# Challenging young children through simple sorting and classifying: a developmental approach.

Simple sorting tasks and classification activities are part of the math or science curriculum in many early childhood programs. Early childhood professionals utilize a number of enjoyable exercises and materials to enhance simple sorting and classifying skills with young learners. Standards set forth by the National Council of Teachers of Mathematics (NCTM) support the use of simple sorting and classifying activities within early childhood learning environments. Within the algebra strand of the NCTM standards, there is the stated expectation that all students PreK-2 should, "..sort, classify and order objects by size, number and other properties" (NCTM, 2000).

Simple sorting and classification are fundamental concepts that help children to organize their thinking about the real world (Reys, 1995). For example, with the development of simple sorting and classifying, children begin to differentiate between plants and animals, day and night, circle and square, and one and ten. Children begin to apply logical thinking to objects, events and mathematical concepts they encounter.

The concepts of simple sorting and classifying help children to understand the notion of belonging to a group and, of equal importance, to understand that objects can be grouped in different ways or regrouped. For example, a red square could be grouped with red objects, squared objects or objects that are red and squared. Later in math, young children may apply these grouping activities to situations such as 9 which could also be viewed as 3+3+3 or 6+3. If they do not remember that 9 and 6 apples are 15 they could mentally regroup (or reclassify) the 9 into subsets of 6 and 3 apples (if they know double combinations) and then add the 6 apples and 6 apples plus three apples to get the answer of 15 apples.

In working with simple sorting and classification children can be challenged at their ability level. Very young children may classify objects that are familiar to them such as pets, type of clothes, body parts, and so forth. Slightly older children may attend to sorting or classifying tasks that are more figural such as shapes and colors (Schultz, Colarusso, & Strawderman, 1989).

This article discusses sorting and classification factors, materials, and strategies that are helpful to individuals working with or developing curricula for young children in the prenumber area of sorting and classifying. Fundamental to the discussion is the premise that sorting and classifying strategies can be used by early childhood professionals to challenge the minds of children in engaging ways through developmental sequences.

Sorting versus Classifying

Sorting and classifying are terms that are often used synonymously when dealing with prenumber tasks associated with grouping objects or attributes. In this article the terms sorting and classification will be presented as two separate levels of logical thinking. Some theorists including Piaget (Lavitelli, 1970) make a distinction between simple sorting and classifying. Simple sorting is viewed as a beginning type of grouping task in which the way objects are to be sorted is shown or told to the child, "give me all the blue tooth brushes". Children are given or told the grouping pattern for the objects. Classifying on the other hand requires children to discovery how a given set of objects might be grouped. "Look at these toothbrushes and show me how you could put them into groups." The children are not told to put objects into groups based on a particular grouping or attribute as the case with simple sorting tasks. With classifying tasks children are provided a set of objects and then asked to group the objects based on their thinking as to how the objects in each group might be the same. In short, for simple sorting tasks young children are told or shown the grouping pattern and with classifying tasks children need to determine the grouping patterns for the set of objects presented to them on their own.

Factors to Keep in Mind

In dealing with sorting and classifying tasks with young children teachers and child care professionals should give consideration to several key developmental factors. Age is an essential factor (Wadsworth, 1971) to keep in mind when working with young children on sorting and classification tasks. Tasks which might be appropriate to challenge a three year old may not be challenging to a four and half year old child. Younger children may be assigned simple sorting tasks in which real objects (fruit) are shown and they are to find all the objects in a group that are like the one shown. Older children may be presented with a set of attribute blocks and be asked to place the attribute blocks into different groups so that blocks in each group are the same in some way.

Perceptions of young children are also critical for early childhood professionals to keep in mind as they plan sorting and classifying tasks (Russell, 1954) for young learners. How things look to children is the basis for their understanding as they engage in sorting and classifying tasks. Things that look more similar may be considered the same as they work through sorting and classifying tasks. In setting sorting and classification tasks for younger children is becomes more helpful to present objects that are more dissimilar at first in their appearance.

How children construct information is another important factor to consider. Young children tend to construct information differently from adults and consequently expected responses for a task may differ between adult and child (Clements, 2001). Adults may anticipate that a young child will sort or classify a group of objects by triangles and circles when if fact the child groups the objects by things that roll or do not roll. In many cases the greatest categories or groupings often come from the children (Smith, 1977)

The initial use of tactile tasks with sorting and classifying experiences is critical and plays an important role when introducing young children to the prenumber skills of sorting and classifying. Touching or kinesthetic tasks permit messages to be sent to the brain most directly and consequently have the greatest value (Zaslavsky, 2001, Richardson, 1999) to young children for learning mathematical concepts including simple sorting and classifying. The use of real objects or models of objects is necessary when providing early simple sorting and classifying tasks to young children.

Quantity of objects is also important to consider when attempting to increase the performance level of young children and when trying to maintain interest on the part of young children. Many three-year-old children are less likely to attend to sorting and classifying tasks if there are too many objects to be sorted or classified. Starting with four to five objects and increasing to six to eight objects should be sufficient when starting with simple sorting and classifying tasks.

Another significant factor to be considered is communication or mathematical talking. There is a need for children to not only sort and classify objects but for them to communicate their thinking as to how they sorted or classify the set of objects provided to them, More recently we have come to understand the importance of discourse in learning the vocabulary of mathematics. Young children can be confused about phrases such as, "so they are the same" when dealing with sorting and classifying and providing them the opportunity to communicate their actions can help clarify mathematical terms and phrases (Corwin, 1966)

Lastly, the factor of fun (Damon, 2001) and providing children with choices (Richardson, 1999) are important considerations when trying to motivate children to attend to sorting and classifying tasks. Providing young children with a number of opportunities to engage in sorting and classifying in fun ways through individual play and group time activities will go far in promoting healthy learning through sorting and classifying activities.

Sorting and Classifying Materials

In setting up tasks for sorting and classifying is it helpful to think about types of objects to use, physical boundaries for grouping, and methods for storing and sequencing simple sorting and classifying materials. When early childhood professionals give time to the selection and organization of materials the opportunity to increase logical thinking through sorting and classification tasks becomes possible.

Materials for sorting and classifying tasks can be found around home and school. Sorting and classifying materials such as buttons, pasta, dinosaur types, attribute blocks, rocks, leafs, coins, types of pockets, and more can be placed in separate tubs. At the start of simple sorting, real objects or close representations of real objects should be used. These will have more meaning to young children. Later attribute blocks and more abstract objects can be used when working with advanced simple sorting or classification tasks.

To assist young children with the notion of grouping paper plates, loops made of string or yarn, small baskets and other dividers can be used by children when sorting or classifying objects. For example, it may be helpful for the younger child to place liked objects in baskets rather then putting them into undefined locations on a carpet. As children begin to demonstrate the ability to group things with organizers there is less of a need to use organizers like baskets, etc. to place their groupings.

Organizing simple sorting and classifying tasks according to levels of difficulty can also be helpful when planning tasks for young children. Often tubs or other containers can be used to separate simple sorting and classifying tasks. Tubs can be coded to identify easier to harder sorting and classifying tasks. In organizing tubs it is helpful to fill initial tubs for simple sorting tasks contain fewer objects, objects that have fewer differing attributes (size, shape, color, thickness, etc.), and objects that are more real life. As children begin to master the initial set of tubs the classifying tubs can be added that include more objects, objects with more attributes and objects that less representative of real life.

While the fun part of sorting and classifying with children is to select a variety of enjoyable materials to interest children, the critical decision to be made by the teacher is how to provide tasks to children that become more challenging and consequently provide the opportunity for more learning.

Logical Sequence for Simple Sorting Tasks

Sorting and classifying provide an opportunity to foster logical thinking in young children (Charlesworth, 2000). Setting up a sequential set of tasks to foster logical thinking as mentioned above is very important when developing simple sorting skills in young children. The selection and use of a variety of materials and the use of materials with varied attributes are important factors in maintaining interest and challenging thinking. Developing logical thinking information on strategies to be used to develop sequential tasks becomes important. To focus on the discussion of sequential tasks to be used with simple sorting, attribute blocks will be used as a common point of reference in the strategies to follow.

Simple sorting tasks are excellent beginning activities for promoting understandings relating to grouping. The teacher's responsibility in working with simple sorting is to provide a set of objects to children and identify how the set is to grouped. For example, the teacher may show children five different fruits and ask the children to pick out all the green grapes. In working with simple sorting, tasks selected can become more challenging by increasing the number of objects to be sorting, by having children consider more attributes, and by giving verbal versus visual clues. The levels to follow can be used to move from easier to harder simple sorting tasks.

Level 1. Young children can initially be asked to complete a number of tasks with objects (4 or 5) that contain only one attribute being different. For example, the child may be given all different shapes with the same color, or size and be asked to give the early childhood teacher all the shapes that are like the one shown, a circle. Children need to sort by shape only. In level one it is best practice to show the object and ask children to place all like objects in a container or in a space provided. Later, when children learn shapes, the teacher can simply ask children to give the circles (verbal cue) rather than a visual cue. Also, teachers may want to get into the habit of having children explain why they picked out the objects they did. This communication component may help teachers gain insight into children's understanding of why they picked the objects they did and help children to clarify their own understanding of the task. More objects can be added (5-8) as teachers work through Level 1.

Level 2. Once children demonstrate the ability to sort with one different attribute they can begin to work with sorting tasks with two different attributes. In this stage the teacher provides children with a number of objects (6-8) that have different colors as well as different shapes. Children are presented an object with two attributes, green-square, and are asked to give the teacher all objects like the one shown. The teacher should include several different shapes and colors in the pile of objects used. The child may see both green and blue squares, green and blue circles, green and blue triangles, etc. Children who select all green objects or all squares are sorting based on only one attribute. Children who select all the green-squares are classifying based on two different attributes. Again, teachers should provide children with the opportunity to communicate their sorting into groups. More objects can be added as the child becomes successful.

Level 3. Once children are successful sorting objects with two different attributes teachers can try using three different attributes, color, size, and shape. Show a large-yellow-rectangle and ask children to give the teacher all objects like this one. Teachers should ensure that the pile contains a variety of shapes, blue-small-rectangles, etc. that represent the three different attributes. The teacher should again observe to see if the child selects objects based on all three attributes.

Level 4 and Beyond. For children who sort based on three different attributes additional attributes can be introduced such as thickness. The teacher can follow the same procedures as in the earlier stages. Additional tasks might include sorting based on functions such as a spoon, fork, and knife. Teachers can have a pile of objects containing objects used for eating and not eating and ask children to give them things they would use to eat with. In working with sorting by function it becomes important for teachers to have children communicate why they selected the objects they did or tell about the objects they selected for each grouping. Teachers might also consider ways to sort objects or items using different senses. Children can taste one food item that is sour and identify other items that are sour. Children can hear one instrument, a drum, and identify other drum like sounds.

When working with level 1 through 4 sorting activities several things should be remembered. First, the teacher identifies the way objects are to be sorted. Initially, showing the object to be sorted is best. As children become familiar with vocabulary, oral requests can be used. Second, to increase critical thinking more attributes can be added as well as more objects. Lastly, it is important for teachers to have children communicate why they sorted the objects the way they did. The more children are asked to communicate the more they may begin to communicate their choices. This sharing by children will provide teachers with a better understanding of the attributes used by children to sort set of objects.

Early childhood teachers can begin to introduce classification tasks to children as they become proficient in simple sorting tasks based on multiple attributes and functions. When working with classification, teachers begin to develop in children not only perceptual judgments but also more formal mental operations (Lavatelli, 1970). When using classification tasks it is important to remember that children are not told how to classify. Children are put in the position of having to share a system by which they come to classify or group a set of objects based on their own classification groupings. As with simple sorting, a variety of materials or activities can be used when engaging children in classification tasks.

When we begin to ask young children to classify sets of objects based on their thinking, it is important that teachers ask children to communicate their reasoning behind their classifications. While a variety of materials may be used to explain the sequencing of classification strategies, basic attribute blocks with color, size and shape will again be used in the levels to follow to outline a sequential set of strategies for developing classification tasks.

Level 2. Once children classify objects based on one different attribute children can be given a group of objects that have several different attributes and be asked to show several ways in which they could be classified into groups. For example, if given attribute blocks with different colors, sizes and shapes the children could first classify them by color and then be asked if there is another way the objects could be put into groups so somehow they are the same, perhaps size or shape. It is interesting to note that young children normally will look first for the attributes of color and shape before the attribute of size. This second level will help children look for many ways to classify a set of objects. Again, it is important to have children communicate why particular objects were placed into certain groups. In this way teachers can gain an understanding of children's thinking and ask for clarification if needed.

Level 3. Once children can classify a group of objects in multiple ways based on increasing number of attributes teachers can challenge children in classification by asking them to classify the objects in such a way that the objects could fit into a specific number of groups. For example, objects in a pile to be classified may include objects with three different colors, two different shapes and two different sizes. The teacher puts out three plates and asks the children to put the objects on three different plates so that the objects placed on each plate are some how the same. The teacher's expectation would be that because there are three different colors, children would classify the pile of objects by color and not shape or size. It is interesting to note that many younger children of four and five years of age who can complete classification tasks for level 2, may struggle at first with level 3 tasks. The intent of this level of classification activity is to have children think logically about the number of possibly ways a set of objects could be classify and deduct from all possibly ways the one way that best fits the specific number of groups being asked for.

Level 4 and beyond. In addition to setting up classification tasks that are more teacher directed as indicated in level 1 through 3 above, it is important that teachers provide opportunities for children to participate in children-to-teacher and children-to-children classification tasks. A child can select a group of objects for the teacher or other children to classify based on a system the child has in mind. This reversal of roles can provide children the opportunity to develop another level of understanding with regard to classification. By setting up tasks for others to solve, children form classification thinking in new ways that can add to and clarify their understandings. These reversal of roles opportunities will also help teachers understand better the depth of classification understanding individual children have.

As with simple sorting, in working with classification activities teachers can use attribute blocks or other child-centered materials that contain different attributes or functions. In challenging children to identify objects that are classified one-way, objects that can be classified in multiple ways, and by having children consider which way of many ways to classify meets a certain criteria presented, children have the opportunity to become more involved in logical thinking activities.

Concluding Thoughts

Children who have the opportunity to work with activities associated with the concepts of simple sorting and classifying can develop understandings that allow them to organize the world around them. Through the use of simple sorting and classification tasks, teachers help develop children's thinking in terms of grouping and regrouping which is important to learning.

Early childhood professionals should give consideration to a number of important factors such as the age of children, tactile involvement with materials, quantity of objects when developing simple sorting and classifying tasks. It is equally important that children be given the opportunity to communicate why and how they complete sorting and classification tasks. In developing sorting and classification tasks early childhood teachers should keep in mind that young children are perceptual learners and what they see is what they understand in many cases. The materials selected for simple sorting and classifying should be of interest to children.

A final consideration should also be given to how simple sorting and classification tasks are organize to ensure that children are being challenged. It is important to start with simple sorting tasks that contain fewer objects and fewer attributes with real objects. As we organize more challenging tasks children care professionals should begin to switch to classifying tasks that cause students to select or determine possible groupings for a set of objects presented. By selecting and developing tasks organized in some sequential manner, children will have the opportunity to extent the ways they think about new situations and assist them in organization new information.

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DONALD L. PLATZ

University of Wisconsin-Stout

Menomonie, WI 54751