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?

Sometimes I dread meetings.  Honestly, I dread most meetings but this past week I attended the annual Board Meeting for the Chicago Children’s Museum (since I am on the Advisory Board of the Tinkering Lab and we were invited to the BIG meeting) and it was exceptionally fun and entertaining.

Once the voting was over and introductions had concluded, a puzzle maker by the name of Sandor Weisz took over the meeting, broke us into groups and together we worked out an interactive and engaging puzzle.  His business, The Mystery League, is all about creating puzzle hunts for groups of people (meetings, parties, etc.).  We worked in teams, hunted for clues, uncovered the hidden meanings and solved the puzzle.

When Jennifer Farrington, the President and CEO of the museum introduced the activity, she reminded us that young children unravel the mysteries of the world much like we approach puzzles.  They examine the pieces and consider how they fit.  They twist and turn them until they make sense. The pieces are complicated and seemingly disconnected yet they try and err and try again. This is the beginning of the lifelong process of assembling understandings and making meaning of their lives, the people around them, and the world they live in.

I love this analogy.  It is accurate and uncomplicated.

PS. In each area of the museum, staff members were there to answer questions and to ask provocative questions in order to scaffold our understandings.  Brilliant.

1.   identify the problem

2.  consider options for solutions

3.  noodle through the possibilities and pick one

4.  try it out

5.  and find out if it worked.

Sounds easy enough, right?  As intuitive as this approach sounds to our seasoned ears, we learned how to move through this process over many years of trial and error and with a lot of support from the adults around us.  As children, we interacted with the material world testing hypothesis and drawing conclusions based on our rudimentary experiments.

When we couldn’t reach the sink to wash our hands, we figured out how to pull ourselves up onto the counter and balance our hips on the edge of the sink, so both hands were free to turn on the faucet, get the soap, and get washed up.  We eventually  had to figure out the “hand-washing problem” when we were faced with a too-high sink and no grown-up to lift us.

The “too-high sink problem” might have also been scaffolded for us if an adult had been present in the bathroom but not available for lifting.  Perhaps we came out of the toilet area, looking around for help – no takers.  Perhaps we tried to stand on tippy-toes – too short.  Perhaps we reached for the faucet – no way.  Perhaps we tried to sneak out without washing – yuck.  Most likely we observed another older child push himself up onto the counter.  Maybe another grown-up suggested, “Try jumping up.”

It may have taken two or three tries but once we got the hang of it, we never needed a grown-up again.  Problem solved.

In Young Children (March, 2014) in an article entitled, “Integrating Mathematics Problem Solving and Critical Thinking Into the Curriculum” the authors argue that we can teach problem solving skills and strategies to children by scaffolding their learning via an intentional problem-solving process.

To do this, follow these 4 steps:

1.  Reflect and ask

2.  Plan and predict

3.  Act and observe

4. Report and reflect

(French, Conezio, & Boynton 2003)

Imagine you have a dad in your program who works for a large corporation.  He comes to you one day, reporting that his business is moving and has all sorts of interesting items that you might like for your classroom.   He describes some old adding machines that have been in storage for the better part of 30 years complete with 10 cases of paper rolls that have never been opened. He says there are 4 machines to donate.  Perfect. 

The following Monday, he brings the adding machines over to your center.  You put the 4 machines on a table and the children are instantly interested.  However, you immediately realize that trouble is ahead.  All of the children want to use the machines at once.

You have a problem.

Frequently, I see teachers solving these types of problems by using their authority and exerting their control over the children.  A typical “solve” might be “First-Come, First-Served” or “10 minute turns”.  Both of these might work, but by solving the problem for the children, they miss the opportunity to solve it for themselves.

Using the 5 steps above, teachers can scaffold the problem-solving strategy.

1.  Reflect and ask – Bring the group to the rug and begin sorting through the issue. “It looks like everyone noticed that George’s dad brought us some new equipment for our classroom.  What do you think of the new adding machines?”  Discuss.

“There are only 4 machines and we have more than 4 children in our room.  What could we do so that everyone gets to play with the new equipment?”

2.  Plan and predict – “So the kids think we should let George play with the machines first, since his dad donated them.  You also think that George should pick 3 kids to play with him.  Is that right?”

“How do you think this will go?  Do you think the kids are going to be OK with this solution? Tomorrow, we will try this new plan to see how it goes.”

3. Act and observe – “This morning George gets to play with the new machines.  He is going to pick 3 friends to play with him this morning.  Go ahead George.”

Observe the play and the responses from the other children.

4. Report and reflect – Later, at group time say, “It looks like George and his friends enjoyed playing with the adding machines today.  Did you?”

“I noticed that the 4 of you didn’t play with the machines for all of free – play time.  Should we come up with another solution so more kids can have a turn when the first group is done?  How do we decide who gets to play with the machines next?”

Problem-solving builds strong critical thinking skills which are absolutely necessary for strong math skills.  Help your children problem-solve, not by leaving them to do it all alone, but by scaffolding with them.

Differentiated instruction does not mean that every lesson is adapted for every child.  That would be crazy.  According to the Illinois Professional Teaching Standards, Standard 3 – Planning for Differentiated Instruction, “The competent teacher plans and designs
instruction based on content area knowledge, diverse student characteristics, student performance data, curriculum goals, and the community context. The teacher plans for ongoing student growth and achievement.

Knowledge Indicators – The competent teacher:
3A) understands the Illinois Learning Standards (23 Ill. Adm. Code 1.Appendix D), curriculum development process, content, learning theory, assessment, and student development and knows how to incorporate this knowledge in planning differentiated instruction;
3B) understands how to develop short- and long-range plans, including transition plans, consistent with curriculum goals, student diversity, and learning theory;
3C) understands cultural, linguistic, cognitive, physical, and social and emotional differences, and considers the needs of each student when planning instruction;
3D) understands when and how to adjust plans based on outcome data, as well as student needs, goals, and responses;
3E) understands the appropriate role of technology, including assistive technology, to address student needs, as well as how to incorporate contemporary tools and resources to maximize student learning;                                                                                           3F) understands how to co-plan with other classroom teachers, parents or guardians, paraprofessionals, school specialists, and community representatives to design learning experiences; and                                                                                                             3G) understands how research and data guide instructional planning, delivery, and adaptation.”

As far as I can tell, the standards do not require individual lesson plans for each and every child, but it does ask that teachers consider each child’s needs and plan accordingly. Most children do not require differentiated instruction; they fall within a typical range of development and ability.  Therefore, classroom planning, curriculum development, and goal setting is done at a global level, with considerations made for any child with a learning difference.

In an ECE program, one way we do this is by providing open-ended materials and activities that are adaptable for children and by the children themselves.  Manipulatives have many uses and are used to scaffold learning. Interest areas are complex and provide infinite possibilities for learning.  Good activity/lesson plans consider CLAD (culturally, linguistically, and ability diverse) children and provide quality learning experiences for all children.  The environment is adaptable as we are not bound by desks and rigid scheduling.  Good ECE programs differentiate learning all of the time.

So the next time a parent asks you how you are planning to meet her child’s needs via differentiated learning, be sure to quote the Illinois Professional Teaching Standards and explain that in early childhood, our entire curriculum is designed for differentiated learning.

I bet most of you already use math sentences with your children all of the time.  When you ask a child to set the table for snack and she comes back to report that she has finished, you might look over at her work and notice that there are 2 chairs that don’t have a place setting.  Rather than telling her that she needs to get 2 more place settings for the empty chairs, you probably say something like,

“Hmmmm. It looks like the table is almost set but not all the way.  How many plates did you put out and how many chairs are there?  So there are more chair than plates.  How many more plates to you need to make sure that every chair has a plate?”

You might also use a math sentence when you are taking attendance.

“If Johnny and Sara are absent,

how many children are absent?”

or

“There are 6 boys and 4 girls at school today.  How many children all together are at school today?

The main point of difference between how older children approach math sentences and how younger children approach them is that older children are reading them and answering on paper.  Younger children are exposed to math sentence because the adults verbally present them and then support them as they calculate the answers.

Most 3 years olds are not going to be able to add 6 and 4 in their heads.  The way that they will get to the answer is through scaffolded interactions, perhaps between themselves and the adult or between themselves and other children.   After posing the question about how many children are in school today, the teacher should then allow the children to try and come up with their own strategies for solving the equation first and the let them try to see if it works.  If, after a couple of attempts, it is still unclear, the teacher can provide a strategy, i.e., “Let’s count all of the children together, both the boys and the girls, to find out,” and then point to each child as s/he is assigned a number.  Remember to stress that the last number you say is the total.

Try and think of number sentences as more than simply asking questions or making statements about math and number, and more as a “plan of action” for including more math opportunities into your interactions with your children.  This intentionality will force you to consider ways to present the problems and then support the children as they figure out the answers.

I remember all of the research about this topic from graduate school.  Most theorists agree that learning takes place when new information conflicts with what is already known and the learner must create new understandings from the conflict.  This process is most generally an active one – meaning that it doesn’t take place like a sponge absorbing water or like writing on a blank slate.  It is active because the brain is required to work at these new understandings ,and is supported through the supportive interactions between the learner and other people.

So, that begs the question…Do children learn when they watch shows like Sesame Street.  I would argue that, “Yes, they do….to a point.”  Television can never take the place of genuine human interaction, and it isn’t meant to.  It can support prior learning by reinforcing what is already knows and by providing a medium for practice.  Good programming, like Sesame Street models appropriate interactions between the regular characters, both the human ones and the Muppet ones.  It is designed to be as interactive as possible, even though children can’t actually interact with the characters on the show.

The way that television works best for learning (if that is what you believe you are using it for) is if it is watched together.  If adults provide genuine human interaction with creative, appropriate, and engaging programming, then children can most definitely get something more out of this passive activity.

This clip from Sesame Street is a great example of the kind of programming we have come to expect from PBS.  How would you watch this with your children to make it more interactive?

Once children have mastered puzzles with less than 10 pieces, it might be time to bring out the next selection. By this I mean, puzzles should be introduced as children are ready for them, rather than having all of the puzzles you have out on the shelves at once.  This is true for several reasons.  The first and most obvious is that the more puzzles you have out and available, the greater the chances that pieces will be lost, mixed-up or placed with the wrong puzzle, never to be straightened out again.  Second, puzzles that are too easy for the children will be ignored and puzzles that are too difficult for the children will frustrate them.  This is the Vygostkian principle of “The Zone of Proximal Development” hard at work.

This requires careful observation of the children and their puzzle skills.  I have seen young 3 year olds complete puzzles that my boys at 10 could not complete- and I have seen my boys at 5 unable to complete the most basic of jigsaw puzzles.  It is a skill (perhaps a talent??) that may be very strong for some children and average for others.  Only you as the teacher will know if that 50-piece puzzle is appropriate for some of the children in your group.

So, what kinds of puzzles might be good to bring out next?  I would stick with the sturdy wooden type, rather than the flimsy cardboard kind.  Children will often try and force pieces into spaces, so you want your puzzles to withstand the constant abuse. I would then choose puzzles that have a theme that children will know and be familiar with and have uneven cut-outs.

Here are some nice ones….Each of these has 10 pieces but you can see how much more complicated they are than last week’s selection.