Subject: metacognition

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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How Do We Build Metacognitive Thinking Through Self-Assessment

We can all agree that metacognitive thinking is obviously beneficial. The environment in which a student feels comfortable enough to be a self assessor can be tricky. What does that look like? What is the goal?

Getting away from the time-honored question, “Is this the right answer?!”

As former students, this is probably the question that motivated most adults as young learners. The response of, “Yes, you are correct!” or “No, you need to work harder.” always seemed to hold a finality of the lesson.

That is where we all decided that we were “great at math” or that we would be lifelong math strugglers. We all have those memories.

So how do we as teachers change that narrative? How do we facilitate students in becoming their own teachers? How do we give them a voice and the confidence to speak to their own capabilities and shortcomings and how is that beneficial?

Learning Goals and Scales

Reflecting back to John Hattie’s book, “Visual Learning”, there are questions that guide a student through the self-assessing process.

Relating to the content each student should ask themselves:

  • Where am I going?
  • How am I going to get there
  • Where to next?

Keeping those guiding questions in mind each student is given a Learning Goals and Scales chart for each chapter studied.

The goals and scales are based on a combination of Common Core Standards and State of Florida Item Descriptors.

Seen within the items are leveled abilities. This is important to guide the learners in their self-evaluation. It is also very helpful for the students to keep the chart throughout the chapter.

This is not a summative assessment or checklist to use at the end of the chapter. The students should have access to help guide their thinking and goals. The goals and scales are written in “kid-friendly” language as “I can” statements.

This is done to make ownership of the goals easily relatable to elementary-age students. In reading each statement the student is then able to designate the color that best fits their comfort level for that item.

As it relates to their feelings about a topic:

  • Red indicates that the student feels that they are not confident in this skill. They feel that they require more work in this area.
  • Yellow indicates that the student feels somewhat comfortable with the statement. They can be effective when leading in whole group scenarios, or with partner support, but may still have questions.
  • Green indicates that the student feels very comfortable with this skill. Not only could they complete the tasks at hand, they could also explain them to a classmate.

Support through Discussion

Learning Goals and Scales and Think!Mathematics US

The students’ responses to their Scales and Goals can be seen below. Those are then used to guide the students through self-assessment by applying the goals to different examples that have been either created in their Math Journal or through concrete examples that the students can demonstrate and explain.

Examples below show the students reflecting on their goals for their first chapter in their mathematics classroom this year.

Students Reflecting on Their Goals and Think! Mathematics US

The students were allowed to use their goals and scales to keep track of their thoughts and their own accountability and then relate those directly to examples.

These discussions are truly the cornerstone of metacognition for the students. Being told that their thinking is more valued than a simple score is the first step in supporting a student in seeing themselves as not just as a spectator in their education but as their own teacher.

Initial Teacher Takeaways

Having a specific routine for this method of accountability and reflection is crucial. There must be a procedure put in place that helps the student guide themselves independently. If these steps are not taken students become distracted in the implementation of the task and the quality of the actual reflection is lost. 

Providing the students with the Scales and Goals (I can statements) is the first step, but the teacher contribution in creating those goals must be instructionally sound and purposeful.

Something as simple as incorporating the math topic in the journal headings allows students to organize their thoughts for their accountability discussions with their teacher.

For example, if the first three “I Can” statements relate to place value and the student feels that they can prove that they are comfortable with that topic, looking back in their journal headings that address Place Value will give them a place to reflect and prove their thinking.

It should also be said that in some of the discussions and pictures seen below you can see that through the interactions the students actually change their ability levels from their initial thinking. That might be the most profound takeaway with these strategies early in the school year.

Accountability and Reflection and Think!Mathematics US

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Communicating Home

Often we share our students progress by sending home “Monday” folders with worksheets that were completed, test or quizzes taken the previous week, or maybe we have a site where parents can go and see the current grade in your class.  Are we informing parents on their child’s progress?  Does the grade or worksheet give an accurate picture of student growth?

I often challenge teachers to give feedback on an ongoing basis.  We should not only assess from the papers turned in but from what we are seeing, hearing and collecting on a daily basis.  Use journal entries or a table with your objectives (I can statements) to allow for a more productive discussion at a parent conference.  The following guidelines can help your conversation whether it be in the form of report card comments, parent conferences or the chat in the pick-up line.

-What area is the child is doing well? (Have pieces of work that demonstrate growth.)
-What area does the child struggle? (Show specific concepts not just a broad topic.)
-What are you doing in the classroom to help?(The learning does not stop after a chapter test. It is your responsibility to help the child learn it!)
-What can they do at home to support you and their child? (Parents want guidance on how to help.)

Attached is an article from the Wall Street Journal – 10.18.17 addressing the idea of a student-run conference.  This conference helps children communicate their progress while building the metacognitive process.  Would love to see this happening more in our schools.

Communicating Home


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