13
THINKING MATHEMATICALLY
mathematical processes, concepts, and symbols
into meaningful counting experiences, dramatic
play activities, games, rhymes, songs, finger
plays, stories, and literature.
When counting the days until a trip, the
educator chooses to count the days using
five as the anchor because it is a number
that most children can understand and
relate to. She puts sticky notes over five
squares on a 5 frame with the numbers 5,
4, 3, 2, 1 printed on each note. As children
count down each day, they remove a sticky
note. Children then see the blank square
and the remaining numerals.
Each day, the children in this scenario see variations
on the partitioning of five, see the numerals in the
context of the count, and they count backwards
in a way that is similar to using a number line.
The educator’s strategy is a more effective and
meaningful way of showing the passage of time
than using the calendar, which is abstract.
Writing numerals needs to occur in the context of
an experience, (writing bills in the class restaurant,
recording the blocks used in a structure, recording
the count in a measurement experience). In other
words, there needs to be a purpose or connection
to writing the numerals. It is not a meaningless
printing or colouring activity.
The big idea for kindergarten educators then, is to
more conscientiously connect children’s natural
play experiences to the more formal language
and symbolism of mathematics. The kindergarten
environment should be filled with materials
readily available to promote mathematical
inquiry. (These materials may include numerals,
found and commercial materials for sorting and
classifying, scales and other measuring devices
for sand and water play, blocks of all shapes and
sizes, containers that promote comparisons and
counting, etc.) For example, Rochelle brought her
shell collection today and Ruman brought his stone
collection. I wonder how many there are in each
collection. How we could find out?”
Copies of homemade or commercial hundreds
boards, big enough for children to count out
their treasures, are essential to capture teachable
mathematical moments for sorting and counting
collections. As children have alphabet strips
at the writing centre, they should also have
number lines which they may use when they are
unsure how to make a particular numeral, or
as a strategy for counting objects. Five and ten
frames, dot cards and dot plates should also be
readily available in order to continually develop
the anchors of the numbers five and ten.
Kindergarten educators can capitalize on
young children’s natural interest in counting,
comparing, measuring, moving their bodies in
interesting patterns through space, and creating
unique buildings using various shapes and sizes
of materials. Since children are naturally inclined
toward mathematics, it is relatively easy to embed
formal mathematics into their play activities.
However, educators need to conscientiously talk
with children to make the essential links to the
mathematics in school.
Disposition:
Why does attitude matter?
What might affect disposition?
The ETFO kindergarten document Kindergarten
Years: Learning Through Play, 2000, suggests
establishing a ‘climate of delight’ in the
kindergarten program.5 In Early Learning for
Every Child Today (ELECT), play is seen “as a
means to early learning that capitalizes on
children’s natural curiosity and exuberance”.6 In
the Ontario Kindergarten Program play is seen as

14
THINKING IT THROUGH: TEACHING AND LEARNING IN THE KINDERGARTEN CLASSROOM
ELEMENTARY TEACHERS’ FEDERATION OF ONTARIO
However, some strands of mathematics might
indicate different intelligences. For example,
geometry could be more related to visual-spatial
than to logico-mathematical ability. Counting and
recalling the names for specific number symbols
could be more related to linguistic intelligence.
Children can be motivated to learn mathematics
through their strength in another intelligence.
Some children may engage in learning to count
through music, chants, or ball bouncing activities.
Others may more easily learn about geometry and
spatial orientation through bodily kinesthetic
activities. For the socially-motivated, learning
mathematics through games and dramatic play
may be most engaging. Some may learn to explore
mathematical concepts and symbols through
literature and/or technology. To motivate children
to learn mathematics, educators must take into
account all of these child-centered possibilities.
Several educator-related factors also contribute
to the child’s disposition to learn mathematics.
Educators who are effective mathematics
educators communicate the enjoyment of
learning mathematics, and have fun with
mathematical challenges and discussions. They
value errors as essential information that help
them learn more.13 These educators:
• help children understand the purpose of
learning math;
• set realistic and interesting challenges
related to mathematics;
• provide children with open-ended activities
that allow them to apply their understanding
at an appropriate developmental level;
• create math-rich classroom environments;
• talk with children about their mathematical
discoveries and ideas; and
• help children learn to evaluate their responses.
Educators need a clear understanding of how
children come to know and understand mathematics
in the early years. Documents such as First Steps®
a vehicle for learning “that provides opportunities
for learning in a context in which children are at
their most receptive”.7
This attention to disposition, natural curiosity,
and receptivity for learning that is so evident in
play-based learning, is at the heart of effective
early education. Lilian Katz identified four
interrelated types of learning that co-exist in any
learning situation: knowledge, skill, feelings, and
dispositions.8 Disposition is the ‘habits of mind’
that become internalized. This quality is particularly
relevant to solving problems in mathematics.
Dr. Douglas Clements identifies the disposition
or habit of mind important for mathematics
learning as: curiosity, willingness to persevere,
imagination, willingness to experiment, and
sensitivity to patterns which are all part of quality
early childhood programs.9 Interest, rather than
cognitive ability, has been shown to be the best
predictor of ability, along with more challenging
comprehension tasks such as those associated
with mathematical problem solving.10
Many factors are associated with creating
interest and motivation for learning, including
novelty, saliency, prior knowledge, and emotions
relative to a particular task, as well as natural
ability or inclination.11 With respect to the latter,
Howard Gardner’s multiple intelligence theories
would suggest that children with strong logico-
mathematical intelligence would have more
natural ability and likely more positive attitudes
and intrinsic motivation toward mathematical
learning than other children, (just as some
children are more naturally inclined toward
language/literacy, music, bodily kinesthetic
tasks, etc.)12
The most effective motivators
are relevance and novelty, supported by the
confidence of successfully completing challenges
that are closely matched to children’s current
level of understanding and skill.