Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
The goals of the NCTM's reasoning process standard are that "in grades K-4, the study of mathematics should emphasize reasoning so that students can-
(NCTM, Curriculum and Evaluation Standards for School Mathematics, p. 29) Video Overview
- draw logical conclusions about mathematics;
- use models, known facts, properties, and relationships to explain their thinking;
- justify their answers and solution processes;
- use patterns and relationships to analyze mathematical situations;
- believe that mathematics makes sense."
Before this lesson, students worked on matching equivalent sets of objects and then on matching the number of objects with a numeral. Students now develop their number sense by exploring number concepts and number relationships. Drama and music connections provide the context for these explorations as students act out a story and sing a song. The children first close their eyes and count to 5. When they open their eyes, they pretend to be in an imaginary forest. Students are assigned roles, such as flowers or bunnies, and are given simple costumes. They role play as they listen to a story about five ants. After the story is told, the class sings "The Ants Go Marching" twice, with some of the children acting out the song during the second round. This lesson connects written symbols or numerals to pictures, physical objects, and oral language for the numbers 1 through 6. The number sequence is emphasized and a distinction is made between cardinal and ordinal meanings for number. Cardinality refers to how many or the quantity of a set (for example, four candles on a cake), whereas ordinal numbers refer to the relative position of an object within a set (for example, the third person in line to buy tickets for the movie). The song also furnishes students with experiences in pattern recognition (auditory, kinesthetic, and visual) as they hear, feel, and see the rhythm of the music. Topics for Discussion
For Teacher workshops
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Developing Number Concepts
- Identify the cardinal and ordinal uses of numbers in the lesson.
- Mr. Clarke used the language "number 2" and "number 4" to designate the second student and the fourth student. A next step is to help the children use the ordinal names, such as first, second, third, and so on. Design a follow-up lesson that would help the children connect the ordinal names to their meanings.
- How did the chart that Mr. Clarke used contribute to students connecting quantities to symbols to number names?
- As Mr. Clarke was identifying six children to role play flowers, one boy called out, "We need three more," demonstrating his understanding of a part-whole number relationship-3 and 3 make 6. What other number relationships did children recognize during the lesson?
- Describe ways to modify this lesson to emphasize more exploration of number relationships.
Connecting Drama, Music, and Mathematics
- How was mathematics a part of the story and the song? What is the value of embedding the study of the number concepts in the story and the song?
- Mr. Clarke likes to begin his lessons with a story. What value exists in telling a story at the beginning of a lesson?
- Instead of just narrating the story, Mr. Clarke had children don costumes and act out the story. Describe the advantages and disadvantages of role playing in this context.
- Mr. Clarke believes strongly that music should be integrated throughout all the curriculum. Identify the reactions of the children to the music, and describe how this lesson promoted sensory integration for the children.
- In the lesson, music is used to engage students, facilitate their language development, and reinforce their understanding of rhythm and patterns. What are some other benefits of using music?
- Could you tell which students had special needs? How might this kind of lesson, with its emphasis on music and drama, blur the lines between paper and pencilchildren with special needs and other children?
ExtensionsAssessing Children's Understanding of Number Representations
Dramatic Plays for Mathematical Concepts The story created for this lesson was simple and short, but it actively involved the children and emphasized some mathematical ideas. Work individually or in small groups to write short plays that emphasize mathematical concepts and that could be used with a class of young children. Each group of teachers working together can perform its play for the other groups.
Develop a set of tasks and questions to assess a child's understanding of the connections among written symbols, quantities, and oral names. For example, to assess the connection between oral name and quantities, ask a child to show three pennies. Be sure also to assess the other direction, from quantities to oral name. For example, display five pennies and ask, "How many pennies do I have?" Develop tasks for all six contexts. Depending on the age of the students, assess their ability to recognize symbols as well as their ability to write them. Then use tasks to assess some children's understanding of the connections among these representations for number.