An analysis of relation between sequence counting and knowledge of place values in the early years of school.
Place value and mathematics for students with mild disabilities: Data and suggested practices.
The students' initial ideas were about adding and subtracting amounts between place values but they soon realised that the only thing that worked across all place values was "getting ten of" and the inverse action of partitioning into ten equal parts.
A unit about decimals was planned for the end of the year as a way to support students to integrate their knowledge about whole number place value and fractions.
The author divides these specialized activities and games into separate sections for early number work, basic calculations for larger numbers, place values
and the fundamentals of time tables, multiplication and division.
The decimal point becomes a "mirror," reflecting the place values to the left of the decimal point on to the right side.
Trissy's application of her understanding of the place value of whole numbers to be mirrored in the place values of fractions of whole numbers is an example.
When asked why they did this, students who made this mistake said that they translated exactly the digits from Hindu-Arabic to Chinese and did not consider the place values
of the digits.
Critical thinking also permits students to place values
on information and respect the role of information in problem-solving situations.
Students reason that: larger numbers must be in higher place values
to create larger numbers; waiting for a 9 for a particular spot in a three-digit number may not be a wise chance-based decision; two numbers to be subtracted must be as far apart in size as possible to create the greatest difference; and so forth.
Students can memorize the names of commonly used place values
and will say that the 2 in 123 means two tens.