Reflection 4: Using Literacy to Teach Mathematics
This generation of students is doing mathematics that is much more than computing numbers. Math is a “language” that has difficult vocabulary, specific syntax, and challenging concepts that require a deep understanding of the content to truly comprehend (Bach, Bardsley, Gibb-Brown, Kester-Philips, 2009). Throughout my own experience in the classroom I have tried to incorporate reading and writing into lessons in order to deepen my students’ mathematics knowledge.
Throughout educational history, reading and writing activities have been mainly utilized during English and social studies. With new types of literacy and the accessibility of information via internet, reading and writing lessons need to be taught throughout adolescents as well (Vacca, Vacca, Mraz, 2011). One strategy for incorporating reading activities in the math classroom is to provide stories with meaningful contexts or model mathematical ideas. For students who may not particularly enjoy math, reading a story with an interesting plot, setting, or characters will help increase motivation in the associated math lesson (Whitin and Gary, 1994). The following activities are examples of lessons that I’ve created for middle and high school students that incorporate reading and writing activities in the math classroom.
One activity that I have outlined, but have yet to use in a classroom is based on the book The Librarian Who Measured the Earth by Lasky and Hawkes (1994). This book is a picture book/short biography about Eratosthenes of Cyrene and his discoveries about fractions and geometry. I would have my math students read the story, and either begin a class discussion, or have students discuss in small groups Eratosthenes’ work, what it must have been like to be him, and struggles he must have faced. I would be able to evaluate students understanding of the lesson through their ability to work with circles. The students would show during activities and assessment their knowledge and understanding of the relationships within circles and calculate certain measures. Some students may feel motivated to do further research on the time frame/area Eratosthenes lived, and find out what/if any major events were occurring during this time. Another possibility is that students may begin to elicit ways in which Eratosthenes work has influenced what they learn in school. The questions and curiosity that the students have after reading the story would indicate the connection between their interest in the story and the development of their geometry skills.
Another similar activity that I plan to use with my class uses the book Real Life Math by Glazer and McConnell (2002) that gives examples of how math topics from the middle school to college level are used/seen in everyday life. I plan on keeping this book in my classroom and asking students to read it whenever they asked the infamous questions “why do I need to learn this” or if they share their future goals with me. They could read this book to determine what math skills will be required of them while having the profession of their dreams. When a student reads this book I will ask them to share their findings with the class. I think it is important that students share their knowledge with one another, even if it is not specifically about the curriculum. By hearing it from their peers, the information can be more valuable than if it comes from the teachers’ mouth. Utilizing a book such as this in my classroom allows my students to make a connection between the math activities they do in school, to authentic scenarios that are related to their lives. As I mentioned in my reflection of the constructivist approach, making math concepts authentic, allows students to connect and see value in the lesson. Because this is personal to them, they would be affected in some way by what Glazer and McConnell (2002) have to say. In addition, some of the vocabulary in this book can be challenging depending on the concepts that are looked at. Students may have questions about terms that they may not have learned yet, and therefore would be broadening their literacy and math vocabulary.
Very often students get bored with typical math lessons, so I have created a Lyrical Mathematics lesson for a future class of mine to complete that will allow them to incorporate songs and math. This lesson requires literacy skills that are not used very often such as analyzing the characteristics of poems or lyrics. Depending on the option they choose, the students will express their knowledge throughout their presentation. I will look for the students’ description of the literary elements of the lyrics, analysis of their meaning, and connection to mathematics. Stories encourage investigation and challenge students in a nonthreatening way (Griffiths and Clyne, 1991). Therefore, in an activity like this, students are practicing their math skills in a nonthreatening way because their focus is on the lyrics rather than a typical, intimidating math problem. As the students completed this activity I would evaluate their learning based on the results of their project, and correct calculations of the light-years or evaluation of our calendar days (depending on the assignment option they chose).
A book that I plan on having in my classroom library is Anno and Anno’s (1983) book called Anno’s Mysterious Multiplying Jar. This book is about a jar in a world that is in a world related to factorials. In my experience, students know how to compute factorials, but do not know what it is they are actually finding. This book is a great resource that connects a popular math concept, with a story and illustrations that will aid in understanding. Whether I read this book to the students as a whole group, or asked them to read it independently, I would probably have them fill out an comprehension worksheet/graphic organizer that would encourage students to write down their ideas about factorials prior to reading the book, and their feelings after reading it. I would see evidence of their learning through their ability to compute factorial problems. By reading the story and discussing the multiplying process, students will begin to understand the process of finding factorials.
Literacy skills are not simply attained through reading. Writing and language expression enhances literacy skills as well. One example of a reading and writing assignment that I used during student teaching was Questioning the Author. For this assignment I asked my class to read the New York Times article and answer some questions about it. After reading the article and given some time to write down their responses, the students were asked to reconvene to discuss the author’s beliefs as a whole group. Student comprehension and understanding was clear to me through the discussion that commenced. One student specifically, who was not a strong student in my class, had very strong feelings about this article because he did not see the relevance of our math curriculum to his life. Although he is not typically expressive during a typical math lesson, this student was evoked to share his thoughts due to the article he had just read. Although I had to warn my class they were beginning to get a little rowdy, it was clear that this reading/writing activity was successful in getting my students to use their language skills as well as think critically and challenge one another. They were highly expressive of their thoughts and concerns regarding the mathematics curriculum and its value to their lives. While this activity did not enhance their understanding of any specific math concepts, it allowed them to develop affective, transformative feelings about the subject. If I do this assignment again in the future, I plan on having the students write their responses so their powerful words can be shared with fellow teachers and administrators if it is appropriate.
Another writing assignment that I have used in various classes is a writing to learn or sentence starter activity in which I write sentence starters on the board and ask students to complete them in their notebooks. These have taken the form of Do Now Activities to sum up a lesson, or clues about previous lessons that activate prior knowledge. One time I used this in my 8th grade, self-contained special math class during student teaching after a lesson on linear equations. The students in this class struggled with word processing skills so completing an activity like this was highly valuable to them (Learning Log). It allowed them to reflect on the material they had learned during the past few classes, and put the lessons into their own words. When reading their responses I had the opportunity to evaluate their understanding of the math, as well as the progress they are making with their writing. Although this was a short assignment many students struggled with expressing their ideas on paper. I remember one student specifically was working with his English teacher on using transition words. When I saw he had used “although” and “however” in his responses I gave him positive feedback that was specific to the progress he had made with his writing. In addition, he clearly indicated the steps for graphing and evaluating algebraic equations. Rather than relying on numbers and equations, the student used language and literacy skills to express his mathematical understanding.
A simple writing activity that can be incorporated into any classroom is a question-answer relationship assignment. Although I have not been able to use this in a classroom yet, this is a simple activity that requires the students to use their text or other resources to answer questions about the lesson. The example I have created tests the students’ ability to look up information about functions and determine what value they have in mathematics. The responses from this activity will not only allow the students to work on their writing skills, but it will also indicate their reading comprehension and effectiveness of using resources. Because this generation is so used to typing what they need to know into Google, requiring them to use textbooks in the classroom is great practice in how to look up research material. “Research literacy” is not something that many students have experience with. Therefore I anticipate a lot of questions will be asked about the “old fashioned” way of looking up information. In addition, this activity will require the students to recall math vocabulary so they can look up the necessary terms to answer the questions. Davidson and Pearce (1988) stated that students benefit greatly from translating mathematical symbols and problems into writing complete sentences. It requires students to think about the problems and use diction that appropriately descries their thought process.
While working with Mr. Castiglione at Newburgh Free Academy (NFA) I used a vocabulary strategy with the students that required them to make verbal and visual word associations. One day I had them complete the graphic organizer using the word “inequality.” As they filled out the boxes I could see them thinking and questioning the various ways they could represent such a seemingly simple word. In mathematics a vocabulary term does not simply take the form of a word on paper. Very often it can be represented symbolically, graphically, or though a picture. Therefore, it was clear that students understood the term inequality because they were able to share the various ways it can be represented. In addition, when completing a lesson that included inequalities I said the word, wrote the various symbols for them on the board, and gave numerical representations of inequalities. When asking students to complete problems or share their ideas, they showed a clear understanding of an inequality regardless of my means of representing it. The writing aspect allowed the students to summarize their knowledge and represent it in a way that was meaningful to them. Writing helps students learn, therefore through these activities, students utilized an additional skill that aided in the development of their mathematical knowledge.
All students are relying on their teachers to provide them with the knowledge and skills necessary to make them successful as adults. I have learned that my job as a math teacher goes beyond teaching numbers. In order to give my students the best education I can, I will continue to incorporate literacy lessons, such as reading and writing activities, into my math lessons. This will allow my students to develop ideas of math concepts in a differentiated way, as well as increase reading comprehension and writing skills. I look forward to using these activities and creating new ones like the ones mentioned in my classroom when I become a teacher.
Appendix
Standard 2- Knowledge of Mathematics |
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Aspect |
Explanation |
Ways I Met the Standard |
Contexts for Mathematics |
Accomplished math teachers understand the connections between concrete math techniques and abstract concepts. |
-By using the book The Librarian Who Measured the Earth I can allow my students to learn a fundamental math problem through the context of a story. -The Multiplying Jar Lesson required me to seriously consider how I can bring more to a topic that is typically taught through a direct instruction, “just remember this” type of way. By incorporating the book into the factorial lesson, I will be able to add a layer of understanding for the students. |
Core Mathematical Knowledge |
Accomplished math teachers understand the various domains of mathematics and ways in which to get students to develop understanding in all of these areas. |
-Because many concepts in mathematics can be shown in different ways, using the vocabulary strategy discussed above allows students to see all forms of a word. This requires the teacher to know all forms of the word and their relation to the content so it can be effectively translated to students. -Taking song lyrics and connecting them to a math lesson cannot be done unless the teacher has a solid foundation in mathematics. Because I understand the basics so well, and how they bring us to the more challenging/abstract concepts, I can bridge teaching gaps using creative lessons such as this lyrical math one. |
Standard 4- Knowledge of the Practice of Teaching |
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Aspect |
Explanation |
Ways I Met the Standard |
Knowledge of Pedagogy Influences Instructional Strategies |
Accomplished math teachers use their knowledge of pedagogy, math, and student development to make informed, appropriate instructional strategies. |
-The incorporation of a Learning Log in a classroom shows that a teacher understands the value of letting students express their thoughts using words. This increases comprehension and helps them organize their thoughts. -Us teachers need to make lessons real and authentic for our students. By keeping Real Life Math in my classroom I can show my students the relevance math has in their lives. |
Standard 8-Reflection and Growth |
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Aspect |
Explanation |
Ways I Met the Standard |
Reflect on Lessons and Continually Improve Practice of Teaching |
Accomplished math teachers reflect on the teaching strategies they’ve use, and continually make adjustments to help improve their students’ knowledge. |
-Although the Questioning the Author lesson got students excited and involved in the ideas and changes in their math curriculum, it got me thinking and reflecting on my own teaching. The students made excellent points about the purpose of school and their feelings towards it that now shapes my instructional decision making. -The Q and A worksheet allows the students to search for answers using the materials around them. I believe watching the ways in which students look up information, or the types of questions they come up with on their own will offer great insight into their learning styles that I can use to guide my decision making. |
Davison, D.M., & Pearce, D.L. (1988). Using writing activities to reinforce mathematics instruction. Arithmetic Teacher, 36, 42-45.
Griffiths, R. & Clyne, M. (1991). The power of story: Its role in learning mathematics. Math Teaching, 135, 42-45
Grossman, F.J., Smith, B, & Miller, C. (1993). Did you say write in mathematics class? Journal of Developmental Education, 17, 2-4
National Council of Teachers of Mathematics (2005). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.
Phillips, D., Bardsley, M., Bach, T., & Gibb-Brown, K. (2009). "But I Teach Math!" The Journey of Middle School Mathematics Teachers and Literacy Coaches Learning to Integrate Literacy Strategies into the Math Instruction. Education, 129(3), 467-472.
Vacca, R. T., Vacca, J. L., & Mraz, M. (2011). Content area reading: Literacy and learning across the curriculum. (10th ed.). Boston, MA: Pearson Education, Inc.
Whitin, D.J., & Gary, C.C. (1994). Promoting mathematical explorations through children’s literature. Aritmetic Teacher, 41, 394-399