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Math Chats Mondays #6: Using Sense-Making to Encourage Math Exploration

A Math Moment with Annie Fetter, K-5 Reveal Math Author

Welcome to Math Chat Mondays, a series where we highlight many of the expert authors, advisors, and thought leaders behind our new Reveal Math K-5 core mathematics program. Each Monday we will introduce a Reveal Math contributor, asking them questions about their mathematical research and expertise, their contributions to the Reveal Math curriculum, and above all, why they are passionate about all things math. Read on to meet our sixth guest, Annie Fetter!

Meet Annie Fetter

Annie Fetter worked on the project that developed the first version of the Geometer’s Sketchpad and was a founding staff member of the Math Forum until it ended in 2017. Currently, she consults with schools, districts, states, and a world-famous art museum and speaks at conferences, encouraging a focus on sense-making and leveraging students’ ideas. She is an author of McGraw Hill’s new K-5 textbook series, Reveal Math, and works part-time for the 21st Century Partnership for STEM Education, continuing the Math Forum’s work on two NSF grants. Her very first Ignite talk, “Ever Wonder What They’d Notice?”, has been used in countless PD sessions around the world. She reads a lot, is an unapologetic beer snob, sings and plays bass at bluegrass jams and in an all-girl band, plays ice hockey goalie, bakes sourdough bread, and is a mother to two of the best dogs a cat lover could have. Follow her on Twitter @MFAnnie.

1. Why have you chosen a career supporting math classrooms?

I decided early on I would be a math teacher, because it seemed like something I’d be good at and I could probably get a job (my 17-year old world view wasn’t very broad!). After college, I joined an NSF-funded grant that was developing the first version of The Geometer’s Sketchpad dynamic mathematics software. When Key Curriculum Press acquired our materials, I ended up helping teachers learn how to use Sketchpad and why they might want to shift their teaching to a more student-centered model.

Our research group also started The Math Forum, the first online mathematics community, and I helped teachers understand how to use the Internet and why they might want to be part of that and how it might benefit them and their students. This was the early 1990s, so being part of an “online community” wasn’t a thing yet, but the advantages of having a community of learners and teachers and enthusiasts was immediately apparent. While it hadn’t been my original plan, I loved contributing to math education in this way, and I continued to work for the Math Forum for another 25 years.

2. How do you encourage students to enjoy math?

One way is to give them interesting math to do! That sounds simple, but isn’t always what people think of when they think “school math.” I’d like students very much to be able to “do” the math that we present in school and that’s in the Common Core Standards, but we need to consider ways to introduce math that makes it seem like something to be explored, rather than something, as we used to say at the Math Forum, “to be over and done with.”

Instead of drilling on procedures and vocabulary for two weeks so that you can solve the problems at the end of the chapter (which often get skipped!), how about starting with those problems?

I first heard this phrased really concisely by Jon Manon, a math educator from Delaware: “Are we learning math to solve problems, or solving problems to learn math?” I hope it comes as no surprise that solving problems to learn math is way more interesting! You’ll be much more engaged if learning some new things will help you answer those questions you already have about an intriguing situation.

I talked about the idea of generating curiosity in an Ignite talk (a 5-minute talk, with 20 slides that automatically advance every 15 seconds) in 2016 at the NCTM Annual Meeting in San Antonio: An Alternative to SWBAT

3. Describe sense-making and why it’s an important component of a math classroom

Sense-making is a habit of mind where you take stock of everything in a situation before you start to “do” anything. What’s happening in the story? What are the constraints? What are we trying to do? What’s going on? In the K-5 classroom, we have a lot of routines in literacy that are focused on sense-making and comprehension, but our routines in math tend to be around “decoding” math (as if it’s magical) and figuring out what to “do,” not about making sense of situations.

I did an Ignite talk about this very topic in 2015 at NCTM in Boston.

4. How might educators utilize sense-making effectively in classrooms and learning environments today?

I think that the most important thing to consider is that students (and grown-ups, for that matter!) should think that math makes sense. It’s not magic and it’s not written in secret code, as much as that might describe many people’s experiences with school math. It’s something that can and should make sense.

Teachers’ most important job is to monitor for sense-making. Do your students think that math makes sense? If not, back up!

“Make sense of problems and persevere in solving them” is the first mathematical practice for a reason. If you aren’t focused primarily on sense-making, then not much else matters.

This story from my blog is one example of what can happen if you focus on sense-making:

5. How did you get involved with Reveal Math and what are you most excited about?

Notice and Wonder is a routine that we developed at the Math Forum, and much of the work I’ve done in the last 10+ years has involved supporting teachers to understand how to do it and the transformations that can happen in a classroom when you start by asking students about their ideas. McGraw Hill had arranged with NCTM to use Notice and Wonder © as a key element of the curriculum and invited me to help them implement it.

I know a number of teachers who’ve told me that Notice and Wonder changed their lives and even saved their careers. While on the surface it’s “just” a routine, it’s really a shift in whose ideas are driving the learning in the classroom. In NCTM’s Principals to Actions, one of the effective teaching practices is “Elicit and use evidence of student thinking.”

As they explain, “Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.” When you are used to “telling” as a teacher, starting with students’ ideas (what they notice and wonder) and really leveraging their thinking isn’t easy, but it’s so worth it! Students are active participants in the classroom, not passive listeners who are supposed to mindlessly parrot ideas and procedures back as quickly as possible.

6. What makes Reveal Math different?

I’ve spent a lot of time helping teachers tweak their “required” textbooks to include more noticing and wondering and to figure out what the students might know about a topic before diving right into telling students what they’re supposed to know. It requires closely looking at the mathematical goals for a particular unit and lesson and paring things down to their essential elements.

It’s always interesting and fun, and many teachers do a really good job and are excited about the possibilities of using the revised tasks in their classroom. However, having a curriculum like Reveal Math that already starts by eliciting students’ ideas lets the teachers use their energy to really listen to students and do the job of teaching, instead of rewriting or developing tasks.

7. What is the most important aspect of elementary mathematics today and how do you see it evolving?

Students of all ages think of themselves as readers. They know that they can’t read everything yet, but they have goals for being able to read at a higher level and they see the progress that they’re making. Imagine the picture books to easy reader to chapter book progression. I’ve had kids tell me excitedly they’re pretty good at easy readers and are reading their first chapter book. There isn’t really an equivalent in math. What progression is visible to students? Not so many students think of themselves as mathematicians, and they don’t have the idea of not being able to do something “yet” as clearly in math as they do in reading. They think of math more as something they can either do or they can’t, and that it’s something done to them rather than something they personally do.

I think that’s changing, slowly but surely.

Teachers are increasingly embracing students’ ideas as important contributions during the math block, and working hard to elicit and leverage those ideas more and more. Instead of hoping that students make it through math, they are hoping that students look forward to math and think of themselves as having important math ideas.

Some teachers have even told me, “I never liked math, because I didn’t feel like I had any math ideas that mattered, and I don’t want my students to feel like that!”

See more on developing a math-positive classroom:

8. What is your fondest math memory?

I don’t know if I would label it “fond,” but the mathematical experience I reflect on the most often happened during a summer enrichment experience after 9th grade. To make a long story short, one day during the math block, we did what would now be called a visual pattern — “How many dots in the next figure? How many in the 10th figure?” That sort of thing. Not only did I not know the answer, I didn’t even have any strategies for figuring it out and I had never seen anything like it. Other than a few weeks in the middle of Algebra I where I was briefly flummoxed, I’d never seen a problem in “school” that I didn’t know how to do and that looked totally unfamiliar.

It turned out to be super interesting! But why did it take until I had finished 10 years of school for me to be assigned a problem that I labeled “interesting?” I was used to doing other math-y things I considered “interesting” — logic puzzles, three-dimensional puzzles, and Puzzles for Pleasure by E. R. Emmet were things I did for fun at home — but nothing like that happened in school. Why on earth not?

Hear more what Annie has to say about the power of math on her blog:

Sign up here to learn more about our brand new K-5 mathematics core curriculum, Reveal Math!

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