Base ten blocks, also known as Dienes blocks after popularizer
Zoltán Dienes (), are a
mathematical manipulative used by students to practice
counting
Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for ever ...
and
elementary arithmetic
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and Division (mathematics), division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathema ...
and develop
number sense
In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by ...
in the context of the
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
place-value system as a more concrete and direct representation than written
Hindu–Arabic numerals. The three-dimensional blocks are made of a solid material such as plastic or wood and generally come in four sizes, each representing a
power of ten
In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power ...
used as a place in the decimal system: ''units'' (ones place), ''longs'' (tens place), ''flats'' (hundreds place) and ''blocks'' (thousands place). There are also computer programs available that simulate base ten blocks.
Base ten blocks were first described by
Catherine Stern
Catherine Brieger Stern (1894–1973) was a German psychologist and educator. Born under the name Käthe Brieger, she developed sets of mathematical manipulatives similar to Cuisenaire rods for children to use in building up their number sense and ...
in 1949, though
Maria Montessori
Maria Tecla Artemisia Montessori ( ; ; 31 August 1870 – 6 May 1952) was an Italians, Italian physician and educator best known for her philosophy of education (the Montessori method) and her writing on scientific pedagogy. At an early a ...
had earlier introduced a similar manipulative, the "golden beads", which were assembled into the same shapes as base ten blocks. Dienes popularized the idea starting in the 1950s, recommending blocks for several
number bases (
two
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number.
Because it forms the basis of a duality, it has religious and spiritual significance in many ...
,
three
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies ...
, etc.), called multibase arithmetic blocks (MAB), so students could concretely compare different number bases and learn about the decimal place-value system as one arbitrary choice among many possibilities. Multibase blocks found support in the
New Math movement of the 1960s. Today, base ten blocks are widespread while blocks for other bases are rarely found.
Use in mathematics instruction
Base ten blocks are popular in
primary-school mathematics instruction, especially with topics that students struggle with such as
multiplication
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
. They are used by teachers to model concepts, as well as by students to reinforce their own understanding. Physically manipulating objects is an important technique used in learning basic mathematic principles, particularly at the early stages of cognitive development. Studies have shown that the use of base ten blocks, as with other
mathematical manipulatives, decreases as students move into higher grades.
[Hatfield, Mary M. (1994)."Use of manipulative devices: Elementary school cooperating. " School Science and Mathematics 94.6 (1994): 303–309.]
See also
*
Cuisenaire rods
Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisor ...
*
Number sense
In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by ...
*
Mathematics education
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical know ...
References
{{Reflist
External links
*
Base Blocks - NLVM
*
Exploring Ones, Tens, and Hundreds with Base Ten Blocks - A Lesson for Third Graders by Maryann Wickett and Marilyn Burns, fall 2005
*
, Susan C. Anthony
*
Progression of Multiplication: Arrays, Area Models & Standard Algorithm, Make Math Moments
Mathematical manipulatives