Ways to Help Children Communicate and Share Mathematical Ideas (page 2)
As we provide children with rich experiences and environments to explore and observe, we also need to provide opportunities for them to communicate and share their discoveries with others. As children explain their observations and the ways they capture these observations, they are making their own thinking more clear and visible to themselves. There are many ways to accomplish the important task of sharing.
Group Sharing and Discussion Format
As children come together as a group during the course of the day, they should be encouraged to express the discoveries and observations they have made. The figure below lists some sample prompts that teachers can use to assist students with collecting their thoughts and expressing their ideas.
Questions that encourage children to organize and express comparisons and measurements.
What did you see? What happened first? Tell us what you think about... How do you know? What do you think will happen next? How tall is your plant? How did your shadow change? How much does your rock weigh?
As children become more skilled at writing their thoughts, they can keep daily journals of their observations. They can keep track of the changes that they are observing and the phenomena that are occurring in their world. For example, if they are exploring their shadows, they may journal about how their shadow changes length at different times during the day. When children make such deliberate attempts at making their observations and their thinking visible, like scientists, they are able to make predictions and develop conceptual schemes about scientific phenomena.
Making a Book
As children have opportunities to observe, explore, and experiment with many phenomena of change and growth, they will be able to build theories about their world. As these theories become evident, a book of “Amazing Discoveries” can be created. For example, when children explore and examine what happens to shadows at different times of the day, they can begin to make claims about the position of the sun in the sky as it relates to the length of a shadow. Class statements can be made such as “When the Sun is high in the sky above, our shadows are shorter than they are late in the evening when the Sun is low.” This concept is certainly an “Amazing Discovery.”
These experiences are valuable for young children because they are the basis for much more complex and abstract concepts. The concrete experiences such as comparing the length of their shadows to the position of the Sun will, over time, expand to an understanding of the very abstract concepts related to the movements of the Earth and sun.
With each Concept Exploration, children’s theories and discoveries should be celebrated and recorded. At the end of the year, you will have constructed a wonderful book that captures the rich problem-solving experiences of the children across many topics of interest. They will have, in fact, written their own textbook, chapter by chapter, of each Concept Exploration.
Modeling Appropriate Mathematical and Scientific Language
As children observe and measure change and growth, it is important for teachers and collaborating adults to model appropriate mathematical and scientific language. As children describe phenomena of change and growth in their own language, we can supply different levels of description reflecting a more specific vocabulary. For example, “Our bean grew six centimeters in ten days,” “Our shadows were the shortest at noon,” “The wind was blowing thirty miles an hour,” “The water in the rain gauge was more than three inches high,” and “The oak tree was more than one hundred feet high.” Examples of measurement problem-solving strategies for young children are shown in the figure below.
Measurement problem-solving strategies for young children.
- Use all modes of instruction—concrete, iconic, and symbolic—and supply language.
- Pose questions and get children to explore and wonder.
- Dialogue with children about what they are measuring, how they are measuring, and what tools they could use to measure.
- Discover and invent together and independently at school and at home.
- Share and see other viewpoints and expressions.
- Make sense out of a lesson.
- Model standard mathematics.
- Have fun!
Relating Rational Counting of Units to the Process of Measurement
In order for young children to solve problems in mathematics, they need to be able to count with meaning. Young children solve mathematical problems with rational counting. As children count how many building blocks long a plant is, it is important for them to count rationally and in a stable order, knowing the appropriate sequence of numbers. Using one-to-one correspondence (that is, touching one object at a time when counting objects in a set and keeping track are important aspects of rational counting. When a child can consistently keep track of which object he touches and which sequences of numbers is used, he will be counting with meaning. When children count with meaning, they know that the last number named in a counting sequence tells how many in the set, that is, it tells the cardinal property of the set.
Rational counting is not simply naming a sequence of numbers. Children who do not count rationally use numbers as they would name people’s names in a group. That is, the counting sequence of “one, two, three, four” is done with the same purpose and understanding as naming “Carlos, Ben, Judy, and Nicole.” When children know that “one, two, three, four” tells how many are in the set, they are rationally counting.
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