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Journalling in
mathematics
What
is journalling?
The
benefits of journalling
Teaching
tips for journalling
Writing
prompts for journalling
References
What
is Journalling?
Journalling
involves students writing about their learning in
mathematics. What they write can be based on a prompt
given by the teacher – for instance, on a topic
currently being covered in class. Alternatively, it can
be more self-directed, with students choosing from a
menu of prompts, or simply free-writing about their
thoughts, feelings and ideas. Teachers will often read
students’ journal entries and respond with comments or
questions. Sometimes this can evolve into an ongoing
written conversation between student and teacher.
Journalling can happen before, during, or after a
session of mathematics learning.
The
Benefits of Journalling
Journalling
has benefits for students, teachers and the mathematics
programme as a whole. These include: promoting
understanding, promoting a sense of involvement with
mathematics, promoting better informed teaching and
promoting teacher student relationships.
Promoting
Understanding
Journalling
promotes understanding by building on the powerful links
between writing and learning. According to one
researcher:
...
writing can engage all students actively in the
deliberate structuring of meaning: it allows
learners to go at their own pace; and it provides
unique feedback, since writers can immediately
read the product of their own thinking on
paper" (Emig paraphrased in Borasi and
Rose,p.384).
Journalling
in mathematics allows students to:
-
establish
connections between mathematical ideas. For
instance, by asking students to explore and write
about various strategies for solving similar
problems;
-
focus
on what they do and do not know;
-
develop
more precise ways of communicating;
-
clarify,
organise, and refine their thinking;
Promoting
a Sense of Involvement with Mathematics
Researchers
report that journalling can help students to deal with
the struggles that are often involved in learning and
doing mathematics. It can also allow students to examine
the nature of mathematical knowledge and what it means
to think mathematically.
Journalling
promotes a sense of involvement with mathematics when it
encourages students to:
-
summarise
goals, strategies, and reactions to mathematics;
-
record
their accomplishments and openly vent frustrations;
-
consider
the relevance of mathematics in their lives.
Promoting
Better Informed Teaching
When
teachers read their students’ journal entries they are
able to gain a new perspective on how individual
students are coping with their mathematics learning.
This information can be used to develop next learning
steps.
Journalling
promotes better-informed teaching by providing teachers
with:
-
formative
data about students' understanding and dispositions,
including students’ emerging ideas about
mathematical concepts;
-
a
basis for learning conversations (written and oral);
-
an
opportunity for feedback and feed-forward;
-
information
that assists in short and long-term planning.
Promoting
Teacher Student Relationships
Journalling
can also help teachers to make deeper connections with
their students. It does this by:
-
enabling
students to actively participate in a dialogue with
teachers though a private, non-threatening means;
-
allowing
students to share ideas, opinions and feelings about
mathematics, the mathematics programme and their own
learning styles;
-
providing
a permanent record for the teacher and student to
examine.
Teaching
tips for Journalling
Careful
management is needed to maximize the potential of
journalling. The following tips provide useful advice
for using journalling as a learning technique in the
classroom.
| 1. |
Classroom
organisation is important. Teachers need to have a
manageable system, especially if they are going to
take part in ongoing journal conversations with
students. This might mean responding to one group
of students at a time, rather than the whole class
in order to give deeper levels of feedback. |
| 2. |
Daily
journal writing is not a necessity. Journalling
should be used strategically to complement the
classroom programme. |
| 3. |
Journalling
is a form of transactional writing. Students will
need time and scaffolding to develop as journal
writers. Teachers can assist students by modeling
examples of journal entries. |
| 4. |
Like
any classroom innovation, the success of
journalling depends on the quality of student
teacher relationships and the belief and
commitment that both parties have to the
journalling process. In particular, students need
to know the benefits of writing in a journal. |
| 5. |
Provide
feedback on what is important. Commenting on
writing conventions such as spelling and
paragraphing, is not as important as providing
feedback on mathematical thinking. |
| 6. |
Students
should look back and reflect upon their own journal
writing experience. This may be done orally, or
in writing. There is evidence that such reflection
makes the students more aware of themselves as
learners. Click on Reflecting
on reflective journalling for a further discussion. |
Writing
Prompts for Journals
Journalling
tasks fall into two distinct groups, self-directed, and
teacher directed.
Self-directed
journalling
Free-choice
journalling is where students choose to write about
whatever they wish. This can be informed by a checklist
of possible starters. Such lists can be developed within
the class. One particular list is referred to on ARB
resource NM1226.
The items on this list are not meant to be exhaustive.
The teacher may encourage students to self-select different
aspects from this checklist over time so that they reflect
more widely on their learning.
Possible
prompts for self-directed journalling
| 1. |
What
I learnt today in mathematics
-
What mathematics did I learn?
-
Describe how a method works.
-
What are my opinions on the mathematical ideas I
learnt today?
|
| 2. |
How
I felt learning mathematics today
-
I was feeling …
-
What did I enjoy or find good?
-
What didn't I like?
-
My feelings about mathematics
-
My favourite thing in maths is?
|
| 3. |
Things
that I need help more on
-
I find … hard
-
I need to practice …
-
I need to remember …
-
I need to improve at …
|
| 4. |
Things
that help me learn, or about my learning
-
Where did I learn new ideas from?
-
How do I learn best?
-
How is my learning progressing?
|
| 5. |
Things
that were useful or interesting |
| 6. |
Things
I found easy or I already knew |
| 7. |
Did
I have an "AH HA" moment |
| 8. |
Any
other ideas you would like to write about. |
Teacher-directed
journalling
Sometimes
the teacher can choose the prompt or topic for journal
writing. This might be a particular aspect taken from
the journalling checklist above, or instead center on
various aspects of the mathematics that the students are
currently encountering. Some general suggestions follow,
along with particular examples.
Possible
journaling prompts regarding mathematical content
| 1. |
How
it works: Students
explain how a strategy works.
For
example: Write instructions to a friend on how
to do front-end estimation. (Go to the ARB resource
NM1217
for more information about this example.) |
| 2. |
How-to’s:
Students explain in writing how to do something.
For
example: Someone tells you that two thirds of the
80 cars in the parking lot are green. Is it
possible to work out how many cars there are in
the parking lot altogether?
How
do you find 25% of a number? (Note the student is
asked for a general explanation, that is how to
find 25% of any number rather than 25% of a
specific number.) |
| 3. |
Definitions:
Students write their own definitions of terms.
For
example: What is a percentage?
When
are two lines parallel?
What
is a triangle? |
| 4. |
Trouble
shooting:
Students explain errors they or their teachers
have identified.
For
example: Joseph was counting up in 0.1s. He went,
"0.5, 0.6, 0.7, 0.8, 0.9, 0.10." What
mistake did Joseph make? |
| 5. |
Arguments:
Students develop an argument to support a point of
view.
For
example: Think of two ways to find ¾ of a number.
Which one do you think is the best and why? |
| 6. |
Problem
Posing:
Students construct (and model answers for) their
own problems.
For
example: Write a problem, which involves finding
the area of a shape. |
| 7. |
Pre-writing:
Students write before a maths session, looking
forward to their learning.
For
example: What can you do to day that will help you
learn in mathematics. |
References
Borasi,
R., & Rose, B. (1989). Journal writing and
mathematical instruction. Educational studies in
mathematics 20(4): 347-365.
ARB
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