Read PDF The Mathematics in Our Hands: How Gestures Contribute to Constructing Mathematical Knowledge

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Not only does it include teaching math-specific terms such as "percent" or "decimal," but it also includes understanding the difference between the mathematical definition of a word and other definitions of that word.

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The following example, used in a presentation by Dr. Judit Moschkovich of the University of California at Santa Cruz, underscores why vocabulary must be introduced within the context of the content Moschkovich, :. In this problem, the student is instructed to "find x. The student even put a note on the page to help the teacher in locating the lost "x".

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The student understood the meaning of "find" in one context, but not in the appropriate mathematical context. I recently helped a math teacher create a Sheltered Lesson, and I was surprised to find that there were some vocabulary words that I didn't understand. My lack of familiarity with the words hindered my ability to do the math problem and gave me a deeper empathy for ELLs who struggle in the same way with vocabulary and comprehending math assignments.

Following is a list of tips for explicitly teaching mathematical academic vocabulary:. Written word problems present a unique challenge to ELL students and teachers alike. In Reading and Understanding Written Math Problems , Brenda Krick-Morales writes, "Word problems in mathematics often pose a challenge because they require that students read and comprehend the text of the problem, identify the question that needs to be answered, and finally create and solve a numerical equation — ELLs who have had formal education in their home countries generally do not have mathematical difficulties; hence, their struggles begin when they encounter word problems in a second language that they have not yet mastered" Bernardo, Teacher Xiao-lin Yin-Croft has encountered this pattern in her classroom of bilingual Chinese students in San Francisco.

She has developed a very creative way to use her students' background knowledge of math as a stepping stone for other language learning. She does this by accelerating math instruction at the beginning of the school year and then building on what students have learned in math in reading and other content areas.

First, we read math word problems; I demonstrate the logical thinking process while translating words into pictures and, finally, into number sentences.


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  • The Mathematics in Our Hands.
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  • Helping Every Learner Identify as a “Math Person”;
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Soon, they start to explain their own thinking after reading complicated word problems that involve several steps. They correct each other, and argue about which number sentences they should use to arrive at the correct final results. As they sharpen their math skills, I capitalize on their enthusiasm to teach them how to extract the most important information from texts, and move them toward the oral and reading fluency they need to understand and discuss more challenging texts. Even if you aren't accelerating math instruction, however, there are a number of ways to help students master word problems.

Krick-Morales offers suggestions in the previously mentioned article, such as explicit instruction of key vocabulary, daily practice of problem solving, repeated readings of the word problem together as a class, and hands-on activities such as movement, experiments, or drawing to help students comprehend the problem. As students become more familiar with math vocabulary, they will be able to solve problems more easily.

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As the opening quote from the Shel Silverstein poem reminds us, background knowledge plays a critical role in math class! My colleague Hillary found that sometimes her students would get "lost" in a problem simply because they didn't understand the context. Following are some tips to help in building background knowledge of students. As I've worked with content area teachers in my district to develop Sheltered Instruction lessons and activities to enhance ELL learning, I've told them, "If a student doesn't say it in your class, they're never going to say it.

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When students learn new vocabulary, the opportunity to use it must be presented in class, because students are unlikely to try it out on their own — especially academic words like "parallelogram" or "function"! Here are some tips to increase student-to-student interaction with academic language in the math classroom:. Technology can also be a powerful tool in math instruction for ELLs.

Here are some ideas ways you can play with technology in a math lesson:. Even if it doesn't come easily at first, there are ways to get ELLs excited about math.

By keeping their language skills and needs in mind when planning mathematical instruction and by helping your colleagues do the same , you will be taking important steps in helping students master mathematical concepts and skills — and who knows? Your students may be the next generation of economists, rocket scientists, and math teachers just waiting for the tools they need! It is inspiring to know that there are talented, creative teachers who are always finding better ways to teach and are willing to share the knowledge.


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The EngageNY website provides materials focused on curricular examples, standards for mathematical practice, and other materials for professional development. Discovery Education: Puzzlemaker. Puzzlemaker is a free puzzle generation tool for teachers, students and parents where users can create and print customized word search, criss-cross, math puzzles, and more using their own word lists.

Catherine Snow: Word Generation. Catherine Snow's new website provides information and resources for educators who would like to learn more about Word Generation and how it is implemented. Includes links to comprehensive academic word list that students need to master to comprehend academic content. PBS Teachers offers a database of multimedia math lessons and activities that can be searched by grade or topic.


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  5. Choose the country or region, and search by curriculum standards, subject and grade level. This worksheet offers the complete poem cited in the article, as well as some fun related activities and questions. This webcast features Dr. Deborah Short and discusses effective instructional strategies for teaching English language learner students in middle and high school, such as the SIOP model. Translating Word Problems. This is a great site for teachers in the elementary levels, as it provides a list of keywords you can teach your ELLs to look for as they read word problems.

    Also included are useful ideas and tricks to better prepare students to understand written math problems. Bernardo, A. Language and modeling word problems in mathematics among bilinguals. The Journal of Psychology, 5 , Dale, T. Integrating mathematics and language learning. Snow Eds. Jarret, D. Portland: Northwest Regional Educational Laboratory. Moschkovich, J. Beyond Words: Language s and Learning in Mathematics.

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    Ethnomathematics

    Ever since then I am fascinated by how gestures are used in mathematical communication and interaction and how they shape how we think about and understand mathematical ideas, both from an individual and from a social perspective. During that time, I also took courses in German Sign Language to understand better the mechanisms of a manual gestural-somatic language.

    The question, how learning math in this language influences what and how mathematics is learned came just natural. My entrance point into this research focus — motivational, theoretical and methodological — is hence my study on gestures.

    Christina Krause

    My further research interests, all centralizing in the questions I am interested related to deaf learners, encompass mathematical conceptualization, metaphorics in mathematics, mathematical epistemology, and aspects of language in the learning of mathematics. Each route had thirteen steps. A step is a part of the route between vertices. Participants were randomly assigned to one of the four conditions co-thought gesture, drawing, hand movement prevented, and no rehearsal , with 28 participants in each condition.

    Participants were tested individually. They were asked to study four routes, one at a time, so that they could later describe the routes to an experimenter. On each trial they were presented with a diagram that showed a complete route on an A4-sized paper i. In order to help them to get familiar with the sequence of steps from the starting point to the destination, participants were told to physically trace the existing route on the map twice with a highlighter.

    They should trace every step and not to pause at any junctions of the route. Then we removed the diagram. In the pilot test, we asked twenty participants, with five in each condition, to view the existing routes each for 20 seconds instead of physically tracing them on the maps twice with a highlighter. However, at least half of the participants in each condition recalled most of the steps in wrong order.

    One possibility was that they did not process the stimuli as routes that navigated from starting points to destinations. Rather, they might perceive them as lines and arcs that formed various visual patterns. Therefore, we changed our protocol and asked participants to physically trace the existing routes. Participants then received different instructions for rehearsal in different conditions. In the co-thought gesture condition, participants were told to rehearse the route from the starting point to the destination with their hands.

    In the drawing condition, participants were instructed to draw the route from the starting point to the destination once on a piece of blank A4-sized paper.