Of the three children who are using the turkey basters as a tool to move the water, none of them are using it the way it is intended.  Since we don’t know the background of the children we can’t assume that they have had or have not had experience using turkey basters or observing others using them.  This may be their first opportunity to play with them in the water table. They appear to understand that somehow the liquid is supposed to go into the tube and the rounded end is for squeezing.  They do not know that the rounded end is also key to getting the water up and into the tube. They are using the basters pretty successfully as tools for stirring the water.

The water table is rich with mathematical experiences for children.  Not only are they estimating and measuring, they are also problem-solving .  In this scenario, we can also see the children motor planning**.  They have to figure out how to use both of their hands simultaneously to hold the cups, pour the water, make the water wheel spin, and hold the baster. Both the turkey basters and the making the water wheel turn require a sequence of coordinated movements to make them work.

Now watch the next video.  In this one, one of the teacher has come over and is providing scaffolding around the use of the turkey basters.  What do you think?

How would you support these children? How specific would you be in offering instruction?  How do you know when to provide exact directions for problem-solving and when to encourage independent problem solving?  When do you “teach” and when do you “scaffold?”

One of the things I consider when deciding which technique to choose is whether or not, through observation and experience, and trial and error, a child could figure how to do something (in this case-manipulate a turkey baster) on his/her own.

In the video, the teacher explains the required sequence of manipulations for the basters to work.  She explains to the child that he needs to squeeze the rubber end, put it into the water, release the end so the water will be sucked in, and then squeeze the rubber end to move the water out.  I don’t know about you, but I think this is a very complicated tool to learn how to use. To be honest, I’ve seen many a grown-up fail to use a turkey baster correctly come Thanksgiving time.

You have to follow the sequence exactly or it won’t work.  For young children, especially those under three, following these multi-step directions is very difficult.  As they focus on one part of the problem, they can’t (or find it extremely difficult) to pay attention to the other details at the same time. They may be able to squeeze the rubber end and put it into the water, but then remembering to release it and let the water rise is probably too many things to expect a very young child to be able to do.  You can see that even after the teacher has explained it a few times, the boy continues to struggle while he little girl uses the baster to scoop the water out of the cup.

In the case of a complicated tool, I would show children the steps to make it work.  However, I would focus on the first step, until the children are successful before moving on to the subsequent steps.  I would also play alongside the children and model using the tool.  Remember to encourage the children to follow the steps by explicitly saying, “First squeeze.  Then put the tip in the water.  Then release and watch the water go up.”  Keep repeating this sequence until the children are able to complete the sequence themselves.  They will be so thrilled when they master this tool.

**Motor planning is the ability to conceive, plan, and carry out a skilled, non-habitual motor act in the correct sequence from beginning to end. 

https://nspt4kids.com/healthtopics-and-conditions-database/motor-planning/

Last week I wrote about the importance of impartial and accurate observations of children.  Teachers of young children need to systematically use observation as a part of their daily practice in order to plan for appropriate and engaging learning opportunities, to set up the environment so it is both challenging and safe, to collaborate with other professionals, and to communicate accurately with families.

Today, I want to look at the video above and consider ways in which to support this child as he actively investigates the ramps.  Let’s tease apart the ways he is already exploring early mathematical competencies and ways we can further support his play so he can go deeper. During free choice time, this particular child came over to the large rug, where a long rubber track was placed along with a few wooden balls of various sizes.  He began exploring the track but before long (a minute or two) he went to the corner of the room and pulled out some wooden ramps and large block.  What you see in the video is what happens next.

Before we begin to analyze his play we need to accurately and objectively observe his play. What do you see? What is he doing?

At first, the child lays down three tracks of the same length from a large wooden block and then adds tunnels to the ends of the tracks.   He rolls a ball down each ramp, one-by-one, smiles and collects the balls to start over. He then uses his hands to hold three balls at the same time, and then places them all simultaneously at the tops of the ramps and releases them at the same time. He runs to where the balls have stopped, collects them and repeats the same action. Holding the balls in his hands, he goes back to the ramp box and takes out one more ramp and tunnel and sets them up next to the original three. He asks his teacher to help hold a ball and then asks me (while I was recording) to hold the last ball.  He indicates what he wants us to do by verbalizing and nonverbal cues, and we all release the balls at the same time.

He goes back and collects eight more ramps and sets them up.  The ramps are in sets of similar lengths and in descending length order. He places them side by side and when he gets to the last one, he puts it off on the end of the block but then moves it and makes room for it with the others. He collects the balls and hands them to his teacher.  He goes and finds a small car and places it at the top of a ramp.  He then uses one of the balls to push the car down the ramp and through the tunnel. 

I LOVE this clip.  There is so much going on during these three minutes there is no way we could possibly discuss it all. But, let’s give it a go.

Where is the math?

1.  Spatial Reasoning – Notice how he places the ramps, makes room for the last ramp, lines up the tunnels at the end of the ramps.
2. One-to-One Correspondence- As he places one ball at the top of each ramp, you can actual see him making this assessment and adjusts his actions to each ramp has one ball.
3. Sorting and Grouping- We don’t know from this observation whether he purposefully sorted the ramps by length and then grouped the like lengths together, but we do see the ramps end up like this.
4. Problem-Solving – He tries to roll the car down the ramp on its own (you don’t see this bit in the video) but it won’t move on its own.  He uses the ball to push the car down.

We could spend more time analyzing the video, but this is enough for now.

The next step is to consider ways to support his explorations and scaffold his understandings.  If you were his teacher teacher, what would you do to plan for this child?

I am going to offer a few suggestions.  They may seem obvious, but often I find that they are not.  I am only offering a few so there is room for readers to offer their own ideas.

1. Bring the ramps and balls out again – In my experience, I have found teachers set up learning activities for one day and then switch them up the next.  Children need many opportunities to explore the same materials over time.  I would even reassure him that the ramps and balls will be out so he can continue playing with them as he might think of other things he wants to add to the play.
2. Add one more element – It may be interesting to add another element to the activity.  Maybe a few more cars of various types and sizes or a ball of yarn (I’ll let you consider ways yarn may enhance the activity).  Don’t add more than one at a time, unless the child asks or comes with the idea himself.
3. Talk about the ramps and balls at group time – Tell the other children about the ramps and balls or better yet, let the child describe what he was doing with the ramps and balls to the other children.  This may pique their interest and some may join him, or he may explain in his own words, what he was doing, what he was thinking, and why.  This could be very enlightening.

Those are my three ideas to further support his play.  What would you do?

So, for the month of June, I will be the guest blogger.

Since the blog debuted on July 1, 2012 there have been 795 posts and over 100,000 readers.  Those are really impressive numbers even when you factor in that we are a small, very-focused, niche blog.  The writers have written about so many aspects of young children and math: teaching young children math, supporting math competencies in the adults who work with children, math learning standards, STEM and STEAM, the list goes on and on. It is clear from the data we collect about the Early Math Counts site, and from conferences where we speak about the site, that there are people all over the country who regularly use and count on the resources provided.

Using Video Observations of Children at Play

This month I wanted to look at ways to support teachers of young children using video clips of children at play.  Even though at first glance, it may not look like the children are focusing on math-related activities, or that their engagement might lead to experiences in early math exploration, but they do. This idea came about when I recently attended a statewide meeting where one of the speakers presented a new way of supporting student teachers – through virtual interactions with young children (the children are avatars.)  It got me thinking about how successful I have been using real video clips of real children to look deeply at play and to consider ways to support it.

I am still very much dedicated to the notion that young children learn through their play and that play should make up the vast majority of a child’s day in school, whether in an Infant/Toddler program, a preschool or during the early grades. I believe that his gift of childhood must be protected at all costs.  One way we can do this is to look at play with educators’ eyes, a focus on development, and through the lens of “play is still (and will always be) the most appropriate way for young children to make sense of the world around them.”  The battle between “learning” and “play” is not real.  Learning and play are one and the same, and it is up to us to educate parents, other teachers, administrators, and funders that young children who are allowed to play freely will be well prepared for school and life.

In the AAS program at Harold Washington College, students practice the skill of “observation of young children” followed by interpretation and reflection in all ten of their early childhood courses.  These are skills that take years to hone and are usually complicated to complete simply because their observations take place in the real world, with no two students looking at the same thing at the same time.  Fortunately for me, I have been the field instructor in the student teaching practicum for many years, and I have been able to videotape children at play throughout that time.  I now have a library of over 200 videos of children at various ages and stages of development, in diverse and interesting settings, and engaging with a variety of other children, adults, and materials.  I use these videos as a teaching resource so that we can observe children at play together and through a series of prompts and questions, students can work on these skills in a controlled setting.

Personal Bias

https://news.yale.edu/2016/09/27/implicit-bias-may-explain-high-preschool-expulsion-rates-black-children

In August, 2017 the Governor of Illinois finally signed a bill that makes it illegal to expel a young child from school or child care. Data from 2005, showed that three times as many Illinoisan preschoolers are expelled than their K-12 counterparts and of those expelled, African-American boys are most likely to receive this ultimate punishment.¹

Personal bias is real and should be addressed as such in teacher education programs and through professional development opportunities.  One way to begin mitigating the negative affects of personal bias is by encouraging teachers to confront their own biases as well as their own “triggers.”  Once they become aware of their own issues, they are better able to recognize them and adjust themselves accordingly.  Last semester, one of my students told me that she has an issue with children who say, “No.”  She was in a toddler classroom, so this was an exceptionally difficult trigger for her to overcome.  After we discussed this, she realized that she was raised in a home where it was unacceptable for children to challenge the adults in any way.  Her experiences, over many, many years, were a very powerful instructor. She believed that children who say, “No” are bad children.

After revealing personal biases, we work on objectivity.  This takes practice and does not happen overnight.  Teachers need copious opportunities to simply observe.  They also need opportunities to write down what they “see” in accurate and factual ways, free from subjectivity and opinion. This is a lifelong process.  Even people who do this well can slip up once in a while or slide backward over time.

Over the next three weeks, I am going to post some videos of children at play so we can practice observing and looking for opportunities to support children’s early math skills.  But, first things first….

What do you see?  Be as factual and objective as possible.

¹http://abc7chicago.com/education/rauner-signs-bill-preventing-expulsion-in-preschool-early-childhood-programs-/2307628/

An early childhood science area is usually made up of tools used for exploring materials and collections of materials. Tools such as magnifying glasses, goggles, light tables, mirrors, magnets, specimen viewers,sorting trays, tweezers and thermometers (to name a few) should be made available to children at all times so they can investigate the “collections” you have in your room.  Ideally, the children themselves helped in developing the classroom collections.  For example, during walks around the neighborhood, the children can collect leaves that have fallen to the ground.  At this time of the year, your leaf collection can be pretty spectacular. Unfortunately, this collection needs to be replaced annually. as the leaves will dry out and fall apart.  That process, in and of itself, is a pretty interesting one for children to explore.

It is nice to have a collection of rocks and stones.  Again, these will range in type depending on where you live. Outside of small pebbles (choking hazard) I would encourage the children to collect all sorts of rocks. The wider the selection, the more attributes they will have. Since Chicago is right on Lake Michigan, we also have a never ending supply of shells.  This collection can take years to build, but shells are an awesome found material that can be explored in a variety of ways.

So what does all of this have to do with math?

It is pretty fascinating to observe young children investigate materials and collections in the science area. I like to consider ways that children might use a variety of materials in authentic ways, with enough time and space to allow for deep exploration. It is a natural instinct for them to separate the items, categorize them, look for common traits or characteristics, order them, sort them, and count them.  The more interesting the collection, the more the children will want to spend time with it. Imagine putting out the container of seashells you see above.  There are a lot of shells all crammed in there.  I am not so sure that this is the best way to encourage deep engagement. Try reducing the collection to a smaller variety and then place those on a tray with a magnifying glass.  What do the children do?  How do they approach the materials?  How can you support their explorations while encouraging their instincts to categorize and sort?In the example above, the teacher has put out 4 shells.  They all have a common shape however, the colors and sizes are different.  This seemingly simple set-up encourages logico-mathematical thinking.  Children are faced with a relationship conundrum.  The shells look the same but they are different. It is in their “differences” that the children are able to identify the relationships between them.  One shell is smaller.  One shell has stripes.  They have to think about “same and different.”  They also have to identify their attributes. It reminds me of the Sesame Street song, “One of These Things is Not like the Other” where three items in a collection are similar and one is dissimilar.  Here, three shells are white and one is not.  Three are big and one is not.  In order for children to figure this out, they have to make sense of the relationships between them.

The differences between these shells is much more subtle.  You can hardly see the color change in the fourth shell.  But, if you provide the science tools, like a magnifying glass, the children will see the differences much more clearly. You can lay shells out on the light table as many of them are opaque or partially opaque.  The light will come through the shells in places and allow the children to see details they might not otherwise notice,

When you put out your your leaf collection, help organize the leaves in some fashion so children can approach them with purpose.  Perhaps start with the green leaves.  These are less likely to fall apart as the children handle them, and may be a little bit easier to study.  They will probably still lay flat so it is possible to put them under a microscope.

This is a leaf from a Birch tree.  You can clearly see the cells and the veins running through it. Depending on the quality of your microscope, the children will see some version of this and can make great observations about what they see.  Point out some of the characteristics of the leaves they are looking at.  Are they symmetrical?  If they are, then the children can fold them in half along the center vein and both sides will match up.  If they are asymmetrical, they won’t.

On another day, bring out the leaves that have begun turning colors.  How are these different?  How are they the same?  Be sure to leave a few green ones out for comparison.  Have the children feel the difference between the textures of the leaves as well.  Observe as they use their math skills to organize the collection into categories that make sense to them.

How else can you use the science area to support early math competencies?

One of the obvious places you could put up a peg board is in your woodworking area.

Rather than having all of your tools all jumbled up in a box under the woodworking table, hang a simple piece of pegboard up over the table and carefully organize your tools so they all fit.  Once you have them in place, lay the entire thing down on the ground and carefully draw an outline around each tool so the children can match the shape and size of the tool with the space where it belongs.  This will keep your tools organized while also asking children to use their math skills to put their materials away.

One of my favorite ways to use peg boards is to hang them up at the children’s eye level and supply the children with a selection of hooks and clips so they can create their own wall project.

Next, put out a box of tubes, yarn, and pegs (the kind you have from your small pegboard collection are perfect). Show the children how the pegboard hooks work.  They may be a little complicated at first, but they will get the hang of it.  Explain how the hooks can be moved around the board to provide anchors for their work.  Provide a few examples of how the hooks can be used with the tubes and the yarn.

This example comes from the hallway at Truman College.  See how the tubes are set up to create a ball run for small balls, like ping pong balls.  The balls move through the tubes and drop down to the next level.  This requires an enormous amount of motor planning and spatial awareness and may take a while for children to create.  Those who are very familiar with marble towers may have a greater understanding of the mechanics behind these kinds of designs. Make sure you also provide buckets or bins to catch the balls when they come to the bottom, otherwise you will have them rolling all over the classroom. Large marbles are another good option.  They move a lot faster than ping pong balls so it might be interesting to encourage children to “race” the balls and experiment with speed.

Notice the addition of the upside down bottle.  The wide bottom allows the balls to drop in and then they come out of the spout and back into the adjoined tube.  They have also added colorful pipe cleaners; a tool that is extremely satisfying to the young child.  They can be bent in any direction and are strong enough to hold stuff together.  Awesome ideas.

Clothespins are another inexpensive and interesting addition you can provide.  They work well when clipped onto the yarn, and if you have the multicolored variety, children can create patterns with them. They can use them to hang things off of their wall project, which sounds easy enough at first, but will require planning and estimating.  Heavy things may slip so the children will have to figure out that they need to use more clips or hangs things that are lighter or smaller. There are so many uses for a board like this but leaving it as open-ended as possible creates a blank canvas on which children can work.

I’d love to hear from you about what you might add to a classroom pegboard?

In order to seize the “teachable moment” we need to be prepared.  If a child runs up to you with an earthworm she has dug up and she wants to measure it, it’s never going to happen if you have to go back inside the building to find a tape measure or ruler.  Although we can’t be prepared for every hypothetical math opportunity, we can maximize our chances by creating this math kit, and adding to it, as needed.

First, find a small to medium-sized backpack.  It doesn’t have to be pretty or new.  Pull one out of the old lost and found bin and use that. Label it in some way, so it is clear that it goes outside with the group and that it is for math (and science) opportunities.

Now, fill it with supplies.  This is a short list of the items I would choose, but if you have additional ideas, please put them in the comments section.

2 small tape measure

2 small rulers (or full-sized rulers)

a small bucket balance

several small, lined notebooks

pencils 

a camera (if you dot have a spare that can be left in the bag, be sure to bring a phone with a camera, or the classroom camera.)

markers

 

small thermometer (This is an analog thermometer.  You may want a digital one.)

 

 

 

 

small field guide to birds (I like this edition.  It is designed for young bird watchers and costs $4.95)

and a small field guide to insects and spiders

Here are some ideas of how to use the Math Kit with the children.

Before bringing it outside, introduce the kit to the children during group time.  Take out each of the items and let the children explore them by passing them around the group.  Allow them to ask questions.  Once you gather the supplies back together, explain that the bag will be accompanying the group outside and the children can use them whenever they want.  You can then go through each item, one by one, and provide concrete examples for how they might be used.  Ask the children for their ideas as they will probably think of things that you never even considered.

I would imagine that depending on where you live, there are ample opportunities to look for birds and bugs in the great outdoors.  Even if you have a small outdoor space, there are probably places to dig and explore.  You probably have a few children who Howard Gardner would categorize as having a Naturalistic Intelligence.  People who are nature smart, have a strong affinity for the outdoors and are very interested in human and animal behaviors.  These children may know where to find bugs even when you don’t.  You can support these observations by using the field guide books to help in identifying the species and the names.  Encourage the children to draw pictures of what they find, take pictures of the bugs or birds, and then help the children think of ways to document their experiences.  Keeping records of their discoveries is a great way to encourage early math skills. Have the children keep count of how many they have found using tally marks, and then how many of each species.  That way they need to think of sets and subsets.  They can sort their categories by attributes (brown birds, red birds, small birds, big birds).  This will also encourage them to categorize their discoveries as they look for similarities and differences.

Use the outdoor thermometer to chart the temperature.  Begin using the thermometer simply.  Have the children look at the gauge and show them how to read the temperature.  Older children will have an easier time with this.  For younger children, you can use permanent markers to show where the “hot,” “warm,” “cool,” and “cold” ranges are.  That way, if they can’t yet read the thermometer, they can tell the range of the temperature.  Keep a daily record of the temperature in one to the little notebooks.

Use the tape measures and the rulers to measure all sorts of outdoor stuff.  Encourage the children to use these tools whenever an opportunity arises.  You may have to remind them that you have these tools in the math backpack and suggest some measurement ideas from time to time.  It might be fun to bring out a longer tape measure and try to measure things like how high the children swing, or how far they can jump. Make accurate records of these measurements in the notebooks and help the children compare the numbers.  Who jumped the furthest?  Who swung the highest?

What other ideas do you have for your Outdoor Math Kit?  Send them along!  See you on the playground.

If you look up Busy Boards on Pinterest, you will see dozens of great examples of homemade versions that are wonderfully constructed, have stimulating and varying materials, and range in size.  My neighbor’s board is HUGE!  That is one of the things I really like about it.  Several children can stand in front of it at once and manipulate the levers and knobs. It is also tall enough that four and five-year olds can stand alongside their younger classmates or siblings and play side by side. It is also solidly made; heavy plywood, securely fastened objects, and softly sanded edges.  I asked my neighbor where she got it and it turns out that her brother built it for her children as a gift.  With a little ingenuity, a dash of elbow grease, and a few hours of work you can build your own Busy Board for your classroom, program, or outdoor space.

You can see that this board is a little weather worn because it lives outside in the backyard.  It has a base that allows it to stand anywhere, but it would be equally interesting if it were to be attached to a fence or a wall as a permanent fixture in any play space.

Take a moment to look at the items that make up this busy board.  There are simple things, such as the mirror in the lower right corner, and much more complex items like the old lock and the accompanying skeleton keys hanging right near it.  Each item is either open-ended, like the chalkboard in the center, or specific in purpose, such as the numbered press lights. (Look carefully, and you can see the spaces where the other three press lights used to be. The kindergartner of the house wanted to build a robot and thought that the lights would work well in his overall design.)

Nearly all of the objects on the board support early math learning in one way or another.  For very young children, opportunities to explore relational concepts such as “on/off,” “open/closed,” “in/out,” and “locked/unlocked” are strewn around the board. Other items focus on other math areas.  The kitchen timer supports early understandings of measurement.  It has the added benefit of ringing when time is up. The stacking rings ask children to use their sequencing skills.  There are hooks around the board that allow you to hang a bag for chalk, or keys to locks.  This design asks that children match their use with other items on the board.

There are latches that slide, buttons to press, knobs that turn, a wheel to spin, and bells to ring.  Each of these actions asks that children consider spatial relationships, and develop ideas about how things work. It is a place for exploration, a place to build and test hypothesis.  If done right, a board like this can meet the developmental needs of a range of children. Yes, toddlers can stay “busy” playing at the board, but older children can also explore the items in ways that are meaningful and appropriate for their ages and stages as well.

How to build a Busy Board

Use 3/4 inch plywood (make it thick enough that screws don’t come out of the back).  Have it cut to size.

Paint the board with a nontoxic indoor/outdoor paint.

Go into you basement, garage, junk drawer or workshop and look for items that might work on the board.

Sort them.

Look for old toys that can be repurposed, like these stacking rings.

Make a list of items that you would like to include and create a “Wish List” of items you can send out to your families.  You might be surprised what people have laying around.

Gather the items. 

Lay out the items on the board and make sure that there is enough space between each item so they can be manipulated.

Secure each item to the board so it is safely adhered and can’t be pulled off.

Enjoy your board!

Here’s a list of items I think would work well.  Some may not work for an outdoor board, but you might make those removable. What can we add to the list?

Thermometer

Any type of clock

Calculator

Wall telephone (A rotary phone would be cool)

Latches

Locks

Pulleys

Push lights

Switches

Wheels

Mirror

A magnet board – magnets

Knobs

Buckles

Locks (with and without keys)

Hooks and eyes