So, I started this blog a few years ago…a week, if I remember correctly, before The Board decided we shouldn’t be using blogs with students unless they were accessed through the something or other that I never have figured out. It’s been sitting idle ever since. I think my last post was in 2008! Seems like the perfect place to start blogging about some math learning.
Confession: When I first learned about the Landscape of Learning in the “Young Mathematicians at Work” books by Cathy Fosnot and Maarten Dolk, I dismissed it. It is a lot of shapes and though it is visually appealing, I didn’t take the time to figure out what all of those ovals and triangles are for. I was too busy teaching!
Fast forward: Last year I did some work with the Student Work Success Teacher. She suggested using it to assess where my students were. I liked that idea! It looked so cool with all the triangle and ovals coloured in with pretty highlighters. But…there were a lot of words I didn’t understand, and I didn’t really understand the difference between the “Big Ideas” and the “Landmark Strategies”. I did understand the tools. Hooray for me!
This year I have been doing some work with other teachers in my school and in the board, and I feel like I am starting to understand the Landscape.
For the past week, my grade 2/3 class has been engaged in Cathy Fosnot’s unit titled “Ages and Timelines”. I thought we were pretty good at subtraction, and number lines. I thought the timeline study would be a good tie in to a timeline we made in Social Studies to go along with the Traditions and Heritage unit. (It has been, but that’s a topic for another day.) I thought we’d spend about 2 weeks on this unit, and then my 2s would stick with it a bit longer while my 3s jumped back into multiplication and division. So far, so good. It is taking a bit longer than I expected, but I am happy with where we are so far. We’ll probably spend one week more than I had originally planned. (That’s the end of me putting the rest of this post into context for you.)
After the first week of our work, we had made it past Day 1 – figuring out how old everyone in the family was when 8-year-old Carlos and 10-year-old Maria were born. We made it past Day 2 – figuring out how many years until Carlos and Maria will reach the ages of their kin, and are in various stages of figuring out how old the folks will be when Marie and Carlos are 33, 35, 55, 57 and 87-years-old. I spent some time on Thursday talking with a few of my groups, focusing on grade 2 students. Then, I came home and filled out some Landscapes while thinking about what I saw in our discussions over the week. Here are some photos:
I started by completely filling in shapes that I saw the students were clearly possessing. The two in yellow have been working as partners for this unit. As I interviewed them, I could clearly see that one was leading the work, but the other wasn’t far behind. One was helping the other by showing him how to get started, choosing strategies for them to use and filling in some gaps. The other was helping too because he was challenging the thinking. I caught him a few times saying, “No…..oh wait. You’re right.” Or, “NO! That’s not right!” and then getting the other to explain his thinking. They both asked for help a few times when things weren’t going smoothly. I found it easy to scaffold them through their thinking because they really had already been scaffolding for each other. They both had their work very organized. They are counting backwards, making 10s, and counting on. But some skills are sort of there, but not 100% concretely. They were using open number lines, but in a way that showed me they are still sort of experimenting with using it on their own, and they often needed me to talk them through drawing it before they got started. I was drawing the end and beginning points, for example, and even though they were telling me what to write it was always with a question mark at the end.
Me: What should we put at this end?
(Repeat for every thing I put down, and with everything they then started putting down for themselves, even after I walked away and they only had each other to confirm the choice.)
They were right every time, but not confident about being right. I could also see that one was “keeping one addend whole and moving to a landmark number” but the other wasn’t as competent with this skill. He could do it, but didn’t think of it on his own or use it independently.
Then I chose a student who is struggling through the unit. I was able to pinpoint some gaps. The yellow students didn’t even think about a hundred chart. They are beyond that. But the person in pink needed one. It was used competently to find an answer, except that it was used for counting by ones, not skip counting, and there were some one-to-one correspondence problems that led to the wrong answer quite a few times.
So…what have I learned? I feel like I know where to go with all three of these children. Today in a PD session, my principal compared the Landscape with running records. It was a lightbulb moment for me. Yes! This is the precise sort of information I have about my students as readers and writers.
So…what’s next? Well, now I have to figure out how I react to having this new information. I am comfortable having all of my students working on ability-level appropriate reading and writing work. I am comfortable meeting with groups of children based on the strategies they need to develop. I clearly need to get comfortable doing this in math.
I know that I am engaged in really good professional development when I feel my world starting to shift. I have resisted the idea of Guided Math for a several years. I don’t want to make it sound like I am lazy, but honestly Guided Math sounds like a lot of work. I mean, I am doing a lot of work now, and sometimes revamping my way of doing something feels like a daunting task. But I think I need to stop resisting and just do it. It will be work, but I am excited about the possibility of seeing large leaps in math like I have become accustomed to seeing in literacy.
Today in our PD session we went through the work of a whole group, and mapped it on the Landscape. We could see where they class was clustering with their skills. We could see some outliers who were both above and below the groups. (I mean, they were doing things close to the top or close to the bottom that others weren’t showing during the activity we observed.) This helped to paint a picture of the whole class and what goals it might be good for them to work on next as a whole. I know that would help me to do some planning for my class. The curriculum is certainly a map of where we need to go each year, but I feel like the Landscape might be a more precise map of how to get from point to point on our journey. I’m thinking of it as paper CAA maps my father-in-law gets for free from the travel agent compared to Google Earth. They’ll both get me where I need to be, but one is going to help me avoid the sandwiches at the Ignace gas station because I’ll know there is a Subway just down the highway!