A New Math Mindset

 

When I was an elementary-school student, I hated math time. My brain didn’t work as quickly with numbers as many of my other friends and peers, and I felt that I was “bad” at math. Unfortunately, I had this misconception until I was 33 years old when I began my three-year goal study at Trinity School.

When I think back three years ago when I decided to focus on the math growth mindset for my goal, I can remember having a feeling of trepidation; however, I knew that I needed major growth in this area if I wanted to be a better math teacher myself. I began my journey by taking Jo Boaler’s online course, which is what I truly believe was the turning point in my philosophy about being “good” or “bad” at math. I not only learned that all math minds are different and have different speeds and ways of thinking about numbers, but I also came to believe in my own heart and mind that anyone can be “good” at math, including me!

It was at that point that I noticed a shift in the way I thought about math and taught it to my own students. I spent nights at home searching for math challenges for my students and myself and felt an invigoration when working hard to complete them. I shared this attitude in my classroom and soon noticed my students were working on these challenges during snack time, way after math time was over, because they wanted to persevere. Soon my twitter account was full of smiling student faces that were posing with pictures of their completed math work and I was hash-tagging the “math growth mindset” numerous times a week. We began celebrating our work together by charting our attitude and successes and in no time the students began using math vocabulary regularly when talking about math and even in other subject areas too! They understood terms such as “number flexibility” and felt excited to not only talk about it, but also prove they could do it.

One of the more exciting highlights from the past three years was when I read the book, Making Number Talks Matter, and began implementing number talks in my classroom. Number talks have been a wonderful teaching strategy that allows the students to feel comfortable with math and helps them appreciate the idea that there are many ways to solve a math problem. It also has helped me informally assess my students’ understandings and given opportunities for every voice to be heard in math.

The completion of my three-year goal study came with a feeling of pride, confidence, and a math attitude change. I have pride and confidence in my ability to teach math to a younger generation of students. Many of these students are young versions of myself who long to feel “good” at math, and I love being able to impart my own newfound math growth mindset on them.

Learner, Thinker, Writer: Sarah Hanzman serves the Trinity School community as a Second Grade Teacher. 

Planning rich mathematics lessons

There is so much to think about when planning and teaching mathematics lessons. At many schools, there is an adopted text that dictates what teachers teach and when they teach it. At our school, the adopted mathematics textbook provides a resource for lessons, but that text is not the mathematics curriculum. This can feel freeing but also daunting. How can teachers be certain they are planning rich mathematics lessons when they aren’t following a lesson from an adopted text?”

As a math specialist at the school I have wondered, “Could a lesson-planning template be helpful to teachers when they plan their own math lessons? And what would that template look like? In order to plan a mathematically rich task, I wanted that template to include:

  • A reference to national standards
  • A context
  • A connection to recently revised progress reports and “I Can” statements
  • A way to provide mathematical progressions (developmental sequences) for the target skill
  • An outline for teaching the lesson – (launch, explore, summarize)
  • Anticipation student responses
  • Connections with the 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein–Anticipate, Monitor, Select, Sequence, and Connect.

Gratefully, I collaborated with Jill Gough about that template. Jill is the director of Teaching and Learning at Trinity School in Atlanta and is my colleague. In addition to her mathematics expertise, she is masterful at listening to ideas and illustrating them through her sketches.

With her help, this is our latest iteration of a mathematics lesson-planning template.

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This is one of the completed templates for Pre-K.

prek-rotation6And this is an example of a completed template for a First Grade lesson.

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I believe the important part of this math-planning template is understanding the mathematics content necessary to effectively plan with it.

Mathematics content knowledge is needed to anticipate student responses for a lesson. Anticipating responses helps us be strategic in providing entry points for the lesson and meeting students where they are during the lessons.

For example, during a lesson asking students to physically act out, and later use objects to model How Many Feet in the Bed?, these were anticipated students responses:

  • Counting the feet by ones to tell how many.
  • Counting the feet by twos to tell how many.
  • Starting the count over to know” how many feet in the bed” after another character gets in.
  • Counting on from the last count when another character gets in the bed to tell ‘how many feet in the bed”.
  • ‘Just knowing’ “how many feet in the bed” without counting.
  • Struggling to count or to tell how many in all as the number of feet in the bed increases.

Content knowledge is also necessary as we monitor what our students do during the lessons.

For example, during that How Many Feet in the Bed? lesson, it is important to notice and note:

Can students model the story with objects?

Are students keeping track of an unorganized pile of objects?

Does a student demonstrate one to one?

Do students know how many after counting?

Can students count on?

Where students are in their mathematical understanding is demonstrated in what they are doing and saying. And what they do and say helps us know what to ask, when to nudge, and what should happen in the next lesson.

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Creating this template reminds me of planning for guided reading. When planning for a guided reading group, I wouldn’t simply ask students to read and then tomorrow pick another book and ask them to read again. I would choose a focus for the lesson: decoding, fluency, or comprehension (the target). Then I would choose a proper supporting text to match the focus (context). During the lesson, I would notice what students know how to do as they read. I would also notice what they struggle to do and what strategies they use to help themselves when they struggle. I would realize what tools students don’t yet have that can help them with future texts (notice and note). I would know how to notice all of this and make instructional decisions because I know what tools students need to become readers. There is a path. Deepening our content knowledge helps us understand the path in mathematics.

So, this math lesson-planning template is a beginning to planning rich tasks. The template helps us think about the content and the path of learning for the lessons. And it is helping us notice what students do.

What’s next:

It is crucial for me to create efficient and useful meeting agendas as grade level teams and I continue to build our collaborative math communities. During 30-minute meetings once per rotation, we have shared our notes, noticed trends across classrooms, talked about content, and discussed future lessons.

The lesson planning template should evolve to explicitly include the math practices. Routines for Reasoning by Grace Kelemanik, Amy Lucenta, and Susan Janssen Creighton states that a math practice goal is a thinking goal. Those math practices describe how students will reason mathematically about a problem.

So this journey continues… 

Learner, Thinker, Writer: Becky Holden serves the Trinity Community as the Early Elementary Mathematics Specialist.

The Art of Badging


Growing up in rural Pennsylvania I was extremely active in Girl Scouting. One of the joys of scouting was earning badges. Badging required me to fulfill a variety of criteria, skills, goals, and objectives in all areas of life. From drawing and painting to sewing and photography, I learned skills that are the basis for my teaching career to this day! Earning badges and awards (specifically the First Class award, equivalent to the Boy Scouts Eagle Award) and receiving it demonstrated to me the skills I had acquired and the honor of receiving the badge or award validated that fact.

gs-badgeswww.pinterest.com/explore/girl-scout-badges/

When Nina Chamberlain, my teaching associate at the time, returned from the 2015 National Art Education Association conference held in New Orleans, she brought back the idea of “badging” to our art classroom. I was totally on board with using them within the Choice-Art studios! She hand-drew over 100 badges for the 10 studios we have in the Choice-Art Studios. We had a “soft opening” last year, awarding the badges to students who demonstrated specific skills with materials, techniques, or concepts in the studios. A big THANK YOU to Nina! Thank you for sharing your talent. I couldn’t have done it without you!

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Photo by Pat Kerner, Art by Nina Chamberlain

This year I have taken the art of badging to the next level. I have developed learning progressions in each of the 10 studios. After demonstrating their skill earning specific badges and fulfilling the criteria in a studio, the student can earn a “ribbon” signifying their attainment of the skills at that level of the learning progression. The Green ribbon signifies the “Novice” level, then comes the Yellow Ribbon for the “Emerging” level, after that is the Red Ribbon for the “Proficient” level, and finally the Blue ribbon for the “Advanced” level. In some studios, such as the Architecture studio, I have changed the names of the levels to reflect historical terminology: Novice, Apprentice, Journeyman, and Master Architect.

drawing-ribbons

Photo by Pat Kerner, Art by Nina Chamberlain

Students have enthusiastically embraced the earning of badges and ribbons, and I am finding their motivation and engagement has increased. Many students are determined to earn all of the badges and subsequent ribbons in a studio to become a master of their craft!

Little did I know that when I was a Junior, Cadette, and Senior Girl Scout that badging would come full circle and become a focus for my work with students in the arts!

Learner, Thinker, Writer: Pat Kerner serves the Trinity School community as the Lead Upper Elementary Department Art Teacher.

Deep Learning…what does it REALLY mean?

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I’ve been doing a lot of thinking lately about what Deep Learning really means? Is it “less”, but “more”? Is it more complex, more work, and difficult? Does technology assist in this? Is deeper learning only for a select group of students, or is it for everyone? What does it look like in the classroom?
How do we create a community of people who truly understand what deep learning really is?

For me, I’ve been grappling with all of these ideas, asking a lot of questions, and trying to gather information about the topic. As our school community begins to look at this topic, do we really understand it? Can everyone articulate what it means? I’m still getting there.


A Rich Seam How New Pedagogies Find Deep Learning

A Rich Seam
How New Pedagogies Find Deep Learning

One resource that I came across, was focused on the use of technology and how the effective integration of it, allows for deeper meaning and understanding from our learners. For years, I’ve been talking about the difference between consuming information (knowledge acquisition) an creating content to share with the world. Applying what they’ve learned in new ways.

~One way that deep learning can occur is through the intentional use of technology in the classroom along with the change/shift in pedagogy from the facilitator.~ According to Michael Fullan and Maria Langworthy,

“the explicit aim is deep learning that goes beyond the mastery of existing content knowledge. Here, deep learning is defined as ‘creating and using new knowledge in the world.’ “

Deep learning tasks are those that re-structure the learning process towards knowledge creation and purposeful use.


Deeper Learning for All is a resource that had me nodding my head YES to as I was reading…it confirmed what MY ideas about Deep Learning are! Mastering core academic content and being able to think critically to solve complex problems. Working collaboratively to learn how to communicate effectively while developing an academic mindset. All of these competencies help us understand what it means…but how to we accomplish these things?

Personalized Learning- LEARN

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Project Based Learning-DO

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Work Based Learning-APPLY

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Competency Based Learning- SHOW

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As I’ve been thinking about what all of this means, and what it looks like in particular, it’s affirming to know that we ARE doing these things, and doing them WELL. Finding intentionality in how we do things will lead us to an understanding of what deeper learning really is.

 

Learner, Thinker, Writer: Marsha Harris serves the Trinity School community as the Director of Curriculum.