“I think that wolf should go in this row, with the pigs,” protests five-year-old Harper. 

“What? Why? He’s a wolf, not a pig!” insists Harrison.

“And he’s not pink!” chimes in three-year-old Evelyn. 

“The wolf will go with the pigs in this row for ‘Stories,'” explains Harper. “You know, like in that book, The Three Little Pigs!”

I wander over to see what this deep discussion is all about. Wow! The older preschoolers are lining up and labeling groups of animals from the basket. This is child-led learning at its finest!

“Oh yeah! That makes sense!” Miguel agrees.

But Evelyn seems puzzled by their reasoning. Math skills such as sorting and patterning are developed in a sequential order—and Evelyn’s early math skills are not as developed as those of her older friends.

At all ages, children classify objects intuitively to make sense of the world. Two-week-old infants can already distinguish objects that they suck on from other objects.

By the age of two, toddlers can form sets of similar objects. By preschool, children can sort and categorize objects according to a given attribute.

When children engage in classification, they are sorting objects according to some established criteria. For Harper, it makes sense to classify the wolf with the pigs. It also makes sense to Miguel when Harper explains his reasoning. 

I look at the list that Harper has created. I chuckle at his phonetic spelling as I read the three categories that he has printed across the top of a sheet of green paper: “Jungle, Farm and Stories.”

When learning how to classify objects, children first learn how to identify and name the attributes that the items in a group will have in common. Then they move on to identifying the attributes that will exclude items from a group.

See Harper’s list in the bottom right corner?  It reads, “Not in a group.”

Wow! This is math! This is early literacy! All while playing and having fun!

Remember back in first grade when we were learning about sets and we had to circle the apples, but not the oranges, on our math worksheets? Our morning of animal sorting is a similar exercise, but the children are establishing the rules.

Hands-on play will beat a worksheet any day of the week. What sticks to the hands, sticks to the brain. 

When children sort objects in their environment, they are using their analytical thinking skills, which are the lifeblood of mathematics. When children engage in organizing activities, it helps them make sense of their world.

Sorting allows children to determine where they think an object belongs and why they think it belongs there. Often, objects will be reclassified from one day to the next. The wolf may be classified as a “Story Animal” today and as a “Forest Animal” tomorrow!

A 2015 research study showed that young children were more creative, more interactive and more verbal when they were playing with sets of animal figures than with other toys (Trawick–Smith et al. 2015). These findings were consistent regardless of gender or background.

The takeaway? Every classroom needs a basket of animal figures!

What’s so great about a basket full of plastic animals? It doesn’t come with a rule book!

When children play with toys such as small animals, people or vehicles, they create elaborate make-believe scenarios and engage in rich discussions about those scenarios. Perhaps best of all, they learn to play cooperatively with their friends. 

As educators, we know that children love to play with baskets of plastic animals. Now we have research to prove what we’ve known all along: that open-ended, imaginative play will naturally lead to sorting and classifying—and you’ll be checking off those early math learning standards in no time!

Looking for an Early Math Counts lesson plan that involves sorting and classifying?  Check out Cereal Sorting!

“I see the daddy cardinal, do you know where the mama bird is?” Four-year-old Noah, binoculars in hand, is busy counting birds in our outdoor classroom.

Are you aware that the annual Great Backyard Bird Count is coming up later this week? This is a great opportunity to create a bird-watching station and knock out some STEM and early learning standards while encouraging family involvement.

Mark your calendars for Feb 12-15 and join us for this fun and educational week!

February and March are good months for bird watching and bird counting in our program. This is a great way to accelerate STEM learning on days when below-zero wind chills make outdoor play impossible.

We have bird feeders set up right outside of our windows so that we can set up indoor bird-watching stations to give the children close-up views of their feathered friends.

We provide clipboards, books, binoculars and our abacus to help with the bird count. We also use this opportunity to teach our students how to tally on a tally chart. We reference the eBird website, which shares local sightings of different bird species.

I take the top ten birds sighted in our area on the eBird website and add pictures of those birds to our abacus. To do the same thing, just add your location to the eBird website and you’ll see which birds are sighted most often in your area. It’s quite fabulous!

We also like The Cornell Lab and the Audubon Society. I have the Cornell Lab Merlin Bird ID app on my phone to help us identify birds by their songs.

Your local U.S. Fish and Wildlife Service may also be able to provide free materials for bird identification. There is a big difference between bird identification books for children and those that were written for mature bird watchers. I would check some out at your local library or bookstore before purchasing.

This is a great opportunity to practice not only counting, but grouping by attributes or close observation of the differences between a downy woodpecker and a red-bellied woodpecker.

We try to keep a ruler nearby for our older children to use to determine whether they have spotted a six-inch downy woodpecker or a nine-inch hairy woodpecker. This offers the children an opportunity to use estimation and practice using real tools for observation.

This is also a great time to introduce Venn diagrams for clarification and documentation.

By creating a comfortable and inviting place for the children to birdwatch—complete with pillows, chairs and tables with baskets of binoculars—you can encourage them to slow down and observe more often.

By planting native plants in your outdoor classroom, you will also attract more birds to your bird-watching stations.

We remind our kids that outdoor birds are hard to spot but easy to hear. We ask them to close their eyes and point to where the song is coming from. I like to teach common mnemonics like the American Robin’s cheery up, cheerio, which can be picked up on almost any bird walk in the United States. Learn some mnemonics for common birdsongs here.

We have tried the inexpensive plastic binoculars from school-supply stores and toy aisles. They really didn’t work well and broke the same day that we brought them out. Smaller, child-sized binoculars are much easier for little hands to manage. Children enjoy using “real” tools and will treat them with much more respect than a pair of cheap plastic ones. I often teach them how to focus the binoculars to get a clear image. I place these binoculars in a basket, along with the identification books. We also stock our bookshelves with a wonderful collection of books about birds, nests and hatchlings.

We talk so much about STEM these days. This is one of the easiest and most magical ways to create a learning hub that can inspire young learners to engage in STEM exploration and discovery.

By participating in these learning adventures, you can learn right along with the children as you observe, ask questions, draw conclusions and discuss your findings with your early learners.

When we observe birds from our indoor birdwatching stations and then take those same observational skills outdoors, we have a deeper understanding of the birds we see and the birdsong we hear.

By adding the technology from the websites mentioned above and building bird feeders from oranges or peanut butter and seeds, we can include engineering in our learning adventures. We can include math as we count the number of birds arriving at the feeder and then subtract the birds that fly away. By grouping, measuring and comparing the birds, we can meet our early learning standards and benchmarks.

I hope you will join us in our Great Backyard Bird Count this year. Birds of a feather flock together. Come join the fun!

Welcome back to week 2 of making graphs with kids! Today we explore rolling out an exploration and pushing students to think more deeply about a concept.

Let’s Make Bar Graphs!

Since I knew the class had only limited exposure to bar graphs going into this exploration, we spent the first two weeks working on bar graphs. This blog will explain how I helped the class move from simpler to more complex graphing problems.

We started this exploration back in January, so I knew what my first question should be: did you like your presents or spending time with family? I knew this was a question the class would easily understand, have firm feelings about, and be excited to talk about. This conservatism is a key aspect my exploration philosophy: introduce novelty in small doses. If I am expecting them to do a completely new thing, then the rest of their thinking should be simple enough they can focus on the new piece. If I had asked them to vote on a conceptual topic, like their favorite character across multiple books, they would have been less able to focus on the graph.

The Rubber Meets the Road

When it came to the actual voting, I had several goals for the process. I wanted to make sure the students couldn’t accidentally ‘vote’ multiple times, that they were able to express themselves through their votes, and to create a physical graph that could be seen and examined over time. Therefore, instead of asking the class to raise their hands, each student wrote or drew their vote on an index card. That card was then taped into a blank bar graph grid I created out of masking tape on our board. I also wrote out sentence stems for the class; while few of the students were able to read the stems, some of them decided to copy them into their exploration journals.

The timing of the voting and discussion was also rather important. The question was on the board from the time the students entered the classroom, which lead to big discussions about how people were voting and why. While this may have led to some politicking or vote changing, the point of the exploration was not to find out how they actually felt. Instead, they were learning to predict how people would vote, how that would change the outcome, and even making sure that everyone understood the question at hand. After all, when I hear one student say to another “Student Z hasn’t voted yet but will probably vote here, so we’re going to win”, that is a great sign that the student understands how to read and interpret a graph.

As the week went on, we transitioned from simple questions about their preferences to more complex questions about the novel we were reading, Charlotte’s Web. I also started encouraging the class to have more challenging discussions about the graph, like seeing how many people voted IN ALL, how much did this option win by, and what would have happened if two people had voted differently. These questions pushed the class to see the graph as a living representation, not a static object to be observed.

Ramping Up the Difficulty

In the second week I transitioned to more complex graphs. Instead of choosing between two options, the class had to choose between three or four. I also took away the horizontal guides so they could see how having the votes misaligned made the graph harder to read. Finally, the class switched from vertical bar graphs to horizontal bar graphs. In keeping with that conservatism I mentioned, the questions I posed to the class reverted to easier questions about who won and how many votes each option got until they became comfortable with these variables.

Throughout this entire process, I continually asked myself how these changes would either

help the class read graphs better or give the class a more intuitive understanding of the relationships between numbers. This helped me ensure the questions and graphs were challenging the class and working towards their mastery goals.

This was just the first half of our exploration, check back next week to see how we took it to the next level.

The difference between an activity and an exploration

Exploration based learning may be all the rage, but not every Pinterest post is an exploration. Explorations are intensive, thoughtful investigations into a concept, while an activity is a solitary project, isolated from any surrounding work. In my Pre-K/K classroom, the emphasis is on explorations that take anywhere from a week to a month or more. In this series of posts, I will explore the groundwork I did to prepare for an exploration of graphing, the work we did with graphs for that month, the benefits of this exploration, and wrap up with some guidelines about how this mindset can be extrapolated to inform other explorations.

The seed of most of my math explorations comes from Little Kids – Powerful Problem Solvers by Andrews and Trafton. While I believe this book contains many great ideas, I’ve often felt it did not do enough to provide a full plan and instead simply explored a single activity. Therefore, when I read that our January exploration was going to be centered around graphing, I was certain that there were ways I’d need to expand it.

Laying the groundwork

I knew we’d be working on graphing in January, so I started several months earlier by seeing what the class already knew. They voted for whether the movie or book version of How to Train Your Dragon was better. After the vote, the class made a bar graph based on the votes cast. While they were working and during our discussion, I took careful notes about what prior knowledge the class already had.

Once the graph was completed, I questioned the class to see how well they could analyze the data. The whole class could tell who won and lost, which was reassuring. Most of the class was also able to tell how many people voted for book and how many voted for movie, another encouraging sign of comprehension. Further probing, however, revealed a number of weaknesses. No one was able to determine how many people had voted or how much the movie had won by. This, therefore, provided the baseline for the scope of my exploration.

While it is not necessary to have a full questionnaire before initiating an exploration, it is vital to check what prior knowledge the students have. You will almost certainly not have to cancel an exploration based on what the class already knows, but it is this tailoring that allows students to best grapple with the material later on.

Setting the scope

If you were going to attempt this exploration, it would be critical for you to determine what goals are appropriate in your setting and time frame. Students younger or you have a shorter time frame? Consider emphasizing the recognition of the larger picture of the graph (who won, what were the categories, etc). Students with a more developed mathematical ability? Push them to create graphs in groups or independently and spot errors in a graph based on the data set. Using this as a capstone to previous graphing explorations for advanced students? Have the class compare multiple representations of the same data to determine the ideal format or study misleading statistics.

With this range of goals in mind, I prepared for this exploration by determining what educational skills I wanted for the class to achieve. By the end of the month, I wanted my students to be have two related skills:

-Tell what information a graph is trying to depict.

-Be able to visualize how a set of numbers would look when graphed.

These were the two goals that all the work within this exploration would be working to address. As we move through this month, these goals will be the lens through which all of the activities will be evaluated.

This scalability is not unique to graphing. Many, if not most, topics in mathematics can be easily adjusted up or down. The final post this month will detail how to do this, but rest assured the teaching moves discussed here are generally applicable.

Creating a Sequence

This is one of the trickiest parts of the process: what is the actual work the students are going to do? I’m a worrier, so the trap I find myself falling into is making a timeline: Monday do this and ask this, Tuesday this and that, etc. However, since the goal isn’t me being able to do these activities, it is unwise to make too precise of a timeline. Instead, it is more efficient to make a sequence of topics or activities the class can cover. This way, I have a vision of where we can go and what to prepare, but I’m letting the class determine the pace. For this exploration, I decided to start with bar graphs and move into pictographs in the third week. In addition, it is useful to consider the breadth of questions that can be asked. This vision of exploration preparation will be explored more in the final blog post this month, so check back for a fuller explanation.

Check back next week as the rubber hits the road and we actually start graphing!

We discussed ways of creating the jars so the children’s number and counting skills would be challenged appropriately; enough to be stimulating but not too much to be frustrating. My student decided to stick with small items that fit easily into empty baby food jars and chose items that at first glance, seemed easy enough to count.

The children came over to the table at their leisure during free choice and my student explained the game to them.  She defined estimation and explained what they should do.  Each child estimated how many of each item were in each jar.  They then wrote the numbers on small pieces of paper and stuck them to a graph next to their names and under the items.

What I found fascinating was how the careful choice of the items created a challenging math exercise for the children.  The pom pons were large and nearly filled the jar but because two of them were red they looked almost like one, making it hard to see where one began and the other ended.  Many children counted the five pom pons as four as they were “tricked” by the red ones.

The beads were straightforward; seven beads in seven colors, easily discernible and easy to count, as evidenced by the chart above.  The marbles were harder as they rolled around the jar a lot and it was hard for the children to know which marbles they had counted and which ones needed counting.  The really challenging jar was filled with Cheerios.  First, there were 8 Cheerios in the jar, which was the biggest number they had to count to.  Second, all of the Cheerios looked the same, so it was nearly impossible for the children to know if they had counted each one once, or if they had recounted some.

These small challenges are important to consider when setting up an activity.  For children with a secure sense of number and solid counting skills, the jars did not allow the children to point to each individual item or to line them up or to separate them for counting.  Many children still use these strategies to ensure they are counting correctly and following the counting rules.  One-to-one correspondence provides a framework for counting so that children know that each separate item has a one number attached to it, no more and no less.  One bead = one and the next bead = two, and so on.  The Order Irrelevant Rule  says that as long as each item is only counted once, it doesn’t matter what order the items are counted in.  This activity challenged both of these rules which is what made it really engaging and interesting both for the teacher, the children, and the observer (me)!

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?

That said, all of these fun winter clothes are a great resource for sorting and graphing as a large group.

This picture shows a large graphing floor mat that is so perfect for preschool children.  They can put their own hats or mittens in the squares (rather than having a teacher do so on a piece of tag board).  This simple physical involvement will make the activity so much more interesting for the children.  Once they have put their items in the separate squares, they are easy to count and provide appropriate visual cues so the children can “see” which has “more” and which has “less”.

I would start with Mittens vs. Gloves and see where it goes!

So, teaching data analysis to young children seems completely contradictory to me.  How do we look at data sets and make sense of it?

Young children need to collect data that is meaningful to them.  This can be in the form of scientific inquiry such as; how many sprinkler days did we have this summer?   or, what is everyone’s favorite kind of juice? The data can then be collected and categorized into data sets.  Usually, we want to explore ideas that yield manageable data sets for young children (2 – 3 sets, ideally).  In the case of favorite juices, children may say orange, apple, grape and possibly one other.

You should tally their responses by using visual cues that can be read by pre-readers. You might draw three glasses on the top of the tag board with one filled with orange, one filled with yellow and one filled with purple.  The colors will visually represent the juice and will make sense to the children.

Under each choice, the children can write their names to represent their choice, or if they are not ready to write, you could put their photos under their choices.  You have now created a usable data set that is analyzed by the children.  The analysis should be readily seen and understood by the children.  You can ask questions of the data, for example; Which juice is the favorite amongst our group?  Which juice is the least favorite?  How many children chose each kind? etc.

Next week we will continue looking at data analysis and the young child.

The graphing mat pictured above breaks many of my “rules.”  Most importantly, once completed, it can’t be kept in the classroom for further study and reflection.  What it lacks in permanence, it more than makes up for in size and usefulness.

This mat is best used with children sitting around the edges of it so they can really participate in the creation of the graph.  The mat can be used to investigate all sorts of classroom questions and rather than creating ways to represent objects, the children can use the actual objects themselves for their data set.

Imagine that the children in your room want to know if more children wore mittens to school or if more children wore gloves.  In a matter of minutes, you could pull this mat out, have the children go to their cubbies and get their gloves/mittens, and then take turns placing them in the graph.  When everyone has had a turn, the children will see, in an obvious and clear way, whether more kids wore gloves or mittens.

You don’t have to purchase one of these (although the ones from the teacher’s store tend to be pretty sturdy).  You can make one with some colored tape and a plastic shower curtain from the dollar store.  Every room should have one of these, as it makes graphing a breeze.

I had an opportunity to observe a wonderful teacher use the children’s classic Caps For Sale as the foundation for a graphing activity.

She first read the story with the large group.  The children knew the book well and read along with her.  They acted out the monkey parts and tried on all sorts of different caps.  They had a blast.

She then told them that during free choice they could come over to the table and vote for their favorite colored cap. She created this wonderful board so they could vote.

Once the votes started rolling in, some of the children stayed at the table so they could watch the results.  There were a couple of children who wanted “blue” to get the most votes, and a couple of children who wanted “red” to win. This became very exciting as the votes for blue and red were neck and neck for a time.  The children had loads of opportunities to talk about which color had more and which had less.  The graphing exercise itself became a vehicle for a lot of conversation about more and less, favorites, counting, counting on, and one-to-one correspondence.

Later, once all of the votes were in, the teacher brought the graph to the rug so the group could revisit their data.  You can see how this all played out in the video below.

After watching the video, do you have any suggestions for improving the activity?  Tell us what you think.