Facilitator Training Module: Developing Early Math Skills and Number Sense

Module Overview

This module introduces a hierarchy for early math goals, starting from pre-number concepts and number sense and gradually moving to counting and symbol recognition. It helps facilitators design developmentally appropriate goals instead of starting with rote “1 to 10” counting.

Learning Objectives

By the end of this module, participants will be able to:

Explain what number sense is and why it must precede rote counting.
Use pre-number concepts (more/less, big/small, same/different, long/short, few/many) in structured activities.
Distinguish the three components of counting: quantity, number word, and numeral symbol.
Plan math activities that use concrete objects and daily routines rather than “counting in the air”.
Use the hierarchy of math goals to identify gaps and step back appropriately for each child.

Section 1: Core Ideas – What Is Number Sense?

Number sense is the intuitive ability to understand “how many” in a set and link that to a number name. Even very young children can see that one pile is “a lot” and another is “less” without counting exactly.

Key points for facilitators

Number sense includes:
Recognizing small quantities at a glance (1–3 objects).
Understanding “more”, “less”, “same”, “bigger”, etc. as comparisons.
Linking these comparisons to real objects, actions, and choices.

Section 2: Pre-Number Activities (Before Counting)

Before formal numbers, we work on comparative adjectives that become quantifiable once measurement or counting is added.

Typical pre-number concepts

more / less
big / small
long / short
few / many
same / different

Facilitator guidelines

Select one or two target concepts at a time (e.g., more/less and big/small).
Use real objects (blocks, crayons, snacks, leaves) to show the contrast.
Ask for actions: “Give me the big ball”, “Show me where there are more blocks.”

These activities lay the foundation for later understanding of addition, subtraction, and measurement.

Section 3: Meaningful Counting – Not “Counting in the Air”

Rote counting without objects does not automatically build understanding of quantity.

Principles for teaching counting

Never count in the air as the main method; avoid chanting numbers without objects.
Always pair number words with concrete items that can be touched, seen, and moved (blocks, beads, toys, fingers).
Embed counting in play and routines:
“Give me 3 cars”
“Let’s count 4 steps”
“Put 2 stickers here.”
Count together as the child hands over or places each object.
The facilitator and the child can do rote counting once the knowledge of number sense is established. Many children enjoy this as well.

This way, “one, two, three, four” becomes attached to how many objects are actually present.

Section 4: Three Components of Counting

Facilitators should explicitly recognize three distinct components:

Quantity (How many objects?)
Child experiences and compares different set sizes.
Number word (Sound)
Child learns the spoken label “one, two, three…” for each quantity.
Symbol (Written numeral)
Child later learns that “1”, “2”, “3” are written forms of those number words.

Effective intervention helps the child connect all three: objects ↔ number word ↔ symbol.

Section 5: Using the Child’s Environment and Interests

After introducing these components, return repeatedly to concrete, meaningful contexts:

Count fingers, toes, body parts.
Count drawings the child loves (cars, butterflies, favourite characters).
Use everyday items: snack pieces, toys, classroom materials.

Daily number sense activities (e.g., quick “how many?” games, simple “more/less” comparisons, number pyramids or small number lines) reinforce the idea that numbers describe the real world, not just worksheets.

Section 6: Hierarchy of Math Goals for Facilitators

Facilitators should think in terms of a scaffolded hierarchy rather than jumping straight to written sums.

Suggested hierarchy

Pre-number concepts
more/less, big/small, long/short, same/different.
Number sense with objects
Quickly seeing “how many” in small sets, comparing which is more or less.
Counting objects with 1–1 correspondence
Touching each object once while saying each number word.
Mapping to number words
Answering “How many?” with the correct spoken number.
Mapping to numerals (symbols)
Matching sets to written numerals, e.g., 3 dots ↔ “3”.
Working from memory
Giving a requested number of items without them being counted together every time.

Understanding this hierarchy allows facilitators to locate the child’s current level and “step back” if needed to fill gaps.

Application Tasks for Training Sessions

You can use these as activities in a workshop:

1. Sort Goals Activity

Provide a mixed list (e.g., “count to 20”, “understand more/less”, “match 5 objects to ‘5’”).
Trainees sort them into the hierarchy stages.

2. Design a Pre-Number Game

In groups, design one play-based activity targeting only “more/less” or “big/small”, using common classroom objects.

3. Three-Component Check

Show a short video or description of a math activity.
Ask: Which components are targeted—quantity, number word, symbol? What is missing?

Math Do’s

Do start with pre-number concepts (more/less, big/small, long/short, same/different) before formal numbers.
Do use real objects (blocks, toys, snacks, classroom items) for all early math work.
Do embed math in daily routines: counting steps, snacks, toys put away, children in class.
Do teach counting with one-to-one correspondence: touch/move each object as you say each number word.
Do link three components: quantity (how many) + number word (sound) + numeral (symbol).
Do start with small sets (1–3, then 4–5) and use subitizing/visual patterns like dot cards or dice.
Do follow the child’s special interests (cars, trains, animals) and count or compare those items.
Do use clear, repeated language (“Show me more”, “Give me 3 blocks”, “Where is 4?”).
Do allow movement and sensory regulation (standing, fidgeting, squeezing a toy) while doing hands-on math if the child remains engaged.
Do track progress along a hierarchy (pre-number → number sense → counting → numerals) and step back a level when a child is stuck.

Math Don’ts

Don’t make “counting 1–10 by heart” your starting goal; it doesn’t guarantee understanding.
Don’t rely on “counting in the air” (reciting number words without objects) as the main activity.
Don’t introduce symbols (1, 2, 3…) too early without secure quantity and word understanding.
Don’t flood the child with large sets (e.g., counting 20 bears) before they are comfortable with 1–5.
Don’t use only worksheets or pencil-paper tasks; early math should be tactile and visual.
Don’t mix many new concepts at once (e.g., more/less + big/small + numbers to 10 all in one short session).
Don’t rush to addition/subtraction before a strong sense of “how many” and “which is more” is in place.
Don’t treat mistakes as failures; treat them as information about which level of the hierarchy you need to revisit.
Don’t compare autistic children to neurotypical peers; compare them to their own previous level on the hierarchy.