One of the most exciting aspects of working with young children is witnessing their sense of joy and wonder in everyday objects.  I often forget that their understanding of many concepts, and their exposure to many tools, is a brand new experience for them.  As an adult, sometimes it is easy to forget this, but children remind us to see the excitement in new things, even if it is just finding new meaning and function in a familiar object.

We all know that young learners find excitement in anything novel and different.  If you ask ten children to collect five objects and create a use for them, chances are you will get many different objects and designs because all children have innovative and pioneering ideas and, rightfully so, they think their ideas are the best! Limitations, boundaries and restrictions are not yet familiar concepts to young children.  Often they are able to express their beliefs, designs and viewpoints about many aspects of their world in a more uninhibited way than adults do; their minds are free to wander, dream and plan to their heart’s content. This is the beauty of witnessing a young child explore mathematical concepts.

For young children, introduction to these new concepts is cultivated through various spontaneous activities and games.  For instance, setting out places for a tea party, counting out spaces during a game of Chutes and Ladders, finding the biggest rock, counting fingers and toes, and going down a slide all incorporate the concepts of number sense, spatial sense, measurement, estimation, and problem-solving and critical thinking skills.  Kids are constantly practicing math skills from birth!

As a stay-at-home-mom, many of the “lessons” that I find my children enmeshed in tend to begin organically.  In my experience, children are much more interested in learning something new when they initiate or present it.  To me, it always feels like they are extending an invitation to the adult to help guide the grasping of a new concept or skill that they innately feel they are ready to learn.  As educators, our learners are advancing at their own level, and our job is to encourage and support each one of them as they succeed at one step, then move onto the next.  I find the process captivating. However, many times these learning opportunities happen at inopportune times (i.e., in the car, away from home, outside) when materials that I would typically use to help supplement my teaching are not necessarily available.  Thankfully, math is all around us; and utilizing what you have or what you can find is much better (and usually more fun) than using nothing at all, or waiting and possibly missing the opportunity.  When they are ready, they are ready – jump right in!

In my last post, I discussed the process of organizing child-centered “learning boxes”  and learning spaces where children are able to explore materials on their own and practice math concepts anytime they choose.  Of course, this is helpful when they are at home or in the classroom, but learning does not just cease once they are away from these two areas. This is where being resourceful and innovative in our own right comes in handy.  Having a small set of available materials in various places (in the car, in the garage, in a bag or purse, etc.) materials are available for times when ideas spontaneously strike.

One example of this occurred recently when we were outside and my daughter excitedly decided she wanted to practice her math skills to gear up for the start of school. Naturally, her brother (preschool-age) wanted to join in as well.  Of course, I wanted to nurture this fertile idea, so I knew my responsibilities would involve keeping both engaged, allowing both ample learning opportunities, and allowing all of us to have fun. The first thing they did was to get out the chalk and a big bucket of rocks we had previously collected.  I then asked my daughter to look in her math box for other materials to assist with her vision. She came out with large foam dice.  After some discussion about our process, we came up with the idea that they could each roll a die and count out that many rocks.

After a few rolls, this proved to be a perfect task for my younger son, but my daughter bored of it quickly.  I could sense she was ready for more a challenging task.  Again, I encouraged her to practice self-reliance and creativity and referred her to her math box.  She came out with a white board and dry erase marker found in her math bin.  She had decided she wanted to practice writing out math problems, which is a new concept for her.  While her brother continued having a blast rolling his die all over the driveway,  counting that many rocks out and then putting them all back in the bucket and starting over (practicing number sense, one-to-one correspondence and problem-solving skills), we worked together on addition and subtraction problems.

She would roll her die and write that number down, then she would roll it again and add or subtract these two numbers together to get solve the problem.   Since she is just learning how to write out a mathematical equation, I helped her better understand this method by drawing two boxes side-by-side.  She rolled the die and place that many rocks in the first box.  Then, she rolled the die again and place that many rocks in the second box.  She then went to her white board, wrote out the problem using the appropriate signs and counted all of the rocks to find the answer

They did this side-by-side for quite awhile.  After a bit, this idea then morphed into both of them working together, the older child teaching the younger how to problem-solve higher-level math concepts.  My part in the learning process became unnecessary, and I was there just as a guide when help was needed, which is exactly what child-directed learning should exhibit.

There are many different ways that math can be engaging and exciting by utilizing everyday objects in a new way.  Often the most spontaneous lessons and activities turn out to be the most fun and rewarding.  Allowing children the freedom to explore math concepts in this way makes learning fun for all!

Differentiated learning spaces are simply areas where children of any ability level can visit and practice skills.  The intention of these spaces is to encourage acquisition of concepts, foster independence, encourage growth and development and promote self-confidence.  The beauty of the space is that it is customizable to learners’ needs because you, the educator/parent/caregiver, design it with the best interests of your students in mind. In my experience, this differentiated environment is all-inclusive and allows children to learn from one another and teach one another, demonstrating boundless real-world experience. Whether you are working with one child or thirty, I have found that creating this type of differentiated learning environment not only offers learners of varied ability endless learning opportunities, but also encourages independence, organization and self-reliance. For example, you may have learners who prefer to work on the floor, or sitting at a table.  Perhaps some of your learners can concentrate better on a task in a quiet environment, while others can easily adapt to noise and other distractions. When in a learning environment of varying ability (and, let’s face it, as educators, caregivers and parents we usually are) it is our responsibility to encourage independence, self-reliance and achievement with each learner.  This is what a differentiated learning environment looks like.

Set-up does not have to be daunting, and you can take comfort in the mantra that nothing is impossible; everything is obtainable with organization and patience.  Furthermore, these spaces do not have to be uniform, and you can take liberties designing the space(s) that best suits you and your learner(s).  The main concept is to create an area (or areas) that engage and invite all learners to explore, together or individually, and will change and grow along with their dynamic development.

Here are some tips:

• Whenever possible, put materials at child’s height – this invites learning and independence.
• Invite children to find a space that will help them learn. Allow them the opportunity to have control over their own learning.  This will give them the confidence and self-reliance they will rely on later in life.
• Label everything: even if the child is not a “reader” yet, exposing him/her to letters and words will only help develop those literacy skills in conjunction with math skills, which enriches their learning experience. Additionally, this will help you stay organized!
• Create “learning” boxes (or ‘fun learning boxes’). Fill a shoebox, cardboard box, Dollar Store container, or basket (whatever you have on hand and works for you) with everyday materials you have in your home (tape measure, ruler, crayons, markers and pencils, dice, blocks, LEGOs, measuring cups, etc.); anything they can use to count and become more familiar with math concepts.  Nothing too complicated or elaborate (for the learner or teacher), just anything students can play with and explore, either with you or on their own.

• Allow children to explore these learning boxes at their own readiness. You may initially invite them to play with you, whereas you introducing the box and you both explore the materials.  You can also explain the traditional use for each tool, and together you can make a list of fun activities to try.
• I find that the adventure of discovering new things gets young children very excited about learning. A few other ideas to try when setting up these math boxes are to invite children add materials they find to the box. Being adventurers and explorers together, you and your children can explore your home and neighborhood to find other math tools to add to the box.
• Include a variety of materials for learners of all ages and ability level. Some helpful and inexpensive tools are:
  • Mini tape measure and/or measuring tape
  • Egg cartons or ice cube trays for 1:1 counting
  • Large foam dice
  • Rocks, LEGOs, small animals or gems for counting
  • Number flashcards for number recognition (you can easily get these from the Dollar Store or make them yourself with notecards)
  • Ruler
  • Paper and pencil; white board, small dry erase marker and erasure
  • Calculator
  • Abacus
  • Inexpensive math counters and math games.

*(Tip: use your local second-hand store or Facebook groups!)

• Allow children to learn and explore on their own, encouraging independence and creativity, while also offering “lessons” and “guided play” as well.
• Keep materials and supplies at their level – this allows them to explore, and invites them to play with the materials whenever and however they wish.
• Allow time for children to discover new materials. They may not know what a tape measure is, but they will enjoy the process of investigating what it can do.  Not to mention, watching them interact with new tools and materials will allow you to assess their understanding and give you an idea of what you can present to them.
• Have a number line located somewhere children can see and access when they need assistance with number recognition and counting.
• Frequently ask children to refer to the learning box in order to become familiar with and utilize the tools inside. For example, if they ask you how tall something is suggest they explore their math box to find a tool that can help with this.  If they need help remembering, “Which number comes next?” direct them to use the available number line you have displayed.  This encourages necessary life skills, such as, independence, self-reliance and resourcefulness. If you teach them now they will have the knowledge for a lifetime.

Learning boxes are a fun way for students to develop early math skills and practice early math concepts.  Additionally, for children with learning difficulties, this type of differentiated setting promotes self-regulation and confidence because its design endorses aptitude and capability, rather than helplessness. This type of learning environment cultivates the development of important self-confidence and critical-thinking skills, which allow children to grow into self-regulating, inventive, capable and creative individuals.

Today, let’s take a look at how tools are used to support mathematical understandings and how tools can be misused so they are not really effective in terms of meeting early math outcomes.  

Here you can see a few sorting trays designed so that children can create, extend, and copy patterns (green tray), sort and organize items by attribute (yellow tray), and graph (blue tray).  

This red one is divided into quadrants so that more or larger items can be grouped or sorted in other ways (I.e., animals that fly, animals that swim, animals that walk on 4 legs, animals that walk on 2 legs).

These all come in a set and are beautifully made, large enough that children can use smallish items with them but not so smallish that they present choking hazards.

So, if you had these in your room, how would you use them?

The day I saw these in a Head Start classroom, they were sitting out on a table with several bins of small manipulatives nearby.  A few children were playing with them and from my observations, it was clear that they did not know or understand the purpose of the trays.  They were using each tray much the same way they might use a plastic plate, as a receptacle for putting the toys, storing the toys, and moving the toys around.  The teacher never came over and neither modeled how to use the trays nor explained how to use them.

Here you can see how one child was putting dinosaurs into the spaces of the tray in a disorganized fashion.  At no time did a teacher support his play by suggesting alternatives, or sitting next to him and encouraging more purposeful use of the materials.

It reminds us that our role as “set designer” and “provocateur”  demands that we do not put materials out in a haphazard fashion but systematically think about our curricula, materials and environment in thoughtful ways.  We  must observe the children to know where they are developmentally and what they need from us so we can support their growth.

These tools are not meant to be put out on a table at the same time without direction.  They are meant to be used to support developing mathematical competencies.  That is NOT to say that young children should not use them to play.  Of course they should.  In fact, before I used them for their designed purpose, I would allow  the children to explore the trays, one at a time, over a period of time, to see how they explore them organically, without direction.  Eventually, I would take one over to group time and show the children how they can make patterns in the green tray or sort items in the yellow tray.  I would show examples and sit at the math table and work on patterns with the children, creating them and asking the children to extend them.  I might ask children to create their own patterns and see if I can extend them. I would set out very specific manipulative that have 2 or 4 attributes so they can be easily distributed in the sorting trays.

I would set the scene and facilitate the play.  I would use math language throughout these interactions and make it fun.  I would show excitement about the challenges these trays present and pose thoughtful and stimulating questions that the children could answer.  I would encourage the children to “try” and get excited at their efforts.

In short, I would do my job by being the best, most thoughtful teacher I could be.

Think before you set up your materials and arrange your space.  How are you going to be the best teacher you can be?