NCSM - Section 4 - Teaching Resources

Section 4 - Teaching Resources

4 - Teaching Resources

How do I use a particular mathematical tool (manipulative)?
What mathematical tool might be used to teach a particular concept?

In this section you will be able to find references to articles from Teaching Children Mathematics, Mathematics Teaching in the Middle School, and the Mathematics Teacher to help you answer questions like the ones posed above. Thus far, we've included the journals from 1995 -2001.

Link to the journal archives on NCTM's website:
-- Teaching Children Mathematics
--- Mathematics Teaching in the Middle School
---- Mathematics Teacher

We've chosen to use the word mathematical tool to describe objects or things that might be used to help teach children mathematics. Mathematical tools include manipulatives, calculators, and other objects.

Concepts to Mathematical Tools to References
Full Lists of Concepts to Tools for:
Elementary -- Middle -- Secondary

Click the E-M-S initial in the columns to view specific references for the corresponding Mathematical Concept by grade level:

Concept
Elem Mid Sec

Algebra/patterns
E M S

Algorithms

E
M S

Amplitude
-- -- S

Angles
E M S

Area/surface area
E M S

Calculus
-- -- S

Cardinal/ordinal/nominal numbers
E -- --

Circular functions
-- -- S

Classification/sorting/making sets
E M S

Coordinate/analytic geometry
E M S

Conic sections
-- -- S

Constructions
E M S

Counting/skip-counting/
one-to-one correspondence

E
M S

Data collection/
management/graphing/
interpretation

E
M --

Decimals
E M S

Dimensionality/3D/2D
E M S

Discrete mathematics
-- -- S

Dow Jones industrial average
-- -- S

Dynamic geometry/mathematics
-- -- S

Equality/equivalence/
inequality/equations

E
M S

Estimation
E M S

Euclidean geometry
-- -- S

Factoring/factors
-- M --

Fact strategies/turnaround facts
E -- --

Fibonacci sequences/numbers
-- -- S

Fractal geometry/chaos theory
-- -- S

Fractions
E M S

Functions

M S

Geometry
E M S

Hamiltonian circuit
-- -- S

Horsepower
-- -- S

Hyperbolic geometry/functions
-- -- S

Integers
-- M S

Iteration/recursion
-- -- S

Latitude/longitude
-- -- S

Linear algebra/matrices/
determinants/vectors
-- -- S

Logistic growth model
-- -- S

Maps
E -- S

Markov process model
-- -- S

Matrix algebra/Punnett square
-- M --

Measurement/scale
E M S

Mental math
E M S

Modular arithmetic
-- -- S

Money
E -- S

Money management
-- M S

Number concepts/operations
E M S

Odd/even/prime/composite numbers
E -- --

Pascal's triangle
-- -- S

Patterns
-- -- S

Perimeter/circumference
E M S

Place value
E M --

Permutations/combinations
-- M S

Physics
-- -- S

Probability/chance
E M S

Problem solving/thinking skills
E M S

Proofs/theorems
-- M S

Pythagorean theorem
-- M S

Quadrilaterals
-- -- S

Quantity
E M --

Ratio/proportion/percent
E M S

Rational/irrational numbers
-- M

Reasoning
E M S

Relationships/connections
E M S

Sequences/series
-- -- S

Similarity/congruence
E M S

Spatial visualization
E M S

Spreadsheets
-- M S

Speed/velocity
E M

Statistics/data management
-- -- S

Symmetry
E M S

Tangent
-- -- S

Tessellations/tiling
E M --

Transformational geometry
E M S

Trigonometry/trigonometric
functions
-- -- S

Variables/variability
-- -- S

Velocity/speed/rate
E M S

Volume
E M S

Weight/mass
E M S

Mathematical Tools to Concepts to References
Full Lists of Tools to Concepts for:
Elementary -- Middle -- Secondary

Click the E-M-S initial in the columns to view specific references for the corresponding Mathematical Tool by grade level:

Tool
Elem Mid Sec

Abacus
E -- --

Algebra
-- -- --

Algebra tiles
-- M S

Arithmetic-mean machine
-- -- S

Astrolabe
-- M --

Attribute blocks
E M --

Balance scale/weights/scales
E M S

Balloons
E -- S

Barometer
-- M --

Base-ten blocks
E M S

Beads
E -- --

Books/journals/newspapers/
portfolios
E M S

Building blocks/Lego
E -- S

Calculators/graphing calculators
E M S

Candy/food
E M S

Capacity containers
E M --

Cardboard/boxes
E -- S

Chalkboard/metal
chalkboard/flannelboard/
magnet board
E -- --

Chemical test kits
-- M S

Clinometer/transit

S

Clocks/stopwatches/
calendars
E M S

Color tiles
E M --

Compasses
E M S

Computers/Internet/
software/spreadsheets
E M S

Costumes
-- -- S

Counters
E M --

Cubes/Unifix cubes
E M S

Cuisenaire rods
E M --

Dice/number cubes
E M S

Drinking straws
E -- --

Elastic Bands
-- -- S

Fabrics/beadwork
E M --

Fractal cards
-- -- S

Fraction models/circles
E M --

Games/puzzles/toys
E M S

Geoboards
E M S

Garbage
-- M --

Geometric shapes
E M S

Geometric solid
E M --

Graduated cylinder
-- -- S

Knitting needles
-- -- S

Hundreds chart/math tables/number lines/10x10 grid/circle chart
E M --

Maps
E -- --

Marbles
E -- --

Miras/mirrors/reflective material
E M S

Models/simulation
E M S

Money
E M S

Nomographs
-- -- S

Paper/origami/stencil patterns/graph paper
E M S

Pattern blocks
E M S

Pentablocks
E -- --

Play centers
E -- --

Polyhedrons/nets
E -- S

Protractors
E M S

Rollers
-- -- S

Rulers/tape measures/trundle wheels/calipers
E M S

Site gun
-- M --

Slide rules
-- -- S

Soap
E -- --

Spinners
E M S

Springs
-- -- S

String/rope
E M S

Tangrams
E M --

Telephone
-- -- S

Ten-frames
E -- --

Thermometers
E M --

Toothpicks/rods/sticks
E -- --

Tower of Hanoi/Atlantis
-- -- S

Video technology/multi-media
E M S

Return to the top of this page

Return to the Sourcebook index

Updated 09/07/03