Lecture presented at the International Conference on Logical Mathematical Thinking

“Are you bigger than my teacher?” four-year-old Jeffery asked his slightly overweight principal on his way to the bus.

Mrs. Hix laughed, responded. “Yes,” shook her head, and thought, “Children always surprise me. I thought he meant weight, I guessed height, and he meant age! A very different view of ‘bigger.' I had no idea that's what he meant!” (quoted from Copley, et al, 2004).

Young children are fascinated with measurement concepts. They are constantly measuring how big, how tall, how much, how far, and how heavy they are compared to their friends. In daily experiences such as choosing the biggest brownie or pouring juice into too small a glass, children use and develop their intuitive notions of comparing volume, area, length, and other attributes they will eventually learn to measure. As adults, we often think of measurement in terms of formulas, rulers, and graduated cylinders. But young children encounter measurement in many contexts every day as they explore and try to make sense of their world (Copley, 2000, p.125).

I spend much of my time observing and listening to young children. In fact, I teach weekly in young children's classrooms and my experiences there combined with research outcomes have greatly informed my understanding of young children's measurement thinking. In this presentation, I want to share some conversations, classroom video clips, and photos of young children as they measure. Please know that what I see young children do often conflicts with what I think they can do and that I am constantly impressed with their abilities to experiment, “play” with new concepts, and make generalizations about their new learning. This discovery is especially true of young children's measurement concepts. In this presentation, I want to share with you some of these discoveries, relate them to research findings, and finally discuss the important role of the teacher in the development of these concepts.

I need to make one important note before I begin with the first video clip. Please know that I believe that measurement activities with preschoolers are exploratory and the goal is not mastery. The teacher's role in developing a child's understanding of measurement is to introduce measurement concepts through a variety of experiences, using the appropriate vocabulary to describe the process. Most importantly in measurement, I believe that teachers should not limit their expectations of young children. Providing a variety of experiences along with reflection and communication about those experiences will result in some surprising results!

Now, let's begin. I will discuss three different measurement ideas in this presentation: 1) the recognition and vocabulary of measurement attributes, 2) comparing and ordering, and 3) the process and behaviors of measuring. Within each idea, I will begin with photos, quotes, or video clips of young children experimenting with measurement. Unfortunately, I will not be able to share copies of the video clips or photos with you; young children's parents have only given me permission to share them during presentations and they are not for widespread distribution. However, we will be able to discuss and identify children's understandings from the illustrations. I will then follow those experiences with research findings that specifically relate to these illustrations, and conclude with a discussion about the role of the teacher in the development of these concepts.

As these few examples illustrate, children naturally use measurement and comparing language to discuss their surroundings and relationship to other animals or objects. Although the language they use is often incorrect or general, young children are aware that there are different ways of describing measurements. They begin to recognize the attributes of length (how long or tall something is), capacity (how much something holds), weight (how heavy it is), area (how much space is covered) and time. However, they often are unable to use the correct vocabulary to describe a particular attribute. In fact, they frequently over-use the words, big or little to describe length, volume, weight, area, and even time. Before children learn how to measure, they must first be able to describe and differentiate the attributes of an object by length, capacity, weight, and area.

First, children compare two objects using a particular measurement attribute. Children's first understanding of length measure involves the direct comparison of objects (Linquist, 1989; Miller and Baillargeon, 1990). First, children compare two objects and describe one as taller or shorter than the other; holding more or holding less than another; heavier or lighter than another, or covering more or less space than another. Initially, children's ideas about the size or quantity of an object are based on perception. They judge that one object is bigger than another because it looks bigger (Piaget & Inhelder, 1967). They can arrange objects side-by-side to compare their lengths. They can hold one object in each hand to compare their weights, if the weights are significantly different. They can lay one leaf on top of another to see which has the greater area—if the smaller shape fits within the boundary of the larger leaf (Clements, 2003). In addition, they can describe events as taking more or less time than another.

The second step would be to compare three or more objects or events and place them in order, a much more difficult task and one that requires many problem-solving, experiences. One of the components of measurement is the idea of transitivity (e.g., if length A is less than length b, and length B is less than length C, then length A is less than length C). This is an idea that young children typically cannot conceptualize without many experiences and discussions.

As active observers, children watch adults measure to solve problems in their world. Young children begin to model measurement behaviors and frequently experiment with both standard and non-standard tools. We know that actual measurement involves assigning a number to an attribute of an object, such as the length of a carpet or the capacity of a jar. Understanding how to measure accurately is a skill that takes many years to learn and is a process that requires many experiences. Four-year-olds can begin to learn the process of measuring with non-standard units. They can lay identical plastic chains end-to-end across the length of a room and count the number of chains. They can cover a sheet of paper with sticky-notes to measure the area of the sheet of paper. They can use teddy bear counters to measure the weight of a toy. Current thinking and research suggests that children can benefit from using rulers and other measurement tools even during beginning activities with measurement. As they have more experiences they can learn that there cannot be gaps or overlaps between the concrete units used to measure length and that the unit lengths on a ruler must be counted rather than the marks above each number (Boulton-Lesi, Wilss, & Mutch, 1996; Clements, 2003).

The process of measuring is based on some fundamental components: Conservation (an object maintains the same shape and size if it is moved or subdivided into parts), transitivity (mentioned in the previous section), unit (the number and size of units is consistently used for the measurement of one object), and iteration (e.g., using teddy bears laid end to end to measure the length of a classroom rug.) To effectively measure, young children can experiment with measuring behaviors using licorice sticks or yarn to measure their height, rice or sand in plastic tubs to measure how much “cookie dough” they need for their party, and rocks or marbles to measure the weight of the class gerbil. This experimentation with nonstandard units is a preliminary step to understanding why the use of standard tools is important for accurate measurement. Research indicates that as early as first grade, children use units to find the length of different objects and they associate higher counts with longer objects (Hiebert, 1981a; 1984). However, they often fail to see the point of having identical units of length measure. They freely mix units such as inches and centimeters, counting them all to “measure” a length (Leher, Jenkins, and Osana, 1998). Recent research also suggests that measurement ideas are dependent on the notions of unitizing and of composite units (McClain, Cobb, Gravemeijer, & Estes, 1999; Outhred & Mitchelmore, 2000). At the early childhood level, experimentation with measurement behaviors is essential to mathematical understanding. As children develop they will learn how to conserve, reason with transitivity, select appropriate units or tools for the attribute being measured, and learn to measure with multiple copies of units of the same size.

What should the teacher do to facilitate a child's ability to measure? Here are just a few suggestions that are supported by both research and my classroom experiences.

Rulers, yardsticks, meter sticks, measuring tapes, balancing scales, centimeter grid paper, and marked cup measurers are tools that should be included in every early childhood classroom. Children should be encouraged to use them “as they want” for their measuring experiments. Similarly, teachers or other adults should use them appropriately as needed in the daily class routines.

There are many measurement opportunities that occur throughout the day in an early childhood classroom. Measuring the length of the classroom when you need a new rug, using the clock to determine how many more minutes you have until lunch, deciding if a stack of books is too heavy to carry, or deciding if a piece of butcher paper is big enough to cover a paint table are all measurement activities. To help children develop an understanding of measurement, these activities need to be explicitly modeled for children. Highlighting what you are doing as you measure will only encourage their exploration with measurement.

An important aspect of any modeling activity is the oral language that is used to describe that activity. Talking aloud as the measurement activity is being modeled helps children focus on the activity and the particular measurement strategy that is being used.

Many problem-solving activities can be used that involve measurement activities. Car races between the teacher's car and the class' car provide good opportunities to measure fairly (especially when the distance the teacher's car travels is measured with tiny licorice sticks and the class' car is measured with long licorice sticks)! Colored paper quilts that must be covered completely by different rectangular shapes require experimentation with area. Making a straw bridge for the Three Billy Goats Gruff creates an opportunity for understanding the concept of weight. Cooking a recipe for no-cook candies for the entire class requires many chances to measure capacity as well as addition operations. These are just a few ideas that were initiated by young children. They are so many more!

While there are many daily experiences that lead to discussion or modeling of measurement concepts, the most obvious is that of time. Deciding how much time is left for interest centers, for outdoor play, before snack time, for clean-up, or before the day care bus arrives are all questions that are answered every day. Take advantage of these daily questions by using a timer that visually shows time passing. A visual timer and the use of comparison words to describe the time will help children understand time measurement.

Most measurements do not need to be exact. Often, only rough estimates are required for length, weight or capacity measures. Children need to hear estimation vocabulary (e.g., about, close to, almost) in context, in real-life situations.)

Assess children's progress and your understanding by observation and asking questions.

To assess children's progress with measurement, you should observe students consistently every few weeks. Observe children in interest centers and in group settings as they use measurement tools, try to fit objects into specific spaces, compare the size of objects, use measurement vocabulary, pour water or rice into containers, or use the term “bigger” to describe something.

As children are completing activities or working in small group settings, ask the following questions:

Which one is longer…shorter?
Can you find something that is longer… shorter than this? How can you show me?
How much ribbon will you need to go around this? How can you figure it out just by looking?
Can you put these three straws in order from the shortest to the longest? How can you show me your answer is right? Where would you put the fourth straw? How did you know?

Which shape can be covered with the most… the least number of blocks?
Will it take more blocks to cover the table or the book? How can you show your answer is right?
What if you used cubes to cover the book? Would it take more cubes or blocks to cover it?

Which is heavier? … lighter? How do you know?
How can you show which person weighs more… less?
Put these three rocks on the balance, one at a time. How can you tell which rock is the heaviest… the lightest?

Which container holds the most… the least? Why do you think so?
How can you find out which container holds the most water?
What if you had three containers? How would you find out which one holds the most water if you could only fill one container at a time?

o What do we do when we come to school? What do we do after that? Before lunch? What do we spend the most time doing in our class?

The development of a young child's understanding about measurement is an exciting and surprising topic. It is one that I will continue to investigate with young children as I observe and listen to their thinking!

Boulton-Lesis, G., Wilss, L., & Mutch, S. (1996). An analysis of young children's strategies and devices for length measurement. Journal of Mathematical Behavior, 15, 329-347.

Clements, D. (2003). Editor. Engaging young children in mathematics: Standards for early childhood mathematics. New Jersey: Lawrence Erlbaum Associates.

Copley, J.V., Glass, K., Nix, L., Faseler, A., De Jesus, M., and Tanksley, S., (2004, February). Measuring experiences for young children. Teaching Children Mathematics. pg. 314-319.

Copley, J. V., (2000). The young child and mathematics. (pgs. 125 – 146). National Council Teachers of Mathematics and National Association for the Education of the Young Child.

Hiebert, J. (1981a). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12, 197-211.

Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children's reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Mahwah, NJ: Erbaum.

Linquist, M. (1989). The measurement standards. Arithmetic Teacher, 37, 22-26.

McClain, K., Cobb, P., Gravemeijer, K., & Estes, B. (1999). Developing mathematical reasoning within the context of measurement. In L. V. Stiff (Eds.), Measuring mathematical reasoning in grades K-12, (pp. 93-106). Reston, VA: National Council of Teachers of Mathematics.

Miller, K. Fl, & Baillargeon, R. (1990). Length and distance: Do preschoolers think that occlusion brings things together? Developmental Psychology, 26, 103-114.

Outhred, L.N., & Mitchelmore, M. C. (2000). Young children's intuitive understanding of rectangular area measurement. Journal for Research in Mathematics Education, 31, 144-167.