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

http://www.aimsedu.org/2016/11/28/subitizing-part-2/

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

### Episode 41 | The Stories of AIMS – Beverly Ford

Beverly Ford, updates us on the progress she and the other members of her team are observing in their work within a particular school setting. She tells a few stories related to how her students are demonstrating various stages of learning. Bev expands on some of the things her partner, David Pearce, discussed in last… Continue Reading

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

### If I Could Turn Back Time

As we come to the end of another school year, our team here at the AIMS Center has been spending time reflecting on the past year of learning from students. We were asked the question, “If you could go back into the classroom, what would you do differently in regards to your math instruction?” I… Continue Reading

### Math Super Heroes – A Reflection on Early Mathematics

I have just concluded my second year at the AIMS Center for Math and Science Education in which our Center’s main focus is to learn how young children come to know math.  Through our partnership with two Head Start early learning programs, the four AIMS early math research associates observed two sites that housed 10… 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

### Episode 40 | The Stories of AIMS – David Pearce

David Pearce, presently a member of our Coordinating Units team spent that last year working with the K-1 students. He relates to us a few instances where he saw the work of Steffe and others come to life, and how it is changing his perspective on children’s mathematics. Continue Reading

### As The Craze Turns, My Two Cents Worth

Fidget spinners have suddenly become one of the hottest topics in education right now. They are the current craze with students all over the United States. Touted as a low-tech toy, they are perceived as being either helpful or harmful, depending who you ask. Countless articles, blogs, podcasts, interviews, etc. can be found each day… Continue Reading

### Small Misunderstanding, Big Difference in Meaning

After one month as a missionary in Argentina I was ready to raise the dead. Or at least that is what the woman at the door must have thought. Let me explain. As we were proselyting door to door, it was my turn to talk to whoever answered the door. A woman happened to answer… Continue Reading

# Divergent Thinking Puzzles

### A Touchy Situation

I am indebted to Robert Benjamin, a scientist from the Los Alamos National Laboratory, for A Touchy Situation. Bob first did this activity with his son when his son was in kindergarten. Therefore, he feels that the activity is appropriate for students at all grade levels. He also notes that the activity works best if students use… Continue Reading

### Relative Reckonings

This week’s Puzzle Corner activity comes from the field of recreational mathematics where people do math just for the fun of it. One of the areas of recreational mathematics is logic. Logic puzzles are usually challenging and are normally resistant to quick and easy solutions.The puzzle presented here, Relative Reckonings, is no exception. This puzzle… Continue Reading

### Shrinking Square Challenge

This week’s Puzzle Corner activity is a seemingly simple one that may prove more difficult than one might expect. In it, students place four pennies on the corners of the square pictured. They are then challenged to move only two of the coins to create a new square that is smaller than the original. Most students will need to… Continue Reading

### Puzzling Over Prices

The Puzzle Corner activity this week is a thought puzzle that presents an interesting paradox. Solving it will require some divergent thinking on the part of your students. Puzzles like this one appeal to some people, but frustrate others. It is my hope that when students solve this puzzle, or see how it is solved by others,… Continue Reading

### It’s a Snap!

This week’s Puzzle Corner activity is an adaptation of a classic puzzle from recreational mathematics. It is traditionally posed as a thought problem to be worked out in your head; as such, it is moderately difficult. However, I have found that many elementary school children can solve this puzzle -if they have manipulatives to make it concrete.… Continue Reading

### Locating Legs

This week’s Puzzle Corner activity has a holiday theme. In it, students are presented with a paradoxical scenario and asked to try to make sense of it. In this scenario a child is hiding under a table at her parent’s holiday party. Looking out, she can count 20 legs and thus knows there are 10 adults in… Continue Reading

### Family Ties

This weeks’s Puzzle Corner activity is a collection of three riddles all dealing with the relationships between relatives. The first one is thought to be many hundreds of years old and is one of the best known brainteasers of all time. I have chosen to leave it in its original form, even though the style of English… Continue Reading

### Alternate Arrangements

Six drinking glasses are arranged in a row. The first three are filled with water; the next three are empty. Is it possible to get the full and empty glasses to alternate by moving only one glass? This classic brain teaser has been making the rounds in recreational mathematics circles for years and is the… Continue Reading

### The Relative Riddle

This week’s Puzzle Corner is a classic riddle requiring reasoning to reconcile. (Please forgive the crude alliteration.) While many of you have encountered this riddle before and already know the answer, the riddle probably caused curious consternation (I beg your pardon once more) the first time you saw it. Riddles like the one presented here… Continue Reading

### Alphabetical Puzzlers

This week’s Puzzle Corner is a collection of puzzles dealing with letters of the alphabet. While they are not necessarily mathematical in nature (although one could argue this point), these puzzles have a place in a well-rounded mathematics curriculum. Alphabetical Puzzlers is a collection of four puzzles that use letters of the alphabet in a… Continue Reading