Math journals, or problem solving notebooks, are books in which students record their math work and thinking during problem solving sessions.

These notebooks can be used to:

Record the solutions to math problems, along with the strategy and thought processes used to arrive at the solution

At times journals may also be used to:

Write about learning: For example, students may be asked to write about "what you already know about ......" at the beginning of a unit or "what you did today, what your learned, and any questions you have", or "your most and least favorite activity in this unit and why."

By dating entries a math journal provides a chronological record of the development of a student’s mathematical thinking throughout the year.

Why Use Math Journals?
While students learn how to "do" math, they must also learn how to articulate what they are learning. It is important to provide many opportunities for students to organize and record their work without the structure of a worksheet. Problem solving notebooks support students' learning because, in order to get their ideas on paper, children must organize, clarify, and reflect on their thinking. Initially many students will need support and encouragement in order to communicate their ideas and thinking clearly on paper but, as with any skill, the more they practice the easier it will become.

Journals also serve as invaluable assessment resources that can inform classroom instruction. Reviewing a student’s math journal provides a useful insight into what a child understands, how s/he approaches ideas and what misconceptions s/he has.

What are the Characteristics of a Good Math Journal Question?
A Good Math Journal Question ….

allows for multiple entry points and recording techniques, thereby allowing all students to work at their individual level of thinking,

provides the opportunity for students to learn by answering the question, and the teacher to learn about each student from the attempt,

may have more than one solution (open-ended),

requires more than just remembering a fact or reproducing a skill,

provides the opportunity for students to show their different ways of thinking,

can be represented with physical materials as well as by drawings,

has clear, concise directions,

provides opportunities for group work and discussion.

captures the interest of children.

The most important thing to consider when developing a journal question is whether the question involves significant mathematics. Closed questions such as "Ben had 5 apples. He ate 2. How many apples did Ben have left?", often seen in early years classrooms, do little to develop a child's mathematical thinking if the child can answer the question before even getting back to his/her seat. The child may spend 15 minutes drawing and coloring apples but mathematical thinking is limited. Changing the question from a closed to an open format such as, 'Ben had 5 apples. He ate some of them. How many did he eat? How many did he have left?' creates greater potential to stimulate mathematical thinking and reasoning when a child is asked to show as many different solutions to the problem as s/he can.

Can Journal Tasks be Revisited During the Year?
Definitely! Good tasks are open ended to allow for different strategies and products to emerge. Many tasks have multiple solutions and students should be encouraged to choose their own method of solving problems and representing their findings. Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On the first occasion the student may be focused on ‘how to do’ the task whereas on subsequent visits recordings often become more detailed.

The methods that children use for recording will also change over the course of a year. Repeating a task provides a record of this growth for teachers, parents and students. For example, in Kindergarten an open ended addition task (see work samples below) may be explored early in the year before children begin to write number sentences. Early in the year most kindergarten students will record their thinking in relation to this problem pictorially and may only record one or two solutions to the problem. As the year progresses symbolic recording will gradually begin to appear and recordings will become more detailed.

Making slight variations to a task (e.g. changing the number that a child is asked to make using dot cards) or changing the materials used to complete a task (e.g. changing the objects in a sorting cup from buttons to coins) will help to maintain interest while students further develop skills and concepts. Some teachers like to introduce math journal tasks whole class and then place tasks in centers for children to revisit at other times throughout the year. Other teachers choose one journal task and repeat it, with slight variations, several times throughout the year as a record of students’ growth to be included in a child’s portfolio.

The work sample above shows a Kindergarten students' attempt to record her thinking early in the school year in response to the task: Vanessa had 5 cupcakes. Some were chocolate. Some were vanilla. How many were chocolate? How many were vanilla?

Three months later this student completed a similar task: Cameron had 6 buttons. Some were green. Some were purple. How many were green? How many were purple? On this occasion the child's recording is more detailed and clearly demonstrates her developing understanding of addition. Although she repeats some number sentences, her drawings show all possible combinations of the six buttons.

How often should I use Math Journals in my class?
This is entirely up to the teacher. Some teachers use them several times a week. Other teachers who have more restrictions on their math sessions due to using a mandated curriculum set aside one session per week for journals and then select a task that correlates with the current unit of study. The important thing is to ensure that students are being given regular opportunities throughout the year to record their mathematical thinking in a way which makes sense to them.

What type of book should my students use as a Math Journal?
My experiences in numerous K-5 classrooms has shown that an unruled notebook produces the best Math Journal results. Although these are not always as readily available as ruled notebooks (and are often more expensive) they have a distinct advantage in that students are not restricted by lines and have the space to choose whether to use pictures, numbers, words or a combination of these to record their thinking.

What strategies can I use to support the development of students' math recording skills?
For strategies to support the development of students' math recording skills please see this page (K-5 Math Teaching Resources)

Interested in using Math Journals in your class?
Please see the following links to find out more about our math journal tasks for Kindergarten, 1st, and 2nd grade based on the Common Core State Standards: Kindergarten 2nd Grade

## Math Journals

What is a Math Journal?Math journals, or problem solving notebooks, are books in which students record their math work and thinking during problem solving sessions.

These notebooks can be used to:

- Record the solutions to math problems, along with the strategy and thought processes used to arrive at the solution

At times journals may also be used to:- Write about learning: For example, students may be asked to write about "what you already know about ......" at the beginning of a unit or "what you did today, what your learned, and any questions you have", or "your most and least favorite activity in this unit and why."

By dating entries a math journal provides a chronological record of the development of a student’s mathematical thinking throughout the year.Why Use Math Journals?While students learn how to "do" math, they must also learn how to articulate what they are learning. It is important to provide many opportunities for students to organize and record their work without the structure of a worksheet. Problem solving notebooks support students' learning because, in order to get their ideas on paper, children must organize, clarify, and reflect on their thinking. Initially many students will need support and encouragement in order to communicate their ideas and thinking clearly on paper but, as with any skill, the more they practice the easier it will become.

Journals also serve as invaluable assessment resources that can inform classroom instruction. Reviewing a student’s math journal provides a useful insight into what a child understands, how s/he approaches ideas and what misconceptions s/he has.

What are the Characteristics of a Good Math Journal Question?A Good Math Journal Question ….

- allows for multiple entry points and recording techniques, thereby allowing all students to work at their individual level of thinking,
- provides the opportunity for students to learn by answering the question, and the teacher to learn about each student from the attempt,
- may have more than one solution (open-ended),
- requires more than just remembering a fact or reproducing a skill,
- provides the opportunity for students to show their different ways of thinking,
- can be represented with physical materials as well as by drawings,
- has clear, concise directions,
- provides opportunities for group work and discussion.
- captures the interest of children.

The most important thing to consider when developing a journal question is whether the question involves significant mathematics. Closed questions such as "Ben had 5 apples. He ate 2. How many apples did Ben have left?", often seen in early years classrooms, do little to develop a child's mathematical thinking if the child can answer the question before even getting back to his/her seat. The child may spend 15 minutes drawing and coloring apples but mathematical thinking is limited. Changing the question from a closed to an open format such as, 'Ben had 5 apples. He ate some of them. How many did he eat? How many did he have left?' creates greater potential to stimulate mathematical thinking and reasoning when a child is asked to show as many different solutions to the problem as s/he can.Can Journal Tasks be Revisited During the Year?Definitely! Good tasks are open ended to allow for different strategies and products to emerge. Many tasks have multiple solutions and students should be encouraged to choose their own method of solving problems and representing their findings. Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On the first occasion the student may be focused on ‘how to do’ the task whereas on subsequent visits recordings often become more detailed.

The methods that children use for recording will also change over the course of a year. Repeating a task provides a record of this growth for teachers, parents and students. For example, in Kindergarten an open ended addition task (see work samples below) may be explored early in the year before children begin to write number sentences. Early in the year most kindergarten students will record their thinking in relation to this problem pictorially and may only record one or two solutions to the problem. As the year progresses symbolic recording will gradually begin to appear and recordings will become more detailed.

Making slight variations to a task (e.g. changing the number that a child is asked to make using dot cards) or changing the materials used to complete a task (e.g. changing the objects in a sorting cup from buttons to coins) will help to maintain interest while students further develop skills and concepts. Some teachers like to introduce math journal tasks whole class and then place tasks in centers for children to revisit at other times throughout the year. Other teachers choose one journal task and repeat it, with slight variations, several times throughout the year as a record of students’ growth to be included in a child’s portfolio.

The work sample above shows a Kindergarten students' attempt to record her thinking early in the school year in response to the task: Vanessa had 5 cupcakes. Some were chocolate. Some were vanilla. How many were chocolate? How many were vanilla?

Three months later this student completed a similar task: Cameron had 6 buttons. Some were green. Some were purple. How many were green? How many were purple? On this occasion the child's recording is more detailed and clearly demonstrates her developing understanding of addition. Although she repeats some number sentences, her drawings show all possible combinations of the six buttons.

How often should I use Math Journals in my class?This is entirely up to the teacher. Some teachers use them several times a week. Other teachers who have more restrictions on their math sessions due to using a mandated curriculum set aside one session per week for journals and then select a task that correlates with the current unit of study. The important thing is to ensure that students are being given regular opportunities throughout the year to record their mathematical thinking in a way which makes sense to them.

What type of book should my students use as a Math Journal?My experiences in numerous K-5 classrooms has shown that an unruled notebook produces the best Math Journal results. Although these are not always as readily available as ruled notebooks (and are often more expensive) they have a distinct advantage in that students are not restricted by lines and have the space to choose whether to use pictures, numbers, words or a combination of these to record their thinking.

What strategies can I use to support the development of students' math recording skills?For strategies to support the development of students' math recording skills please see this page (K-5 Math Teaching Resources)

Interested in using Math Journals in your class?Please see the following links to find out more about our math journal tasks for Kindergarten, 1st, and 2nd grade based on the Common Core State Standards:

Kindergarten

2nd Grade

Kindergarten Math Journal PromptsMonthly Math Journal PromptsMonthly Journal PreviewMath Journal Prompts by DomainDomain Journal Prompts PreviewNovember Journal Prompts

December Journal Prompts

January Journal Prompts

February Journal Prompts

March Journal Prompts

April Journal Prompts

May Journal Prompts

Measurement and Data

Operations and Algebraic Thinking

Geometry

## Math Journal Expectations