The best time to plant a tree is twenty years ago.
The second best time is now.
- Proverb
As children, most of us learned math through a collection of disconnected procedures. However, effective teaching of fractions (and math) means understanding overarching concepts and knowing what skills, problem-solving strategies, visual representations, and mathematical language bring those concepts to life.* So, we must first really, truly understand what we are teaching.
The second best time is now.
- Proverb
As children, most of us learned math through a collection of disconnected procedures. However, effective teaching of fractions (and math) means understanding overarching concepts and knowing what skills, problem-solving strategies, visual representations, and mathematical language bring those concepts to life.* So, we must first really, truly understand what we are teaching.
Lesson One: Why do we multiply by the reciprocal when we divide?
TEXT VERSION (Informed by www.jamestanton.com) |
Lesson Two: Why is it "undefined" when zero is in the denominator?
(From www.jamestanton.com) |
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Want more professional development?
Here are some resources vetted and recommended by colleagues.
Here are some resources vetted and recommended by colleagues.
Workshops
Summer Institutes at Mt. Holyoke Offers a mix of math content and pedagogy that is CCSS aligned. Supposedly really, really good. Summer Elementary Mathematics Lab at University of Michigan Very much a learning lab, participants spend the morning pre-briefing, observing, and debriefing Deborah Ball teach ~30 upper elementary schoolers. Afternoons are spent in workshops. Workshops, Summer Institutes, and On-Site PD from Mathematics in the City (NYC) Part of The City College of New York, MitC offers training in creating inquiry-based math workshops in your classroom. |
Web sites
Dan Meyer Math teacher & math education scholar at Stanford University. Check out his "three act math" stories. National Council of Teachers of Mathematics A math-specific teacher resource site. Check out their 60-minute E-Seminars. Teaching Fractions According to the Common Core Standards From the University of California at Berkeley, Hung-Hsi Wu's dense yet teacher-friendly guide is worth a complete read. It is divided into chapters by grade levels. Check out the introduction and any relevant chapter(s). Annenberg Learner A teacher resource site produced by WBGH, Boston. Check out math Interactives and Lesson Plans. They also offer college-level math modules. |
Books
Ball, D. Numerous articles, including Magical Hopes: Manipulatives and the reform of math education. Deborah Ball is one of the go-to experts on math education who keeps it real by still teaching elementary kids. If you are a math teacher, read her work; we promise you won't be sorry! Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational numbers for teaching mathematics in grades 3-5. NCTM published this text written by a bunch of math professors and consultants. It's legit. Moreover, it's filled with activities and math problems to get at some of the key ideas we highlight on our resources page. Chapin, S., O'Connor, C., and Anderson, N. (2003). Classroom discussions: Using math talk to help students learn, Grades 1-6. From the Marilyn Burns folks comes this book that explains the rationale behind classroom discourse (learning, cognitive, & social benefits) and outlines how to do it in a math classroom. Several fraction-specific examples. *Confer, C. & Ramirez, M. (2012). Small steps, big changes: Eight essential practices for transforming schools through mathematics. Long-time math resource teachers and coaches in high-poverty schools wrote this well-organized book about making math education work for kids. It's an easy and inspiring read filled with things you can do in your classroom tomorrow. One chapter is devoted to learning through classroom talk. Another shows how teachers can connect overarching ideas, skills, strategies, helpful visual representations, and mathematical language. Yet another outlines effective math-specific instructional methods. Read this book. Grant, C. et al. Lenses on Learning. Written for school leaders, this set of resources provide: a broad overview of math education and modules about teacher learning for math, observing math, and supervision of math teachers. This was a grant-funded project and piloted in the Boston area. Lamon, S. (2012). Teaching fractions and ratios for understanding. The title pretty much sums it up. There is page after page of math problems you can use tomorrow in your classroom. The companion text More! Teaching fractions... is kind of like an answer key, but it includes rationale. Lampert, M. (2001). Teaching problems and the problems of teaching. In this gripping text, Lampert examines a year of her own practice within a fifth grade classroom. She opens the door, not only to her classroom, but to her mind, sharing how to thinks, plans and acts in service to her students' learning. She illuminates problems of teaching - how to simultaneously balance many different priorities and matters - as well as the instructional approach of teaching through problems. Sullivan, P. & Lilburn, P. (2002). Good questions for math teaching: Why ask them and what to ask, Grades K-6. Again, a Marilyn Burns production. Totally teacher-friendly and practical, this book lists generative questions by grade level, suggests materials that can help kids explore the questions, and tells teachers what to look for in their responses. There's a chapter on fractions. |