Gibney, Thomas

Lamb, Phyllis

KnowledgeBank at OSU

=~q 3 (r) 1- 7= I 0 The third evening was spent on introductory experiences with a calculator. Students became familiar with the ,keyboard, adding 1 more, 1 less, and were shown some ways to practice basic math facts with the calculator. The fourth evening centered around logical thinking and some measurement activities. In addition to the handouts, each family received a "Math Toolbox" at our first session. The toolbox contained a tangram set, dice, odd and even counters, two-sided beans, and a deck of cards. 24 SERENDIPITY IN THE PRIMARY GRADES Thomas Gibney and Phyllis Lamb The University of Toledo Toledo, OH 43606 The National Council of Teachers of Mathematics in its Curriculum Standards for Grades K-4 states that the need for curricular reform in K-4 mathematics is clear. Such reform must address both the content and emphasis of the curriculum as well as approaches to instruction. A long-standing preoccupation with computation and other traditional skills has dominated both what mathematics is taught and the way mathematics is taught at this level. As a result, the present K-4 curriculum is narrow in scope; fails to foster mathematical insight, reasoning, and problem solving; and emphasizes rote activities. Even more significant is that children begin to lose their belief that learning mathematics is a sense-making experience. They become passive receivers of rules and procedures rather than active participants in creating knowledge. I The Standards emphasize involving children in doing mathematics in grades K-4 by interacting with materials and other children. The National Research Council reports that the teaching of mathematics is shifting from an authoritarian model based on "transmission of knowledge" to a student-centered practice featuring "stimulation of learning. 11 2 Teachers need to explore, develop, test, discuss and apply ideas. 3 William J. Bennett, as Secretary of Education, stated that, "what our children need are lessons that explore unfamiliar possibilities, and that play on their imaginative capacities." Referring to mathematics Bennett stated that, "American students are doing poorly because mathematics is too often taught as isolated formal skills rather than a means of solving real problems. 11 4 Teachers' Roles Teachers must prepare their students to be challenged by situations they and their students have not met previously. Students will be unsure about how to start the solution to a problem and unaware of how much time and effort it will take for a reasonable solution. Attitudes of the teacher and students will be important. Students must have confidence that their problem-solving strategies are adequate to solve the problems presented to them. Teachers should search for and examine good problem situations to determine if the problems are appropriate for their students. With young children, working and playing are synonymous. Free play happens naturally. Children learn many mathematics concepts while playing with blocks, puzzles, games, the 9 housekeeping center, cooking corner and the woodworking bench. Many of these pleasant, worthwhile activities lend themselves to problem-solving - weighing, measuring, seeing spatial relationships and determining quantity. Teaching problem solving requires a teacher to help students become willing to solve problems. Problem-solving strategies must be taught so students can solve problems. Teachers must teach students to think their way through problems to reasonable solutions. The skills taught should include listening and reading skills, skills related to following directions, and the skills that relate to the use of numbers, relations, and operations. Strategies Strategies are techniques for finding answers or explanations for questions or situations that present uncertainity or difficulty. There is no specific strategy to enhance successful problem solving. The only criterion is that the problem be solved in an efficient manner for the problem solver. Suggested Problem Situations for the Primary Grades Teachers of young children need to be able to rise to the occasion of a spontaneous experience such as the "teachable moment" of a special show and share time. Show and Share Upon returning from a Spring vacation in Florida, a child who had enjoyed exploring the ocean beach brought to class a collection of beautiful shells. After discussion, show and tell, and sharing, the teacher led the group to more discovery involving: 1. classification - kind of shells, recognizing same and different kinds 2. shape - comparing various shapes 3. size - measuring; weighing; using terms of more, less, bigger, smaller 4. looking for patterns; grouping 5. counting Displays using the skills were set up according to problem-solving activities. Learning and discovery games with shells were created using the skills. One special activity was a "Lotto" game created by using the shells. Six lotto cards were made 10 As a pre-activity each week, there was an estimation jar filled with things such as gumdrops, goldfish crackers, or pretzels. Each person would make a guess and the winner would be announced at the end of the evening. Families were given an estimation project to do at home, such as, estimate the number of shoes in your house and then count to check your answer. Another one was to estimate the number of times in a day the refrigerator door was opened. The first evening's topic was spatial visualization. Tangrams and grid games were used as a way to introduce geometric ideas. The second evening was spent on basic facts of addition and subtraction using manipulative materials. Odd and even counters and two-sided colored beans were used and various games were taught that could reinforce children's understanding of numbers and basic facts. 23 had a parent and two siblings so there was a total of about 45 people involved. Most of the students were first and second graders. Before our session began the parents and children were given an attitude survey. The parents stated they were willing to spend twenty to sixty minutes a week helping their child, but they felt they didn't know enough about current math instruction or were insecure about their own math ability. The children were also surveyed. Most of the students had a positive attitude toward math and felt confident about their ability in math. The things they liked most about math involved counting and addition activities. The thing they liked least was subtraction. The format of the program was a meeting one evening a week for an hour. During that time the parents were given a brief introduction of the topic and then shown several activities to do with their children at home. After each activity was demonstrated, the parent and child were given an opportunity to practice their game and ask questions. At the end of the evening, the children had a snack while I talked with parents, distributed take-home materials, and answered questions. 22 on pieces of cardboard. Outlines of six shells were made on each card. The real shells were placed in the middle of the table. Four to six children sat around the table. Each child reached out and "drew" a shell, held it up and placed it on the card where it matched. This sequence went on until all cards were filled. The teacher guided the discussion and directed the activity. Cooking Experience The everyday experiences in preschools and kindergartens provide numerous problem-solving activities involving the preparation of nutritious snacks. Each day a new plan is presented which follows a format such as: 1. Introduction and discussion of the snack for the day. Example: "Bugs on a Log" 2. Recipe on a large chart is presented: 1 large celery stalk 8 raisins 1 teaspoon peanut butter 3. Children proceed to prepare the snacks for eating: Remove green leaves on celery. Wash celery stalk. Spread peanut butter on celery. Place raisins along stalk. Another example is the Honey Balls recipe: Combine: 1/2 cup powdered milk 1/2 cup honey 1/3 cup peanut butter Put in bowl and stir. Chill. Roll into balls. Through these activities, children learn to identify numbers, count, measure, and classify objects and act out the solution to the problem of equal food distribution. They can act out and see the difference between 1/3 cup and 1/2 cup. The recipe charts are important for the child to see the pictures and "read" the directions and ingredients. Shapes and Sizes Geometric shapes are explored through the use of crackers with the various shapes of circles, squares, rectangles, and triangles. Children can also find these shapes around the room - in table-top games, toys, furniture, and other objects within their environment. Building blocks of all shapes and sizes fit right into the scheme of discovering geometric forms. A good supply of blocks includes a variety of shapes and sizes. 11 Through all of these activities, the teacher assists in the learning experience by guiding discussions and introducing problems. These activities provide readiness for the use of attribute blocks in the primary grades and allows the children to discuss and act out the solutions to problems presented by the teacher. Estimation Kindergarten children should be asked to estimate answers regarding real life situations. Children should record their estimates on a sheet of paper and then discuss the estimates with their teachers. Types of questions that could be asked are: l. How many people in this room are left-handed? 2. How many people in this class have a dog? 3. How many people in this room are wearing glasses? 4. How many people in this room have a birthday in November? It is important that all children estimate an answer. Interesting questions may arise relating to whether contact lenses are glasses and to whether the teacher is a person in the room. These provide the teacher with ample opportunities for problem-solving questions to relate children's responses to real world situations. Summary Children live in a world of mathematics. A good environment for using mathematics in kindergarten and the early primary grades is essential so students have the opportunities to discover and solve problems. Do not underestimate the ability of primary grade students to solve problems. Often students will use strategies that teachers are unable to predict. Students in the primary grades are able to make estimates, keep records of their observations, account for all possibilities, and make decisions on the basis of what has or may happen in a given situation. Students must be taught to believe they can solve a problem and must also be confident when they arrive at a reasonable answer. Problems in the primary grades must be difficult enough to present some challenge, but easy enough so that solving them instills confidence. A student's tolerance time for dealing with a problem before giving up will be gradually increased as the student understands more strategies for solving problems. Problem solving in the primary grades should not be dependent upon reading ability. Students should have problems read to them before and after they have learned to read. Students in the primary grades need to begin to develop a variety of strategies for solving problems and these strategies need to be identified and 12 INVOLVING PARENTS IN THEIR CHILD'S MATH INSTRUCTION Sue Showers Hamilton County Office of Education Cincinnati, OH 45215 Knowing the importance of parent involvement and its influence on a child's learning, I have been looking for ways to encourage parents to take an active part in their child's mathematics education. Several avenues have been explored. One way was a monthly newsletter that contained ideas and games to be. tried at home that was co-ordinated with the current curriculum. Another idea was to explain manipulatives and games to parents during conference time and then send the materials home with parents to use with their children. Summer calendars with math activities and packets with manipulatives were also sent home to reinforce math concepts and skills and to encourage parent-child involvement. All of these things helped, but I felt there was a need and an interest to further involve the parents and children. So many times at conferences, parents would make comments such as the following: "I would like to help my child, but I really was never any good at math" or "Math has changed so much since I was in school, I really don't understand it." Many parents seem to lack confidence in their math ability and have a negative attitude toward mathematics. In the past several years, I had become aware of the Family Math materials from the University of California and have been anxious to try to involve parents and children in such a math class. Last fall, I began a parent-child math group for grades 1-3. This group met for four evenings and the objective was to have parents become comfortable with mathematics and become aware of current math trends. I had hoped to have ten families involved in the program; instead, I had seventeen families. Several families 21 Math Lotto is an example of a simple team game that can provide effective practice in computational algorithms and other tasks that require 30 or more seconds to complete. (The game does not work well with basic facts and other instant recall questions.) For a class of 29 or 30 students, the teacher prepares three sets of the numbers 1-15 written on slips of paper. One set is given to the members of each team (in a class of 29, one student receives two numbers), and the third set is put into a small box. The teacher picks a number from the box, but does not immediately announce the number. A problem is given to the class , and the students are allowed time to start working on it . The teacher waits until students have had enough time to get a good start on the problem, then announces the number. The first of the two students with that number to show the correct answer (e.g., by raising his paper) scores a point for his team. The slip of paper is put back into the box. In Math Lotto, each student works on every problem because he knows that he might be called on. Since the slip of paper is put back into the box, even a · student who has just been called on might be called on again . One additional procedure can further improve the game. When the teacher hands out the numbers, some of the pairs of students can be matched on ability. (This can be done for four or five pairs of students without having it become obvious to the class.) During the playing of the game, the difficulty level of the problem can then be adjusted to the abilities of the pair of students whose number has been drawn. At a time when our society is expecting more from our schools , we need to find ways to provide more effective instruction to our students. By more careful selection and management of instructional games, teachers can ensure that all students are actively engaged in learning. Bright, George W., John G. Mathematics Games. Monograph No . 1. Mathematics, 1985. REFERENCES Harvey, and Margariete M. Wheeler. Learning and Journal For Research in Mathematics Education Reston, VA: National Council of Teachers of Brown, Byron W., and Daniel H. Saks. "Measuring the Effects of Instructional Time on Student Learning: Evidence from the Beginning Teacher Evaluation Study." American Journal of Education 94 (August 1986): 480-500. Lasley, Thomas J., and Ronald Walker. "Time-on-Task: How Teachers Can Use Class Time More Effectively." NASSP Bulletin 70 (May 1986): 59-64. 20 discussed with the students as helpful actions to use in solving problems. The "teachable moments" can come through a variety of ways such as : l. a spontaneous occurrence - something not even in the lesson plan book -such as a weather phenomenon like a sudden rainbow or tornado , or a child bringing into class something for show and share. 2. a teacher-planned event which leads up to discovery and new understanding. 3. introducing or culminating a unit . Take advantage of the serendipity experiences in teaching and look for those magic "teachable moments" . 1NCTM. Curriculum and Evaluation Standards for School Mathematics. Reston, VA: The National Council of Teachers of Mathematics , Inc.; March 1989; p. 15. 2Hill, S.A., Griffiths, P.A., & Bucy, J .F. Everybody Counts - A Report to the Nation on the Future of Mathematics Education. Washington, D.C.: National Academy Press, 1989; p. 81. 3NCTM. Curriculum and Evaluation Standards for School Mathematics, p. 17. •Bennett, William J . "Elementary School Curriculum Reform Urged By Bennett". Toledo Blade; September 3, 1986; p. l. 13 

Serendipity in the Primary Grades

https://kb.osu.edu/bitstream/1811/86549/1/OJSM_16_Summer1989_09.pdf

Serendipity in the Primary Grades

Abstract

Similar works

Full text

Available Versions

KnowledgeBank at OSU