What Makes CFLM Different? Part One: Landscapes of Learning
How is CFLM different than a traditional curriculum?
- Our Landscapes of Learning (developmental trajectories) are used to interpret and move student thinking forward to ensure progressive development.
- Children have opportunities to do what mathematicians do every day.
- Contexts serve as the source for new learning not just an application of what students already know.
- Students generate models from contexts, rather than being shown or “taught” models.
Below, we elaborate on the first of these pieces, the Landscapes of Learning. In later blog posts, we will continue sharing more about the others.
1. Landscapes of Learning.
Our landscapes are not trajectories comprised of stages; nor, are they linear pathways. They are comprised of big ideas, strategies and the use of models as tools to think with. They are used, not to level and prescribe objectives, but to interpret and document learning, and to help teachers move student thinking forward.
While teaching with the CFLM units, teachers are developing their capacity in the areas that matter most for student achievement: deepening their beliefs about what it means to do mathematics, strengthening their enactment of research-based teaching practices, and building mathematical knowledge for teaching.
Focusing on the landscapes over time, years of time, deepens teachers' mathematical knowledge for teaching and drives everything they do from how they question, how they make adjustments in real time, how they facilitate discussions, how and what they assess, and on and on.
Not familiar with what a landscape is? Take just a few minutes to listen to Cathy as she talks about the multiplication and division landscape that is the backbone of several of our 3rd-5th grade units.
While many curriculum companies claim they use trajectories to build their materials, very few, if any, actually provide those trajectories for teachers to use every day. With CFLM, every unit includes a one-page Landscape of Learning that provides a road map of development that students will traverse throughout the unit. As teachers allow students to mathematize the rich contexts in the investigations, they need a guide for interpreting what students are doing and saying. Let's face it, kids don't raise their hands and say "Teacher, I am over here using partial products, can you please confer with me to move me further along in development?"
Teachers need to spend time analyzing student thinking with developmental trajectories like our landscapes so they understand the significance of what each of their children are doing, and what is just on the horizon for them that they can nudge towards. Without research-based landscapes, teachers are left with just asking generic questions like "Why don't you draw a picture of what you're doing?" or "Maybe you can do it another way?" These questions are just not powerful enough to support progressive development, so thinking about and using landscapes is absolutely critical for both teachers and students to move forward.
Many people are familiar with Cathy's landscapes from years ago, but all of our new units include new landscapes like the following:
- Addition, Subtraction and Number Sense
- Navigation and Shape
- Systems of Measurement
- Linear Measurement
- Area and Perimeter
- Data Representation and Analysis
- Place Value
- Fractions, Decimals and Percents
- Area and Volume
- Coordinate Plane
- And several more!
Having the paper version of each landscape in the units is great, but we also highly recommend the videos on our P2S2 platform where Cathy and other authors actually build the landscapes on screencasts and connect them to the contexts and investigations in each respective unit.
Finally, our dynamic assessment application provides a landscape for each child so teachers can document the journey of each child as they construct the most important big ideas, strategies and models. As students work on the rich investigations, teachers can take pictures or video of their work and attach it to their landscape. But even more, within the app we provide provide written assessments for teachers to give to their students to not only assess where students are on the landscape, but also use our rubrics to know how to respond to what they're doing. More on that in a future post, but for now you can check out the assessment app here and sign up for a free trial.
With all of the amazing supports, it's no wonder that CFLM is transforming classrooms all over the world...and only growing!!
Stay tuned for the next post as we discuss how children in CFLM classrooms have opportunities to do what mathematicians do EVERY DAY!