Abstract Understanding literacy in Math means more than just knowing the basic skills of addition, subtraction, multiplication and division. Mathematics is made of letters, numbers, symbols, and a vocabulary that form a language all its own. It is important for teachers to understand the complexities of Math and how to share strategies of learning for student success. Some research suggests a lack of prior knowledge and basic skills and others suggest a breakdown in the system.
Regardless, student success is dependent upon an understanding of the literacy of Math and the ability to teach all students to be successful. Introduction Math is all around us. We learn Math in school and use it in our daily lives; often not realizing we are performing Math functions. Literacy in Math is essential; however, there are many factors that are preventing students from succeeding in the Math. Research shows that reading and writing in Math are critical to success in Math. If students are fluent in reading, one would assume fluency in Math as well. However, this is not the case.
According to the National Assessment of Educational Progress (NAEP), 32% of eighth graders have attained a “proficient” level on reading scores leveling many children who are not as fluent in reading materials, making inferences, and thinking critically as teachers expect or would like (Richardson, Morgan, and Fleener, 2006). If only 32% of students are proficient in reading, what does that do to Math scores? Math is a language unto itself and is often a challenge to many students, but if you cannot read well what does this to do achievement scores in Math. My research has indicated that literacy in Math is the key to success in Math.
Therefore the answer should be simple: teach students to understand the language of Math. However, research indicates that many students lack prior knowledge, basic facts, ability to read, mathematical thinking/interpretation skills, and confidence (Amen, 2006). Lui (2006) stated No Child Left Behind produced a policy environment with no one left responsible for the “savage inequalities” between affluent schools and those in poor communities of color. Regardless of who may be to blame for the breakdown in the education system the only way out of this is to focus on educating our students.
My goal is to teach Math to secondary students. To achieve this goal, I need to understand literacy in Math, its importance, and how to help students become successful. This paper will examine literacy in Math and the importance of reading and writing in the Math class to fully comprehend the functions of Math. Literacy in Math Kilpatrick (2001) identifies five strands of mathematical proficiency. They are conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. Conceptual understanding refers to a student’s comprehension of mathematical concepts, operations and relations.
Procedural fluency refers to a student’s skill in carrying out mathematical procedures appropriately. Strategic competence is the student’s ability to formulate, represent, and solve mathematical problems. Adaptive reasoning refers to the capacity for logical thought and for the reflection on, explanation of, and justification of mathematical arguments. Productive disposition is the student’s habitual inclination to see mathematics as a sensible, useful, and worthwhile subject to be learned, coupled with a belief in the value of diligent work and in one’s own efficacy as a doer of mathematics.
Based on Kilpatrick’s definition of mathematical proficiency, it is clear that Math is a very complex subject and requires much understanding. As a result, literacy in Math is a necessity because Math is a language all its own. It is far more than just words on a page. It is numbers, letters, symbols, and most importantly, it is vocabulary. Students must understand symbols that represent concepts, syntax of a mathematical sentence, and the vocabulary of mathematics (Kester Phillips, Bardsley, Back & Gibbs-Brown, 2000).
Fuentes (1998) stated each word and symbol read in mathematics text must be read and understood with precision. It is a misconception that Math is nothing more than addition, subtraction, multiplication, and division. Vocabulary is very important to understanding Math and an important part of the learning process. To be successful, students need to be fluent readers, but they must also read the text in a specific manner. Dr. Kevin Lee (2010), a professor at Purdue University, suggested the following tips for reading Mathematics: * Focus on concepts not exercises * Read the text more than once.
* When reading through for the first time, scan for big ideas * The second time through, fill in details * Read with paper, pen and calculator * Read the narrative * Study the examples * Read the pictures * Learn the vocabulary and the language * Use the index and the appendices. Know what every word means * Make a note of things you don’t understand, ask for help afterwards Following these steps may be timely, but they are necessary if one truly wants to understand the lesson. As students read, they should make notes to the side and go back to those notes to define any words that they don’t know.
Students should also study all examples and pictures. Examples and pictures are included for a reason. They are used to help convey the message of the text and explain how to perform functions and calculations. The Breakdown In the introduction I mentioned the breakdown in literacy in Math. The two main reasons I mentioned was that the No Child Left Behind legislature left gaps in responsibility for the differences in affluent schools versus poor communities of color and the lack of prior knowledge and basic facts.
Amen (2006) concluded that students have lower achievement in Math because they lack prior knowledge, basic facts, ability to read, mathematical thinking/interpretation skills and confidence. In Amen’s experience in her own classroom, children of poverty come with fewer opportunities than the children of the middle class. In addition to battling the issues that many of them face at home each day (hunger, neglect, physical abuse, substance abuse, and non-permanent homes) I also have to deal with the fact that they also come to school less academically prepared than their middle class counterparts.
Amen was not suggesting that these students are not able to learn, but that they lack many of the basic skills and knowledge more readily available to students from middle or upper class areas. In his study of the social injustices of reading and writing in Math, Yang (2009) looked at the textbooks and available extensions (audio, video, etc). Yang looked at the social injustices from both the teacher and student perspectives. Yang’s findings showed that students needed to rely on outside mentoring and tutoring to understand the textbooks. The textbooks were highly technical and students from the poorer communities had many challenges.
Now that it is clear there is a breakdown in Math literacy, the question is what to do to rebuild and teach students to become literate. The solution is to determine where students are lacking and focus on building on the skills required and the confidence needed to be successful. The reading tips mentioned earlier are important, but they are not enough. The ability to read and understand Math and its vocabulary is essential but if students are lacking in the prior knowledge and basic skills of Math, we must address the importance of how to teach those concepts to students.
To teach literacy in Math, teachers need to address the two key factors essential to achievement for students: writing in Math and vocabulary development. Importance of Writing in Math According to Schwarz (1999) writing and vocabulary development is necessary in all curricular areas, especially Math. Writing in Math does not necessarily mean writing an equation. Writing equations is definitely part of fluency and comprehension of math, but when thinking in terms of literacy writing in Math means that students can put into their own words what each
lesson means to them. Writing can play a vital role in developing literacy and understanding. According to Blessman and Myszczak (2001) writing in mathematics class seems to demonstrate a student’s knowledge of material being taught and it allows for an outlet for true authentic assessment. Much of the research indicates writing serves as a means of helping students organize, analyze, interpret, and communicate mathematical ideas, leading to a deeper understanding of content concepts (Burns, 2004, Holliday, Yore, and Alverman, 1994).
Writing in the Math classroom can help students by allowing them to put together their thinking by requiring them reflect on their work and clarify their understanding of the ideas of the lesson. Many researchers suggest the use of journals in the Math classroom. Writing can help student gain relevant knowledge and experience in preparing for new activities, review and consolidate what is known or has been learned, and reformulate and extend ideas and experiences (Langer and Applebee, 1987).
In addition to Langer and Applebee, Kelly (2008) stated journals provide students the opportunity to 1) sort out experiences, solve problems and consider varying perspectives, 2) examine relationships with others and the world, 3) reflect on personal values, goals and ideals, and 4) to summarize ideas, experiences, and opinions before and after instruction. Wilcox (2011) identified two levels of integration that teachers may use as a beginning point. Writing without revision, the first level, can be readily worked into mathematics instruction.
Writing with vision, the second level, may take more time but enables teachers to connect the writing process more fully with mathematics instruction. Each level can be appropriate under differing circumstances. Regardless of which level of writing is used, the benefit to the student is a great tool in teaching students to become literate in Math. To put the benefits of journal writing into perspective, Kostos and Shin (2010) conducted a study with a group of second graders to analyze how the use of journals affected their communication of Mathematical thinking.
The results of the study found that the use of journals to enhanced second grade student’s mathematical thinking through math communication. Kostos and Shin findings showed improvement on student’s mathematical thinking through math communication, an increased use of Mathematics vocabulary and math journals worked as an assessment tool for student mathematical thinking. One area in which is beneficial is that of problem solving. Writing increases understanding, achievement, problem solving skills (Bangert, Drowns, Murley, and Wilkinson, 2004, Borasi & Rose, 1989, Steele, 2005, 2007, Herrick, 2005, and Clark, Waywood and Stephens, 1993).
It has been reported that low achieving students tend to be impulsive problem-solvers: they jump into a problem without understanding (Charles and Lester, 1984). Huggins and Maiste (1999) stated children have an implied understanding of the word order of problems but their experience with verbal forms doesn’t connect their understanding. In other words, students understand the numerical form, but once in word form, most feel they lack skills to solve the problem.
With journal writing the problem solving breakdown can be improved because students will have a better understanding of the word order and verbal forms because they are consistently using journal writing as a regular part of their Math instruction. As the research has shown, journal writing has many benefits to students and teachers. Students can learn from their writings by processing information received from instruction and putting down on paper in their own words what they think they have learned from the lessons.
In return, the teacher can review these journals and make assessments about what the student has learned and give additional instruction if patterns arise in the journals indicating that students do not understand the material. Importance of Vocabulary We have seen how writing is important to literacy in Math, now we will look at the importance of vocabulary. According to Fletcher and Santoli (2003), vocabulary of math is not usually taught in school and if students are not reading good textbooks, then they have no place to read math terms.
As mentioned earlier, Yang’s study on textbooks showed students needed assistance from outside sources to fully understand the complex texts. As teachers, we cannot always select the perfect textbook; we use what we’ve been given so it is us to the teacher to make the most out of the text. Math vocabulary plays and important role in a student’s ability to understand daily lessons, complete homework, discuss ideas in groups, take tests and be successful in achievement tests (Amen, 2006). If vocabulary plays a primary role in so many aspects of math then it is important that vocabulary development be a part of Math instruction. Teachers need
utilize strategies such as word walls, vocabulary journals, and other activities to stimulate the use of vocabulary in Math instruction. Amen suggested the following strategies for achieving an understanding of math vocabulary: * Require use of mathematical language within the classroom * Create a glossary of terms that is available to all students and grows with each chapter * Use of word walls as a review of terms * Daily problem solving activities * Pre and post vocabulary inventories Amen also stated in her research that the direct instruction and support of math vocabulary increased test scores and confidence in test takers.
This is encouraging news when so much focus is placed on achievement test scores. The use of vocabulary activities in the classroom to help students more literate in math will also narrow the gaps in students who are lacking many of the basic skills, prior knowledge, and mathematical thinking stated earlier by Amen. Strategies for Teaching Literacy Writing and vocabulary are a very important part of Math literacy. For students to become literate, teachers need to include strategies in the classroom for students.
During the study conducted by Kester Phillips, Bardsley, Bach, & Gibbs-Brown (2000), as teams worked on lessons and making connections they began to realize that not only was their job to teach children mathematics and literacy skills and strategies, but it was also their job to help their students make connections between them and help them transfer these skills and strategies to other content areas. These strategies need to be a part of every lesson and used every day. Many students learn by repetition and the daily use of these strategies will drill these key pieces of information home.
Strategies should be introduced slowly but diligently. Implementing a number of changes will intimidate students and teachers will not see any improvement. When developing strategies for direct instruction and individual and group activities, teachers need to consider two things: the students in the class and the needs of those students. Not all students will be on the same instructional level and some students in the class may need accommodations or extensions. Recommendations for teaching adolescents with difficulty learning math were
recently described in a reconceptualization of teaching and learning called the Key Model (Bottge, Heinrichs, Chan, & Serlin 2001). The model suggests that leaning is enhanced when teachers attend to the following: * Providing meaningful problems that motivate students * Affording opportunities for students to use their prior experiences * Situating learning in contexts that help students connect their new knowledge to future applications * Helping students build confidence in their ideas in “safe” groups before expecting them to reveal them in high-stakes settings * Keep expectations for all students high.
* Continuing to emphasize foundation skills In addition to the Key Model, Smith (1996) stated that because proponents of school mathematics reform prescribe neither content nor method of instruction, math teachers may feel less sure of what it is they should teach and less capable of employing methods to teach it.
Smith suggested that teachers do the following: • expand problem choice to include problems from a variety of situations that are part of students’ lives now, not just in the future; • continue to be experts in their content fields so they are able to predict student reasoning; • give students opportunities to express themselves through mathematical discourse as they work to construct and refine their mathematical thinking; • balance students’ constructions with selective, judicious telling in order to help them gain terminology; • model mathematical ideas; and.
• assist students in their mathematical reasoning. Based Strategies can be simple and become more complex as students present and understanding of Math skills. Selecting strategies for all students can present a challenge because it is difficult to please the entire class, but if the teacher will listen to the students and observe students response to activities, creating strategies will come with ease. The first and most simple of activities is for students to keep a journal.
Journals were mentioned earlier and are an excellent way for students to record information from class instruction such as definitions, calculations, formulas, and other key information. This journal will include specific information provided by the teacher and written in the journal per teacher request, information the student deems important, and reflections by the students about what they learned from the lesson. This portion can be looked at by the teacher as an assessment that the students understand the instruction and have an understanding of the material.
Another writing exercise for students is the use of post-it-notes in the textbook. Students will use the post-it-notes to write key reference words and stick to the page in the book that relates to the information on the post-it-note for the students to reference when needed. This will help students understand their textbook and the post-it-note will make for quicker access so students don’t have to waste time struggling through the text to find the information. There are many vocabulary strategies students can use to learn everything from terms to formulas.
These strategies include the use of word walls, a vocabulary journal, flash cards, and word games (crossword puzzles, word searches, etc). Word walls are important because they stay on the wall and are added too as new vocabulary is introduced. These walls can be used as reference at any point. A vocabulary journal can consist of a team journal which involves group writings and readings using as many vocabulary words as possible with prizes going to the group that uses the most words. Another journal exercise is a journal prompt.
The teacher gives a statement that includes a math problem, students will write out directions to complete the problem. Not only does the student demonstrate how to complete the problem, but how to verbally express in words problem solving skills. Another activity for students is a lesson summary. Students will be given a worksheet with three boxes. Each box contains an exercise: take notes, make notes, and summary. Students will take notes during the lesson then create questions about the notes they took and lastly, they will summarize the lesson in five sentences.
Crossword puzzles and word searches are always fun for students. They will learn both the vocabulary word and the definition. Probably the most fun activities for students would be to play games they can relate to at home. Using board games such as bingo or taboo can be fun for students because many of these students may play these games at home. To find out whether students would be interested in the game, I would suggest a survey to for the students. Ask questions about the types of games students play and the types of other activities students like. Getting to know your students will make strategies much easier to create.
Depending on the responses of the students, if a board game idea good but there are too many games to choose from, have the students get into groups and create their own board game. Students can receive a set of guidelines for creating the game such as number of players, number of vocabulary words to be used, or the concept to be learned in the game. There are many activities for students to use to learn math in the classroom. Teachers need only be creative and select activities that the majority of the class will like. Knowing your students is very important and the best way to do that is talk to your students.
Ask questions. Listen to what students have to say. Let the students be part of the lesson. Use student ideas to make the best of the class. Literacy in Math may be easier than anyone thought and the results of every teacher’s efforts will show in student confidence and higher test scores. Conclusion There has been a serious breakdown in literacy in Math over the years. To recover from this breakdown, teachers and students need to set aside the arguments about responsibility for this breakdown and get down to the basics of teach students to become literate in Math.
To understand what it means to be literate in Math one must first realize that Math is a language unto itself. Students who are fluent in reading may not be fluent in Math because of the much of the language of math contradicts the concepts learned when learning to read and write. Letters can now represent numbers, symbols represent words or actions, and many vocabulary words have additional meanings such as the word plane. Teachers need to understand their students. Teachers need to know the instructional level of their students and also need to know information about their background.
Many students are not exposed to the language of math and therefore are at a disadvantage to students that do have prior knowledge. Teachers will be challenged by having students that lack basic math skills, lack the ability to read and any number of other challenges that may not have been mentioned in this paper. To know their students will enable teachers to select activities that will accommodate the entire class. This paper also discussed the importance of both writing and vocabulary in being literate in Math. The best way to utilize writing in the classroom is to have the students keep a journal.
This journal will allow students express thoughts and ideas, demonstrate an understanding of the materials being taught, write out problem solving ideas, and write out key pieces of information. The best way to teach students to become literate in Math is through a variety of student activities. These activities can include word walls, word games, journals, and any number of games to stimulate learning. For these games to be successful, they need to be student friendly and able to accommodate any student having difficulty in Math.
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