Showing papers in "Teaching children mathematics in 2001"

Representation: An Important Process for Teaching and Learning Mathematics

Abstract: By the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. NCTM is not responsible for the accuracy or quality of the translation _________ ___ __ _________________________________ ____________________________________ ידוסיה ךוניחב הקיטמתמל יצרא םירומ זכרמ http://mathcenter-k6.haifa.ac.il 1 גוציי : הקיטמתמ לש הדימלו הארוהל בושח ךילהת Representation: An Important Process for Teaching and Learning Mathematics

Using Student Interviews To Guide Classroom Instruction: An Action Research Project.

Abstract: Guide Classroom Instruction: An Action Research Project D uring the 1999–2000 school year, the teaching staff, including teachers and instructional assistants, at Jefferson Elementary School, Jefferson, Oregon, engaged in an action research project to investigate how student interviews would influence the way that teachers present mathematics in the classroom. For the purpose of this article, action research is defined as the process of asking a worthwhile research question, collecting credible evidence to answer the question, and using the evidence to guide further improvement in a school. Action research is similar to traditional research in that it embodies a desire to inquire and understand and a commitment to use data to guide improvement efforts. Unlike traditional research, which is usually conducted by university researchers to construct general theories, action research is conducted by school personnel to build local knowledge. Although action research can yield results that can be generalized outside the local school setting, the outcomes of action research are primarily directed toward meeting the needs of children in a school through changes made by the school’s teacher-researchers.

Using Representations to Explore Perimeter and Area

Abstract: n an elementary school classroom, as in reallife, the lines between the content areas shouldbe blurred, particularly between mathematicalproblem solving and mathematical situations con-textualized in good literature. For that reason, Ialways look for interesting books about mathemat-ical situations. Why use children’s literature toteach mathematics? A good story often placesmathematical problems in the context of familiarsituations and is similar to, yet a much more elab-orate version of, mathematical word problems.Assertions that children’s inability to solve wordproblems results from their inability to read or tocompute effectively simply are not true. The prob-lem is that children do not know how to choose thecorrect operation or sequence of operations tosolve the problem. To solve a problem situationpresented in words, children need to be ableto connect computational processes withappropriate calculations. Their difficultieslie in the fact that children simply do notunderstand the mathematics well enoughconceptually to make the connection with the prob-lem-solving situation. Using books with authenticproblem situations may help children see thatlearning computation serves a real-life purpose.One of the ways that we can help students makesense of mathematical problem situations is byproviding contextualized problems that are rich invarious representations of mathematical concepts.We know from research that “there are differentlogical or experiential paths that lead to the sameideas; similar experiences may lead to different yetvalid ideas; and different models help different stu-dents construct ideas” (Graeber 1999, p. 202). Byusing different representations of mathematicalconcepts, we give children many opportunities todevelop intuitive, computational, and conceptualknowledge.The ability to connect conceptual understandingto the processes for determining perimeter and area

Developing Number Sense: What Can Other Cultures Tell Us?.

Abstract: Volume: 7 Issue: 6 Start Page: 312 ISSN: 10735836 Full Text: Copyright National Council of Teachers of Mathematics Feb 2001 Linda Lai's thirdand fourth-grade mathematics students in the Edith Bowen Lab School of Utah State University are studying a variety of counting systems used by people around the world and throughout time. Activity and voices fill the room as students use books, reference materials, and even the Internet to conduct their research. As the students work, many show surprise when they learn about and experience the many ways that people have counted and recorded numbers. From finger counting to number words that relate to our fingers and toes; to concrete materials, such as sticks, strings, and pebbles; and, finally, to the numerals invented by various societies, these students are enhancing their number sense by learning about the systems of other cultures. Additionally, the students are gaining a cultural appreciation for the diverse ways that we all use to count. Across the country Bianka Crespo's fifth-grade class at Salome Urena Middle Academies, IS218M, in New York City is involved in an integrative investigation to study the history and mathematics of the Inca. The Inca (also spelled Inka) controlled a vast area along the Pacific coast of South America until the Spanish conquered their civilization in the sixteenth century. Lai and Crespo are two of a growing number of educators who are emphasizing culture in their mathematics instruction. This article describes how they implement these ideas to create an exciting mathematical environment, one in which students not only study important mathematical concepts but also learn to value the mathematical contributions of people who are different from themselves. Acquiring Number Sense \"Imagine that you are in another country. You see some delicious-looking bananas in the market. How can you tell the market vendor that you would like to buy three bananas? You cannot speak the language of the market woman, and she cannot speak yours.\" I have often used that introduction with classes of children of various ages, as well as with groups of teachers. The usual reply is, \"Point to the bananas and show three with your fingers.\" I say to the children, \"Think how you would show three, then raise your hands and show three on your fingers. Keep your hands up, and look at your neighbors' signs for three. Are they like yours, or different?\" Most raise three fingers on one hand, but a few raise one finger on one hand and two on the other hand. Some bend their fingers rather than raise them. Which fingers do they use? Are the three fingers in consecutive order? Which gestures are the most efficient? Depending on where I am teaching, the gestures are often different, but they seem perfectly appropriate in that setting. The number of \"correct\" answers amazes students and even some teachers. How do you show three on your fingers? How would you or your students signify two or four to represent a consistent system of finger gestures? I might repeat the exercise with a larger number, perhaps eight, which would require using two hands. Still, the choices are numerous.

Second Graders Circumvent Addition and Subtraction Difficulties.

Abstract: and ones, Mrs. Underwood planned a sequence of activities about her Aunt Mary’s candy making (see Cobb et al. [1992]; Cobb, Yackel, and Gravemeijer [1995]). She explained that her Aunt Mary distributed candy to various community charities, and the charities sold it to raise money. Because her candy was selling rapidly, Aunt Mary needed a more efficient way to package the pieces to keep track of large amounts of candy. After Mrs. Underwood introduced Aunt Mary’s problem to her students, the class spent several days exploring different ways to package candies efficiently. During one of the lessons, the children wrote letters to Aunt Mary to convey their suggestions. On the following day, Mrs. Underwood explained that she had telephoned Aunt Mary and had found out that her aunt planned to follow some of the children’s suggestions to package her candies in groups of ten. During subsequent lessons, as the children solved problems about Aunt Mary’s candy, they, too, packaged candy in groups of tens whenever possible. As they did so, they developed different “packing” (addition) methods to determine the amount of candy that Aunt Mary had made. They solved such problems as “Aunt Mary has 37 candies on the counter and 25 in the pan. How many does she have altogether?” The children also developed different “unpacking” (subtraction) methods to determine how many candies remained after Aunt Mary delivered candy to various community functions. These problems included “Aunt Mary has 63 candies. Her church bazaar orders 27. After she delivers the order to the bazaar, how many will she have left?” This article shares one packing and one unpacking problem to highlight the solution and recording methods that Mrs. Underwood’s students developed for sensibly adding and subtracting large amounts of candy. The methods that they developed helped the children avoid some of the difficulties that they had experienced earlier in the school year.