Blogstitute Post 5: On Being a Mathematician

June 30th, 2014

Welcome back on this lovely Monday to our Summer Blogstitute! We have a lovely post from Kassia Omohundro Wedekind this morning, author of Math Exchanges and How Did You Solve That? Kassia talks about how her students’ attitudes change throughout the year when it comes to thinking about themselves as mathematicians. And while Kassia talks about math here, the question could be asked in all classrooms: “What is the legacy of our (math) classrooms?” Be sure to leave a comment or ask a question for a chance to win a package of eight Stenhouse books! Last week’s winner is Terri R. Keep commenting!

On Being a Mathematician

2014-02-19 11.48.08In the last days of the school year I always think about how far we are from the first days of school. So much change and growth happens in a classroom between September and June, and as a math coach I get to watch these changes happen in many classrooms and throughout many grades. I had been thinking specifically about how students’ mindset about mathematics can change throughout a single school year when fifth-grade teacher Mary Beth Dillane and I sat down for a coaching session to reflect on our work together this year.

The fifth graders in Mary Beth’s class began the year with a variety of different feelings about math. Some hated it. Some loved it. Some loved it as long as it came easily and quickly. One cried at Mary Beth’s table in the back of classroom, “I’m bad at math. I’m always going to be bad at math.” And most had just not thought much about themselves as mathematicians: people who construct meaning and contribute mathematical ideas.

And yet the first day I visited Mary Beth’s classroom, about midway through the school year, I could immediately tell how much she valued community. The students huddled together in groups working collaboratively on chart paper, lingering over a single problem. A class-constructed number line labeled with fractions, decimals, and whole numbers from zero to two hung in a prominent spot on the wall. Above it were the words and ideas of Mary Beth’s students. (“Connor and Khalil’s rule: Decimals and fractions are the same shown in different ways.”) At the front of a class was a hand-written quote from Mary Anne Radmacher, “Courage doesn’t always roar. Sometimes it is the voice at the end of the day that says I’ll try again tomorrow.” Already Mary Beth’s students’ ideas about learning and what it meant to do math were expanding and changing. We continued to work on this throughout the year, explicitly teaching behaviors and practices of mathematicians.

So it didn’t surprise me when our last coaching sessions turned to the topic of how the students have changed as mathematicians and how they view the learning of math in general. We discussed our own ideas about how each student had changed (“Did you see how they persevered on that problem? They spent the whole class working on it and didn’t want to stop!”), but we wanted to hear from the students themselves too. So, a couple of weeks before the end of the school year, I decided to interview some of Mary Beth’s students about how they viewed themselves as mathematicians and their general mindset about math. I asked them several questions (Who is a mathematician? How do you feel about math? What is math? Are there some people who are just good or bad at math?). I want to share just a few of their ideas and words with you.

Kassia Omohundro Wedekind

Kassia Omohundro Wedekind

Who is a mathematician? What kind of person is a mathematician?

“A person who looks at different perspectives to find their answer.”

“A mathematician is a thinker, a strategy person, shares ideas.”

“A mathematician is a person who, like, thinks, thinks about the problems . . . risk-takes about the problem. If they think it’s hard, they still do it.”

“A mathematician is a person who checks and checks if it makes sense.”

What is math?

“Mostly calculating.”

“Numbers—decimals, fractions, everything.”

“Like, stuff. Like diameters, circumference.”

As we talked about the student interviews, Mary Beth and I realized that while the students had broadened their understanding of what kind of people they are as mathematicians, they still have very narrow definitions of math. We know that so much of math isn’t about calculating and numbers. It’s more than the “stuff”—it’s the thinking. We know we need to explore different ways of communicating that to our students.

I think asking these kinds of questions of our students is important. (Next year, Mary Beth and I plan to do a similar interview with students during the first week of school as well as at a couple of other points in the year so we can reflect on how we are helping them grow as mathematicians.) But perhaps it is even more important to ask these questions of ourselves as teachers. What is the lasting legacy of our math classrooms? We hope that it is deep understanding of mathematical content. But just as much, we hope that it is the sense that all people are mathematicians who are capable of the problem solving and persistence required of mathematics.

As Mary Beth’s class of fifth graders prepares to head off to middle school we both ask ourselves, “Are they ready? Are they independent enough? Do they know enough about fractions?” We think about our students who have struggled this year, who have made so much progress, but who still would be thought of by many as “behind.” Like overprotective parents we’ll have to fight the urge to drive over to the middle school in the first days of the next school year and peer through the windows of their classroom, shouting, “Brian, use the number line in your head!” “Giselle, think about what makes sense!” But we won’t. We’ll watch them go, those mathematicians, and take on the world. And we’ll keep working on helping kids be “thinkers,” “strategy people,” and sense makers.

 

Entry Filed under: Blogstitute,math

22 Comments Add your own

  • 1. Lisa C  |  June 30th, 2014 at 6:17 am

    I have found, in my 14 years of teaching, that as the number of worksheets I hand out in math class decreases, my students’ love of math increases. Math self concept really is so important!

  • 2. Joanne M.  |  June 30th, 2014 at 11:48 am

    How do you create a feeling of confidence in students who are intimidated by Math due to bad experiences in other grades?

  • 3. Dawn Sunderman  |  June 30th, 2014 at 12:28 pm

    Great post. Really has me thinking. I will be adding your interview questions or similar ones to my math survey that I plan to do at the beginning and ending of the year.

  • 4. Jaclyn Karabinas  |  June 30th, 2014 at 12:49 pm

    Excellent instructional strategy! A great approach that is used so often in literacy (you are the reader/writer) and not nearly enough in math.

  • 5. Rhonda P.  |  June 30th, 2014 at 12:56 pm

    Having taught 6th grade math for 3 years and 3rd grade math for 21 years, I have seen many students who love math and those that hate math. I feel that a student’s confidence in math can be built up despite previous experiences in other grades. They need to first of all realize that everyone learns at different rates, which does not mean that if you take longer that you are not just as smart. They also need to realize that because math is going to be a part of every grade level, they need to just buckle down and work hard. Identifying these struggling students is, as we all know, essential at the beginning of the school year. They need patience and extra encouragement from us. I always tell my students that their “light bulb” may not turn on the first time trying something new. They need to wait for it, but it will turn on. Positivity is the key!

  • 6. Lindsay Foster  |  June 30th, 2014 at 1:01 pm

    Love how you are helping students to reflect on their learning and offering continuous improvement.

  • 7. Tammy Petty Conrad  |  June 30th, 2014 at 1:17 pm

    Loving these blog posts on education and learning. Like the idea of surveying students at the beginnng and end of year. Think I will incorporate that into my classes. Thanks!

  • 8. Tracy  |  June 30th, 2014 at 1:45 pm

    “We know that so much of math isn’t about calculating and numbers. It’s more than the “stuff”—it’s the thinking.” Such an important point! This past year I really focused on those kids who are perceived as naturally good at math because they are quick calculators. But these same kids frequently are the ones who can’t explain their thinking or share a strategy. Using a lot of math talk in whole group, and introducing small group math exchanges a copuple of times a week, really helped to stretch everyone’s thinking…including my own!

  • 9. Brian  |  June 30th, 2014 at 4:40 pm

    Unfortunately, too few classrooms focus on creating mathematical thinkers because they are driven by formulas, procedures and “right answers”. Great article. Keep up the great work!

  • 10. Terje  |  July 1st, 2014 at 2:36 am

    In literacy instruction the teachers are expected to spend time building a community, share their passion for reading and writing and model who they are as readers and writers. I believe the same is true for mathematics. The teachers who are problem-solvers, who have found the beauty of math, discovered the patterns, connections and core of different concepts, have an easier time igniting love of math. For the ones whom math seems a bit scary a math coach or having a supportive inquiry/book study group could help to grow and change, always keeping the students learning as the focus. I enjoy Stenhouse blogstitute for nudging thinking and providing resources for further learning.

  • 11. Sandi  |  July 1st, 2014 at 5:44 am

    Thank you for this thoughtful post. As a kindergarten teacher, I work hard to start the process of helping students see themselves as capable mathematicians and to notice Math in their world.
    I especially want them to leave knowing that it’s important to keep trying, that faster isn’t better, that it’s OK to take risks and make mistakes, and that talking about their thinking is an important part of being a mathematician.
    I could definitely relate to the author’s last paragraph. Watching my kids leave that last day, knowing some of them will struggle and may start to see themselves as “bad at Math” makes me sad.

  • 12. Lindsey  |  July 1st, 2014 at 12:28 pm

    I taught a 1/2 split this past year. Initially I intentionally incorporated math talks as a way to engage both grade levels and to see where we were with number sense. At first the first graders were quiet participants but by the end of the year anyone visiting my class could not distinguish between the grade levels. Confidence was built, collaboration increased and a love of math prevailed.

  • 13. Jill  |  July 1st, 2014 at 2:14 pm

    I love the idea of interviewing the students at various points throughout the year to see how their thinking changes. I plan to try this in the upcoming school year.

  • 14. MJ  |  July 1st, 2014 at 5:25 pm

    I teach kindergarten. Making math fun and hands-on is important to me. I want my students leaving kindergarten in love with books AND math!

  • 15. Vishal Upadhyay  |  July 2nd, 2014 at 12:02 am

    It’s really an informative and well described post. I appreciate your topic for blogging. Thanks for sharing such a useful post.

  • 16. Valerie Black  |  July 3rd, 2014 at 4:42 am

    As I read your article, I thought of course about my own students. I teach in a resource room and math is often something that they feel good about – a strength. Not because they are able to work at the grade level math and find a lot of success, but because when they look at numbers so many times they can successfully do many of the basics while reading continues to be elusive. Your article makes me want to explore with them more of the reflective parts of working problems – it is hard for many of my students to articulate what they are doing in problem-solving situations and we spend time giving words to our processes. I would like to include some of these types of reflections. Thank you.

  • 17. Julie  |  July 4th, 2014 at 8:10 am

    Hi Kassia & Everyone — It was so refreshing to read a post about math that focuses on classroom community and growth mindsets. I love the examples of a class created number line and student designed math “rules.” During the upcoming school year I hope to work with my students to design big idea posters for each math unit. I’d also like to conduct math interviews but need to find a way to really use those to inform instruction.

  • 18. Patricia Maia  |  July 4th, 2014 at 1:02 pm

    Kassia,
    I am intrigued in finding ways to make this work in middle school. I have spent the last few days moving my classroom, which required me to move all the retired English teachers materials. As I was packing the boxes, I saw things like editor’s checklist and book talks. I am thinking of math checklists and problem solving talks to help build mathematical thinking skills.
    Thanks,
    Patricia

  • 19. On Being a Mathematician &hellip  |  July 8th, 2014 at 4:29 pm

    […] some of these thoughts, and share some stories from a great 5th grade classroom in my blog post, “On Being a Mathematician,” over at Stenhouse’s Summer Blogstitute […]

  • 20. Jen  |  July 8th, 2014 at 8:28 pm

    I have recently worked with a enrichment group where the `what is maths?’ question kept arising. The children were concerned that we weren’t `doing’ maths because we weren’t solving number problems! The more I questioned, the more I realised that their concepts of maths were very limited – so far as to say that unless there are (written) numbers involved it is actually NOT maths! I have to admit that this was the first time I had actually thought long and hard about my understanding of maths and what the children I teach understand maths to be. There is plenty more to think about here.

  • 21. Janet  |  July 8th, 2014 at 9:23 pm

    Wonderful to read your writing and think about your ideas. Mindset is so important. (Everybody read Carol Dweck’s! work.) Kids inventing and being excited about math comes from a safe space to experiment and risk and “come back and try again tomorrow.” What a gift to have two thoughtful teachers supporting students. I hope your sweet family is having a wonderful summer. Your work has changed my work.

  • 22. Amber garbe  |  July 8th, 2014 at 9:33 pm

    Thanks for this thoughtful post! I’ve been gathering literature to help students see mathematicians in action, to spark their ability to see themselves as a mathematician. Two titles I’ve added to my list of such books are The Boy who Loved Math and a Beam of Light. Does anyone have others?

Leave a Comment

Required

Required, hidden

Some HTML allowed:
<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

Trackback this post  |  Subscribe to the comments via RSS Feed


New From Stenhouse

Most Recent Posts

Stenhouse Author Sites

Archives

Categories

Blogroll

Classroom Blogs

Tags

Feeds