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Blending K8 Math Instruction with Cathy Fosnot

Helping students take ownership of their math learning

With students coming to the classroom with a variety of backgrounds and skill levels in math, it can prove difficult to meet each of their needs. By combining high-quality curriculum, instruction and digital tools, blended learning has the potential to meet each student’s individual needs at their own pace. In this webinar, educators from the United Nations International School (UNIS) in New York City discussed how the school has transitioned to a 21st century math program by combining Cathy Fosnot’s Contexts for Learning Mathematics with adaptive technology to give students more autonomy and to inspire them to take ownership of their math learning.

Professor Emeritus of Childhood Education
Founding Director of Mathematics in the City
City College of New York

I find that when I talk to people about blended learning, they often have very different preconceptions about it. So I’m going to start off with a definition that I find helpful: I look at blended learning simply as a blend of the best of both technology and in-person instruction. In other words, it’s a no-brainer that in this day and age we should be using the best of technology and we should be making use of the best of human interaction. When we put the two together, we create a powerful learning situation.

Whether we’re talking about human interactions—the teacher and students—or whether we’re talking about the interaction that occurs when a child is on a computer, we
need to be talking about deep student-centered learning. If it isn’t deep, if it isn’t about students’ ideas, if it isn’t putting the control of learning in the hands of students, then it’s not powerful.

Both teacher interaction and computer interaction need to make use of research-based trajectories. I’ve seen so many things on the market not making use of researchbased trajectories, but just compiling a host of activities to learn the Common Core objectives.

When a teacher is working with a student, we try to understand their strategies. We need to support them to bring the mathematical strategies to fruition, and to go from inefficient to more elegant, more efficient strategies.

We’re not just interested in their answers. We’re interested in how they are modeling the problem mathematically. Adaptive technology needs to be doing the exact
same thing. So if we’re going to have blended learning and we’re going to have children doing things with computers, then we need to make sure that it’s authentic adaptive learning in regard to strategies and ways of modeling, not just coding and looking at children’s answers.

As teachers assess students through human interaction, it’s in the moment. We sit and confer with students as they work. We’re studying how they’re starting, what tools they thought would be helpful, what they used to work through the problem. We’re making mental notes as we look at their strategies. This is formative assessment and it is continuous through every moment of interaction.

Computer technology needs to be doing the exact same thing. It needs to be truly formative and continuous. A teacher in the classroom needs to hook students with interesting scenarios that they want to investigate. We need to treat students as mathematicians at work. And then we move around the room mentoring and listening. We need to involve students, have them justify their thinking, have them write up their arguments and present them to their community of peers. They need to be able to reason abstractly and to quantitatively model the mathematics.

This is what’s critical: We don’t need computer companies developing digitized drill sheets. We don’t need computer companies grading and pushing out data on grouping so a teacher can do 26 different targeted lessons to 26 different kids. We need computers to adapt to each child in the same way that powerful human interaction does. We need the computers adapting to each child in real time so no student falls through the cracks.

Math Coach
United Nations International School (N.Y.)

It’s important to be very clear about what your intended goal is when you start implementing a blended learning model, and also to remind yourself that technology is just a tool to help you achieve your goal. Learning in the classroom needs to be purposeful and intentional, and this includes sessions when using an adaptive learning system.

Adaptive learning systems are not intended to drill, nor do they replace the math workshop that provides meaningful discourse in the classroom. Instead, it needs to support the mathematizing in the classroom so that students can practice their strategies using specific tools in an individualized format.

Originally, back in 2012, we had a whole-class format. As we began to become comfortable with the system, we transitioned to more of a rotation model. Students work in small groups on different things. Those settings can be facilitated and divided based on the needs of the students as you monitor and make mental notes of their work.

Regrouping is frequent. You have to be dynamic about how you are blending. These small-group settings offer small class sizes with more opportunities for individual interactions with teachers.

Assistant Principal
United Nations International School (N.Y.)
Queens Campus

Using a rotation model has served us well in an elementary school, because most of our teachers were already very familiar with a station format. Many teachers who have taught young children have used stations in some form, so it was an easy transition.

Murry: I’d also like to emphasize that learning is not linear, it’s a journey. So we need to be mindful of that when we are looking at technology. We need to ensure that the PD for both teachers and parents provides the same journey. We should conduct a full investigation of the potential of an adaptive learning system not only for students, but also for parents and teachers.

Kennedy: Implementation almost always has bumps along the way. Tech support for the hardware, which is usually in-house, and the software, which is usually from the product side, are critical. Don’t let any of the bumps discourage you, because most of us go through more than a few when anything new is introduced.

What is also crucial to a smooth implementation is to ensure there’s enough planning so that teachers are comfortable. Our school year begins after Labor Day, so we began professional development in August so that teachers could get comfortable with the technology, and so they would know what students would be experiencing.

Murry: Also, the students need orientation in September. We look at two perspectives: How do we help new students, as well as students who forgot over the summer? The webinars and student support that DreamBox provided have been very helpful. They also have a help screen for kids that unpacks common misunderstandings students have when they are answering something. DreamBox is very helpful in responding right away. So that has clarified a lot of our student questions early on in September.

Kennedy: We also wanted parents to be comfortable, because we use the adaptive technology for homework. We wanted parents to understand if their child was assigned
15 minutes using DreamBox, how they can support that in a way that is appropriate. Communication is very important. We hold parent workshops. We do an orientation for them and let them use the program. And we are also very clear about the parameters we set up for homework.

To watch this web seminar in its entirety, please visit: