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The and reports of the National Assessment of Educational Progress NAEP writing as ses sment National Center for Education Statistics, , administered to 8th and 12th graders, show an increase in writing scores. Applebee and Langer's analysis of NAEP data as well as other sources published during the decade preceding their review revealed that the more frequently students reported writing one or more paragraphs in science and social studies, the higher their writing achievement.
The results, however, were lower in mathematics. Indeed, many teachers find it more natural to integrate writing and science e. Wolsey examined the complexity of student writing and vocabulary learning in a cross-disciplinary writing project involving English, science, and social studies. Where was mathematics?
That we see so few examples of the integration of writing and mathematics in educational literature seems surprising, considering that the mathematics education community has affirmed the importance of such integration for many years. In , Countryman's book, Writing to Learn Mathematics: Strategies That Work, K, captured the attention of mathematics educators amid a flurry of interest and ideas e. Almost a decade later, NCTM specifically stressed writing as "an essential part of mathematics and mathematics education" p. Still, many teachers struggle to link writing and mathematics and honor the integrity of both disciplines at the same time.
Teachers of writing might say that if students are assigned to describe the process they used in solving a problem with no revision or editing, the quality of integration is drawn into question. Teachers of mathematics might say that if students are asked to write a report on a famous mathematician they may not be engaged in developing mathematical reasoning no matter how many drafts they write. Although the appropriate balance may be elusive, the endeavor is nevertheless worthy of being undertaken e. There are two levels of integration that teachers may use as a beginning point.police-risk-management.com/order/spouse/bum-dati-cellulare.php
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Writing without revision, the first level, can be readily worked into mathematics instruction. Writing with revision, 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. In Carter's description of writing tasks in her mathematics instruction, both levels are reflected. She had her students write in what she called "mathematical notebooks" p.
She also had her students write about mathematics in a process-oriented way during writing workshop. Although Carter's reflective mathematical journals and stories about mathematical concepts in writing workshop may not represent an ideal solution, they demonstrate one teacher's exploration of the possibilities. This article presents six additional examples, including student work, in which teachers have attended to the goals of both writing and mathematics.
By no means are these ideas new. Teachers may have been introduced to them before, but perhaps not in the context of mathematics. Although the following suggestions are not exhaustive, teachers have found them to be a promising place to begin. As students start class, they are given a prompt to which they respond for a few minutes in writing. The task is not designed as a mathematics problem per se, but rather to encourage students to focus on mathematics.
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One fifth-grade teacher typically used learning logs to review previously learned material. On one occasion, the prompt she posed was, What did we learn about mean, median, and mode?
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Most students wrote at least a half page filled with definitions and examples see Figure 1A. While studying probability, one student wrote the following definition: "The 'probability' of something is how likly your gonna get, pick, or find something. Figure 1A: Learning log entries by fifth graders — definitions and examples of mean, median, and mode.
Figure 1B: Learning log entries by fifth graders — definition and examples of probability. This teacher found that the quality of the learning logs improved as students shared their work: "[When a student shared] a log that showed clear understanding, this provided others with an example to follow.
Learning logs honor the integrity of writing when students write their own connections and examples. At the same time, they foster mathematical understanding by engaging the minds of students in transforming information from facts to be memorized to the construction of meaning e. Teachers often ask questions and count on having at least one or two students raise their hands.
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One fourth-grade teacher tried to involve everyone in the class by allowing think time and expecting students to write before sharing. For one think-write-share, she asked, "What is an equivalent fraction? In reflecting on the use of this strategy, the teacher commented,. I assumed that everyone understood [what an equivalent fraction is], because we've done it for a while. To address this misconception, the teacher strategically selected students to share based on the thinking she had seen demonstrated: "Kids who were getting it wrong, kids who were getting it a little, and those who knew it well.
Figure 2A: Think-write-shares by fourth graders — example showing a clear understanding of equivalent fractions. Figure 2B: Think-write-shares by fourth graders — example of equivalent fractions, before and after revision.
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The think-write-share strategy heightens student engagement in writing. Concurrently, students are held accountable for their own mathematical understanding. Students may be accustomed to taking notes, but now ask them to make notes as well. Along with listing the main points of a lesson, students can write their own reflections and perceptions.
She asked her students to fold their papers in half vertically. On the left side, she directed students to define integers and construct number lines to demonstrate relative size of integer pairs. On the right side, students wrote their own reactions and observations. One student wrote, "I will remember that on the negitive side the bigger it gets the smaller it is. I thought that was cool. Smaller to larger with zero. Zero and C aren't small, big, high, or low" see Figure 3.
It encourages students to make connections between new concepts and previously learned material and their personal experiences. A third-grade teacher used shared writing with her students to review what they had learned in their geometry unit. Using chart paper, the teacher recorded a student-generated word bank that included face, edge, vertex, congruent figures, and polygons.
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On subsequent sheets, the teacher used a black pen to record in sentences what the students shared about their learning. Next she guided them to suggest revisions and additions to their shared writing and recorded those suggestions with a different colored pen. Some changes related to word choice "learning about geometry" became "learning and exploring geometry" , while other changes related to geometry concepts. In the shared writing, students had listed 3-D shapes such as spheres, cones, cubes, and cylinders and had given real-life examples.
During revision, students added the following sentence that went beyond visualization to include attributes: "Some 3-D figures will have vertexes corners , edges, and faces. Figure 4: A shared writing about geometry composed and revised by third graders and their teacher. This teacher valued shared writing as an engaging strategy to help students internalize mathematics:.
Using Children’s Literature for Mathematical Investigations
I feel that this experience has helped them go beyond recording the information in their math journals and just doing our assignments I think it helped to make it more personal and [validate] what was important to them. Because the mathematical ideas are constructed through group interaction, students help one another learn to communicate mathematically. Using a similar process, a teacher can make a class book with students. Once a shared writing is completed on chart paper, the teacher numbers the sentences and assigns each student a numbered part to write as a final draft for a page in the class book.
Here you will find a Musical Museum, loaded to the brim with almost 2, kids song lyrics, organized alphabetically, and by category with a search engine. Musical activities designed for newborns through age 7 are presented here.