For children in the early elementary grades, experiences with classifying and sorting are important to their development of reasoning. When children sort and classify, not only do they develop reasoning skills for algebra, but also skills that will be important in terms of data analysis.
Having children sort everyday objects such as buttons or lids is one example of the type of activities that can be done in this area. However, one important thing to remember about sorting is that in order to sort, children need to know something about attributes. We as adults take this information for granted, but it is important before having children begin to sort items, to hold up a particular item such as a button, or lid, or attribute block, and ask kids to describe it. Focusing their attention on the shape, size, color, texture of an object will help them to develop a sense of attributes or properties of an object. This will be helpful for getting children to sort items in a logical manner.
This link will allow you to download the GSP file sorts.gsp . This file is set up to develop children's understanding of Venn Diagrams and give them another type of sorting experience.
Introducing the sketch
This sketch has circles and squares that vary in size, color, and in border thickness. The students have the option to work the sort using either one, two or three loops. They also must label the loops with a given attribute such as : circles, big objects, red objects, thick borders, etc. Once they have done so, working in pairs, the students should take turns placing all of the objects in the diagram.
I suggest working with one loop to begin with to develop the idea of the complete space of the diagram. For example if I was playing with one loop marked squares, the squares should all be placed inside the loop and all other objects should be outside of the loop, but in the plane of the game space. Emphasizing the idea of "not" something is just as important as the ideas that something does fit the category. This idea is once again something that we s adults understand that needs to be made explicit for children.
I would begin with a whole group demonstration, using just one loop, and asking the PST to choose an attribute to sort by. Then as a group, we will decide what should go where and asking others to judge / justify choices. This approach is important for me to model the type of discourse and discussion that is appropriate during whole group instruction with technology. I understand that there will be times when not all students can be on their own computer, and for my PST it is important for them to see that technology can be effectively employed even when it seems you do not have enough resources.
Activities and Challenges - Here are some of the activities that could be used with PST in this environment. In doing these activities it a good idea to have students keep track of their methods and ideas so there can be some sharing of problem solving approaches during a wrap up discussion of the activity.
1. The One Loop Game - Just as was described above, the players choose an attribute, and then all shapes must be placed correctly in the game space. Each player should take turns placing an object. The partner should check for validity.
2. The Two and Three Loop Game - This time employing either two or three loops. This can make the game a bit more challenging and at the same time push the development of considering multiple attributes at the same time. In introducing this idea, it might make sense to start with two loops that do not overlap and ask children to put all squares in one and all red objects in the other. Have your students think about how to resolve the issue of what to do with the red squares.
3. Loop Games with Conjunctions - An extension of the loop games can be made by changing the rules for the lables of the loops. By including conjunctions such as "and, but not, or" the game can be altered to be even more complex.
4. Mystery Loop Games - Instead of having students choose the labels for each loop and displaying them, we have them chosen, but not revealed to the other player(s). One person selects the categories and becomes the judge for the task. Then this becomes a problem solving exercise as the goal becomes to identify the labels for each loop by placing a shape somewhere in the game space and having the judge tell if it is correctly placed or not. This process helps to develop generalizations, conjectures, and the beginning of proof. This game can be played with any number of loops, and with any number of mystery loops.
This sketch is useful because it allows students to access materials that may be too time consuming, or expensive to produce for everyone. This is one activity that can bring technology into this are of need for elementary children but in no way should suffice as the only experience PST (or children for that matter) should have in sorting and classifying.