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

# Toothpick Puzzles

### The Goalpost Puzzle

The Puzzle Corner activity this week is an adaptation of a classical matchstick puzzle from recreational mathematics. As has been noted before in this column, these puzzles date back to the nineteenth century when matches were first manufactured and began to proliferate. Most matchstick puzzles can be broken into two general categories: those that are geometric in… Continue Reading

### Arrow Arrangements

This particular puzzle comes from The Moscow Puzzles. The puzzle is found in the section entitled “Geometry with Matches,” which offers a selection of matchstick puzzles as “geometrical amusements that sharpen your mind.” Arrow Arrangements is one of the more difficult puzzles in this section, and requires students to understand and apply some basic geometric… Continue Reading

### Toothpick Puzzlers

This week’s activity consists of five related puzzles that should challenge students. Matchstick (I have substituted toothpicks) puzzles have been a staple feature of recreational mathematics for years. The puzzles presented here were adapted from some that appeared in The Moscow Puzzles by Boris Kordemsky (available from Dover Publications, Inc.) This type of puzzle often requires patience… Continue Reading

### The 36 ‘Picks Puzzle

This puzzle comes from a rich historical tradition that dates back to the 19th century when matches were first manufactured. Invented in 1827 by the British chemist John Walker, matches soon replaced the tinder boxes and flints that people had formerly used to light fires. As matches grew in popularity and became ubiquitous later in… Continue Reading

### The Three-to-Five Triangle Puzzle

This week’s Puzzle Corner activity comes out of a rich historical tradition that dates back to the 19th century when matches were first manufactured. Invented in 1827 by the British chemist John Walker, matches soon replaced the tinderboxes that people had formerly used to light fires. As matches grew in popularity and became ubiquitous later… Continue Reading

### Reducing Squares

Reducing Squares belongs to a category of puzzles called “matchstick puzzles” which were very popular in America during the last century. Most adults in those days carried small boxes of matches with them to light the many candles or lamps in their homes. Many of these same people had a favorite repertoire of matchstick puzzles… Continue Reading

### Flipping Fish

This puzzle has been around in various forms for a number of years. All forms begin with eight toothpicks or matches arranged in the shape of a fish. One version challenges you to move exactly three toothpicks to make the fish face the opposite direction. Another version challenges you to move just two toothpicks to… Continue Reading