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
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.
As Brayden went to get Filip a bandaid, he realized that there was a math opportunity here. Did some counting back. As you can hear, I got a little distracted at the end. pic.twitter.com/hRuBEkj6Ae
— Aviva Dunsiger (@avivaloca) May 18, 2018
He really needed to get Leah a bandaid, and not Filip. My fault! I wrote the wrong name.
— Aviva Dunsiger (@avivaloca) May 20, 2018
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
Just as I suggested, Brayden went back to list the children that each needed a band-aid on Friday. If he continues to do so as more children use them (we may need to work on smaller printing), then he can also comment on this data as he collects it. More authentic math from a box of band-aids. #ctinquiry #iteachk #teachersofinstagram #engagemath
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
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?