A math journal, or problem solving notebook as they are sometimes referred to, is a book in which students record their math work and thinking. They can be used to:
entries the 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 question ….
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?
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. Subsequent visits provide an opportunity for students to communicate their mathematical thinking and reasoning more clearly.
that children use for representing their thinking 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 representations will gradually begin
to appear and representations will become more detailed.
Making slight variations to a task (e.g. changing the numbers, context, or materials used) will help to maintain interest while students further develop skills and concepts. Some teachers like to introduce 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 the development of math skills and understandings for student portfolios.
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 written representation 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. You may choose to use some tasks as quick warm ups or as assessment or homework tasks. The important thing is to ensure that students are being given regular opportunities throughout the year to represent their mathematical thinking in a way which makes sense to them.
What type of book should my students use as a Math Journal?
Our experiences in numerous K-5 classrooms have shown that an unruled notebook produces the best 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 representation skills please see this page.
Interested in using Math Journals in your class?
Click on the links below to learn more about our journal tasks for Kindergarten - 5th grade aligned with the Common Core State Standards: