This course for K-6 educators explores the power of student reflective journals in building students’ mathematical knowledge and practices.

## Session 1: Explore the Inquiry Topic & Reflect on Your Current Practice

Outside-of-class meeting | Time: 1 hour | Materials: Recent Student Journals (class set) and board photographs for several recent lessons

### Focus

A well-organized board provides a model for students to organize their own journal writing. On the board, students can revisit the problem, solution strategies, and big ideas that developed during the lesson and use these to reflect on what they learned. Likewise, student journal-writing provides a key resource for teachers during the lesson, allowing teachers choose and sequence student work to be presented at the board and to pitch the discussion so that it responds to the needs evidenced across all student journals.

### 1A: Examine Journals and Reflect on Current Practice

- Examine students’ journals and jot notes in response to the following questions
- Do journal entries have the elements you expect at your grade level? For example, have students written the date, problem, their solution attempt, and any other elements you expect (friend’s idea, summary, reflection)?
- Do the journal entries show a coherent flow of ideas across a lesson? For example, can you understand the problem, what strategies were used to solve it, and what the class learned from comparing and discussing these strategies? Can you understand the new learning for the class as well as for the individual student? (For younger students, you may only be able to identify the problem and how the student solved it.)
- Does your students’ journal-writing allow you to see their thinking so you can strategically choose students to present at the board? Does it enable you to grasp where all students are in their thinking, so you can hit the “sweet spot” in the whole-class discussion?

- Reflect on your board writing (using photos if available) and jot notes in response to the following questions
- In what ways does your board writing provide model the qualities we hope for in students’ journal writing–logical, neat, accurate, complete, etc.?
- Does your board provide a coherent record of the lesson that helps a viewer grasp the problem, solution strategies, what was learned, etc.? (Such a record can be valuable to help students look back on what they learned during a lesson, or look back later in their notes).
- Does your board accurately represent what is in the selected students’ journals? (Would students see it as an expression of their own thinking?)
- Is your board use consistent, so students know where to look for key information, such as the problem, friends’ ideas, summary, etc.?

### 1B: Learn about New Strategies

The preceding reflection questions suggest ways that board writing and journal writing support each other. Ideally, the board provides an organized model for journal writing, and journals capture student ideas that spark the learning of the whole class when shared on the board. Diagrams and mathematical expressions can be shown together with written explanations on the board, and, unlike fleeting verbal comments, board work remain available throughout the rest of the lesson (and later in the students’ journals). The board also allows students to see and simultaneously compare several solution strategies (rather than try to remember what has vanished from a document camera). Some strategies to build synergy between board and journals include the following.

- Work on elements of your board writing that improve it as a model for your students’ journal writing: completeness, consistency of elements and their placement, neatness, accuracy, crossing out and updating mistakes (rather than erasing), etc.
- Add elements to your board writing designed to spark students’ awareness that the board represents their thinking. For example, use thought bubbles with student names to note important ideas that you want students to be able to review. Some teachers have small magnetized tags with every student’s name or self-portrait, so these can be used to show students’ predictions, solutions or sides in a mathematical debate.
- Try to make the student work shown on your board a large-scale, legible but otherwise exact replica of each student’s work, so that students see their ideas represented faithfully, not an altered version of their ideas (unless changes are made explicitly and at the student’s request)
- Using photos of the board at the end of the lesson, analyze the progression of student work and ideas on the board, to see whether it accurately captures the flow of important mathematical ideas across the lesson; for example, can the important mathematics and how it was learned be reconstructed from looking at the board?
- Analyze the board photograph and the whole class set of journals from a lesson, and revisit your choice of student work for the board. Would you make the same choices again? Why or why not? Ideally, every student in your class should be able to understand the student work on the board and see their own struggles represented and solved. For example, if some students are having difficulty counting accurately, the board work may include work from a student who crosses off counted objects and explains why, so struggling students see that others shared their struggle and solved it. Analyzing the class set of journals and board photograph together can help you strengthen your skill in anticipating and sequencing student work, so that your lessons more consistently hit the “sweet spot” of discussion, in which students all learn from the board work.

### 1C: Plan to Try New Strategies

- Identify one or more strategies you will try in your classroom, designed to improve your use of the board and strengthen the connections between board and journal use
- Identify evidence will you look for on the board and in journals to inform you about the impact of the strategies

## Session 2: **Try New Strategies in Your Classroom **

In class | Time: 3-5 lessons over 1 to 2 weeks

- Try out the strategies in your plan for approximately 3-5 lessons in which journals are being used
- If possible, jot down notes during or soon after each lesson to capture your experiences with the strategies that you tried
- Photograph the board at the end of each lesson
- Bring your notes, board photos and the class set of students’ journals to the next session

## Session 3: Examine Evidence and Refine Your Plan

Outside-of-class meeting | Time: 30-60 minutes

### 3A: Examine Evidence from Lessons and Revise Plan

Examine student journal entries, board photos and any notes you kept. Reflect on (or discuss) the following questions:

- What do you notice about your board as a model for student note taking? What are the strengths of your board writing and what would you like to work on further? For example, what do you notice about clear flow of the mathematical ideas of the lesson, legibility, accuracy, and highlighting of student thinking?
- What do you notice about the connections between student writing in their journals and student work on the board? For example, does the work on the board allow all or nearly all students to see their struggles represented, and also show the path to a new understanding?
- What strategies were successful, and what did you find challenging, as you tried to build students’ habit of reflection on their learning?
- What strategies would you like to carry with you in your next week of instruction and what refinements, if any, might you make, to enhance benefits to your students?
- What new strategy(ies) would you like to test our in the next week?

### 3B: Make a Plan for Your Second Round

- Identify new or refined strategies you will try in the next 3-5 lessons to improve board use and the connection between board and journals
- Identify the evidence will you look for to help you assess the impact of your work

## Session 4: Test Your Refined Approach

In class | Time: 3-5 lessons over 1 to 2 weeks

- Try out the strategies for approximately 3-5 lessons in which journals are being used (about 1-2 weeks)
- If possible, jot down notes during or soon after each lesson to capture your experiences with the strategies that you tried
- Take a photo of the board at the end of each lesson
- Bring the board photos, your notes and your students’ journals (class set) to the next session

## Session 5: Examine Evidence and Reflect on this Inquiry Cycle

Outside-of-class meeting | Time: 30-60 minutes

### 5A: Examine Evidence and Reflect

Examine student journal entries, board photos and any notes you kept. Reflect on (or discuss) the following questions:

- What do you notice about your board as a model for student note taking? For example, what do you notice about clear flow of the mathematical ideas of the lesson, legibility, accuracy, and highlighting of student thinking? Do you notice any changes since you last examined these?
- What do you notice about the connections between student writing in their journals and student work on the board? For example, does the work on the board allow all or nearly all students to see their struggles represented, and also show the path to a new understanding?
- What strategies were successful, and what did you find challenging, as you tried to improve board use and strengthen its connection to journals?
- What strategies would you like to carry with you into future instruction, and what additional changes do you want to try?

### 5B: Reflect on this Inquiry Cycle

- What did you learn that might inform future inquiries–for example, how to collect data, collaborate, find useful resources, etc.
- Is there anything from this inquiry you would like to share more broadly at your school or with the profession? How will you do this?