What Makes CFLM Different? Part Two: Doing What Mathematicians Do

How is CFLM different than a traditional curriculum?

1. Our Landscapes of Learning (developmental trajectories) are used to interpret and move student thinking forward to ensure progressive development.
2. Children have opportunities to do what mathematicians do, every day.
3. Contexts serve as the source for new learning not just an application of what students already know.
4. Students generate models from contexts, rather than being shown or “taught” models.

In the most recent post, we looked at how the Landscapes of Learning are essential tools for interpreting student thinking and for teachers to question and confer with students in powerful ways to support progressive development.

#2 Children have opportunities to do what mathematicians do, every day.

Let's take a look at the discipline and think about what mathematicians really do. Mathematicians work on big, juicy, challenging investigations for long periods of time. Sometimes they work alone, sometimes they work in pairs. They share ideas with each other, gain insights, get stuck. When they think that they've cracked something, they bring it to the community for feedback. They hear from other mathematicians about what they think about the insights they've had. They challenge each other's thinking. They go back and revise their thinking, their models, their proofs and arguments. When they are ready to publish, they share it with a larger mathematics community and try to convince other mathematicians of what they've discovered, define what's true and under what circumstances. All the while, their efforts are intended to move the entire mathematical community forward.

Every CFLM unit uses the math workshop model every day. This is the model that CFLM provides so that children are treated like young mathematicians at work every day. They do what mathematicians really do.

Here's Cathy sharing how we think about math workshop.

Developing contexts versus giving word problems

In CFLM, contexts that all kids can imagine serve as a source for learning, not just an application of it. In the sample clip below from our online classroom video library, notice how the teacher knows the difference between giving a word problem and developing a context in one of our 2nd grade measurement units, Tanisha and Tamika's Toolbox. CFLM contexts are used to hook children, to give them something they can imagine, to give them something they can mathematize from their own lived worlds. They generate the mathematics from carefully crafted sequences of contexts.

Teachers support the investigation

Many people think that teaching through inquiry means that the kids discover everything. CFLM is not discovery math. Just throwing a rich task out to kids and allowing them to choose a strategy and draw a picture is not sufficient in moving kids further in development. We need to sequence contexts didactically to ensure progressive development. This means that when kids are mathematizing contexts from their own lived worlds, teachers need to leverage the power of carefully crafted sequences of contexts to question and confer in ways that move kids further along the landscapes of learning. They need to understand where kids are in development, what big ideas and strategies they're trying to use, celebrate those ideas, get underneath them and challenge them. Here's another sample clip from our online platform of Cathy questioning and conferring with a group of 3rd graders in an investigation from Groceries, Stamps and Measuring Strips.

Gallery walk and congress

Mathematicians are committed to moving the entire mathematical community forward. As mathematicians discuss what they've been doing with other mathematicians, new mathematics often comes out of that discussion. They construct viable arguments and critique the reasoning of each other.

The math congresses in all CFLM units promote these features:

• Moving whole-class discussions beyond just a share of what each kid does. 
• We raise the bar and up the ante thinking. Teachers are supported to think, "What's a conversation that we can use student thinking to get started to move the entire community forward?"
• Teachers employ teaching practices that build communities of mathematicians and keep the dialogue ball moving amongst the kids, rather than a back and forth volley between the teacher and kids.
• The goal of each congress is to help kids see something new coming out of the congress than they knew going into the congress.

The clip below is yet another sample of one of many clips of teachers using the CFLM units with real students on our online platform. This clip comes from a portion of a congress from a 2nd grade unit, Beads, Shoes and Making Two's where a teacher is facilitating a congress after students investigated various egg carton designs that work and do not work for creating cartons of two rows. Notice how the teacher addresses each of the 3 bullets above to go beyond just a show-and-tell of strategies so kids get to do what mathematicians actually do.

Math workshop enables students to be treated as mathematicians every day. Instead of the teacher trying to transmit the mathematics on students, students have opportunities in every unit, every investigation to do what mathematicians actually do by mathematizing rich contexts with low floors and high ceilings so that all kids have a way to get started, and all kids have room to grow.

Allowing students to reinvent strategies and big ideas is no easy task. However, the curricular materials that teachers use play a critical role in lifting some of the burden of "teaching" off the teacher. With rich sequences of investigations in every unit, teachers are freed up from having to force the mathematics on children and can instead work on teaching practices that support progressive development such as posing purposeful questions, facilitating meaningful discourse and supporting productive struggle.

Join us in our movement to transform all classrooms into communities of young mathematicians at work!