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# Importance of Informal Mathematics Knowledge (page 2)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

Both quadrilaterals because of their four straight sides, a trapezoid is a quadrilateral with two parallel sides; a rhombus is a quadrilateral with both pairs of opposite sides parallel (also called a rhomb or diamond).

Informal mathematics knowledge is also important for older students. It may be harder to extract informal from formal learning and some misconceptions may be more rigidly held by older students, but teachers need to assess prior knowledge in whatever form for better connections to new mathematics learning. For example, Jamie is a student in Mrs. Banks’ third-grade class and was taught in previous grades that applying multiplication to whole numbers would result in larger numbers. This concept was confirmed with Jamie’s experiences grocery shopping with her mother. If one apple costs 20¢, then four apples cost 80¢. Buying a six-pack of soda for \$2.50 was cheaper than buying six sodas at the individual price of 50¢. Mrs. Banks is attempting to explain why would result in a smaller number. She could begin with Jamie’s understanding that six sodas 50¢ would result in a \$3.00 purchase. Shown another way, that would be of a dollar, or 3 dollars.

Misconceptions of older students are often caused by inadequate concept development through a wide enough range of examples during formal instruction or by limited informal experiences. For example, if a child had only cube-shaped blocks to play with, he could not compare other three-dimensional shapes and their properties. Viewing a diagram of a pyramid would be confusing for this child.