Successful family math programs use the knowledge of stages of development outlined below to develop activities that correspond to the stages of children in their groups. This knowledge helps parents know what to expect and what not to expect from their child’s math thinking. An awareness of the stages may help parents be patient with the child as he moves through them, and be tolerant of what seem on the surface to be mistakes, but are really only indications of the stage the child is at. Similarly, the fact that the child is ready to deal symbolically with numbers, to read and write the figure associated with the concept of “6,” only as he reaches school age, will show the fruitlessness of using workbooks or flashcards while the child is younger.

0–3 years

• The child’s representation of understanding is often physical (twirling to show roundness or a circle, or using a marker to make a line while saying “Vroom, vroom” when asked to draw a truck)
• Explores quantity, size, shape, distance, and pattern in rhythms
• Can “subitize” at a few days old (that is, can recognize a group of three objects, and is surprised if an object is taken away or added by stealth)
• Parents support this learning by providing experiences and adding language, such as “up and down,” or “just two more sleeps.”

3 to 5 years

• At about four, the child wants to count everything
• Will focus on number if environment supports it (sees parents using calendars, calculators, doing sums, estimates, etc.)
• Learns number names, one-to-one correspondence between number name and thing, that the last number named is the number of the group, that you have to start at 0 to count accurately
• Can invent number systems or representations of numbers; measures by non-standard units
• Stories, songs, rhymes are important to learn number names in the right order
• Concrete play is more important than abstraction, e.g., count ants or forks or popcorn as you eat it

From 5 years

• Children begin to be ready to represent ideas or objects with symbols
• Schools need to build on what kids already know, rather than insisting on a single method, and move from concrete to abstract

Family Math Programs

In Canada, Great Britain and the United Kingdom, family math programs have been implemented by many school boards, ABE programs and community groups. According to an ERIC digest on family math by Wendy Schwartz (1999), the most comprehensive program is “Family Math” which was developed by the Lawrence Hall of Science in Berkeley, CA; in Great Britain, the IMPACT program (Inventing Maths for Parents and Children and Teachers) is widely used. In Ontario, the Esso Family Math program, developed at the University of Western Ontario, has spread widely around the province.