacy are in Harmony

Teaching

By: Hunter Thompson, University of South Carolina Pre-Service Music Educator

Teaching students how to read music is basically like teaching students how to be literate in another language. As you learn more and more of a language, the rules and guidelines for reading, writing, and speaking that language become increasingly complex. Music educators should approach teaching students music like they are preparing students to be literate in the complexities of music, and we all know how complex music can become (we’re all looking at you, Schoenberg). Music students should not only be literate in musical literacy, but they also need to be literate in traditional literacy, numeracy, communicative literacy, and even technological literacy to be successful in today’s music classes. Students must be literate to comprehend expressive markings such as accelerando or rallentando. The basis of teaching rhythm is contingent on the assumption that students are numerate, and we also use mathematical structures within music theory. Watching a conductor’s gestures and expressions requires students to be literate in the nuances of communication. The rising popularity of electronic music and the usage of online notation software requires students and teachers to be technologically literate. All of these forms of literacy converge in our music classrooms, so this means that we must adapt non-musical strategies for usage in our lessons.

Close Reading is a task that students are expected to do in essentially every class that they will ever take; however, it is a skill that is unintentionally not as well-developed and practiced outside of typical English Language Arts courses. Without clear guidelines for how Close Reading is applied to subjects like music, art, physical education, dance, and other classes that are necessary for educating the whole child, students will not be able to put these strategies into practice. Therefore, it is crucial that we, as music educators, make our approach to Close Reading essential to our lessons, and instead of relying solely on music-specific structures to achieve this, we should also model our approach off of existing structures. Although Close Reading is a strategy that was originally created for use in English language arts courses, Close Reading (with some minor adaptations) will help to engage students in a deeper analysis of music that they are performing and to which they are listening.

Wolsey and Lapp’s Approach to Close Reading for Traditional Print Texts

Close Reading strategies have historically been applied to print texts, but texts come in all sorts of shapes and sizes. There are two types of text: print and non-print texts. In a music classroom, an example of a print text could be a student’s individual part or a conductor’s score. Print texts have traditionally been the dominant of the two in classroom settings, but there is still an enormous amount of information that students can gain from working with non-print texts. With regards to music classes, an example of a non-print text could be a live or recorded performance.

Thomas DeVere Wolsey and Diane Lapp outline Close Reading for traditional print texts like this. First, you must select a complex text for your students to study, and think about priming questions that you could ask your students before introducing them to the text. Next, have students complete an independent reading and annotation of the text. After that, complete partner sharing activities so that your students are able to hear a diverse range of perspectives. Following that, re-read the text (as an independent reading, student-led reading, or teacher-led reading) with specific goals in mind, and conduct a group discussion to reinforce particular ideas. Re-read the text as many times you deem necessary and conclude with a written extension, reflection, or explanation of the text that highlights a specific skill concept.

This approach to Close Reading has been highly effective in countless traditional literacy settings to help students gain a deeper understanding of complex print texts, but what does this process have to do with music? Close Reading, by definition, uses “text-based questions and discussion,” and “students are guided to deeply analyze and appreciate various aspects of the text” (Brown & Kappes 2012).

Close Reading Adaptations for Music Classrooms

Music teachers do these things on a daily basis, whether we realize it or not. Additionally, music teachers want their students to develop the skills necessary to perform and listen to complex pieces of music with much deeper analysis. It is extremely important to remember that this level of analysis will require multiple visits with the same text. With every close read, students will pick up on more nuances and important details which will ultimately lead to a greater understanding of the composer’s and/or conductor’s craft.

In music classes, we constantly ask our students to perform and listen at the highest level; therefore, students must develop a more advanced skill set to analyze complex works. Resultingly, I have adapted Wolsey and Lapp’s outline of Close Reading for performing music and listening to music. The adaptation for performing music is geared more towards a band, choir, or orchestra class while the adaptation for listening to music is geared more towards a music appreciation or music history class. However, they can be used in any music classroom with minor adjustments.

Adaptation Chart of Close Reading for Performing and Listening to Music

Wolsey and Lapp’s Close Reading for Traditional Print Texts	A Close Reading Adaptation for Performing Music	A Close Reading Adaptation for Listening to Music
Select a complex text that relates to instructional purpose (use Lexile Levels to help with this)	Select a complex text that relates to instructional purpose (use state grade categorizations to help with this and resources provided by sheet music retailers) Example: Music List: Concert Festivals	Select a complex text that relates to instructional purpose
Provide priming questions: What are you thinking as you read? What words do you not know? What techniques is the author using? What is the author’s message? What is the impact on the reader?	Provide priming questions:What is the tempo? What is the key signature? What is the time signature? What is the pitch range? Are there any accidentals? Are there any difficult rhythms? What kind of signs, repeats, dynamics, and articulations do you see?	Provide priming questions: What do you hear? What genre is this piece? What is the instrumentation or orchestration? What is the structure of this piece? What style period is this piece from? What message or emotions is the composer attempting to convey?
Number the paragraphs.	Number the measures.	For listening with a score, number the measures. For listening without a score, segment the recording using time stamps.
Independent reading (use paragraph numbers to chunk text for greater analysis)	Independent sight reading (use measure numbers to note difficult and important sections in the music)	Independent listening with a score (use measure numbers to chunk the score for greater analysis)Independent listening without a score (use time stamps to chunk the piece for greater analysis)
Text annotation – writing on paper; using highlighters and/or pens to “mark” the text	Text annotation – writing on music; using a pencil to circle/star/box any notable parts of the music	Text annotation (with a score) – writing on the score; using colored pencils or pens to mark melodic lines and harmonic analysesText annotation (without a score) – write down notes about the piece with time stamps included
Partner sharing – discussion with language frames	Partner sharing – discussion with language frames	Partner sharing – discussion with language frames
Rereading (independent, student-led, or teacher-led) with analysis on how text was written and writer’s craft	Re-examining (independent, student-led, or teacher-led) with further analysis of sequences, modulations, intervallic relationships, and other patterns	Re-listening with a score (independent, student-led, or teacher-led) with analysis of compositional techniques and composer-specific musical idiomsRe-listening without a score (independent, student-led, or teacher-led) with analysis of how different time stamp segments are similar and dissimilar
Discussion to reinforce academic vocabulary and interpretation	Discussion to reinforce academic vocabulary and interpretation	Discussion to reinforce academic vocabulary and interpretation
Written extension, reflection, explanation of the piece, or demonstration of the skill concept through writing	Written extension outlining performance goals and practices and/or a summarization of elements of the composer’s style	Written extension (music critique or analysis), reflection, explanation of the piece

Will Close Reading Consume My Already Precious Class Time?

Believe it or not, you are probably already doing parts of activities like this in your classroom. However, it has not been made clear to students that these activities are part of the larger process of Close Reading. It is critical that we are intentional, from the very beginning, in choosing what texts we use, and for music, it is important to take into account the musical abilities of each student if you intend to perform a chosen text. Additionally, we must be purposeful in the strategy we use to teach the musical complexities that our students will encounter within the chosen texts.

You most likely are using some of these steps within your classroom, but Close Reading works best and benefits more students when the full process is completed for specific texts. If your wind ensemble is playing Holst’s First Suite in E-Flat for Military Band, it may prove wise for students to complete several close readings of their own part and several close readings of the score. Since this piece is public domain, you can find the score online from the International Music Score Library Project (IMSLP). If you are unable to provide each student with a conductor’s score, you could also use a document camera and projector to display the score during class for a teacher-led close reading of the text. Vision is the dominant sense, and many of our music students may be visual learners, so it could prove very beneficial to those students if they can see how their individual part is connected to other parts. If you are teaching a unit in a music appreciation course on dance rhythms, you could complete a close listening of Bernstein’s Symphonic Dances from West Side Story, which might be more recognizable and engaging to students than a Baroque dance suite. Remember, we could choose any school-appropriate text for our students to work with, but it is important that we know exactly what we want students to learn from that text and that we know exactly what strategies we will use to teach the text.

One concern about implementing a Close Reading strategy in your music classroom is that it will take a large amount of time from technique building and preparing for performances. However, Close Reading is a method of keeping students engaged with a text. If students simply go through the motions, rehearsing the same set of pieces day after day, then students will begin to lose focus while performing. If we take class time to purposefully implement Close Reading strategies into our routines, then it will help students to better understand individual and ensemble performance goals for that particular piece. Ultimately, a strong foundation of technique and fundamentals mixed with the implementation of Close Reading and other literacy strategies will set students up for musical success.

Adapting Other Literacy Strategies to Grow Students’ Music Literacy

Additionally, I urge music educators to avoid what Laura Sindberg refers to as “music teacher isolation” (Sindberg 2011). Look for ways outside of your school’s Fine Arts Department to adapt literacy strategies. Regularly ask your colleagues in the Science, Mathematics, English, History, and Foreign Language Departments about how they adapt traditional literacy strategies in their classrooms. Remember to talk to the other Fine Arts teachers in your schools who do not teach music as well, and do not forget to share your ideas too. Readers’ Theatre is a literacy strategy that requires small groups of students to create and perform a dramatic script based on a provided text. When adapted to a music appreciation class, you could assign small groups of students a recitative and aria or an ensemble song. Make sure the libretto of the assigned opera is translated for your students. Then, they can create their own script to perform their adaptation in front of the class. If you have enough groups and pick out key parts of the opera, your class will be able to summarize the plot of an entire opera with short scenes that they have created. When you have amassed your own stockpile of creative strategies, you will be able to impact a more diverse group of learners because of the numerous options from which you have to choose.

Just as students in an English class will not be able to comprehend William Shakespeare, Toni Morrison, Harper Lee, and Oscar Wilde if they cannot comprehend Dr. Seuss yet, students in a music class will not be able to comprehend the masterworks of great composers like Ludwig van Beethoven, Jennifer Higdon, Eric Whitacre, and David Maslanka if they cannot comprehend their beginner technique books. Literacy looks different in each discipline, and it is our job to make sure that our students can read, perform, listen to, analyze, and critique increasingly complex texts. This blog post is by no means a critique of the strategies currently employed in music classrooms, but in actuality, it is a call to broaden the literacy strategies we are using in our music classrooms. I encourage us to do what music teachers do best, and use our imagination to see what kind of ways we can incorporate creative adaptations of literacy strategies, like Close Reading, into our lessons.

References

Brown, S., & Kappes, L. (2012). Implementing the Common Core State Standards: A primer on “close reading of text.” Washington, DC: Aspen Institute.

Sindberg, L. (2011). Alone All Together—The Conundrum of Music Teacher Isolation and Connectedness. Bulletin of the Council for Research in Music Education, (189), 7–22. https://doi.org/10.5406/bulcouresmusedu.189.0007

Wolsey, T. D.V., & Lapp, D. (2017). Literacy in the Disciplines: A Teacher’s Guide for Grades 5-12. Guilford Press, a Division of Guilford Publications, Inc.

About the Author

Hunter Thompson is a junior at the University of South Carolina, where he is majoring in Music Education. He grew up in Hartsville, South Carolina, and he participated in his school band program beginning in sixth grade and continuing to his senior year of high school. He would like to thank several educators for the tremendous impact they had on him: His mother, Elizabeth Thompson, who will always be his biggest educational influence; his high school band director, Cameron Watkins, who always believed in his musical abilities; and one of his college professors, Dr. Jennifer D. Morrison, who provided him with an amazing opportunity to write about a subject that is very important to him.