An analysis of relation between sequence counting and knowledge of place values in the early years of school.
Beginnings of place value: How preschoolers write three-digit numbers.
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.
Recognise that the place value system can be extended to tenths and hundredths.
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.
6) suggest, "prior knowledge of whole numbers and fractions can both support and interfere with construction of a correct concept of decimals." 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.
The Chinese numeration system is one of many numeration systems that can reinforce a student's conceptual knowledge of place value. Through the use of Chinese numeration representations, students reviewed the base-ten place values in other contexts.
Reys (1998) explains that place value is the foundation of our numeration system.
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.
Test results from Connecticut substantiate the difficulty that students have with the concept of place value
. Students can memorize the names of commonly used place values
and will say that the 2 in 123 means two tens.