The Count! Counting and Estimating: First Cousins

In previous weeks, the Museum of Teaching and Learning has expressed concern for America’s relative lag in mathematical abilities and, among some adults, an outright disdain for math. See earlier articles published through our helpful platform, Network for Good:  "Attitude Adjustment” and “Getting a Grip on a Trillion.” Perhaps that is why some individuals saw the MOTAL Marble Guess last Saturday as “fun” and others were adamantly in the “no thanks” category.


Anyway, MOTAL is thrilled to have met our goal of providing an opportunity for fun for some supporters and some “dough” to help carry on with business as a charitable organization in the category Enrichment. As promised, the winner will be announced today. You will learn the name toward the end of this e-blast.


But first, a bit of insight about counting and estimating, for they are prominent activities in real life—in the kitchen, the supermarket, at the political rally, or after the rock concert. Estimating amounts can be helpful for adults in all walks of life. But the skills of estimation are developed through practice in counting and augmented by abilities in logic and calculation. Estimates certainly do vary from individual to individual based on innate abilities but also in the strategies In use.


Real World Math: 6 Everyday Examples

The two skills of counting and estimating are entwined. Children are able to start counting at a very early age (between ages two and four) as parents help them use fingers and toes, followed by gradually more mature activities such as putting blocks in a container, then crayons in a box, later beans in a jar. Counting accurately one-by-one requires concentration and vocabulary as the amounts increase. When she was three, a young woman who now supports MOTAL was known to say, “ . . . ten, eleven, twelve, thirteen, nexteen, nexteen . . .” when her memory for the right words wasn’t yet in place nor did she have the system to figure it out

Estimating can be developed in young children as well, but it takes knowing parents and teachers to encourage it. Simple activities such as If you take a handful of grapes, how many are in it? And how many are in my (teacher’s) hand? Why are they different? The link that follows describes many good ideas for developing estimation abilities.


18 Estimation Activities That Take the Guesswork out of Teaching Math

Speaking of estimates, the range of estimates submitted for the MOTAL guessing contest went from 300 to 5,000. To refresh your memory, the picture of the vintage pretzel can shows the top layer of marbles and the dimensions are: eight inches tall, six inches in diameter, and weight of eleven and four tenths pounds. The marbles were the schoolyard winnings from the marbles champ in the 1940s. A few contestants mentioned in passing that they counted what they saw but then looked up sizes and weights of marbles to assist in their calculations.

Counting is a skill learned by young children, but older children (and adults) have the capacity to visualize and count by groups. It is a precursor to effective understandings in multiplication. In other words, count by twos, threes, . . . tens, twelves, fifteens. Few people practice beyond that, but some do!


MOTAL’s process for counting marbles was established by the first team of counters. P. Nagel, M. Mena, and G. Nagel placed groups of 100 in Styrofoam bowls by grabbing handfuls of marbles and counting out exactly 10. They noted each set of ten with a tally mark on the side of the bowl so as not to lose count. The team discovered that marbles do come in sizes; some marbles were smaller than others and only one large marble (a “boulder”) was buried inside the can of normal marbles. They also found one small hard rubber ball that they did include in the count. The second team of counters (C. Stewart, A. Hammer, and G. Nagel) came on to verify the results. They had to ward off the temptation to simply recount a random sample of bowls, but the math teacher’s words prevailed: true verification did require counting each and every marble again. Their patient counts matched the results obtained by the first team, except for one bowl that got dubbed “The Haunted Bowl.” It took four recounts to settle on the fact that the actual number was two less than the original.

So, now that you readers have some information and thoughts about counting and estimating, MOTAL is pleased to announce the person with the guess that was the closest to 969 actual marbles in the can (without guessing a number over the amount). It was MOTAL fan and supporter, Mary Deming. Mary also serves as the secretary of the board, but since nobody knew the real count prior to the contest, her victory was on the up-and-up. She had no “insider’s knowledge.” Mary will be awarded two day passes to Disneyland! Congratulations!


Submitted by Greta Nagel
MOTAL President and CEO
We Educate People About Education


P.S. Before we sign off, a few parting comments. Yes, somewhat preachy. A persistent and worrisome theme, reflected in recent comments by a talented high school math teacher, is that adults freely reflect their own dislike of math and often say things like, “I was never good at math,” or “I hated math too.” Permission to be poor in math is passed on from generation to generation, not through anything genetic, but by frequent modeling. Math teachers end up having extra work to do in undoing lukewarm and/or negative attitudes. Humans do have the capacity to change negative attitudes and behaviors. We can start by saying nice things (even if it seems like pretending at first). We can catch ourselves “being good.” We might reward others’ behaviors with smiles, and share pleasant activities. Doing math takes organization and patience. The next generation is watching and listening.