Structuring School Opportunities

Independent Activities in Mathematics for Young Children

Free play time. Materials are here and here. See what you can do. I am here to watch.

Independent activities are the center of mathematics learning. Independence necessitates a prepared environment, which means the work for educators goes on outside of the school day. Creating the right kind of opportunities is lots of work, which is the reason, I think, this approach to mathematics in the preschool is rarely found. Many materials are required needing organized storage. The range of materials requires flexible sequencing, often different for each group of children. Generally activities are changed once a week, some staying a week or two and disappearing for a month or two, gradually building upon the children’s natural interests.


Independent Time Versus Group Time

Independent activities are free; group times follow an adult agenda. Independent is Yin to group time Yang — distinct but interconnected: one gives rise to the other. In the independent side, the children do what they want to do in an environment open to their choices, whims, and distractions, without adult control or prescription. It can be unpredictable, for sure. On the group led side, the children participate in demonstrations and games, formal and informal, that unite the whole classroom in shared understandings. One fits into the other or envelops the other or something like that. This part, the independent activities part, is where you get to watch, document, and marvel as children construct deeper ideas about mathematics than you could ever imagine 3 to 6 year-olds being able to do.

Cream being poured into coffee

When I discuss the distinction between the two, I call attention to the current context of leader and participant. As the presenter I do most of the work, while the participants are sitting politely and attentively. I note that whether the experience of my session or class is beneficial or not depends upon what I do. If they aren’t engaged, it’s my fault. In stark contrast, we have break time, where participants get up and do whatever they choose to do and take care of their own needs. Whether their actions in the break are beneficial or not depends on them. Only they can know. As the presenter I don’t intercede to make their break better; I don’t supervise their need to use the restrooms or monitor how much cream goes in their coffee. They are independent and trustworthy actors. It’s the same for children.

Workstations Time

This is the name I use for an independent time for Mathematics and Design. I would guess that you are like many of the visitors here and have never seen workstations as I present them. Workstations are not like Montessori workspaces; there is no procedure to follow, and children are free to move about. Workstations is a routine part of the day when nothing is available other than a set of prepared activities offered as free play. Just as we offer free play in activity areas indoors, where children get to freely choose among activities, and free play outdoors, where children are free to run, climb or sit with friends, we offer this short free play time with a limited set of boxes or containers. The adult is simply present and available, like when they go off and do their thing outside. The worst thing would be to sit with them and “teach” them things, which would be like supervising the amount of cream in their coffee.

In order for this openness to work, the educator has to be sure to acquire and sequence attractive, carefully chosen materials to add to the containers before the children arrive. As the children play in workstations, the educators sit, attentively watch, document interesting developments, respond to children who take initiative and become engaged, comment on what the children accomplish, risk going with the flow, allow the children the opportunity to solve their own problems, and remain calmly present through the necessary messiness and silliness that always happens in the beginning. The children do what they want to do, while the other activities are temporarily closed. If you understand the concept of the environment as the third teacher, you know how to trust this third teacher to do the work. I promise you will be a believer in creating this kind of workstation experience for some short period in the children’s day once you have tried workstations long enough to experience the joy of having a classroom hum with amazing creativity and excitement. Hopefully by April. (~_~)

What is inside those containers has to be pretty cool to use, and the time has to be short. I usually expect 8-10 minutes in the beginning, gradually approaching 30 minutes four months later. I plan five different stations for a group of 18-20 children to give enough options so groups of 3 to 6 children play together. Five stations provides a slight press to be with others and less opportunity to be alone. I expect the activities in the boxes to stay the same for a week. The next week some or all of the options are different. It should never feel old and boring.

overtopChildren are free to move, free to float, free to sit and talk to each other, but not free to use anything else in the classroom. “This is workstation time now.” “Workstation boxes are going.” When the bell for cleanup rings, the children put the materials back in the container, return the container to the shelf, and go on with the regular day. I try to signal the cleanup a bit after the interest peaks and before boredom starts crazy time.

Workstations in Action at the First of the Year

I made a video of four-year-old children at the very beginning of a school year (September) encountering workstations on the second day of school. This particular school was for low income four-year-olds in a subsidized housing area where the children arrived from the neighborhood. Each cardboard container had an assigned place on a table or on the floor. We labeled the boxes and their corresponding areas with pattern block shapes. I have also used numerals. In this classroom workstation time was at the beginning of the day, before breakfast even, as children trickled in.

Masterful Facilitation

I have used this video clip hundreds of times as a provocation to describe how Ms. Noris Daniel “teaches” the children to use Workstations. If you would be interested in my definition of how we really teach others, simply watch Ms. Daniel. She is a master teacher. See how smooth and simple mastery is?

She modeled. She demonstrated being friendly, interested, observant, and responsive. She demonstrated authenticity and full presentness to everyone. She modeled being on the floor, using the unfamiliar materials, and even dumping the box so others could have access.

She informed. Everything she said was informative — sharing information about what the children could see or hear — without placing demands on the children to respond to anything on her agenda. There were no directions. Her two “question-like” comments were rhetorical, “What are we going to do with you?” “Did you notice that?” Since neither expected an answer, they are non-demanding. Her informative statements gave the children information about the names of things, what we do with things as norms of this school, what children have in common, and the names of the other children. Give. Give. Give. Give. Gently. Warmly. Respectfully.

She responded with attention and interest to what she valued. She noticed initiative. She noticed solutions. She noticed entry. She noticed completion. She noticed interactions. Each recognition marks that action as normative conveying the message that this is what we do at school.

Three domains of action, which is how the most powerful leaders in the military and in business act, too. They don’t make others obey their ideas, instead they personally represent the values of the organization in every statement and deed. They inform the leadership team and everyone of the facts, conclusions. goals, opportunities, descriptions of progress, challenges ahead, etc., so the members of the organization can generate the ideas and solve the problems. In response to those good things, they are careful to ensure they express their authentic personal pleasure as well as provide tangible rewards, all of which strengthen the norms in the workplace.

The success of independent activities in mathematics and design directly depends on the adults following these guides. No demands. High information. Personal warmth. Enterprise Talk addresses this further.

Workstations in Action Six Months Later

Now you can see the same children at workstations time six months later. Back at the beginning the activities in the boxes were open-ended toys to play with. Over time the activities began to shift, as you see, to mathematics and design. As you also may note, Enterprise Talk guided adult action. The children discovered playing with these items to be interesting without any direction or encouragement from adults. Of course, the adults responded warmly to tricky ideas, commented upon certain things, photographed creations, and created displays in the classroom.

I think you can see the culture in the behavior of the children. I think this is the right way to educate children in mathematics. Things are right, in my mind, when two conditions are met:

  1. The children are doing things I value.
  2. I am being authentic, open, truthful, and acting in accord with my best wisdom in the moment.

I don’t know any way to articulate more simply what I have sought to be able to do all my professional life.

Jumping Off a Cliff

I know it can be scary to simply put out the stuff and cross one’s fingers. I had to face my own fears of this. It was easy to imagine the worst case scenario of wild animals going crazy and children being hurt. I would think a visit to that page in Troubling Behavior, Clarifying Responsibilities, might remind you how the adult remains the community leader, always firmly clear in his or her own responsibilities and clear in transferring responsibility to the children. The essential component, of course, is good stuff to play with that matches these children, this week. That wisdom comes from documentation and dialogue with others. I have always found it beneficial to talk to others about the next opportunities to provide to build workstations as an independent time.

I find these guides exceedingly helpful.

  1. I stay closely attentive to the children’s interests and choices; I think of it as being “behind the children.”
  2. I stay in control of myself; I do not push, direct, encourage, assist, or mediate.
  3. I spend my time watching very closely for the good things, which I describe, narrate, and record.
  4. If there are problems, I bring them up at a later time for a group discussion.
  5. 80-20I am focused on having 80% of the children involved in the activities. In a group of 20, four children can wander around or crawl under the tables if they want, but not five. I’ll work on that fifth person to get back to four. When 80% are involved, gradually a culture of engagement and discovery will become the norm. In the video you saw, we had 100% involvement, which didn’t happen rapidly. I tell myself that I can wait through October, November, December, January, and February, if I have to. The carrots can have months to grow. I can be patient. I can trust that the culture of the 80% will dominate.

I can empathize with your doubts, if you have them. Depending upon the children’s experience outside of school, it can be very messy in the beginning. I’m excited to show you some great stuff to make this work.

Sub-Topics Navigation Problem

Navigation warning: the menu design of WordPress, which I am using, will not guide you further. These five pages of workstation information are all under Independent Activities with no submenu available. To help you navigate in this furthest basement of the site I have provided this bottom section on each page.

The big sign at the bottom of each page takes you through the series in this order. If you want to jump around you use this section.

Materials for Workstations presents the kinds of activities that work well. So many are they that they flow on into successive pages. This introductory page sets the tone with beautiful puzzles and challenges

Design Materials continues with a selection of the best materials I have found for intellectually aesthetic arrangements.

Writing Materials provides materials for pencil control, scissors, and writing numeral practice.

Mathematics Materials shares the advanced materials in number, sorting and classifying, and measurement for five- and six-year-old children, bridging to first grade.

Planning and Rotation Scheme presents a simple system for scheduling throughout one year.

Next Materials for Workstations