Subject: teaching

Welcome to Coaches Corner

Coaches Corner with Amy Belik mathodology

Meet Amy Belik-Math Instructional Coach FXW School- Chicago

Coaching Vision

I coach to empower both teachers and students to see math as an open, visual subject that is full of connections. I coach teachers and leaders to teach in a way that empowers learning to take an active role in making sense of math and take ownership of their own learning. Through self-reflection and collaboration, we can all improve in our craft. I coach people to find their own power and to empower others so that we can transform FXW, our community, and our world. Over the next few months, we will follow Amy as she sets goals with teachers and works to support each teacher to meet their goals. What goals do you have for 2020?

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Building Visualization in Students

2019 Lesson Study Take-Aways

mathodology ban har sarah schaefer

Class Discussions / Structured Exploration

In our study on visualization, I learned that as a teacher I should have a less is more approach. Specifically, teachers should focus on the ideas presented in discussions and not just the answers. We should allow the students to provide details in problem-solving strategies and methods. To promote more visualization, teachers can slow down, ask questions to prompt thinking and allow students the time to discover the answer. Teachers should ask the big questions and provide structure for exploration. Students need time for verbalization of ideas, but without structure, the time is not used effectively.

Physical Movement

Carpet time allowed children to move about the room and partner with someone not in their discussion group. Additionally, moving to carpet or floor helped eliminate distractions. Students were then able to reflect on the pages of the textbook, discussing the multiple methods and (if relevant) could then make connections between the textbook and methods discussed in class. Students were able to better visualize the textbook concepts than at desks with base tens and other distractions.

Questions To Prompt Visualization

○ “Can you imagine?”
○ “Is it possible?”
○ “Is there a different way?”
○ “I wonder…

One is my biggest take a way’s from this lesson study was the power of visualization when teaching and exploring mathematical concepts. What does it mean to visual something? How formidable visualizing is in creating and solving problems. Visualization is a powerful cognitive tool in problem-solving and enhancing this process in children is paramount in helping them solve and create.  I enjoyed collaborating with the teachers to give the children better tools to visualize numbers concepts. 

Our lesson study with Ban Har and Sarah was as valuable as any professional development I’ve ever attended. The ability to plan, create, and revise a lesson with such an experienced group, was beneficial in all subject areas. The small group setting allowed the collaboration to be thorough and specific to the needs of our students.

The in-depth discussions leading up to the lesson planning were worthwhile and relevant. Being able to have different grade levels involved in the planning provided useful information. It was eye-opening for all of us to talk through the skill sets taught in the grade level (2nd) before the intended lesson(3rd) and the grade level after (4th). Being able to see this progression was important. 

I found the lesson study to be a more productive form of professional development. Watching the teaching of the lesson gave me such insight into ways to improve my own teaching. Observing the students as they worked through the lesson, showed us ways we could improve for the next session. 

The discussions (from our lesson study group) following the first lesson were helpful to dissect everything from student strategies used, journal entries, ways to improve the lesson. Everyone brought unique ideas to the lesson and the collaborative sessions highlighted important information. 

Being part of the lesson study is a commitment for the members and requires support from administration (allowing for substitutes/meetings etc. . .); however, it was such a positive experience that provided me valuable insight. The goal is to teach best practices to the students in all subject areas . . . the lesson study project certainly helped me be a better teacher.

I think the lesson study was a great way to examine in depth how to best teach a lesson using strategies to help the children dig deeper and not only solve the problem, but more importantly be able to share and put into words what they learned to see if the concept was truly mastered or if the teachers needed to go a little further. I really liked how the teacher input was very limited in the actual teaching of the lesson. It was by using manipulatives and talking and discussing with their peers and with very strategic open-ended questioning by the teacher that helped the children continue to dig deeper and truly understand the concept.

As we prepared for the 3rd-grade math lesson study, it was noticeably beneficial for the teachers involved to become very familiar with the related previous lessons, which were building blocks for the focus lesson. Just as beneficial was researching the lessons that would follow the target lesson. This helped us more fully understand the future skills and goals for the students. As the lesson was prepared, we also strived for a clear presentation of the lesson, allowance during the lesson for perseverance to explore with concrete materials, multiple methods for problem-solving, and time for students to explore efficient strategies for problem-solving. Along with the goal of the academic unit skill mastery, we strived to promote student discussions leading to a deeper understanding of the skill and visualization. 

After the first lesson was observed and we had ample time to share our observations, we planned strategies we believed would help to improve the lesson. These strategies included offering the students a more detailed explanation of the problem to be solved, encouraging verbalization and visualization before manipulatives were provided, and allowing more time for exploration with manipulatives.

After the lesson, we reviewed the students’ journal entries showing specific problems to be solved. This observation step provided even more opportunities for teacher reflection and validation of the success of the lesson.


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Lesson Study & Visualization

Lesson Study on Visualization with Mathodology

Follow our Journey. Lesson Study with a Focus on Visualization.

Jugyou kenkyuu, a Japanese phrase gives us the term “Lesson Study”. Introduced in the U. S. in the late 1990s, interest in Japanese lesson study remains strong in the education world throughout the United States. Our Lesson Study this year will focus on visualization and metacognition.

Lesson Study & Mathematics

Lesson study works well across education and in particular, in improving mathematics education. We will wrap up professional summer reading on visualization in September with a look into the routines we create in classrooms that promote visualization. During “Introduction to Lesson Study” in October, we will explore what lesson study is, how it works, how to use it, and best practices with a focus on creating metacognition in students.

Pre-Lesson Study Questions

We engaged our focus group from St. Edward School in Vero Beach by asking the following questions:

What attracted you to this Lesson Study?

Overall the participants felt this lesson study would improve their ability to use visualization strategies in their own classrooms. They felt the experience would allow them to “dig deeper” into learning the best way to improve their teaching skills to build visualization.

What do you hope to learn from this Lesson Study

Participants generally responded similarly, wanting a deeper understanding of the science behind visualization, learning how to integrate visualization into their daily teaching, and using visualization to help students see concepts in a different way.

What is visualization to you?

It is creating a picture in your mind, being able to ‘see’ what you are hearing or reading to help you better understand the lesson, and it brings life to situations, assisting a student in understanding the concepts being taught.

What do you feel you already know about visualization? (before reading)

The response to this question was consistent with all participants. All felt that visualization was a way of seeing something in your mind to better or fully understand it and using it in math as well would bring life to situations and assist students in better understanding the concepts being taught.

Ideas on how to get kids to visualize math?

  • Using various concrete and pictorial models
  • Incorporating color in our board witing to connect ideas
  • Relating ideas especially in the operations
  • Have children create a short movie in their minds with each math concept so they can ‘see’ the process and verbalize it before computing

What questions do you have before we start the lesson study?

  • Can all students visualize?
  • How are other teachers using visualization?
  • Does the brain have any physical limitations with visualizing?
  • How do we teach visualization to students so they use it seamlessly when seeing a math problem?
  • What forces the brain to want/have to visualize?

We will be holding a private Lesson Study at St. Edward’s School, Vero Beach, FL in September.

Follow us through this Lesson Study.

We’ll be at Oak Hill High School in Nashville, TN, October 2, 2019 – October 4, 2019. Seats still open!

Click here to register for this event and for details on this Lesson Study.

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