Monday, January 9, 2017

Hit Pause

I took this picture while riding on a mule down into Bryce Canyon in Utah. It was an incredibly beautiful ride, and also very scary.

I am retiring this blog for now. It's been fun! It is still a great resource and I will leave it up so you and I can continue to find things here when we need them.

These days I tend to post things I like on Twitter. I hope to see you there. @karynvogel


Sunday, October 9, 2016

Space for All Learners

In my ongoing quest to find great math resources on Twitter (not hard), I started following Steve Wyborney (@SteveWyborney). Steve is a math teacher and coach in Oregon. He has been posting high quality math activities immediately usable by elementary teachers. I will share a few of them here.

Teachers often struggle with math tasks that feel just right for some students but not others. Steve’s activities are accessible by a wide range of learners in the elementary grades. They provide access points for many but also opportunities for challenge within the realm of grade-appropriate number sense, place value understanding, and additive or multiplicative reasoning.

Steve has created this subitizing/number patterns video that teachers can show to students, pausing at a certain spot to allow thinking and noticing. It couldn’t be much easier. He provides a printable page to give to students. Simple to try, powerful results.

Watch Steve’s video of ideas for how to use this resource. Then you can get the interactive powerpoint slide he created and try it with students. I can’t get it to work on a Chromebook, so you probably need a computer with Powerpoint installed.

These are simple tools, already frequently used in elementary mathematics, but often without the kind of exploration and reflection encouraged by Steve.

If you explore Steve’s blog, I’m on a Learning Mission, you will find lots more high quality instructional strategies as well as tools that are immediately usable with students.

Saturday, April 9, 2016

The Project School Visit

Recently, a group of educators from the Burlington School District visited The Project School in Bloomington, Indiana. This was part of an ongoing partnership with Daniel Baron, one of the school’s founders.

We had three amazing days of quality time with students in classes and meetings with the school staff.

Some takeaways:

School climate matters. When the staff is happy, it shows. Everyone knows it, especially the students, and it creates a healthy, happy, productive learning environment.

Decision-making based on student needs rather than adult needs feels very different. Adults at The Project School have shared core values that guide their decisions. They are flexible, positive, and student-centered. They shift schedules, resources, groups, and plans throughout the year as needs change.

Multi-age classes have many benefits. Observers noticed all students seeming to rise to the level of the oldest students in the class.  We saw a high level of peer support for learning, greater acceptance of differences, and increased self-sufficiency and student leadership.

Having a really great mission and vision matters. Here is theirs. You can read more on their website.
The mission of The Project School is to uncover, recover and discover the unique gifts and talents that each child brings to school every day. Our school works collaboratively with families, community members and social service agencies to solve real problems, as well as to create art for public spaces. Students graduate from The Project School as stewards of the environment with the will, skill, capacity, and knowledge to contribute to the greater good.
The vision of the Project School is to eliminate the predictive value of race, class, gender and special abilities on student success in our school and in our communities, by working together with families and community to ensure each child’s success.

Student voice and choice is critical. A 1st through 8th grade multi-age daily class called Passions helped us see how school can be more enjoyable for everyone.

Themes and big questions are powerful. This year they are focusing on Struggle and Progress.

Problems, Projects, and Place make up the P3 framework used by The Project School. Students do integrated, relevant, compelling projects throughout the year.

Wow! The trip gave me a lot to think about. Our group will continue to meet relative to this experience and our work in Burlington.

Thanks to Daniel and the rest of The Project School staff for helping us see some different ways of thinking about and doing education.

Sunday, December 13, 2015

Fix It

I appreciate Marilyn Burns’ presence on Twitter and her blog. She offers great contributions to the math education community.

Marilyn's recent blog post, entitled Fix It: An Activity for Ordering Fractions, is a well-written reflection of a lesson she taught to fifth graders. Marilyn describes how she used an engaging format and includes details of some masterful scaffolding for a student who needed help. It's worth reading the whole thing.

Fix It Fractions reminds me of the Clothesline Fractions activity Rebekah Thomas did with her summer school class. Before class, she’d hang a set of fractions (using clothespins) on a length of string in her classroom. A different student was in charge of “fixing” them each day (putting the fractions in order). The student presented his or her work to the class along with an explanation.

In Marilyn’s activity, students create their own Fix It Fractions sets for others to try.

There is something inherently compelling about fixing. It is different than doing math work that involves simply performing a calculation or solving a problem. Students look at the work of someone else that may be intentionally or unintentionally incorrect and perform an error analysis. There are lots of formats for doing this, including My Favorite No, or presenting two or more solutions and asking students which is correct and why.

I always appreciate when I see error analysis type tasks in Eureka Math lessons, Smarter Balanced Assessments (both of which we use in our district), and other materials. When I think back to different jobs I have held in my life, I think the majority of my time was spent interpreting, analyzing, adapting, correcting, and reimagining work that had been begun by others.

Let’s think about how to include more of this type of approach for students, and see if it improves their school experience.

Tuesday, December 8, 2015

If I Had a Hammer

Peter, Paul & Mary

I just read a great blog post by Tracy Zager. Her blog is called Becoming the Math Teacher You Wish You’d Had.

It is about getting students out of the normal (sometimes boring) routines they’ve become accustomed to in math class.

Tracy describes being in a workshop with Brian Hopkins and doing a bunch of math problems in groups. Her group solved a problem and then there was discussion and learning about the mathematics that best fit that problem. When Brian posed a seemingly similar problem, Tracy assumed they would be applying that same mathematical construct to the new problem. That was not the case, which surprised Tracy.

“...Brian disrupted the predictable, pitter-pat routine of math class...

What I see in schools is we cue kids to know what tool to use. If we’re two weeks into a unit on fractions and we give them a story problem, the kids figure fractions are involved. If the name of the chapter is “Multiplying Two-Digit Numbers” and it’s written on the bottom of the worksheet, the kids are going to assume they should multiply some 2-digit numbers. If we’ve written an objective about linear equations on the board, kids figure the answer is going to involve linear equations. If my new tool is the hammer that divides fractions, I’m going to use that hammer until my teacher tells me it’s time to switch hammers.”

As educators, we are often frustrated by our students’ lack of ability to make sense of and solve problems (the first Common Core math practice standard). Yet, are we giving students experiences in math class that help or hinder their ability to solve problems?

Sunday, August 23, 2015

Wind Map

Wind Map during Hurricane Sandy, October 30, 2012
My friend, Michael Lye, just showed me a live wind map you can access online at

The above picture is a saved image of the wind map during Hurricane Sandy.

School is starting soon. This would be something to put up on the screen as students enter the room. Ask them questions like...

What do you notice?
What do you wonder?
What information are you being given?
How do you interact with the map?
How was this map created? What do you think the creators needed to know and be able to do?
When would you most like to look at this map?
If you had created the wind map, how would you have done it differently?
What other data might lend itself to being displayed in a similar way? 

Sunday, July 26, 2015

Redefining Math (still)

I find myself thinking a lot about redefining math, and posting things on this blog about that topic. Here, again, is a quote from a brilliant mathematician that forces us to rethink our idea of what “math” means.

I must include a paragraph from this article verbatim. Terry Tao, math prodigy.

That spring day in his office, reflecting on his career so far, Tao told me that his view of mathematics has utterly changed since childhood. “When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed,” he said in a lilting Australian accent. “I sort of imagined a committee would hand me problems to solve or something.” But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. “It’s as if your only experience with music were practicing scales or learning music theory,” he said, looking into light pouring from his window. “I didn’t learn the deeper meaning of the subject until much later.” (p. 46, 7.26.15 NYTMag)

Read more here, and add this to the “How do we redefine mathematics in school?” pile.

NCSM 2015, Boston. Tuesday

NCSM Boston Tuesday Notes. Not the band, the math conference, but I liked this picture better than generic pictures of Boston.

Elham Kazemi
Developing a school-wide culture of risk.
Teaching mathematics well is both possible and difficult.

(She spoke for a bit, then asked attendees at her session to tweet questions to her. Nice use of twitter to get audience participation.)

How do we organize schools for teacher learning?
1. Fostering and developing an intellectual culture establishing a vision for working on practice together, how we get better at practice and offering opportunities for teachers to deprivatize their practice and work on it together. It takes a lot of trust. Take risks. Foster that culture.

2. Strategizing and planning for accountability and assistance.
Who will be applying pressure and support?

3. Developing and elaborating a shared set of principles and practices for teaching shared vision for math instruction. Developing tools, establishing routines.
Facilitating a common language for talking about practice among principals, teachers and coaches.

You can change teachers thinking about something without changing what those teachers do in classrooms. -Dylan William

They used something called “Math Lab” that is like lesson study. While the lesson was being taught, they would use something called Teacher Time Out. Teachers would collaboratively make a decision or confer for a moment about what to do next. Students sometimes gave their opinions also. Students see that teaching is about learning.

Talking is not teaching.

They used the term “open-source teaching”.

They shared this website:

Karen Karp
Teaching K-5 Students Who Struggle in Mathematics
I sat next to Sandi Stanhope at this one and we just laughed because Karen is so engaging and funny.
This was partly about RTI, and she was happy to see NCSM’s position paper on that topic.
Relational understanding versus instrumental understanding.
Teachers help students make connections.

There is data showing that Tier 2 Interventions aren’t helping.
Kids are getting worksheets. The kid didn't get it with a teacher, now why would they get it with a worksheet?
Kids sitting at computer with a generic program, essentially a worksheet on a computer. They are practicing what they don’t know.

Karen talked about misconceptions and rules that teachers should not teach. She wrote a great article about this in Teaching Children Mathematics called 13 Rules that Expire.

You can't think just about your year. You have to think about the future of these ideas.
What is our responsibility to the teachers that come after us?

Telling isn't teaching.

Told isn't taught.

Explicit instruction isn't telling.

At all grades, students who struggle see each problem as a separate endeavor.

They focus on steps to follow rather than the behavior of the operations.

They tend to use trial and error - disconnected thinking not relational thinking.

They need to focus on actions, representations and general properties of the operations.

Create scenarios. When do I add? What does it mean to add? Not just addition problems.