On the campus of

Count Anything and Everything

A few weeks ago, I was walking across campus and found myself counting the number of steps it had taken me to get from our office to the campus bookstore. After realizing what I had unconsciously done, I purposely counted my steps on my return trip to check for accuracy and, to my surprise, I was off by four. I was perturbed. How could it have taken me four additional steps to get back? Was my gait off? Did I miscount? Did I veer slightly off my original path? What happened? Rather than go out again and recount (the temperature in Fresno was over 100 degrees that day), I just sat and wondered.

Why had I counted my steps? I did not leave the office intending to count, it just happened. I was counting for the sake of counting. I often find myself counting things for no reason, the number of white vehicles that I pass on the freeway, the number of trees on the street, the number of red lights I had to sit through, the number of people at bus stops, the number of items in my shopping cart. I literally count a lot of things for no real reason, which reminded me of a comment made by Dr. Les Steffe during his visit to the AIMS Center this past Fall, when he said, “Students need to be presented with many opportunities to count. Have them count anything and everything.”

Whether children are counting the number of other children in line, how many books in the library, the number of teddy bear counters at a center, or prepared counting collections (with a variety of materials), it’s important for us (the adults) to pay attention to how they are engaging in their counting. Here are three questions to ask yourself to guide your observations.

  • When counting by rote (verbal counting), are they simply learning the list of numbers, to ten or twenty? Does it sound like they are singing the ABC’s just with numbers? Is it an arbitrary list of numbers? Is it a sequential number word sequence?
  • When counting small collections are they able to subitize (recognize small sets of objects without counting)? If so are they moving from being a perceptual subitizer to a conceptual one? (can you link to my 2nd, 3rd, & 4th blogs:

The Only Way to do Great Work is to Love What You Do


Subitizing Part 3 – The Why and the How

  • When given objects to count, are students able to touch and count objects that have been organized in a row? Do they have one-to-one correspondence? Do they understand that the last number stated tells “how many” (cardinality)? Are they beginning to compare quantities (more than, less than)?

Reflecting on these questions can help adults think more deeply about children’s counting and can assist in providing appropriate counting experiences for your young child.

In closing, I want to share my favorite video clip of a young boy counting, as it serves as a great reminder that children should count anything and everything!

Preschooler Learning to Count with Real World Examples



AIMS Scholars Engineer Festively!

The AIMS Center for Math and Science Education, the working arm of the AIMS Education Foundation, has committed to helping teachers in the greater Central Valley of California pursue their Master’s degrees at Fresno Pacific University. To this end, funds have been set aside to scholarship teachers interested in earning one of the two MA… Continue Reading

What Will You Read?

Children ran from school buses with shrieks of excitement and expectations of what the next two and a half months might bring, the telltale sign that school is out for the summer in my town. Teachers have left their classrooms for a well-deserved break. Over the next two and half months they will imagine, think… Continue Reading

Partners in Education

We have talked a lot about partners in the work we are doing here at the AIMS Center. Typically, we refer to our Head Start or school partners, but today I would like to broaden that description. I was invited to join a statewide group known as the California Community of Practice around Mathematics, sponsored… Continue Reading

Miscellaneous Puzzles

Cups and Downs

Cups and Downs

This week’s Puzzle Corner activity is a magic trick with a mathematical, as well as a slight-of-hand, component. I first came across this trick in one of Martin Gardner’s many books on recreational mathematics. I liked it so much that I have been stumping students, friends, and family members with it ever since. In order to make… Continue Reading

Tower Trade

Tower Trade

Tower Trade is a paper adaptation to the traditionally wooden Towers of Hanoi puzzle. In the classic version, a wooden base supports three equally spaced dowels, usually aligned in a row, although the earliest version of this puzzle is reputed to have had the dowels arranged in an equilateral triangle. Six – this number varies —… Continue Reading

Total Count-Ability

Total Count-Ability

How many different answers can you find and justify for the nursery rhyme Going to St. Ives? As I was going to St. Ives I met a man with seven wives. Every wife had seven sacks, Every sack had seven cats, Every cat had seven kits. Kits, cats, sacks and wives, How many were going… Continue Reading

Ocean Anagrams

Ocean Anagrams

This week’s Puzzle Corner activity has an ocean theme. In it, students are presented with a number of anagrams. Anagrams are words or collections of words whose letters are rearranged to form new words or collections of words. For example, an anagram for canoe is ocean. Anagrams have a long history in the puzzle community. Lewis Carroll, who was really… Continue Reading

The Age Game

The Age Game

This puzzle features a series of computations involving, among other factors, the student’s own age and birth month. After the computations are completed, students are asked to find a pattern in their answers. This is best done in groups and is not difficult if no computational errors have been made. After students have discovered the… Continue Reading

How Many Squares?

In this week’s puzzle students are asked to find out how many squares are in the figure shown. This is not a difficult puzzle, but it does require some careful observation, organization, and counting. I encourage you to turn to the puzzle right now and give it a try before reading on. This will help… Continue Reading

Time Marches On

Time Marches On

This week’s Puzzle Corner activity is a simple problem with surprising results. The question posed in the puzzle is: “How many times during a day (24 hours) do the hour and minute hands of a clock point in the same direction?” The obvious answer seems to be 24, yet this is not correct. Students are… Continue Reading