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/

So far, we’ve seen what it takes to prepare an exploration, a graphing progression, and a discussion about what kind of questions can be centered around an exploration. To wrap up our month, I’m going to extrapolate from a specific example to a general framework for explorations.

A General Framework for Explorations

One of the most fundamental aspects of an exploration is the materials the students use. In the graphing exploration, the materials mainly stayed the same, index cards or paper pie slices and tape. Other explorations, however, can be greatly varied based on the material. For example, say I wanted to lead an exploration about how textures impact painting. If I wished to alter the materials, I would change what they used. Maybe one day we would paint on standard paper, then silk to see a smooth texture, and then painting on tree bark to see how that differed. Conversely, we could paint every day with a different substance mixed into the paint (rice, sand, and then flour) to see how the texture of the substance affected their art. Especially with young children, they are very sensitive to changes in the physical materials they use and benefit from these varied exposures. In my experience, these are the easiest pieces of an exploration to change.

A second aspect of an exploration that can be altered is the constraints placed on the students. Constraints, as generally understood, are restrictions on how students can use their materials. This is an overlooked aspect, as teachers generally only restrict the final product students can create or the general amount of time that can be spent on an activity. This is shortsighted, as there are incredibly nuanced and powerful changes that can result from properly applied constraints. In the graphing exploration, the class had constraints based on who they could vote for, how they voted, and the representation of their votes. To continue with the painting and texture example, students could paint with their eyes closed to see how the slick paint felt when spread over the rough paper. While the distinction between materials and constraints may be nebulous at times, it remains a valuable lens through which to view explorations.

The final aspect of an exploration is the focus of the students, which is directly impacted by you the educator. Through your questioning, you help students realize what they should be paying attention to or thinking about in an experience. To be clear, students can and will surprise you by noticing things you never expected, but it is also important to plan an exploration around key questions and vocabulary. For example, in the graphing exploration, I drew students attention to the relationships between the numbers of votes instead of just who had more. In the painting and texture example, the focus would include questions like “How does this feel different than that” and “How did this texture affect your painting”. Focus work would also include highlighting vocabulary that would be useful, like ‘rough’ or ‘smooth’ in the texture example. This questioning and vocabulary should expand as the exploration progresses, encouraging the students to think more deeply or analytically about the process.

Some Examples of the Framework in Action

In general, I have found it best to alter either the products OR the constraints day to day, not both. This allows the students to more easily reflect on a specific change from the prior activity. This is not a hard and fast rule, just a general guideline.

In order to provide a launching off point for future explorations and help explain the three aspects of an exploration, here are couple of examples of explorations and how their aspects can be modified.

Building

-Materials: unit blocks, legos, paper towel tubes, rocks

-Constraints: goal (height, representation of specific object, volume), time limits (15 seconds, 30 seconds, 1 minute), blindfolded, only using one hand

-Focus: “Is it easier to have a wider base or a narrower base?”, “Do you think you’ll be able to build as much in 30 seconds as you did in 1 minute?”, balance, symmetry

Color

-Materials: shading paint (a single color with black and white paint to alter shade), colored paper, stained glass (tissue paper on a light table), magnetiles and flashlights

-Constraints: painting in colored lenses or light, painting in dim light (colors appear washed out and gray), colored shadows

-Focus: “How did you make that color, since I didn’t put out any orange?”, “Why doesn’t this look as red as it did on the white paper?”, shade, blend

Hopefully, with this framework and these examples, you’ll be able to take a great idea and expand it into a full-fledged exploration. After all, there’s nothing wrong with doing something fun!

Pictographs and Pie Graphs

I’m going to start this week with a frank statement: I messed up this part of the exploration. When I was planning the scope of the exploration, I intended for the class to spend two weeks on bar graphs and two weeks on pictographs. I knew that pictographs are a struggle for students and I frankly didn’t have any idea how to implement pie graphs in a way that made sense. However, halfway through week 3, I realized how it could be done and altered the scope accordingly. I’m going to present the exploration as it actually went, but keep in mind if you’re teaching this that I would actually do pie graphs before pictographs, just because pictographs can be so challenging.

Pictographic nightmares

For as long as I’ve been teaching math, pictographs have been problematic. A pictograph appears simple enough, as it’s just a graph that uses pictures to represent the data (like a smiley face to represent a vote). However, students often struggle to interpret them correctly. This is particularly common because pictographs will often alter the key and make each image worth two or more votes. When this is the case, students will often count the pictures, not the votes. I knew, if I was going to teach this skill to my students, I would need a way to represent this to them and let them find ways to think through it.

I saw how the students appreciated being able to have their own index card and decorate their ballot in the first section. Therefore, I felt that tweaking the ballots but keeping that basic format would be appropriate. On the first day of pictographs, each ballot now came with half of a circle on both sides. The students then decorated each side to show which option they were voting for. When they attempted to cast the ballots by taping them up, however, I explained that each ballot needed to be connected to one of their classmates’ votes to make a whole circle. We also discussed how the last person might not be able to make a circle and what a ‘half’ of something means.

When it came time to talk, the class did surprisingly well. There was definitely confusion about the difference between how many CIRCLES were in a category and how many VOTES were in a category, but we talked through it. We also discussed why it was important to put the votes together into whole circles instead of leaving them floating around.

As the week went on, I provided less support when they were casting their ballots, which allowed them to talk together about how to combine their votes to create a whole picture. The class also talked about how important it was to color on both sides, since you didn’t know which side you would have to use on the board.

By Thursday I felt the class was ready for a greater challenge, so we transitioned from each picture taking two votes to each picture taking four votes. Once again, I simplified the questioning and provided more support, but the students adjusted smoothly and were able to vote with little support on Friday. Throughout this entire week, I kept many of the questions from

the previous two weeks, like which team won and how many people voted, while adding questions about how many pictures were created and how many votes it would take to finish a picture.

Pie Chart Parade

As I said at the beginning of this post, I really struggled with how to allow the students to create their own pie graphs, at least how to do them without the use of technology. After all, if one of the students was absent and didn’t vote, the pie chart would either need to have bigger slices or be left with a whole in it. Thankfully, I realized that I could create an ‘absent’ vote, which I would place when necessary. That hurdle overcome, I realized I was ready to start our final week of graphing.

To make the pie graphs, I cut paper-plate sized circles out of multiple colors of construction paper and cut it into 12 equal pieces. I also traced a paper plate on the board to provide a template. The students would then pick a pie slice that matched the color of their vote (blue for dogs, red for cats, as an example). That pie slice would then be decorated and arranged on the template into ‘teams’. Our discussion afterwards centered on seeing which team had more votes, how many votes each team got, and how many people voted in all.

As the week went on, I transitioned into providing less guiding on placement, which led to a great discussion about why the teams needed to be together, and offering more options/colors. This week was actually far less challenging than the pictographs, which is why I would recommend switching them if you implement this exploration.

Taking Stock

As we wrapped up our week of graphing, I felt the class had done a great job being able to compare numbers and read the data from graphs. I actually saw them going back and looking at the graphs we had already done and using their new understanding to think about them more deeply.

Next week, I’m going to wrap up the graphing exploration as well as provide some guidelines on how to structure an exploration. I hope you’ll join me then as we get ready to take what we’ve learned and start applying it to the classroom!

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!

Math can be hard, but don’t panic.

Not everything comes easy to us.  This is true for all people.  Being an educator for over twenty years, I have worked with many students who have struggled to conceptualize mathematics.  Each individual brings a different story.  While some truly do have issues that need to be addressed, often children enter school without having had much exposure to numbers; or developmentally they need more time and just aren’t ready.  In these cases, what they need is a patient parent, caregiver or educator to assist them as they learn at their own pace. Keep in mind, we don’t all potty train at the same time. We don’t all walk at the same time. And similarly, we may not be ready to learn math concepts at the exact same time. So, what can we do to help the late bloomers navigate through math successfully?

Your speed doesn’t matter. Forward is forward. Slow and steady wins the race.

Late bloomers can finish the math race too.

As a teacher, there is a curriculum to follow.  As a parent, there are concepts to be reinforced at home to help children “make the grade”.  When a child is not grasping math, it can be frustrating for both the child and the adult.  As an educator, I often find myself calming parents down.  Panic is the first feeling to emerge in these situations.  But rather than panic, what can we do?

Check the foundation.

Rather than trying to play catch up and rushing through the lessons or concepts missed, it is much more productive to back-up and look at the foundation.

*How is number fluency?  Just as there is fluency in reading, you can bet there is fluency in math too.  How well can your child count?

Can they count forwards? Backwards? Can they count by 1’s, 2’s, 5’s, 10’s?

Learning math can and should be fun.  Number fluency has such potential to be exciting for children.  Use several 100 charts, highlight the numbers you are working on and allow the child to count while singing or playing catch.  Think of this fluency work similar to how children sing chants while jumping rope.  It is meant to be repetitive so the child can eventually memorize the numbers. Don’t be afraid to allow the child to look at the highlighted numbers as they practice. Eventually, they won’t need that chart.

For slightly older children the concepts advance, but the method stays the same.  Does your child know their addition facts?  Subtraction facts?  Multiplication facts?  Division facts?  These can be fun too. There are many tricks to be utilized, games to be played to assist in learning these.  Knowing these facts fluently will assist them with math for all of their years in school.  These facts don’t go away but are integrated into much more complex mathematical concepts.

This fluency and ease with the movement of numbers will build a foundation for your child to learn more complex mathematical ideas.

*Is your child comfortable with the hundreds chart? Can they maneuver to the right? The numbers get bigger by one.  Can they maneuver to the left?  The numbers get smaller by one.  How about up?  They get smaller by 10.   Down?  They get bigger by 10.

Understanding movement of numbers and adding and subtracting of bigger numbers with the number chart is foundational.  If the number gets smaller by one, the digit in the ones place gets smaller. If the number gets bigger by 10, the tens digit gets bigger by one.  Similar to puzzles, understanding how the relationships with numbers on the hundreds chart allows children more ease when manipulating numbers.

*How is their number comprehension?  Yes, just like reading, there is comprehension with numbers too.  Do they understand just what 5 looks like?  Not just how to write the number 5, but how many is 5?  Can they comprehend that 95 is bigger than 93?  Is there an ability to visualize number amounts?  Do they understand how many pennies are in one quarter? What does half of something look like?

This image and ability to visualize the number is important.

Acquiring these foundational skills does not happen overnight.  But it certainly doesn’t happen any faster if everyone involved feels panicked and frustrated.  What has to happen to move forward?  I have found that, ultimately, we have to move backwards a bit to finally be able to move forward.  Without the foundation set and secure, adding more new unknown concepts will only compound the challenges with math.  Instead, take a breath and remember the tortoise and the hare.  Now be the tortoise.  Slowly assist your child in building the important foundation that will benefit them in their mathematical life to come.  

Math really is fun.  It can be misery trying to teach it, but magic when you integrate it into your child’s everyday life.  

It’s a mystery to me why some children have a natural affinity for numbers while others show no interest or may even resist them.  It may be no different than why I chose to participate in gymnastics as a child while my best friend’s sport of choice was soccer.  We veer toward subjects and activities that come easily and steer away from those that are confusing or tricky.  As a parent of four young children and a learning specialist, I know how difficult it can be to get a child to participate in something they think is hard or boring. Pushing concepts on young children will prove arduous to both the adult and child, so what are some fun ways parents and educators can engage young children with math?

Too often we turn to the computer for answers, .  Or the apps on a smartphone.  While some of these are fun, my children already spend enough time in front of screens.  There are many workbooks that reinforce math concepts, but if your children are like mine, they aren’t going to be motivated by more ditto sheets.  Instead, I propose thinking more organically about numbers and mathematical concepts; they are hiding within so much of what we do everyday.  Very often, we can explore mathematical language and concepts without it ever seeming to our children that we are “working on math”.  If there are two words that don’t go over well with children, the top two might be “work” and “math”.

Some examples of how to bring math into everyday life:

*Put a timer on the microwave. Tell your child how much time you’ve put on the timer. Challenge them to pick up their toys or clean their room before the timer beeps. If they finish early, do a countdown with them while watching the numbers on the clock. You could even hold up fingers for the 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 countdown.  If it was not enough time, talk about how much MORE time could have been added to the timer.  If it was too much time, how much LESS could have been used.

*Have your child study their cereal box in the morning.  Any aged child loves to look at the colors, the characters, and the games or stories on the back of the box.  But cereal offers many other rich math opportunities:

-Talk about the numbers they see in the ingredients. Discuss which character on the box is “bigger” than another. Take the cereal box apart, cut the pieces and measure them with a ruler or just lay them next to one another and decide which is taller and which is shorter.

-Pull a handful of cereal out and count.  How many “marshmallows” are in the cereal  (if you like the junk cereal variety)? Separate by color. Sort piles of like shapes. The amount of opportunities to get the math brain curious is limitless.

*Near your child’s bed, create a Mathematical bulletin board. My youngest son sleeps on the bottom bunk in a bunk bed. I created a beautiful (not too visual so as to keep him awake) collage of mathematical concepts for him to peek at before he closed his eyes at night.

After we read, I count with him. We find numbers. We look to see which number is “bigger”. We play riddle games. “I’m thinking of a number”. When he is tired, I never force it. When things get old, I switch it up. It is fun because he never knows what is going to be on the board next.

*Is your child physical? Make movement mathematical. How many times can you throw the ball back and forth or roll it if catch proves difficult. Create a dart board (out of plain paper) with numbers on it. Make paper airplanes and see what numbers you can both hit.

Get a jump rope and sing a number song or count. Kick a soccer ball and keep tally marks on a sheet of paper to track how many goals are made by each player.

*Cook and bake with your child. Both offer very rich opportunities to sneak numbers in. There are fraction opportunities but also looking at temperature on an oven. Talking about how long the item needs to cook. How many minutes does the batter need to be mixed? Etc.

*Play games. Dice games, card games, matching games. There are a plethora of board games that include mathematical concepts.

-Sleeping Queens (A family favorite- enjoyed from my 5 year old up through both parents!)

-War: an easy way to compare numbers. You can add and have each player turn over two cards. The bigger number after you’ve added keeps all 4 cards.

-Rat a Tat Cat (Another family favorite that involves your wanting to keep the “low” numbers and get rid of the “high” ones)

-Shut the Box: Roll the dice and close the doors on the numbers you roll. Try to “shut all of the numbers” to end with the lowest number.

-Memory: Who could forget Memory? What a wonderful game. The cards can have shapes on them or numbers. While playing and matching, talk about the shapes they see, count the images on the card together before making matches.  

These ideas are not new and this list is far from complete- there are so many more hidden opportunities to learn math. They are things that many parents are already doing with their children everyday. However, when it is not obvious that Math is being taught, it can be easy to overlook the Math hidden right in front of you. Before you turn on a computer or buy a workbook, try to find the hidden math in your everyday life. To insert mathematical language, concepts and games into their life can make all of the difference. After working in a few more of these ideas, I think you’ll see your child building a math brain from everyday life.

Note: Strategies provided in all four of February’s blog posts can be facilitated in both the home and the classroom, as well as other contexts. 

Young children are often intrigued by the sense of magic that today’s technology seems to possess.  Though there is not magic in the devices, we can harness that intrigue to introduce new and innovative ways to explore mathematics using technology.  ChatterPix, created by Duck Duck Moose (also ChatterKid), is a tablet device application that allows for users to add a mouth animation providing a voice for a character. These animations are saved in the form of a video which can be shared via email, social media, text, etc.  This video shows a quick tutorial for how this application works:

Caption: At this time, ChatterPix is available for iPad and iPhone only.  If you are interested in ChatterPix on other devices, I encourage you to reach out to Duck Duck Moose, they are very responsive to feedback: https://duckduckmoose.zendesk.com/hc/en-us

Price: FREE

As you can see there are endless possibilities for how this application could be used.  As Director of Education Technology at Catherine Cook School in Chicago, I am always amazed by the ideas teachers come up with to support collaboration, creativity, communication, critical thinking, character, and other skill development.  We have used this application in a multitude of ways, such as providing a voice to familiar story book characters. In the consideration of early mathematics, children could use Chatterpix to create their own animated number stories.  Consider this process to help the child(ren) create a plan for their number story video:

1. Identify a character
   1. Will it be the child themselves?
   2. Will it be a favorite book or movie character?
   3. Will it be a brand new character they create?
2. What are the items being added or taken away?
   1. If it’s the child themselves, do they have a favorite toy? Food?
   2. If it’s a favorite book or movie character, what do they know about the character that could give them some ideas?
3. What is the story around the addition or the subtraction?
   1. Is this a true story?
   2. Is this a story made up in the moment?
4. How will the illustration be created?
   1. Pencil? Paint? Sculpture (clay)?
   2. Photograph of actual items and individuals?
   3. An application-based illustration?
5. Who and how would we like to share this video?
   1. Remain on family/school device?
   2. Share with family members or friends?
   3. Post to an eportfolio resource such as Seesaw?

In the example I created below, I decided I wanted to include myself in the video and then tell a simple short story of how I once shared a chocolate chip cookie with my sister which left me with two cookies to enjoy for myself.  Parents and teachers may consider creating their own number story videos to not only provide an example but to also get familiar with the application and discover the fun while enjoying art, technology, and mathematics. The most powerful experiences with technology is when multiple subjects or disciplines come together.

screenshot provided by Brian

Outside of number stories, what other ideas are coming to your mind?