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Today's
Child
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Math |
What is Math?
- it is more than computations (the
traditional Mathematics);
- it is a study of patterns and relationships;
- it is a science and a way of thinking;
- it is an art, characterized by order and
internal consistency;
- it is a language, using carefully defined terms
and symbols;
- it is a tool.
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Why Focus on More Than Computations?
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Mathematics is an understanding; it is a connection in people's minds
Mathematics is not just about memorizing formulas and concepts but it
is the ability to apply them; it is the 'light bulb" that goes off
when one understands.
Knowing mathematics means being able to use it in
purposeful ways.
Students learn mathematics well only when they
construct their own mathematical understanding and see relationships
among these concepts
Math
learning
is
not
a
spectator
sport
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Things to Think
About
Quote from a Student
(when asked for school projects focusing on
math):
"projects
with math?? No. Math is: solve this equation that has nothing to do with
anything and you'll never have to use it ever in your life.
The only thing you need to know about math is
adding / subtracting, multiply division. Fractions and percentage.
That's it!" Jennifer, Age 20
The Constellation Analogy
Imagine the stars in the sky.
Each experience in a child's life makes a connection from one star (one
concept) to another. By providing more experiences, the
understanding becomes more complete.
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We learn by doing, by manipulating, by thinking, by
exploring, by questioning, not just memorizing. With each new experience
we build on our present "constellation". Our level
of understanding, our "schemas" will affect how we perceive
and interpret new information.
ex. A toddler sees a four-legged animal and says:
DOGGIE.
The child has made an association between animals on
four legs and the word 'dog'.
Someone then points out that the animal has horns and says
"MOO-COW". (The child has a new piece of
information about dogs: no horns!)
The child then is confronted with a goat, sees the
horns, and says
"Moo-cow". Based on the limited knowledge as well as the
images of dogs and cows, the child is able to determine that the new
creature is a cow, not a dog.
It is over time, with a vast
amount of experience that the child is finally able to distinguish
between all types of four-legged animals.
The key to effective teaching and learning is
helping children to be active, reflective thinkers so that their
minds will be working and forming relationships, making connections,
and integrating concepts and procedures.
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Keys to Teaching Mathematic Skills
- changing the concept of "math" from facts to processes
- providing opportunities to build connections
- helping students develop these connections as well as provide the
math concepts, terminology, and facts
- building on the old information to understand the new
Teachers might help make this connection by asking reflective
questions such as the following:
- How does this fit with what you already know?
- In what ways is this problem like other
problems/situations you’ve experienced?
- What is it about this problem that reminds you of
yesterday’s problem?
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Obstacles to Using Hands-on Approach
- personal beliefs that students and teachers bring
to the classroom
- assumptions held by administrators, parents, and
society about mathematics, curriculum, teaching, and learning
- belief that "new math" will go away
- beliefs that students need to be comfortable with
computations before problem solving
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Six ways that teachers might structure lessons to promote reflective
thought :
- create a problem solving environment
- use models, manipulatives, drawings, calculators
- encourage interaction and discussion
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- use cooperative learning groups
- require self-validation of responses
- use consistent, correct terminology
- listen actively
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Provide experiences that are
experimenting first-hand with physical objects
and having concrete experience before learning abstract
mathematical concepts
Minds-on: build the basic concepts and
thinking processes, making sure they are understood so they can be build
upon and used to make new relationships, new
"constellations"
Authentic: use real-world problems, things that
are relevant and interesting to the student to help them explore,
discover, discuss, and build on their mathematical concepts
Students' Roles:
- to listen to, respond to, and question the teacher and
other students
- to interact with each other, building on one another’s ideas
- to justify answers
- to rely on a variety of tools to reason, make
conjectures, solve problems, and communicate
- to be a team member in discussions, adding input,
questions, and strategies, as well as problem solving during
"conflicts"
- to search for patterns and question inconsistencies
that puzzle them:
- to look for connections and use prior experience and
knowledge to solve problems
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Kindergarten Math Curriculum
- is much about vocabulary as about numerals
- is more concerned with consolidating understanding
than with rote knowledge
Basic terms
- more/less/ same/different/ equal /
group / set
- Spatial: near/far / in/out/ above/below/
up/down/top/bottom/ front/back/open/closed/right/left/to/from/empty/full
between/beside/across/first/next/last
- Comparison: talls/short; big/small/long/short/
tall/taller/tallest; short etc; small etc; long
- Numerals: rote count to 20; identify numerals to
20; order (1st, 2nd) ; group, match
- Shapes: entry into geometry
- Time: morning, afternoon, later, tomorrow,
- money : recognize coins
- weight: heavy light,
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