1.  How do you promote problem-solving skills with your children?

2.  When opportunities arise for children to “figure things out” on their own, do you let them?

3.  Are you often tempted to do things for children that they can do for themselves?

4.  Is it easier and quicker to solve children’s problems than allowing them the time and support to solve them for themselves?

Yesterday, I was in a 3-year-old classroom where the teacher has spent the better part of the year focusing on supporting children’s independence, autonomy, and problem-solving skills.  I was sitting on the rug while she read a story when I noticed a boy trying very hard to tie his shoes.  He glanced over at me and I found myself whispering, “Do you want me to help you tie your shoes?”  He looked at me like I was speaking Latin.  I then remembered that the children in this room are encouraged to solve their own problems, figure things out for themselves, and work diligently to get hard jobs done.  Although it took a long time, and the laces didn’t look too secure, he did get those shoes tied without my help.

This interaction reminded me that even though I like to be helpful and fix things, this is not ideal for young children as they develop autonomy.  What makes me feel good and useful is not and should not be the focus of my interactions with children.

I know that this is the reason a lot of teachers only allow certain areas of the room to be open at a time, or why they put baskets of toys up on high shelves.  It is simply too much to clean up every single day with very small children. 

Organizing the classroom manipulatives in ways that boost children’s attempts at cleaning up while supporting the early mathematical concept of sorting and categorizing can also  help you out.  Imagine having bins put together like the ones above so that toddlers can see what toy goes where.  At the bottom of each bin, put a colorful picture of the type of toy that belongs in the bin so even if emptied out, the children can easily see that what each bin is for.

Having baskets with labels on them is also a good idea.

I don’t think you need to frame the pictures (although it is a nice touch) but with a little bit of effort, your camera cell phone and a color printer, you can make labels that clearly let the children know what belongs inside.

I also like these buckets although I would have drawings or pictures of the toys in addition to the words.  They now make chalkboard paint that you can put virtually anywhere.  Once dry, you can write on the surface and erase it just like an old-fashioned chalk board.  Using this method allows for flexibility and multipurpose use of organizing materials. At clean up time, allow the children to sort the toys to the best of their abilities.  They will not always get it right and will still need a lot of adult supervision and intervention, but developing a system that allows the children some autonomy in the efforts is a good thing, for them and for you.

Rather than spending your time reinforcing correct answers and correcting wrong answers, time is better spent allowing  children to exchange ideas with their peers so they can discover and uncover number concepts on their own.  If children become accustomed to adults as their only source of feedback, they don’t learn to trust their own instincts and argue or defend their positions.

Think about a time when a child looked up at you after completing a task (let’s say, distributing a classroom newsletter into each of the cubbies) to find out if she is right.  Imagine now, that you don’t tell her that she is or she isn’t, but encourage her to ask her friends to help her.  That means that rather than “fixing and responding” you “wait and see” how the children figure out how to solve the problem.  The friends might come over and examine each of the cubbies to look for the newsletter.  They might find an empty cubbie or a cubbie with multiple letters.  Those children will have to figure out how to explain why the task wasn’t completed accurately and then help correct it.  This interaction requires social negotiation by both parties as well as a pooling or skills to fix it.

It is the conflict between the children that creates the space for negotiation.  It is the negotiation that requires a deep and meaningful examination of each child’s own number concepts in contrast to their peer’s.  This internal chaos demands the child to examine her own belief’s or understandings and then make the necessary adjustments to construct new understandings.

Kamii explains that children who only look to adults to reinforce their ideas only find approval and disapproval.  Rather than encouraging autonomy in children, this sustains heteronomy and children continue to mistrust  their own abilities to solve mathematical problems.

This portion of Chapter 3 concludes with a discussion of group games as a wonderful vehicle for an exchange of ideas amongst peers.  Games provide a format for children to check each other’s math – “You moved 4 squares, not 3”-and children are then required to go back and investigate the mathematical question.

Kamii lays out her 6 Principles for Teaching Number broken down into three categories. The first principle of teaching number is about creating all kinds of relationships (I discussed this a coupe of weeks ago).

Principle 1 – The creation of all kinds of relationships.

Encourage the child to be alert and to put all kinds of objects, events, and actions into all kinds of relationships.

The teacher’s role is to create the “social and material environment that encourages autonomy and thinking.”  If we agree that children construct their own understandings of the world around them, then they need ample opportunity to do so with ample materials to do so with.  We want children to think for themselves and not simply do what they are told so adults must provide an environment that indirectly encourages this.  As children problem-solve, play, pretend, work, and engage with their peers, they are developing and examining all sorts of relationships in a wholly organic way.

Kamii even explains that conflict creates opportunity for children to put things into relationships.  Notions about fairness and equality are rooted in perceived hierarchical relationships.  As children develop logical thinking as well as morality these relationships adjust accordingly.  Negotiating conflict resolution requires that children consider fluid alternatives to problem-solving.  The less a child is required to simply “obey” adult authority, the more they are able to negotiate human relationships, choices and outcomes.

Kamii describes this through the following vignette:

 

When two children fight over a toy, for example, the teacher can intervene in ways that promote or hinder children’s thinking.  If she says, “I’ll have to take it away from both of you because you are fighting.”  Alternatively, the teacher can say, “I have an idea.  What if I put it up on the shelf until you decide what to do? When you decide, you tell me, and I’ll take it down for you.”  Children who are thus encouraged to make decisions are encouraged to think.  They may decide that neither should get the toy, in which case the solution would be the same as the one imposed by the teacher.  However, it makes an enormous difference from the standpoint of children’s development of autonomy if they are encouraged to make decisions for themselves.  ….An alternative solution might be for one child to have the toy first and for the other child to have it afterward.  Traditional ‘math concepts’ such as first, second, before-after, and one-to-one correspondence are part of the relationships children create in everyday living, when they are encouraged to think. (p.30)

More often than not I observe teachers responding to the described conflict the way the first teacher did.  The teacher takes it upon herself to solve the conflict which may be the easier of the two choices, and definitely the quicker of the two.

What I tell my students and what I am telling you now, is that every time you solve a problem for a child, you rob him of the opportunity of solving it for himself.  When you think of it in terms of “robbery” it becomes much easier to make the more difficult and time-consuming decision.

Next week we will look at another Principle of Teaching Number.

When autonomy becomes the aim of education, educators will attempt to increase the areas of overlap between the area of overlap between the two circles.

In Chapter 2 of Number in Preschool & Kindergarten, Kamii  lays out one of the most basic principles of Piagetian theory.  According to Piaget, the goal of education must be to develop the child’s autonomy, the ability to self-govern.  Because schools rely heavily on the use of rewards and punishments (grades, stickers, teacher approval, time-outs, etc.) children spend the vast majority of their time in these structured learning environments governed by others – heteronomy.

She goes on to elaborate that it should not be the goal of education to simply create obedient children, as obedience is about a fear of consequences rather than an internal gauge of right and wrong.  When we apply this to learning, children who learn in order to please others or because they are afraid of the negative consequences of not doing what they are told, most often, cannot think for themselves.

What do you think of that?

Next week, I will finish exploring Chapter 2 “Objectives for Teaching Number” where Kamii discusses the difference between the “construction of number” and the “quantification of number”.  I hope you are looking forward to it as much as I am.