While most of my reading this Winter Break consisted of mystery/thriller/suspense novels, I did make my way through one professional book: Taking Shape. I thought about reading this book after a professional development Staff Meeting on math, and after perusing my vice principal‘s copy, I decided to buy my own. I wanted access to the activities, and I knew that I would need to read this book more closely to really think about the pedagogy and ideas in it. Having discussed my own visual spatial difficulties in the past, it’s no surprise that this book brought with it many stressful moments as well as many insightful ones.
Taking Shape spoke about the value in a spatial approach to math, especially in the early years. I will admit that I’m torn on this one. I did really well in math throughout elementary school, high school, and university, but not when it came to geometry. I often needed diagrams provided for me, I still have not a clue how to read a map, and mentally manipulating objects is a real struggle for me. As I read this book, I wondered, would I ever have succeeded in math if my teachers took this spatial approach? I may be the anomaly, but I’m always drawn to those “student anomalies” and what we do to support them.
That said, I also started to think about some of our recent student work with the pattern blocks. It’s quite remarkable how many math concepts are addressed and extended with this one manipulative.
I started to wonder if the addition of a line on the light table might even extend this shape play for after the Break: allowing for conversations around symmetry, which we have not had before.
Taking Shape mentions many times that there can be growth in spatial sense. Could this also be true for adults? I began to wonder if a spatial approach to some math learning might even allow for growth in my skills. I’m torn here.
I recently discussed this topic with my parents … both educators. My step-dad got me to reflect on my growth already in spatial skills. He reminded me of many years ago when I drew a picture on a whiteboard as a model for a class activity. He mentioned that years before that, I would have never been able to use up so much of the page, made my picture as symmetrical, and created an object that actually resembled my intended one. Growth.
This had me, unexpectedly, thinking about my #onewordONT goal: pausing. If I pause for a minute and really think, maybe there are other spatial areas where I have improved. While my parking is usually far from perfect, a back up camera and some perseverance have certainly resulted in improvements.
I backed into a spot in a busy parking lot (first try) with a person on either side of me. Perfectly parked too, if I do say so myself, and with the grown up way of backing in. Christmas miracles do happen. 🙂 #backupcameraschangedmylife pic.twitter.com/Ez1OrSBr1Z
— 𝘼𝙫𝙞𝙫𝙖 𝘿𝙪𝙣𝙨𝙞𝙜𝙚𝙧 (@avivaloca) December 22, 2019
A student even inspired me to do some recent visualizing, which led to the extension of a math talk that I did not expect. I could “see” things now that I struggled with seeing when I was younger. More growth.
I’m starting to wonder if it’s my fear of spatial tasks that negatively impact on how I view myself as a mathematician. Maybe I need to believe in myself more, and push myself uncomfortably into the geometry and spatial sense realm. Could Taking Shape inspire the conversations with my teaching partner and our students that will allow for this push? It just might. How could it change my impression of myself as a math thinker and learner? I’m curious to see. Maybe one day, I will even be able to read a map correctly. I’m trying hard to not dismiss the possibility.
Yes, so much recognition here! I was a kid who excelled at maths EXCEPT for geometry. I dreaded it. The older I got, the worse it got… flips, rotations? All on paper and none made any sense. Maps I loved (much time reading fantasy novels when young meant lots and lots of maps). But to use one, I had to turn the map when I changed direction. I wish I was joking.
In teacher’s college at OISE we took the multiple intelligences test (now mostly discredited but interesting ideas behind it). No surprise to me I was 10:10 for verbal intelligence (hee hee) and also naturalistic. Spacial? A resounding zero.
Here’s where it gets interesting… I rode my bike daily up until my son was born. Riding means you don’t have to follow the same routes daily, in fact can veer off and change routes as many times as safety and time permit. I got to know my city so well, at least the Southwest/downtown streets. My mental map grew as I took the TTC across town to the beaches, or north to Yorkdale or points on the Yonge line. Driving, too, helped me create a larger map of the region that meant I could always orient myself. Easy when the lake is south… visiting St Catherine’s was really confusing because the lake is north?!
The other reason my spacial sense developed is because of David and Frances Hawkins (yes sorry it does always go back to #hawkinslearning for me). Messing about with blocks, paper, cups, string… using my hands. And at OISE, learning about Andy Goldsworthy. Those were my inspirations: Goldsworthy, Hawkinses… play. Playing with real objects opened the world in a way it never was open. I think back to how stupid I felt, and it makes me frustrated… it’s why I think blocks are more powerful learning materials than almost anything else. Dewey backs me up there, too.
One last possible thing that has grown my brain immensely: learning to play the tamborim in the samba class. Brazilian samba is incredibly beautiful and difficult to learn for a non-musician such as myself. Intricate poly-rhythms that threaten to warp my brain, and when I think I’ll never get it, I catch myself dancing with my feet in 4/4 and my drumming in 3… so the patterns don’t resolve in the same place. It used to feel like tripping down stairs. Now I catch myself. Now I can get it, even if my technique is still weak (should practice more).
So I love your post. I love that we have this in common. I just ask you to be patient with yourself because it’s possible to learn at any age. And how better to teach young kids?
Thank you so much for your comment, Laurel! I love reading about your experiences, and appreciate the connection to #HawkinsLearning. You’ve taught me a lot about Hawkins over the years, and I find myself reading your tweets to also find out more. I love how you made the link here between “play” and growth in these spatial skills. It actually takes me back to the time when I met up with you and Helen before starting to teach Full-Day Kindergarten. You helped me appreciate the link between adult play and learning, and I see that again. You also have me thinking more about block play. Many of our kids this year — both boys and girls — are immersed in block play. I wonder if watching some of this play in action also made me think more about TAKING SHAPE and the value in starting with this spatial learning. Now I wonder if the book will help me see (and extend) this block play in some new ways.
I also love your link to music. When I taught Grade 1, our Arts Consultant at the time (now the teacher in the Learning Commons at my current school) helped me make links between math and music. It really resonated with our kids. I never really considered the benefit for adult learning, but it’s clear from your comment that this music connection has been incredibly beneficial for you.
Thanks for reminding me to be patient with myself. Hearing about other people — their struggles and successes — I think help with this. I have a feeling that I’ll be revisiting this comment as Paula and I also talk about this book and classroom possibilities for the new year.
Amazing – both your post and Laurel’s response. Me, too , friends. That rotating the map thing? Oh, yes, absolutely – though for some reason Google Maps has helped me navigate a ton! (I also learned this holiday that we three should not go to Australia, because the sun is in the wrong spot, if you try to use it as a navigation aid).
I, too, have grown. Back up cameras have been huge for me, coding helped immensely with transformations (it made the Cartesian grid make sense), and having at one of my children be very strong spatially (and wanting to share his world with me) has made a big difference. Thanks, Aviva, for the encouragement to pause and acknowledge that I am getting somewhere. My husband will likely always have to steer me around people-obstacles in the aisles at Costco, but I think that’s okay.
Being gentle with ourselves and honouring our progress is excellent practice for doing it with students.
Thanks Lisa for your comment and adding to this discussion! I must admit that reading your comment and Laurel’s, and knowing that I’m not alone when it comes to these spatial needs, actually brings me a lot of comfort. It makes me feel as though we’re all learning together. I find your comment about Google Maps interesting. I wonder why it’s helped you navigate better. I must admit that I appreciate the written directions on Google Maps (as long as I can avoid highways, but that’s for another blog post 🙂 ).
Back up cameras are also great for me, but coding has actually been very stressful for me. I quickly get overwhelmed by what I need to do, and the correct directions to give. I’m better with left and right, but east and west continue to confuse me. In TAKING SHAPE, there’s a math problem example that includes “east.” I drew the whole diagram in my head completely backwards to the one in the book. I’m still not sure why, and if it matters. That said, I didn’t make my diagram just a picture of the balloon, so I feel as though that should count for something. 🙂 Maybe though my stress with coding comes from my own concerns around spatial activities. Am I assuming that I can’t be successful without trying first? I wonder if a growth mindset of some degree might need to make it into play for me. More to work on in 2020! 🙂
Reading your comment and Laurel’s reminds me of how much richer a blog post becomes with conversation. I have to say that your last line here is my favourite: “Being gentle with ourselves and honouring our progress is excellent practice for doing it with students.” Something to continue to remember as we head back to school in a couple of days. I can’t help but make the link to Susan Hopkins’ “soft eyes.” The same holds true here.
I’ve always been great with spatial thinking. I did dance and gymnastics as a kid. But I was never great at math. When I started learning about number lines, I realized that they are useful for because they connect to my strong spatial sense. I sew (from patterns). I used to quilt before I had children of my own! If only this connection in math (arrays, a teacher illustrating my thinking with a drawing, etc.) had been made earlier for me.
I grew up in the Rocky Mountains, and when I moved to the East Coast, and eventually to Ontario, I had a hard time orienting myself in the world because I didn’t have the mountains as a marker to help me with direction. Still, when my husband and I go to a new place I am the one who does the driving because I get to know my way around more easily than he does. He, on the other hand, is great at moving furniture, knowing if things will fit, parking (even a trailer backed into a spot!), packing a moving van. Can’t find his car in the parking lot if he parks in a new spot, but can look at a room full of furniture and tell you which thing needs to go in the truck first, second, third…
The human mind is so interesting!
Lisa, I love this. The human mind is indeed fascinating.
I was active as a kid too (figure skating, biking, climbing all the trees). Not sure why the physical literacy didn’t translate except that it was the 2D nature of our textbook/paper math classes (no hands-on).
So, I forgot about this: I had an aha years ago that I have always struggled with spacial sense (moving an object in my mind, flipping furniture, etc,) I have always had good volume sense. I watched my husband use jars twice the size of the food he was packing, or way too small. He’s got a mind many point out for being clever, having an amazingly detailed memory, ability to learn. I realized this container mismatch rarely happened to me… and that my hands-on experiences with cooking (measuring ingredients, pouring) and washing dishes (stacking dish rack, pouring water) meant it was always easy. I just didn’t think about it. When I did catch on, it just reinforced the importance of the water and sand play, block play, drawing, mapping, climbing on playground equipment. Brains grow with whole-body experience.
Laurel, thanks for chiming in again and sharing this aha moment of yours. I must say that as poor as my spatial sense skills are, I am actually usually pretty good at estimating volume (e.g., finding the right sized container to hold leftovers, etc.). I never made the connection to cooking and even sensory play before, but both probably assist me with this. I do a lot of measuring as I cook and bake, and I also play with kids in the sand, water, etc. I do a lot of filling containers, and you start to get a sense of size and volume. I never linked this measurement to spatial sense, and yet, the link is certainly there. Again, your comment takes me back to the value of play … for both kids and adults! Makes me wonder what kind of play opportunities we can offer for kids and teachers beyond kindergarten.
Goes to show how vast the topic is! I suppose I have a different view simply because I grew up in the USA and have had to learn as an adult to measure using the metric system. At first, I needed to know and do the conversions: 4 inches = 10 cm, 250 ml = 1 cup, etc. Now I just know how much each of these things is. 5 cm of snow makes sense to me on its own.
The container thing is interesting! I’m going to have to notice that. I’m also thinking about how to teach this in a grade 2/3 classroom.
So interesting, Lisa! I have no understanding of different metric systems. I just had to renew my passport, and needed to write my height in centimetres. I had to Google a conversion. But for small amounts, like 5 cm, I actually have a picture in my mind of what that looks like. It all depends on the measurement.
I wonder if some hands on experiences might help your Grade 2/3’s when it comes to volume. Do they need playing time too? Any extra sensory bins available at your school? If not, a large Rubbermaid bin can work well, especially ones that are longer and not too deep. Curious to hear what you do.
Thanks for sharing, Lisa! Your stories are so intriguing. You show why this spatial approach to math would have been so valuable to you growing up. I actually did gymnastics for a bit when I was younger, and I never would have thought about the connection here to spatial sense, but it’s certainly true. This actually makes you see things differently.
I wish that I had a better sense of direction. I went to the restroom in a restaurant recently, and it was like a maze getting there. I might have gotten lost on my way back to the table (and it wasn’t even that far away). 🙂 Your husband’s ability to look at furniture in this way is also really intriguing. It makes me think about room arrangements, and the value in having this skill when organizing furniture in a classroom. I could definitely use this kind of assistance … especially at the beginning of a school year. Thank goodness for my amazing teaching partner, who can think in this way, and then move the furniture with me to help me see her thinking in action. 🙂 The human mind is very interesting indeed, and this discussion is certainly making me think more about this.
This is a remarkable discussion. Laurel – I am fascinated by the container comment, and Lisa, I think your husband much be must like the men at my house (though 2 of them also help me find my car ),in terms of that Tetris ability.
I have shared with Aviva that I had this incredible epiphany this past year in June and September. I get incredibly stressed out at taking down and putting up (for lack of a better word) my classroom each year. One of Aviva’s posts helped me realize that I really struggle to visualize what something is going to look like – where things will fit best! That makes me somewhat of a puddle on the floor at the end and beginning of the year. Actually brought my teenaged kids in this August to help me think about things, and it helped.
Lisa, thanks for chiming in again on this discussion. You made me think back to that earlier post of mine and the link to spatial sense. I wonder if a more spatial approach to math, especially in the early years, would help both kids and adults with this mental manipulation of furniture. Until I started teaching, I never worried too much about this, but every last week of August, then became another attempt at classroom design. I remember one year (when I was teaching a 1/2 class) that I think I tried every piece of furniture in every area of the classroom before I settled on a design that worked. I probably would have saved the floor, my back, and some time if I could have manipulated the furniture mentally. Now, working with Paula, I realize that I really need another person to lend insight into this classroom design. Before working with her, and after this furniture rearrangement experience, I started to take photographs of the empty classroom and show them to my step-dad. He’s also a teacher, but with far better spatial skills than me. He could mentally manipulate what I couldn’t, and gave some ideas when I was at a loss of where to begin. Kind of like what you did with your teenaged kids this past year. A good reminder that even as adults, it’s okay to ask for help. What a fascinating conversation!
P.S. As for the parking lot, I always try to park by a visual clue (a sign, post, etc.). I often then walk to the sidewalk, and give myself directions on which way I will need to turn to get back to my car. Sometimes, if they’re confusing, I might also write them down. With a new car, my clicker also works well, so I often listen for the sound of the beep to lead me back. 🙂 Minus this last point, maybe I use a few more spatial skills than I think.
My husband has helped me set up my classroom many times! He’s a social worker, but I he seems to instinctively know where the shelves and tables will fit best. (Plus he’s good at heavy things!) I rarely end up moving things after he places them. (Except student desks.)
So interesting, Lisa! Such a great example of how spatial skills are used even as adults. Interesting how so many of us also look for help in this area. Help is definitely not just for kids.