Making Math Happen by dfgh4bnmu


									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
further ideas.

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
                                                                                                something, they
                                                                                                have learned it.
                                                                                                It’s like when you
                                                                                                have to teach
                                                                                                something – that’s
                                                                                                when you know
                                                                                                if you really
                                                                                                understand it,”
                                                                                                Paziuk says.

                                                                                                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
math instruction.
                                          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
Happen series.
                                          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
                                                                                               for including
                                                                                               as part of
                                                                                               a mathematics
                                                                                               program are
                                                                                               to help students
                                                                                               make sense of
                                                                                               what they are
                                                                                               learning, and to
                                                                                               help the teacher
                                                                                               understand what
                                                                                               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, 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

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