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

## 3.1 – Module Goals

In this module, you will:

- Examine all the student journals from your class
- Update your journal plan

## 3.2 – Examine the Journals

This section asks for three different analyses of your students’ journals. As you do each analysis, we suggest that you:

- Look at the student journals from your class and classify or rate the journals as suggested by the prompts, focusing on a single lesson in which students learned a new mathematical idea or procedure.
- Based on the analysis, identify areas where you would like to see student growth, and consider steps you could take to support that growth.
- Update your journal plan (at the end of this module) with the steps you plan to take.

#### Analysis 1: What do the journals tell you about student learning of the new mathematics of the lesson?

On the sheet Journal Analysis 1, record the key new mathematical idea or procedure that you planned for students to learn in the lesson, and then analyze the journals as follows.

Begin by classifying the journals into 3 groups:

- Shows clear evidence that the student grasped the new mathematics (the idea or procedure that was the goal of the lesson)
- Shows clear evidence that the student has
*not*yet grasped the new mathematics - Doesn’t provide evidence to judge whether or not the student grasped the new mathematics

Next, on the sheet Journal Analysis 1, record the number of journals that fall into each group, and closely examine at least one journal in each group, using the prompts on the sheet.

Then, based on the category that most journals land in, note in your journal plan the next steps would you like to take. For example:

- If journals indicated a common misconception, perhaps you want to revisit it in an upcoming lesson and ask students to analyze the misconception
- If journals did not allow you to judge student understanding, perhaps you can strengthen journal writing routines that expect and support articulation of thinking; this might be done by highlighting models, posing specific prompts to the class (e.g., write about what is still confusing), or asking students whether another student reading their journal could identify their learning
- If very few students articulated the expected learning, look back on your lesson to try to understand why that occurred. Students may miss the big mathematical learning of a lesson because they are focused on quickly getting a correct answer or following a procedure, rather than on thinking about the underlying mathematical ideas. Consider how you might design future lessons so that more students have the opportunity to really grapple with a novel problem (for which they have not previously been taught a procedure) and come to a powerful “aha.”

#### Analysis 2: What do the journals tell you about students’ mathematical skills, practices and mindsets?

Review the class set of student journals and identify some strengths (even if they are just evident in one or two journals) and some areas where would you like to see improvement over the year, with respect to:

- Skills (e.g., legible writing, correct numerals)
- Mathematical practices (e.g., writing mathematical expressions, explaining and justifying, creating precise diagrams)
- Mathematical mindsets (e.g., persistence, identifying what is confusing, learning from mistakes)

Use Journal Analysis 2 to record your observations, along with examples. Consider next steps you would like to increase the strengths and to reduce the areas of need. Some examples follow.

- Strategically choose several students’ journal reflections from the prior lesson to begin each lesson. Select reflections that model the skills, practices, and mindsets you are trying to develop.
- During class, notice and highlight the skills, practices, and mindsets you want students to build–for example, notice the helpfulness of mathematical expressions, precise diagrams, or corrected mistakes in student work shared with the class.
- Model on the board the processes you want your students to develop, such as lining out and correcting mistakes, rather than erasing, and adding a bubble to explain the mistake.

#### Analysis 3: What is the quality of students’ journal reflections?

The reflections section of the journal is a place for students to summarize their own learning, insights and confusions during the lesson. It differs from the lesson summary, which is written on the board by the teacher (ideally, summarizing student-voiced ideas), allowing students to copy a correct summary of the lesson into their journal. In contrast, reflections ask students to look back on their own learning over the course of the lesson, and to explain their new insights, how their thinking changed, what they still find confusing, and what questions the lesson sparked for them.

Dr. Akihiko Takahashi uses a 3-point rubric to gauge the quality of student reflections, as follows:

Level | Comment Types | Examples |

1 | General comments | “I learned a lot,” “I liked the lesson.” |

2 | Specific mathematical ideas. | “I learned that the same equation can show different ways of counting.” “I liked Tom’s idea to multiply and subtract the overlapping tiles.” |

3 | Applying ideas to current or future learning. | “I would like to try Rashid’s idea with other problems.” “I wonder which approach will be most useful if the number of tiles on a side changes.” “I thought it must be 7 X 4 but when I saw Jamal’s idea I realized I double-counted the corners.” |

Examine the journals, looking at the reflections from one lesson. Categorize the reflections into one of the three levels above.

- How many of the reflections fall into each of the three categories above?
- What steps might you take to raise the level of reflections? Some strategies to consider are outlined below.

#### Strategies to Increase Quality of Student Journal Reflections

- Begin mathematics lessons by sharing several students’ journal reflections from the prior lesson. Select reflections that model the qualities you are trying to develop, such as mathematical specificity and connecting ideas to new learning. Ask students to notice what is helpful about these reflections.
- During class, notice and highlight the kinds of student thinking you hope students will do in their reflections. For example, when students raise key mathematical ideas as they consider or discuss a problem, some teachers record these ideas as quotes on the board, accompanied by a thought bubble and the student’s name.
- During class, pose the kinds of questions that you hope students will learn to ask themselves, such as “Will this approach always work?” or “What is the same and different about these two solution methods?”

## 3.4 – Pre-Work for Module 4

- Implement the changes you identified in your journal plan, and use for at least 4 lessons
- Bring class set of student journals to the next session

## 3.3 – Update Your Journal Plan

The journal plan provides a place to record the action steps you will try in your classroom, based on each of the inquiries you conducted. It is designed to support you as you consider:

- The changes in student journal writing you would like to see over the next 4-6 lessons.
- The classroom action steps you will try, to support those changes
- The evidence you will look for in the next set of journals.