THIS MONTH’S BIG IDEA: Counting
Dear Families: One of our goals is improving our math instruction in order to increase the development of mathematical concepts in children. According to the authors of The Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (Erikson Institute Early Math Collaborative, 2014), “Counting seems very simple, but it is really quite complex. By developing a sophisticated sense of what counting is and what kind of counting we ought to emphasize in teaching, parents and teachers can better assist children with the development of counting skills and mathematical thinking (p. 47, 2014).” There’s more to counting than just 1, 2, and 3! There are two kinds of counting, rote counting, which is the reciting of number names in order, from memory. Then, there’s rational counting, which is matching a number name in order to objects, as well as understanding that when you have counted the last item in the set, that number represents the total of the objects in the set.
BIG IDEA #1 (Counting): Counting can be used to find out “how many” in a collection. The science/math parents should know…
Finding out how many things are in a collection is the primary reason to count, and knowing how many allows preschoolers to do several important things, such as conduct number operations, compare sets (more or less), and identify equivalence (sameness).
Dr. Gwen Dewar, author of an article called “Preschool Math Lessons: A Developmental Guide for the Science Minded Parent, states, “Numerosity is the conceptual bedrock for most basic math skills. Kids who don’t grasp numerosity…have trouble understanding the counting system. They also have more difficulty with arithmetic and making measurements (Booth and Siegler 2006; Siegler and Booth 2004). How can we help kids learn about numerosity? Recent experiments on American first graders suggest that approximation activities are helpful. Show kids two sets of objects and ask them to judge which is bigger — without counting (this is called subitizing) (Hyde et al 2104). Such activities might help preschoolers, too. But very young children have a lot more to learn. They need to know that specific numbers signify, or map onto, specific quantities. And this understanding may improve with practical, hands-on experience with real sets (Dehaene 1999; Hirsh-Pasek et al 2003).”
Recently, (and I cannot remember who said it or where it was written) but I heard something we want to share with you. Often as parents we get hung up on having our children count to high numbers such as 30 or 40, in the same way we like to hear them recite the alphabet. However, reciting numbers to 35 does not mean they understand the meaning of numbers no more than reciting the alphabet means that they can read. Instead, counting should connect to daily concrete experiences. Use personal interests, daily life, objects and sets of objects around the home, and play opportunities to count concrete items with your children—it’s more real and less abstract.
BIG IDEA #2 (Counting): Counting has rules that apply to any collection. The science/math parents should know…
There are 4 rules to counting that are developed in preschoolers in the following order, which experts agree that rational counting can happen only after all 4 are mastered (p. 51-54, 2014):
1. Phase 1: Stable Order
This principle is that counting words have to be said in the same order every time. The order, 1, 2, 3… is fixed—it’s always the same.
2. Phase 2: One-to-One Correspondence
This means that one number is named for each object. Here, it’s important that they coordinate their physical movement of the finger and eyes across the objects to match one number to one object.
3. Phase 3: Order Irrelevance
This is the idea that the order the objects in the group are counted in will not matter—the end result is the same. For example, if we are counting 8 goldfish crackers, we can put them in a line right to left and count, push them away into a pile and count them, put a mark by them to count them, or even make groups of 5 and 10 to help count large sets.
4. Phase 4: Cardinality
With this concept, the child applies the numbers to the objects, uses the correct number sequence, counts them each only once, and then once he stops counting, they reuse the last number counted to name the total in the set.
What do these Big Ideas about Counting mean to me as a parent?
Stable Order Ideas:
· Sing counting songs—include movement as you do
· Count up and pack from any number
· Post and reference a 1-10 number line that uses dots and numbers when you are working on counting
· Once counting 1-20 is mastered, work on skip-counting by 2s, 5s, and 10s.
· Interrupt a count and have them count backwards down to 1 again.
One-to-one Correspondence:
· In daily routines, like giving crackers
· Use music and movement such as marching to a drumbeat.
· Play “Shutes and Ladders” again and again and again!
· Help them to coordinate their hands, eyes, and objects to point to each object for each number name.
Order Irrelevance
· Arrange and rearrange a collection to confirm the count (line it up, stack it up, clumps of 5…)
· Teach them to group objects by 5s, 10s, etc. to make it easier to count.
· Model and talk out loud about how your method for counting, such as lining objects up, group objects, counting by 5s or 10s.
Cardinality
· Label the set by “how much” or “how many” items there are in total at the end
· As you are counting objects, practice labeling at the end, such as 1, 2, 3… 3 crackers for snack.
Thank you for your on-going connection to what we are working on in school. Thank you for your partnership with us as we work together to provide opportunities for children to grow and develop as strong mathematicians.
Sources:
Collaborative, Early Math. Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know. S.l.: Pearson, 2014.
Dewar, Gwen, PhD. “Preschool Math Lessons: A Developmental Guide for the Science-minded Parent.” Preschool Math Lessons: A Developmental Guide for the Science-minded Parent. Parenting Science, 2008-2014. Web. 17 Nov. 2014.