Making Lesson Plans
Making Math Happen in the Junior Years,
a new release from ETFO, provides
teachers with a vast array of ideas to
incorporate into their math program.
It is the second in ETFO’s Making
Math Happen series. In this issue of
Voice, Jennifer Paziuk, one of the lead
authors, describes the importance
of communication in a successful
math program. An excerpt
from the curriculum provides
Susan Gregoire with her students,
Charles R. Beaudoin Public School,
Halton District School Board.
FALL 2004 | etfo voice A1
“When children can
talk or write about
have learned it.
It’s like when you
have to teach
something – that’s
when you know
if you really
Students at Clairlea Public School,
Toronto District School Board.
One teacher’s approach: An begin, she asks them to talk or write problem. As a result of having a focus,
interview with Jennifer Paziuk about what they did, what they learned, during our class discussion students
and what they have questions about. are able to answer these questions
During her 15 years as a teacher,
“It is important to do a lot of with more detail.
Jennifer Paziuk has become a math
modelling in the beginning,” Paziuk “We also brainstorm for strategies
maven – or, more, a maven of
says. “The students talk and the that might work and previous problems
teacher models how he or she would that are similar that might help us
Paziuk had always liked math
put together a journal entry.” decide on a strategy. I create a strategy
but took her undergraduate degree
As the year progresses, the focus wall with them that stays up during
in science and French. Today she is a
of the journal is varied to include a the year, and we add to it as the
math specialist (she took her training
variety of writing: “How to” instruction, year progresses.”
while on maternity leave), and she
creative writing, reﬂective writing, She also has word wall in the
is one of the lead authors of ETFO’s
explaining a solution. classroom. “Because space is limited,
math curriculum, Making Math
This is a particularly effective I post a new chart for every unit. As
Happen in the Junior Years. It is the
strategy in her grade 6 class, Paziuk students are working on an activity,
second book in ETFO’s Making Math
believes, because students that age they are asked to focus on the math
are more reluctant to ask questions language they ﬁnd themselves using.
“Math became a real interest for
in front of the whole class. Students These words are added to the word wall
me when my eldest daughter started
who are identiﬁed as having learning during our discussion time. It becomes
school. I was trying to help her learn
problems or who have English as a word reference sheet for that unit.”
and really understand rather than
a second language are especially Students also keep a “things I need
memorize – I wanted her to really
reluctant to do so. to work on” list at the beginning of
understand the math,” Paziuk says.
“They are already self-conscious. their journal. Each time students receive
That experience helped transform
They often write that they need extra feedback from their peers or their
the way she approached the subject
help. This way they can ask in private.” teacher, they add the ideas to their
with her own classes. She became
“When first starting out, it is list, and it becomes an individualized
more and more convinced of the
important to offer prompts or sentence learning plan for them. “Giving
importance of talking about math and
starters,” Paziuk says. As well she does productive feedback is one of the
enabling her students to do so as well.
a lot of pre-talking with her class. most important things a teacher can
“When children can talk or write about
This helps students verbalize and do. Stating simply, ‘Good Job!’ does not
something, they have learned it. It’s
clarify their thoughts before they give the student enough information.
like when you have to teach something
are asked to write them down. What was good? Let them know and
– that’s when you know if you really
“At the beginning of an activity I they will be sure to repeat it.”
understand it,” Paziuk says.
give the students a focus: for example, “The most important thing to
One of the mainstays of Paziuk’s
looking for patterns in data. I ask them remember is that the effort of integrating
teaching strategies is the math journal
to think about the math language a communication component into
in which students communicate their
they ﬁnd themselves using or speciﬁc your math program is worth it.”
thoughts about a math activity. To
strategies they used to solve the
A2 etfo voice | FALL 2004
Making math happen understand what the students are (These strategies are described in
by talking about it learning. As well, teachers have more depth in Making Math Happen
the opportunity to discover any in the Junior Years.)
Here is an excerpt from Making Math
misconceptions that students
Happen in the Junior Years. To create an environment for effective
might have and can assess attitudes
communication, it is important
Communication in its varied forms towards mathematics.
to schedule math periods so that
(e.g., reading, writing, speaking) is a At ﬁrst oral communication is the
you have large blocks of time. You
tool to help students think about what main vehicle for expression, as written
may have to be creative in your
they are learning. In language arts, communication may not be adequate
scheduling, but it is very difficult to
students go through the writing process, to give a clear picture of what students
have meaningful opportunities for
which includes brainstorming, pre- have learned. However, throughout
communication if you only have short
writing activities, drafts, conferences, the junior grades, as students’
periods of time. It is ideal if you have
etc. All of this leads to a ﬁnal product communication skills improve, they
a 60-minute block each day.
which is hopefully clearer than when will be able to use an increasing
the process began. Students also learn variety of strategies for demonstrating
to use story maps to organize their what they know. Encouraging Communication
thoughts when communicating about In all cases, students should be through Math Talk
what they have read. It should be provided with opportunities to It is very important to set the tone
the same when communicating in verbalize their ideas before recording of your classroom right from the start.
mathematics. Students take an idea them in a written format (e.g., writing If we want our students to improve
and go through a process to express in a math journal). Think-Pair-Share is their communications skills, they
it in a clear manner. The difference is an excellent strategy for fostering oral must be given the opportunity to
that the focus is on the mathematical communication in math class. Many communicate. If we want them to see
reasoning. other co-operative group strategies, the importance of communication,
The main reasons for including such as Round Robin and Jigsaw, can we must show it to them.
communication as part of a also be incorporated in math class The teacher’s role in promoting
mathematics program are to help to promote the sharing of ideas. verbal communication in the math
students make sense of what they class is critical. Teacher modelling
are learning, and to help the teacher of “thinking aloud” throughout the
The main reasons
as part of
to help students
make sense of
what they are
learning, and to
help the teacher
the students are
Students at Clairlea Public School,
Toronto District School Board.
FALL 2004 | etfo voice A3
One way to get students talking about math is to invite
them to work in groups to discuss what they have learned.
Afterwards, each group can be asked to share its ideas and
ask questions for clarification in a whole-class discussion.
problem-solving process provides Ideas for Encouraging 4. Give students the opportunity to
students with an idea of how to Math Talk share their strategies orally with
describe the mathematical reasoning the class. Explain: “In math you
that occurs as they try to solve 1. Start building a math word wall can use different strategies and still
problems. from the ﬁrst day of school and come up with the same answer.”
Students need to get comfortable keep adding to it throughout the After a number of strategies have
talking about math before they can year. You could also create a word been offered, ask which strategy the
progress to writing about it. Therefore, wall for each new unit if space students preferred, and have them
when ﬁrst starting out, it is important is limited. Have students discuss explain why. All strategies are not
to have lots of time for “math talk.” vocabulary that they used while created equal, so it is important to
Instead of having students write their working on an activity. Let them guide students to the conclusion
ideas down, have the students talk add it to the word wall. Word walls that some strategies are more
about them. can take different forms and may efﬁcient than others.
One way to get students talking include mathematical words only;
mathematical words and deﬁnitions; 5. Invite students to create their own
about math is to invite them to work
or mathematical words, deﬁnitions, problems, either on their own or
in groups to discuss what they have
and examples or diagrams to with other students. These could be
learned. Afterwards, each group can
demonstrate meaning. extensions of problems they worked
be asked to share its ideas and ask
on during class, or problems that
questions for clariﬁcation in a whole- 2. Model math language by constantly they thought of because of other
class discussion. In the latter case, the making students aware of the math activities. Students could then be
teacher should act as a recorder, and words they use in conversation asked to trade their problems with
create a “class journal.” Modelling outside of math class. For example: other students and solve them.
serves the purpose here of allowing “Mark, you used the word ‘chance’ Discuss solutions as a large group.
students to see how orally expressed when talking about your team in
ideas can be translated into writing. gym. What is meant by ‘chance’ 6. Above all, encourage math talk
The journal (and others that are and where do we use this term when students are working. Your
created) should be posted in the in mathematics?” math class should not be silent!
room for future reference.
Math talk should be an important 3. Post a “question of the day” on Making Math Happen in the Junior Years
part of every math class! A way to the board or use a gimmick such as was written by Jennifer Paziuk, Susan
encourage ongoing math talk is to use wearing a hat or carrying a sign that Pitre, Ruth Dawson, Joanne Languay,
a gimmick, such as wearing a visor with displays a question. Try to use open- and Mike Davis. Contributing authors
a math “question of the day” on it (e.g., ended questions such as: “How did were Jane Bennett, Jason Johnston,
What strategy did you use?). Explain you do it?” or “How did you know?” Troy Parkhouse, and Roz Thomson.
to the students that they will need to Tell students that this is the question
answer that question when you come they will have to answer when The book is available from shopETFO
to their group. This type of prompt you arrive at their table. This helps at a cost of $17 (plus GST). To order
helps students focus their learning, and students focus their discussion online go to www.etfo.ca, click on
discuss speciﬁc aspects of mathematics. while working. “Publications” and follow the links.
The following are more suggestions to
get the math talk ﬂowing.
A4 etfo voice | FALL 2004