Young children use sorting and classifying skills to help them organize the world around them.
Both of these skills, which emerge around the age of three, are essential in developing a child’s understanding of the real world. As these skills develop, children begin to recognize the differences between plants and animals, day and night, and different geometric shapes. They enhance their number sense and their intuitive understandings about how to manipulate numbers during mathematical operations. As a result, they begin to apply logical thinking to the mathematical concepts they encounter.
Platz (2004) offers the following suggestions ifying skills.
fying are terms that are often used synonymously, on how to teach young children sorting and class
Sorting versus classifying. Sorting and classi
but they really represent two separate levels of logical thinking. Sorting is a beginning type of grouping task in which the student is told how the objects will be sorted: “Give me all the green blocks.” Classifying, however, requires students to discover how a given set of objects might be grouped: “Look at these different blocks and show me how you could put them into groups.” Unlike sorting tasks, the students are not told to put objects into groups based on a particular attribute. With classifying tasks students must decide how the objects in each group might be alike.
Keep the following key developmental factors in mind when selecting activities for young students on sorting and classification tasks.
• Age. Tasks that challenge a three-year-old student may not be challenging to a four-year-old student. Younger students may be assigned simple sorting tasks in which real objects, such as fruit, are shown, and their task is to find all the objects in a group that are like the one shown. Older students may work with a set of attribute blocks and be asked to place the attribute blocks into different groups so that the blocks in each group are alike in some way.
• Perceptions. How things look to students becomes the foundation for understanding their environment. As they engage in sorting and classifying, things that look more similar Teaching young students sorting
and classifying skills enhances their number sense and their intuitive understandings about how to manipulate numbers.
may be considered the same. Thus, for younger students it is more helpful to use objects that are more dissimilar at first in their appearance.
• Constructing information. Because of their limited experience, young students construct information differently than adults. Adults may expect that a young student will sort or classify a group of objects by triangles and circles when the student actually groups the objects by things that roll or do not roll. Students often see categories or groupings that adults do not anticipate.
• Tactile and kinesthetic tasks. Even before young students learn numbers, using tactile or kinesthetic tasks with real objects permits signals to be sent directly to the brain about the numerosity of items. This has great value for learning mathematical concepts that include sorting and classifying.
• Quantity of objects. Three-year-old students are less likely to attend to sorting and classifying tasks if there are too many objects involved. Starting with four to five objects and increasing to six to eight objects should be sufficient when starting with sorting and classifying tasks.
• Mathematical talking. As students sort and classify objects, they should communicate their thinking aloud as to how they sorted or classified them. We know that task-related talking is important for learning the vocabulary of mathematics. Providing students the opportunity to communicate their actions can clarify mathematical terms and phrases.
• Make it fun and offer choices. Providing students with various opportunities to sort and classify in fun ways through individual play and group time activities will promote healthy learning as they engage in these activities.
Levels of sorting. Sorting tasks are excellent beginning activities for promoting understandings relating to grouping. The teacher’s responsibility here is to provide a set of objects to students and identify how the set is to be grouped. For example, the teacher may show students five different fruits and ask the students to pick out all the red apples. In sorting, the tasks can become more challenging by increasing the number of objects to be sorted, by having students consider more attributes, and by giving verbal instead of visual clues. Platz (2004) suggests the following four levels for moving from simple to complex sorting tasks (Figure 4.6).
Level 1: One different attribute. To start, the students complete a number of tasks with four or five objects that contain only one different attribute. For example, the student may be given all different shapes with the same color or size and be asked to indicate all the shapes that are like the one shown, perhaps a square. Students need to sort by shape only. At this level, show the object and ask the students to place all like objects in a container (or similar
space). After the students learn shapes, ask them to give the squares—a verbal cue instead of a visual cue. The students should also explain why they picked out the objects they did. This communication component helps teachers gain insight into the students’ rationale for picking the objects they did while helping students clarify their own understanding of the task. Increase the number of objects to five through eight as they work through Level 1.
Level 2: Two different attributes. Provide students with six to eight objects that have different colors as well as different shapes. Show the students an object with two attributes, such as a red circle, and ask them to give you all objects like the one shown. Include several different shapes and colors in the pile of objects used. Students who select all the red circles are classifying based on two different attributes. Again, provide students with the opportunity to talk about how they are sorting into groups. You can add more objects as the student becomes successful.
Level 3: Three different attributes. The next step is to sort objects with three different attributes: color, size, and shape.
Show a large green square and ask the students to give you all objects like this one. Make sure that the pile contains a variety of shapes that represent the three different attributes.
Level 4: Adding more attributes. Another attribute, such as thickness, is added as the students become more successful in their sorting. A different task might include sorting based on a function, such as a spoon, fork, and knife. Have a group of objects containing objects used for eating and not eating, and ask students to give you things they would use to eat with. When sorting by function, ask the students to explain why they selected the objects for each grouping.
Levels of classifying. As students become proficient in sorting tasks, teachers can introduce classification tasks. When using classification tasks, the students are not told how to classify. When asking students to classify sets of objects based on their thinking, teachers should also ask them to
Level 4
Figure 4.6 These are four levels of sorting tasks for children in preschool (Platz, 2004).
explain their reasoning behind the classifications they have made. Basic attribute blocks of different colors, sizes, and shapes are useful for the four levels of strategies for developing classification tasks (Figure 4.7) (Platz, 2004).
Level 1: One different attribute. Initial classification tasks follow similar strategies used in sorting tasks.
Start with four to five objects that have only one different attribute. For example, the objects may have the same color and size but have different shapes. Ask the student to put objects into different piles that are alike in some way. If the students do not classify them by shapes, the teacher puts the objects back into a pile and ask them to show another way they can be classi-fied. Any reasonable explanation by students as to how objects were classified is acceptable. As students work through level 1, add more objects.
Level 2: Several different attributes. The next stage is to give students a group of objects that have several different attributes and ask them 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 students could first classify them by color, and then the objects could be put into groups of the same size or shape. Normally, young students will look first for the attributes of color and shape before the attribute of size. Here again, the students should explain why particular objects were placed into certain groups, giving you an insight into the students’ thinking and an opportunity to ask for clarification, if needed.
Level 3: Classifying by groups. This level challenges students to classify objects in such a way that the objects fit into a specific number of groups. For example, a collection may include objects with three different colors, two different shapes and two different sizes. Ask the students to put the objects into three different groups so that the objects in each group are alike in some way. Some students 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 is to have students think logically about the possible ways a set of objects could be classified and deduce the one way that best fits the specific number of groups being sought.
Level 4
Figure 4.7 These are the four levels of classifying tasks for children in preschool (Platz, 2004).
Level 4: Student-selected tasks. Beyond the teacher-directed tasks in levels 1 through 3, provide opportunities for student-to-teacher and student-to-student classification tasks. A student can select a group of objects for you or other students to classify based on a system the student has in mind. This reversal of roles provides students the opportunity to develop another level of understanding with regard to classification. By setting up tasks for others to solve, students perform classification thinking in new ways that add to, and clarify, their understandings.
By using sorting and classification tasks, teachers help develop students’ thinking in terms of grouping and regrouping, which is important to learning mathematical operations. By selecting and developing tasks organized in some sequential manner, students will have the opportunity to expand the ways they think about new situations and assist them in organizing new information.
WHAT’S COMING?
We have looked here at some basic activities in mathematics for students in preschool and kinder-garten. The focus has been on assessing number sense, helping students to learn to count, and devel-oping sorting and classifying skills. With brain growth and development proceeding at a break-neck pace, students moving into the elementary and middle school grades are ready for more difficult and complex challenges. The next chapter examines the components and strategies that teachers of ele-mentary and middle school students should consider when constructing lessons in mathematics.
Chapter 4 — Teaching Mathematics to the Preschool and Kindergarten Brain
Reflections
Jot down on this page key points, ideas, strategies, and resources you want to consider later. This sheet is your personal journal summary and will help to jog your memory.
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