Tag Archives: Mathematics

What is Cognitively Guided Instruction?

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What is Cognitively Guided Instruction? Why do we do it?

Early on a Saturday morning a few weeks ago, I had a conversation with more than 200 teachers and administrators (and a few school board members) about Cognitively Guided Instruction (CGI). The conversation started when I posed the questions, “What is CGI and why do we do it?”

The response was inspiring, thought-provoking, and humbling.

  • Inspiring because the ideas shared highlighted the wisdom and commitment to young people.

  • Thought-provoking because the response pushed me to reconsider my own ideas of CGI.

  • Humbling because it reminded me about the power of collective work and how even in the most challenging times for education, together we can push back and work to change the status quo.

Before sharing what the group came up with, I want to explain why I began this conversation. Over the last year I have found myself needing to define or position CGI in particular ways. As I considered how I might do this, I recognized that CGI is not mine to define. CGI is not mine. It’s not even Tom Carpenter and Eliz Fennema’s. And it never has been.

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In Math, Context is Critical

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Today's math teachers have a lot to balance. From following the Standards for Mathematical Practice, to incorporating real-life application into math problems, to finding resources that are flexible enough to meet a range of students' needs. 

Cathy Fosnot's Contexts for Learning Mathematics is a rigorous K-6 classroom resource that uses a workshop environment to bring the Standards for Mathematical Practice to life. Rich, authentic contexts provide a backdrop for fostering the use of mathematical models as thinking tools, tenacious problem solving, and the reading and writing of mathematical arguments and justifications to ensure the development of a positive growth mindset.

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How the Standards for Mathematical Practice Support Teachers

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How can we break the cycle of frustrated students who “drop out of math” because the procedures just don’t make sense to them? Or who memorize the procedures for the test but don’t really understand the mathematics? Max Ray and his colleagues at the Math Forum @ Drexel University say “problem solved,” by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core.

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The Role of Community in Math

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Today's math teachers have a lot to balance. From following the Standards for Mathematical Practice, to incorporating real-life application into math problems, to finding resources that are flexible enough to meet a range of students' needs. 

Cathy Fosnot's Contexts for Learning Mathematics is a rigorous K-6 classroom resource that uses a workshop environment to bring the Standards for Mathematical Practice to life. Rich, authentic contexts provide a backdrop for fostering the use of mathematical models as thinking tools, tenacious problem solving, and the reading and writing of mathematical arguments and justifications to ensure the development of a positive growth mindset.

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What Makes Math Intimidating for Teachers?

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Raising students’ math achievement doesn’t mean ripping up your planning book and starting over. In Accessible Mathematics Steven Leinwand shows how small shifts in the good teaching you already do can make a big difference in student learning. Thoroughly practical and ever-aware of the limits of teachers’ time, Steve gives you everything you need to put his commonsense ideas to use immediately.

In this video, Steve talks about the intimidation that mathematics gives teachers when they are accustomed to simply knowing how to get the right answer, and how to combat it. He states: "the issue of intimidation is a natural tension when you know you're being asked to do things that you're not prepared to do." 

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Shifts and Challenges in Teaching Math

1Math in Practice is a comprehensive, grade-by-grade professional learning resource designed to fit with any math curriculum you are using. It identifies the big ideas of both math content and math teaching, unpacking key instructional strategies and detailing why those strategies are so powerful.

Rather than providing another sequence of lessons and units to take students from the beginning to the end of the year, Math in Practice focuses on developing deep content knowledge, understanding why certain strategies and approaches are most effective, and rethinking our beliefs about what math teaching should be. 

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