The main features of this file are:
Recommendation 1: Teach number and operations using a developmental progression.
Recommendation 2: Teach geometry numbers, patterns, measurement, and data analysis using a
Recommendation 3: Use progress monitoring to ensure that math instruction builds on what each
Recommendation 4: Teach children to view and describe their world mathematically
Recommendation 5: Dedicate time each day to teaching math, and integrating math instruction
throughout the school day.
Teaching Math to Young
This training provides five recommendations to
teach math to young children.
Teach number and operations using a developmental progression.
Teach geometry, patterns, measurement, and data analysis using a
Use progress monitoring to ensure that math instruction builds on what each
Teach children to view and describe their world mathematically
Dedicate time each day to teaching math, and integrate math instruction
throughout the school day.
Teach number and operations using a
Subitizing is the ability to instantly recognize “how many” in a small set.
To identify the number of things by quickly looking at them—not by
counting them one by one.
An example often used to explain this, is to think of dice – we immediately
recognize the number of dots without having to count each one individually.
Meaningful Object Counting: Counting one-to-one and recognizing that the last word
used while counting is the same as the total.
Cardinality- Understanding that the last number word is the total of the collection.
A child who recounts when asked how many candies are in the set that they just
counted, has not understood the cardinality principle.
Counting-based comparisons of collections larger than three:
Once children can use small-number recognition to compare small
collections, they can use meaningful object counting to determine the
larger of two collections.
Number-after knowledge: Familiarity with the counting sequence enables
a child to have number-after knowledge; to enter the sequence at any
point and specify the next number instead of always counting from one.
Mental comparisons of close or neighboring numbers:
Once children recognize that counting can be used to compare
collections and have number-after knowledge, they can efficiently and
mentally determine the larger of two adjacent or close numbers.
Number-after equals one more:
Once they can mentally compare numbers and see that “two” is one
more than “one” and that “three” is one more than “two” they can
conclude that any number in the counting sequence is exactly one more
than the previous number.
What could our mathematical manipulatives be in the early years?
• Loose parts: Natural objects (stones, plant seeds, sticks, etc.) manmade
objects (bottle tops, keys, washers, buttons, etc.)
• Manufactured mathematical resources: Counters, blocks, interlocking cubes,
five and ten frames, mechanical clocks, pattern blocks
Teach geometry, patterns, measurement, and data
analysis using a developmental progression.
Help children recognize, name and compare shapes, then teach them
to combine and separate shapes.
• Take children on shape walks and ask them to point out the shapes
• Ask children to bring in things from home that illustrates a particular
shape or locate shapes in the classroom.
Identify patterns as well as, extend correct and create patterns.
• Introduce children to basic repeating patterns.
• Help children lean to extend patterns
Promote children’s understanding of measurement by
teaching them to make direct comparisons and to use
both informal and formal units and tools.
• Children can compare objects as they sort, arrange and
• Measurement using non-standard and standard tools.
Help children collect and organize information, and
then teach them to represent that information
• Math Room Quest
• Describe, Describe, Draw
• Interactive Word Walls (Subject)
Visual supports help make language and
mathematics more comprehensible.
Use progress monitoring to ensure that math
instruction builds on what each child knows.
Use introductory activities, observations, and assessments to determine
each child’s existing math knowledge, or the level of understanding or
skill he or she has reached on a developmental progression.
• Use introductory activities to present a new concept to determine how much of the activity
children are able to do independently.
• Observe using a math activity that addresses a specific skill and observing how children try to
complete or solve the task.
• Use formal assessments to help teachers direct their instruction to particular goals.
The flow of progress monitoring.
Tailor instruction to each child’s needs, and relate new
ideas to his or her existing knowledge.
Teach children to view and describe
their world mathematically.
Uncommon technical terms
that are typically associated
with a specific domain.
Amino Acid, Peninsula
Deliberate direct instruction
needed. It helps students build
a web of word knowledge.
Distribute, secure, contribute,
parallel, predict, contrast
Commonly used social
language. We generally acquire
these words through basic
or natural exposure.
bed, happy, sad, cold, hungry
Speaking and Listening strategies:
Dedicate time each day to
teaching math, and integrate
math instruction throughout
the school day.
Plan daily instruction targeting specific math concepts and skills.
• Introduce a concept for the first time or illustrate a concept through an
example that is relevant to children’s everyday lives.
• Embed math in classroom routines and activities.
• Highlight math within topics of study across the curriculum.
Why We Need Math Read Alouds?
• One of the best ways to introduce a new math concept or math skill is by
using books, poems or songs. Math read alouds are a visual way to show
math concepts and the stories help promote a high level of student
engagement by sparking their imaginations.
• Math achievement when they enter kindergarten can predict reading
• Foundational skills in number and operations sets the stage for reading skills.
Create a math-rich environment where children can recognize and meaningfully apply math.
Use games to teach math concepts and skills and to give children practice in applying them.
These can provide an engaging opportunity to practice and extend skills.