I’m taking X.MTHED-404: Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12).
Here are my notes from Session 7, Building and Sustaining the Culture of Problem Solving in our Classroom, with Fawn Nguyen
I am struck by Fawn’s initial purpose. Building and sustaining a culture of problem solving in our classrooms demands vision with plans and commitment with continual growth through feedback.
How to we make use of structure in our planning to narrow our resources to build and sustain coherence and connectedness? Wen we plan, are we intentionally connecting to standards and intentionally stepping away from them to promote problem solving, visual learning, and deepening understanding?
What tasks do we select? How much time do we spend? And, most importantly, how do we show faith in our learners to promote productive, creative struggle?
Conferring with Young Mathematicians at Work: The Process of Teacher Change Cathy Fosnot
If children are to engage in problem solving with tenacity and confidence, good questioning on the part of teachers during conferrals is critical. Questioning must engender learner excitement and ownership of ideas, while simultaneously be challenging enough to support further development. Video of conferrals in action will be used for analysis, and a Landscape of Learning on the process of teacher change is shared as a lens for coaching.
Principles to Actions describes effective teaching practices that best support student learning. In this session we will focus on one of those teaching practices: “build procedural fluency from conceptual understanding.” Ensuring that every child develops procedural fluency requires understanding what fluency means, knowing research related to developing procedural fluency and conceptual understanding, and being able to translate these ideas into effective classroom practices. That is the focus of this session! We will take a look at research, connections to K–12 classroom practice, and implications for us as coaches and teacher leaders.
How to Think Brilliantly and Creatively in Mathematics: Some Guiding Thoughts for Teachers, Coaches, Students—Everyone! James Tanton
This lecture is a guide for thinking brilliantly and creatively in mathematics designed for K–12 educators and supervisors, students, and all those seeking joyful mathematics doing. How do we model and practice uncluttered thinking and joyous doing in the classroom, pursue deep understanding over rote practice and memorization, and promote the art of successful ailing? Our complex society demands of its next generation not only mastery of quantitative skills, but also the confidence to ask new questions, explore, wonder, fail, persevere, succeed in solving problems and to innovate. Let’s not only send humans to Mars, let’s also foster in our next generation the might to get those humans back if something goes wrong! In this talk, I will explore five natural principles of mathematical thinking. We will all have fun seeing how school mathematics content is a vehicle for masterful ingenuity and joy.
How might we attend to comprehension, accuracy, flexibility, and then efficiency? What if we leverage technology to enhance our learners’ visual literacy and make connections between words, pictures, and numbers? We will look at new ways of using technology to help learners visualize, think about, connect and discuss mathematics. Let’s explore how we might help young learners productively struggle instead of thrashing around blindly.
When Steve Leinwand asked if I was going to sketch our talk, I jokingly said that I needed someone to do it for me. We are honored to have this gift from Sharon Benson. You can see additional details on my previous post.
How might we gain time without adding minutes to our schedule?
What if we mathematize our read-aloud books to use them in math as well as reading and writing workshop? Could it be that we gain minutes of reading if we use children’s literature to offer context for the mathematics we are learning? Could we add minutes of math if we pause and ask mathematical questions during our literacy block?
Becky Holden and I planned the following professional learning session to build common understanding and language as we expand our knowledge of teaching numeracy through literature. Every Kindergarten, 1st Grade, 2nd Grade, and 3rd Grade math teacher participated in 3.5-hours of professional learning over the course of two days.
I can make sense of tasks and persevere in solving them.
I can work with equal groups of objects to gain foundations for multiplication.
I can skip-count by 2s, 5, 10s, and 100s within 1000 to strengthen my understanding of place value.
I can represent and solve problems involving multiplication and division.
I can use place value understanding and properties of operations to perform multi-digit arithmetic.
Here’s what it looked like:
Here’s some of what the teacher-learners said:
I learned to look at books with a new critical eye for both literacy and mathematical lessons. I learned that I can read the same book more than once to delve deeper into different skills. This is what we are learning in Workshop as well. Using a mentor text for different skills is such a great way to integrate learning.
I learned how to better integrate math with other subjects as well as push pass the on answer and look for more than one way to answer the question as well as show in more than one way how I got that answer and to take that to the classroom for my students.
I learned how to integrate literacy practice and math practice at once. In addition, I also learned how to deepen learning and ask higher thinking questions, as well as how to let students answer their own questions and have productive struggle.
I learned that there are many different ways to notice mathematical concepts throughout books. It took a second read through for me to see the richness in the math concepts that could be taught.
I learned that there are many children’s literature that writes about multiple mathematical skills and in a very interesting way!
How might we notice and note opportunities to pause, wonder, and question? What is to be gained by blending learning?
How might we make sense and persevere when making estimates? What is our strategy and can we explain our reasoning to others?
Students were asked for a reasonable low estimate, a reasonable high estimate, and then an estimate for how long the song is based on the visual. My favorite 5th grade response:
Well, you asked for a low estimate and a high estimate, so I rounded down to the nearest 5 seconds and doubled it for my low estimate. I rounded up to the nearest 10 seconds and doubled it for my high estimate. For my estimate-estimate, I doubled the time I see and added a second since it looks like almost half.
Strong teams regularly self-assess how well they function within their norms – the hopes and dreams for how they are when together. As we learn and grow together, we pause to reflect, revise, and recommit to strengthen our teams by reviewing our community norms.
We commit to collaboratively design the agenda for each team meeting and that the agendas are shared ahead of the meetings. (ALT)
We commit to fostering a growth mindset with our learners and ourselves. We embrace the power of yet. (Carol Dweck)
We commit to use technology as a tool for learning and not as a barrier between us. (ALT)
We commit to speaking about our learners as if they are in the room with us. (Katherine Boles, Harvard)