Parental Resistance to Educational Change

The greatest challenges facing parents stem from their own school experiences. Every adult has been educated in some way, and the methods their teachers used usually shape the values they carry with them and color their perceptions of how education “should be.” These learned values are very powerful and can be seen in the ongoing controversies that manifest in social media regarding the Common Core State Standards and math instruction, for example. The notion that there is a critical-thin...

 Number Scrabble: Numerical Tic-Tac-Toe

In psychological research on problem-solving, sometimes the game of Tic-Tac-Toe is employed, which, though very simple to learn and play, still offers sufficient problems to the investigator in that it is not at all clear what heuristics are used by the subjects, except avoiding the winning move of the opponent. The same is apparently true for the isomorphic game of Number Scrabble, which is based on the fact that there exists a 3 X 3 magic square, of which rows, columns, and main diagonals a...

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...

 We Teach Kids Mathematics in the Wrong Order

The familiar, hierarchical sequence of math instruction starts with counting, followed by addition and subtraction, then multiplication and division. The computational set expands to include bigger and bigger numbers, and at some point, fractions enter the picture, too. Then in early adolescence, students are introduced to patterns of numbers and letters, in the entirely new subject of algebra. A minority of students then wend their way through geometry, trigonometry and, finally, calculus, w...

 Conservation Tasks and Reason

Piaget had his own way of assessing brain maturation during this period, using his now-famous "conservation" tasks, try this one out on your tour-to-eight-year-old: fill two identical short, squat glasses with equal volumes of water, and ask your child, "Do the two glasses contain the same amount of water, or does one have more?" Now, pour all the water from one of these 'lasses into a tall, narrow glass, and ask your child the same question. Four-year-olds almost invariably say that the ta...