If “Math Is Everywhere,” What Does This Mean And What Does It Look Like?

Math is everywhere! I hear this saying a lot, and I even believe in these words. I’ve used them before, and will likely do so again. But I’ve been doing a lot of thinking lately about what I really mean when I make this statement.

I remember a number of years ago now when I taught Grades 1 and 2. I just came out of Kindergarten, and was excited to teach a new grade. I spent a lot of time creating math centres for my students. They rolled dice, they graphed, they wrote numerals, they added and subtracted, and they even did some counting. These centres were largely game-based, and upon reflection, required very few thinking skills. But my kids seemed to love them, behaviour problems were limited during this centre time, and if you looked around the classroom, you could see “math everywhere” and children excited by the possibilities. I probably even blogged at the time about “math being everywhere,” and used these centres as examples. Now I wonder though, does this really illustrate the idea that “math is everywhere?”

Fast forward way too many years and schools to count (or maybe I just feel old when I do 🙂 ), and now I have some very different thoughts around this statement. The more that I learn and immerse myself in play-based and inquiry-based learning, the more that I believe that we don’t need to create math activities, but instead, help students see, think about, discuss, and understand the math in their world. Kids think mathematically, but they don’t always have the language to name the math that they’re doing. They can also benefit from adult prompts to ask questions and extend this math learning and/or apply it in different ways. Our Kindergarten Program Document supports this approach to math, but it’s not something that has to end in Kindergarten. Some experiences on Friday though made me realize just how rich these authentic math opportunities can be. 

This all started out in the forest, as a group of our students were climbing trees. As they climbed, a couple of children started to discuss birthdays. One child mentioned that he would always “be older” than his friends. He was trying to get to the idea that his birthday comes before the other two birthdays, so he will always turn a year older before the other two boys. I really wanted to hear more of his thinking here, but an issue took me away from the discussion, and when I returned, the conversation changed. I would like to further explore this connection between the months, the passage of time, and ages. What other truths can they explore based on this passage of time? Just a few minutes after this conversation, I heard some children commenting on the height of one child in the tree. What’s a safe height? It was interesting to note the intersection between standard and non-standard measurement in their discussion. Having the students explain their thinking to me, helped me further understand their estimations and their measurements. This discussion may be a good starting point for other discussions in the forest around measurement. What kind of standard and non-standard units can we use to measure height, and how can we use this information to better estimate and/or compare other heights?

Tree climbing today resulted in such varied learning opportunities. For Trinity, it was all about taking some new safe risks and meeting with success. Look at her big jump and smile on the last video. Pure joy! For Wyatt, Brady, and Brayden, this tree space was perfect for some social interaction. I liked the discussion about the birthdays and how they knew that Brayden would always be the oldest. I’d love to flush this out more. The side discussion pulled me away for a bit, but no worries, the kicking was accidental. I also liked the measurement discussion. What is a safe height? What does non-standard measurement look like? So much potential here for exploring measurement more. Some great learning, thinking, and discussions in the trees! ❤️ SWIPE ⬅️ FOR MORE. #iteachk #teachersofinstagram #ctinquiry #engagemath

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It was a little later that day that a child started a math discussion around a box of band-aids. He went to the office to get us some more band-aids, and one child took one from the box. As I was reading with some students around the eating table, another child asked me for a band-aid. I asked the child that got the box of band-aids to get one out for his friend. I thought nothing else about this, until this child, commented on the total number of band-aids in the box. (He was reading the information on the front of the box.) Then he noted that one child got a band-aid for his paper cut, and now he needed to take another band-aid to give to his friend. How many are left in the box? Listen as this child counts back, and figures out the total. He then further counts back when another child requests a band-aid. Writing the new band-aid totals on the box allowed him to work on his printing of numerals, and he even matched these numbers up with the children that used the band-aids: giving some meaning to these numbers. While children in Kindergarten really only have to recognize numerals up to 10, it’s clear that this child recognizes more than that. This authentic math opportunity though gives us a chance to later go back and explore number patterns. If there were 80 band-aids in the box instead of 50, what would the new total be? What remains the same and what changes as we count up and down with different number amounts? By writing the names on the box, he can also explore any patterns that he sees with children that use the band-aids. Are there certain children that use more band-aids than others? Why might that be? What can he infer from this data he collected? As more people also start to record the band-aid usage, they can also become more involved in this discussion, and the different learning opportunities that evolve from it. 

Leah needed a bandaid for a little cut, so I asked Brayden if he could get her one from the new box. That’s when Brayden saw a math opportunity. He saw the sign that showed that there were 50 bandaids. But Filip already took one. How many were left? He initially thought 40, but as he knew that didn’t seem right. He kept thinking about it, and figured out 49. But then Leah needed one. Now how many? 48. I suggested he write down the number left. That’s when I noticed the reversal of the 4, and suggested he look at the number chart to figure out the problem. He did, and made the change. But then he gave away another bandaid, so he decided to write down 47. I suggested that he list the children that are using bandaids on the other side, and he went back to do so. Literacy and math, just by asking for a bandaid. I love these authentic reasons to explore math. ❤️ SWIPE ⬅️ FOR MORE. #iteachk #teachersofinstagram #ctinquiry #engagemath

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Please don’t get me wrong. There may be times that we want to use different manipulatives or math activities to help better support the understanding of a particular concept. That said, I think it’s important for children, parents, and educators to distinguish between these types of activities and true examples of “math is everywhere.” Why? If we don’t, how do we get students, parents, and other educators to understand the value in this authentic math and how they can further mathematize the world around them? In our class, we talk about math all the time as we notice mathematical concepts evolving during play or during conversations. We give kids the vocabulary to also name the math that they’re seeing and thinking about as they play.

Ben was telling me about the picture the first page in his story. After he told me a sentence out loud, I drew lines (one for each word) for him to write it down. Brayden saw what I did, and said that he had to, “write ten.” Ten words? How did he know? “I subitized.” In my 17 years of teaching, this is the first time, through play, I have ever had any child tell me they did this. Incredible!! He then explained exactly how he subitized. This started as writing, but connected with math. Meanwhile, I love seeing Ben’s increased confidence in writing. A few vowel sounds are hard, but he’s sounding out even longer words independently. Really working on having him use his writing to tell a story. ❤️❤️❤️ SWIPE ⬅️ FOR MORE. #iteachk #teachersofinstagram #ctinquiry #engagemath

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And yet, even though we talk math all the time, we still have some students tell us that they’re “excited to do real math next year in Grade 1,” or that they “do real math at home in their workbooks.” What makes this math “real?” What makes it better? My hope is that the more that we move away from contrived math opportunities indoors and outdoors, and the more that we help students and parents see the value of math in the everyday, the more that this math will be seen as “real.” How do we work past preconceived notions of what “math is everywhere” really means, and what it can look like in any grade? For a playful approach to math doesn’t need to end in Kindergarten, and the same examples that I shared here, could be easily extended to other grades, making authentic links to addition, subtraction, non-standard and standard measurement, and elapsed time. Math REALLY is everywhere, so what’s needed for us to truly embrace the math in the everyday? Imagine the rich thinking, dialogue, problem solving, understanding, and positive attitude towards mathematics that could come from this kind of approach. I think it’s worth it. What about you?

Aviva

Plasticine And Self-Reg: What Do You Do When Brands Change?

Just about every educator I know spends their own money on something. I’m no exception to that rule. One of the things that I buy the most is plasticine. Most Kindergarten educators are big play dough users. My teaching partner, Paula, and I have tried to use play dough in the classroom, but with little success. As strange as it sounds, play dough almost seems to be a little too soft for our kids. Instead of it being a calming option for children, it actually dysregulates most of our students. But plasticine is different. It’s not quite as soft, it requires a little more manipulation, and it lends itself to such wonderful oral language and storytelling opportunities, while also being the perfect sensory play that many of our kids use to self-regulate. We usually go through about one package of plasticine a day. I found the perfect plasticine at Dollarama a few years ago. You’d think that all plasticine would be created equal, but it’s not. We want our kids to be independent, so this plasticine is perfect.

  • They can easily go and get their own package of it.
  • They know how to quickly and easily break each stick into smaller pieces: around four or five little pieces that they can share with their friends.
  • It’s pliable enough that it allows for the formation of beautiful creations, but not too pliable, that it creates the same problems as play dough.

I seriously cannot say enough wonderful things about this plasticine … which is why I started to feel incredibly dysregulated this morning when I realized that my favourite Dollarama store no longer sells this brand. Oh no! What am I going to do now?

Here I was this morning thinking that I could quickly run into the Dollar Store, buy my plasticine, and leave, but instead, I spent close to 30 minutes just staring at the shelves. 

  • There is a new plasticine available that is in smaller bundles, but it feels really soft. Will it be too soft? Will this result in the same problems that we have with play dough?
  • There are the big blocks of plasticine available. They’re similarly malleable to the type that we prefer, but students will not be able to be as independent with taking them from the drawer and dividing up the pieces. Can I cut the bigger blocks into smaller sections to still allow for this independence? How much will I need to buy to equate to the other packages?

I went back and forth with the options, and eventually decided on buying a big block of each colour, plus one package of the new plasticine to try out. I didn’t leave feeling good about my decision though. We know that there are a core group of our children that rely on this plasticine play for self-regulating, and would this small change in material significantly change how students respond to it?

As I drove home, I decided to stop by another Dollarama closer to my house, and I was thrilled to find some packages of the old, familiar plasticine that we love. I bought all of them! 

While I can at least start this week feeling better about our plasticine options, what will the next week bring? And the week after that? There are so many things that stuck with me after I took The MEHRIT Centre’s Foundations 1 Course, but the positive and negative impact of sensory items on the classroom environment, is one of many things that continue to stick with me. Now I can’t purchase anything without wondering, how will the children respond?

  • In the past few years, I’ve spent countless hours searching for no-scent or low-scent shaving cream, and then sometimes, even the feel of the shaving cream is too dysregulating for some children. Is it the social nature of this play that also results in dysregulation for some kids?

  • Then there are the times that I’ve purchased flowers or plants for some observational drawings. How will students respond to the smell? Is it too powerful? Will it overwhelm the whole room and not just impact on one little section of the room?
  • This year, we also used vinegar in our sensory bin, as a way for students to help clean the acrylic paint off the floor. We needed to couple this vinegar with a little additional water and some soap to help reduce the scent. In a small room, the smell seems to travel even more. 
  • Some scents seem to work better than others, as we noticed with the rice in our sensory bin. While the cinnamon and peppermint scents were somewhat strong, they were also calming. Students were really attracted to this sensory bin when they wanted a quiet space to self-regulate. Maybe the pouring helped. Maybe the quiet conversations also made a difference. And maybe, a different group of students would have responded differently. When it comes to scents though, I think we now spend hours smelling, thinking, and making changes to sensory experiences before children ever partake in them. 

Today’s plasticine experience reminded me of how something seemingly so small can have such a big impact on student learning and the classroom environment. Thinking back to my experiences of the past, before I even heard about Stuart Shanker, Susan Hopkins, and The MEHRIT Centre 

  • I would have purchased another brand of plasticine without a second thought.
  • I would have chosen the shaving cream based on which brand was on sale versus which brand had the least amount of scent.
  • my school shopping expeditions were a lot shorter, and involved less time feeling and smelling items before buying them.
  • I definitely thought less about the decisions that I made.

In the end, I might have saved some money and time without these Self-Reg considerations, but what impact did my past decisions have on the kids in my class?

  • Did I blame the dysregulation on the children that just couldn’t control themselves?
  • Did I neglect seeing opportunities to change, and the positive possibilities that might come from these changes?
  • Did I manage not to make a difference for a kid that I could have made with just a few small changes and a little extra money and time?

A search for plasticine today has made me think even more about Self-Reg, and the impact that our decisions can have on children. Imagine if it’s not just about plasticine, but creating a learning environment where kids are calm, ready, and able to learn. What would you do if you were me? Here’s to hoping that there are other Dollarama Stores that still carry our favourite classroom necessity, and if not, carry the perfect substitute. Soon we’ll be entering into the last month of school, where year-end activities, field trips, and school events often lead to an even bigger need to focus on Self-Reg. Varied, calming sensory options might be even more important than before, and now hopefully you can understand why a plasticine product is most definitely blog post worthy.

Aviva

When Parking And Driving Is Like Lining Up And Getting Dressed …

Let me tell you a story. I learned to drive when I was 22 years old. I was about to begin my first placement in the Faculty of Education. I needed a car to get from my house to the placement, and so out of necessity, I figured out how to make this car work (safely). 

  • I took lots of classes. I even paid for some additional ones.
  • I practised regularly with my step-dad: a very patient man, who helped me learn how to feel comfortable enough to move from driving in an empty parking lot to out on the road. 

I could have learned to drive six years before I did, and if it wasn’t for this placement, I probably would have waited even longer to learn.

This wasn’t because I was lazy or scared. This was because many people with my kind of visual spatial needs never learn how to drive a car. I needed to figure out strategies to determine where I am on the road and where I need to be. This is why I started driving in an empty parking lot, and moved closer and closer to real cars before moving onto the road. 

  • This is also why I drive predominantly on city streets that I know.
  • This is why I never drive on the highway, where I need to balance speed with multiple lanes of traffic and numerous cars.
  • This is why I always park far, far away from other vehicles, and almost always in a pull-through spot, where I can drive out easily instead of estimating distance when backing out.

I share this story with you, not just because I love another reason to blog about parking (which I do 🙂 ), but because, when I see the world through a driving/parking lens, I see things differently. It’s then that I understand the thinking which for years I didn’t: if we know that a child can’t do something then why are we asking them to do so?

I realize that there are certain things that we expect kids to be able to do when they get to school.

  • Sit and listen.
  • Line up.
  • Wait their turn.
  • Use the washroom independently.
  • Get dressed on their own.
  • Pack their backpack.
  • Feed themselves.

This is definitely not an exhaustive list, but it does highlight many things that are expected of school-age children. As Kindergarten educators, we realize that we might need to support some of this learning, especially in the early days.

  • There are always those children that might benefit from sitting up close to the teacher, or even sitting on a chair, and require a prompt or two to listen quietly.
  • There are always those children that might need a bathroom schedule or reminders to go.
  • There are always those children that might need to learn the “coat flip” or require some help with zippers or buttons.

  • There are always those children that might need help opening or closing containers, even as the year goes on.

And while some students might need more help than others, the assumption is that children will quickly learn how school works and what the expectations are, and they will conform. Conformity is not necessarily a bad thing. There are reasons that we have all of these expectations: from independence to ease in instruction to student safety. But as I’ve learned over the years, the reality is that not all children are at the same developmental level, and for a variety of reasons, what we expect may need to vary. 

  • Pushing harder isn’t going to work.
  • Yelling and demanding isn’t going to make things better.
  • Punishing isn’t going to help increase the speed at which these skills are developed.
  • And accepting this reality, while truly seeing the individual needs of children, doesn’t mean that we’re being “soft” … and even if it does, being kind, caring, understanding, and compassionate are not bad things.

I think that I also needed this final reminder, and at times, have needed to stop and tell myself the importance of this again. For in its own way, it’s just like me with the driving/parking.

  • Would someone have forced me to get my license at 16?
  • Would yelling at me make me a better driver?
  • Would rewards and punishments help me develop these driving/parking skills at a quicker rate?
  • Would comparing me to every other driver out there, help somebody support me better?

When framed in this way, I think that it seems outrageous to have the same expectations for every individual, so why should this be true in any other case? I know why we have our school rules, and I know the benefits of having students follow them. But what if they really can’t? Is it okay to expect something different, while slowly and kindly supporting students in developing these lagging skills? I think back to a post that I wrote a while ago now, where I wondered if our goal is to punish or to understand. In my opinion, it’s the latter, even when at times this can be challenging. For if I didn’t have some people who understood me 18 years ago, and worked to support me, I wonder if I’d ever conquer the challenges of driving and parking. Now think about our kids, and imagine if something like the challenge of lining up, was just as hard and as frustrating as that. 

Aviva

Is It Time To Change The Social Construct Of “School?”

Earlier this week, I saw a tweet from Matthew Oldridge, which inspired a response of my own. This tweet and my reply has been on my mind ever since.

On Friday, we decided to change our dramatic play/block space into a school. Students created a school in here earlier in the year, and looking at the different ways that they’ve been teaching each other lately, this seemed like a logical extension. Kids got involved in moving the furniture, packing away some blocks, and brainstorming ideas for the school. Yesterday they began to play.

My teaching partner, Paula, and I were really interested in seeing how they used this new space and what they did, so we spent a lot of time watching the play in this area. Here’s what we noticed.

Then Tomek did some writing in the school (he was proud of writing a sentence in his book, which he read to me), and Addison thought we needed a SMART Board. “The whiteboard can be one,” she said. Edward thought that we needed a schedule, so she wrote one on here. She sounded out “gym” (we still need to work on the phys-ed word), play, and library. Carly wanted to write a schedule too, and copied hers. Then Trinity came along and read what she wrote. Addison and Carys started to add rules to the board, and Trinity added an alphabet. Tomek and Carly also worked on one. Carys thought about counting the paintings, and then worked on printing numerals as she added the numbers to the back. This is when Tommy and Carly sat down to look at a book together. They told the story based on the picture cues. On Monday, @paulacrockett or I want to get into this space to see how we can extend the play. Maybe the little play spaces around the school microcosm can grow or change. 🙂 SWIPE ⬅️ FOR MORE. #iteachk #teachersofinstagram #ctinquiry

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We both found it so interesting that the traditional view of school is so strong, that even though our classroom doesn’t run in this way, their creative one did.

1. All kids were doing the same thing at the same time. (It took some questions from us to have this slowly change.)
2. A lot of time was spent in rows watching and listening to the teacher instruct at the front of the classroom.
3. Even when children eventually started to play, they made each other a lot of worksheets to trace letters and print numbers.

Paula and I spent a long time discussing these observations. At the end of the day, we even spoke together with the kids on the flow of our day, and what they do throughout the day at school. We wonder if this might change what their school looks like on Monday.

In the meantime, watching this dramatic play evolve has me thinking about what we’re communicating to kids about “school.”

  • How is school portrayed in our classrooms?
  • How is it portrayed at home?
  • How is it portrayed in books, movies, and television shows?
  • Are there messages that need to change, and how might we change them?

I keep thinking about a wonderful Ministry Document, How Does Learning Happen? Our Kindergarten Program Document supports the thinking in here. Yet, even considering all that we know about how children learn best, our youngest learners are still creating “schools” and “classrooms” that support the practices our Document discourages.

I know that there are many schools and classrooms out there that support a learning model that is …

  • student-based.
  • play-based.
  • inquiry-based.
  • parent supported and solidify strong home/school bonds.
  • rich in experiences and allow for diversity so that all children can succeed.

But does this view of school only exist within the walls of these classrooms, and is a contrary view so strong, that even the children in these environments view school more traditionally? If our kids continue to see “school” in a more stereotypical view of full class instruction only, rich in worksheets, with the teacher being the holder of all knowledge, I wonder what it will take for our changes to really make an impact. Changes in our individual classrooms are important, but is it time that we now look at how to change a system and a social construct? These are much harder changes to make!

Aviva

How Do We Get A Little “Mary” Into Our School Days?

Yesterday, I had the pleasure of seeing our school‘s last performance of Mary Poppins. Thanks to the terrific direction by Michelle Fawcett and Janet Raymond, not to mention various other educators throughout the years, Rousseau has been putting on musicals every other year for the past 10 years. Before I even started teaching at Rousseau, I used to go and see these performances. I still remember The Little Mermaid and The Lion King, and how blown away I was by the talent of the students and the support of the community.

Now though, I get the pleasure of seeing these musicals through the eyes of an educator that knows many of the student performers. And it’s this different perspective, which has caused me to do a lot of thinking since the curtain went down last night.

I’ll admit that I continue to be amazed by the singing, dancing, and acting skills of these students, but I also realized that for some of these students, Mary Poppins changed their view of school … and for the better! 

  • Imagine seeing the child that struggles with reading and writing, but beautifully expresses herself through song.
  • Imagine listening to a parent share how her daughter is too shy to talk in public (including at school), but is a shining star on stage.
  • Imagine seeing even the youngest of performers capture the audience through their words and actions, and wondering, do their in-class contributions capture others in the same positive way?

This Mary Poppins performance had me thinking about the Kindergarten Program Document, and how The Arts (i.e., visual arts, music, drama, and dance) are viewed as languages: different ways that children can express themselves. This makes me think about the 100 Languages of Children. 

I wonder how we could support these languages even more across the grades. How might we view those struggling children differently if they were able to express themselves in different ways? Would they still be seen “struggling” after all? I can’t help but reflect back on a recent blog post by Kristi Keery-Bishop, where she discusses some of her scheduling woes. Might a more integrated approach provide even more of the wonderful that I had the pleasure of seeing last night? My tuba playing days of years ago and my singing voice of today will guarantee that I will never be able to do what Michelle, Janet, Laura, and others did last night, but I’d still like to support kids in expressing themselves as our student performers did.

For some kids, these kinds of opportunities, give them a different, more positive view of themselves, and even change how others view them. Don’t all of our children deserve that? Our Board tagline emphasizes curiosity, creativity, and possibilityThis kind of Arts integration definitely supports the latter two, if not all three, goals. How do we provide these rich, Arts opportunities in a school setting, and what impact might this have on kids and their learning? I think that all children deserve to feel as proud, confident, and accomplished as the Mary Poppins actors and actresses felt every night that the curtain went up.

Aviva