Disciplinary Literacy in Algebra

1)Disciplinary literacy in Algebra 

1. Types of questions:

• Questions involved in this discipline must require an explanation of the rationale, require proven steps to be followed, and an answer. 
• Examples of these questions are open ended, up for interpretation, quantitative, and questions that stimulate higher order thinking.
• (Aquirre and Delrosario Zavala, 2013) and (Averill, Anderson, Easton, Te Maro, Smith, Hynds, 2009). 

1. Methods of inquiry

• Exploration, Discussion, Collaboration, Selecting and Sequencing.
  • Description of the standards and expectations of how disciplinarians in Algebra answer their questions
• What does it look like?
  • Exploration: Allowing students to ‘play around’ with mathematical concepts in order to further their understanding of that concept.
  • Discussion: Allowing students to discuss their thinking and rationale in order to gain insight into various ways of solving the same problem.
  • Collaboration: Allowing students to work together to discover new ways of thinking.
  • Selecting: Allowing students to share and discuss what they find in class.  The teacher would select certain solution paths for students to share out.
  • Sequencing: students will develop mathematical ideas from their understanding of the lesson through the “selecting” stage.
• Citations on relevant sources
  • Van de Walle, J., Karp, K., Lovin, L., & Bay-Williams, J.. (2018). Teaching student-centered mathematics. Pearson.
  • Boston, M. (2019) Mathematics lesson planning based on the 5-practices Model. Melissa Boston.

1. Types of texts 

• Word Problems, Textbooks, Data-based, equations, algorithms, etc.
• All of these texts assist in the learning and teaching of math, as well as to justify work/build upon the study of mathematics. They are produced by mathematicians and published by various education publishers. 
• As stated above, these texts are excellent in furthering mathematical skills and thinking within students, teachers and professionals. Word problems allow students to practice using their “math diction” skills to dissect these types of problems and use correct procedures to solve. Textbooks give teacher helpful tips on teaching the content within their class as well as giving students numerous chances to practice concepts before they engage in summative assessment or build further upon their skills

BOOK DESIGN FOR TEXTBOOKS. (n.d.). Retrieved from https://designforbooks.com/textbook-design/.

1. Disciplinary literacy practices

• Mathematicians justify their work with textbooks, equations, algorithms, and proofs. 
• The Pythagorean Theorem is an equation that has been used since Pythagoras discovered this around 580 BC. This Theorem has been used to justify work by mathematicians ever since. Elementary Geometry (1892-1893) by Andrei Petrovich Kieselev is one of the most important texts on Geometry ever produced. 
• Kiselev, A., & Rybkin, N. (1972). Geometrii︠a︡; dopolnitelʹnyĭ material dli︠a︡ 8, 9 klassov. Moskva: “Prosveshchenie”.

2) Ideas for teaching

1. Engaging Students in Cycles of Inquiry
   1. What specific ways can teachers engage students in authentic disciplinary cycles of inquiry (think back to the video you’ve watched)
      1. In some classes, students are allowed to do projects with an outline from the teacher.  Students will have to explore to make connections and make their project relevant. One example of this, might be learning decimals and a student making their own business and deciding what they want on their menu, or prices of their services to be .  They could then figure out the tax for certain orders and decorate their business.
      2. Using manipulatives when being introduced to a topic such as fractions.  One useful manipulative in mathematics might be base 10 blocks. We have discussed this quite a bit in our college level “teaching mathematics” course and allows students to explore the discipline with the teachers guidance.  
   2. What are the benefits and limitations of the specific examples you provide?
      1.  Benefits
         1. Students can explore the discipline
         2. Students are in charge of their own learning
         3. Connections between the curriculum and the manipulatives will be made
         4. Students will be more independent in and out of the classroom.
      2. Limitations 
         1. You have to have manipulatives available to you.  Some school districts don’t have this.
         2. Some students may do better with a more structured setting and the teacher would have to accomodate this.
2. Engineering and scaffolding success

• What specific ways have you seen teachers engineer and scaffold students’ success as they invite them into disciplinary practices?
  • Asking questions and following the standards will lead students on a trajectory to success in disciplinary literacy in mathematics. 
• What are the benefits and limitations of the specific examples you provide?
  • Benefits
    • Keeps students learning tied to the PA math standards
    • Helps students understand the foundation of the problems they are learning
  • Limitations
    • Fall behind in curriculum
    • Standards aren’t always implemented correctly
    • Students with disabilities 

1. Examining words and ways with words

• What specific ways have you seen teachers invite students to examine disciplinary ways with words? (perhaps in the field, articles, videos)

The article “A Literature Review on Disciplinary Literacy HOW DO SECONDARY TEACHERS APPRENTICE STUDENTS INTO MATHEMATICAL LITERACY?”  they talk about the importance of students being able to explain math problems through vocabulary and methods. We also watched a video that shows a 4th grade classroom explain whether a problem was true of false. Within this video, the teacher had the students use math vocabulary within their explanations to show their understanding of the problem. The way teachers can invite students to examine their words is by having them write out explanations for problems and to have class discussions to have a safe place to have discussions. This article also talks about the importance of the process not just the correct answer. 

• What are the benefits and limitations of the specific examples you provide?

One benefit is this method gives students a way to learn vocabulary and have a space to use that vocabulary within the classroom. Another benefit is that this method allows students to fully understand the vocabulary and the concepts behind the math. One limitation of this is the lack of class time. If there is not enough time to discuss the math process then some students may feel that they are falling behind. Another limitation is that some students may need more help and may not be able to understand the vocabulary based on a learning disability. 

1. Evaluating claims and ways with words
   1. How can teachers help students evaluate the quality of claims according to real standards in the discipline?
      1. Teachers can encourage students to voice their explanations and justifications using mathematical terms. Ann Marie Hillman states “In the second, third, and sixth standards, we see a view of the language valued in math classes”. (Hillman, 2013, 400)
      2. Teachers can show students the importance of wording in mathematics. The explanations in math are far different than other subjects. (Hillman). Example, teachers can have students share out their explanations of how they got their answers and have other students revoice their answers. This creates active listening.
         1. https://www.teachingchannel.org/video/formatively-assess-fraction-knowledge-sbac
   2. What are the benefits and limitations of the specific examples you provide?
      1. Benefits
         1. Complete understanding of mathematical diction
         2. Applying the knowledge of understanding vocabulary to explanations of math problems.
         3. Allows students to practice having a voice within math classrooms and their learning in general
      2. Limitation
         1. Limited class time
         2. Students not understanding vocabulary
         3. ELA students