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Wednesday, August 10, 2011

Common Counting Errors for 4 and 5 Year Old Children

 I've been working with my two-year old granddaughter on counting. (Can you say "Overachieving Grandma?") In this picture we are painting TWO monsters after reading "My Monster Mama Loves Me So." This book  is about the relationship between a monster and his mother. As the title suggests, the monster lists some of the reasons he knows his monster mama loves him. Those reasons include the monster mama baking cookies that are filled with bugs. (Doesn't that sound delicious??) All of the examples the monster gives are funny and heartwarming.


Given the fact that I have a passion for both my granddaughter and MATH, I started thinking about the problems children have when they learn to count.  I've been reading the book, "Mathematics Learning in Early Childhood: Path Toward Excellence and Equity", and I found a list of Common Counting Errors.
As a teacher, I found these words interesting:
"As with many physical activities, counting will improve with practice and does not need to be perfect each time. Teachers do not have to monitor children’s counting all of the time. It is much more important for all children to get frequent counting practice and watch and help each other, with occasional help and corrections from the teacher."

After reading Debbie Diller's book, "Math Stations" this quote provided even more support for the use of math stations at the early learning grades.

Just in case you are interested,below is a direct quote from this book about common counting errors:
"There are some common counting errors made by young children as they learn the various principles that underpin successful counting. Counting requires effort and continued attention, and it is normal for 4-year-olds to make some errors and for 5-year-olds to make occasional errors, especially on larger sets (of 15 or more for 4-year-olds and of 25 or more for 5-year-olds). Younger children may initially make quite a few errors. It is much more important for children to be enthusiastic counters who enjoy counting than for them to worry so much about errors that they are reluctant to count. If one looks at the proportion of objects that receive one word and one point, children’s counting often is pretty accurate. Letting errors go sometimes or even somewhat frequently if children are trying hard and just making the top four kinds of errors is fine as long as children understand that correct counting requires one point and one word for each object and are trying to do that. As with many physical activities, counting will improve with practice and does not need to be perfect each time. Teachers do not have to monitor children’s counting all of the time. It is much more important for all children to get frequent counting practice and watch and help each other, with occasional help and corrections from the teacher.

Very young children counting small rows with high effort make more errors in which their say-point actions do not correspond than errors in the matching of the points and objects. Thus, they may need more practice coordinating their actions of saying one word and pointing at an object. Energetic collective practice in which children rhythmically say the number word list and move down their hand with a finger pointed as each word is said can be helpful. To vary the practice, the words can sometimes be said loudly and sometimes softly, but always with emphasis (a regular beat). The points can involve a large motion of the whole arm or a smaller motion, but, again, in a regular beat with each word. Coordinating these actions of saying and pointing is the goal for overcoming this type of error. For variety, these activities can involve other movements, such as marching around the room with rhythmic arm motions or stamping a foot saying a count word each time.
Counting an object twice or skipping over an object are errors made occasionally by 4-year-olds and even by 5-year-olds on larger sets. These seem to stem from momentary lack of attention rather than lack of coordination. Trying hard or counting slowly can reduce these errors. However, when two counts of the same set disagree, many children of this age think that their second count is correct, and they do not count again. Learning the strategy of counting a third time can increase the accuracy of their counts. If children are skipping over many objects, they need to be asked to count carefully and don’t skip any.

Young children sometimes make multiple count errors on the last object. They either find it difficult to stop or think they need to say a certain number of words when counting and just keep on counting so they say that many. When they say the number word list, more words are better, so they need to learn that saying the number word list when counting objects is controlled by the number of objects. Reminding them that even the last object only gets one word and one point can help. They also may need the physical support of holding their hand as they reach to point to the last object so that the hand can be stopped from extra points and the last word is said loudly and stretched out (e.g., fii-i-i-ve) to inhibit saying the next word.

Regularity and rhythmicity are important aspects of counting. Activities that increase these aspects can be helpful to children making lots of correspondence errors. Children who are not discouraged about their counting competence generally enjoy counting all sorts of things and will do so if there are objects they can count at home or in a care or education center. Counting in pairs to check each other find and correct errors is often fun for the pairs. Counting in other activities, such as building towers with blocks, should also be encouraged."

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