Author Archives: Aileen Rizo
Defined as “a strong desire to know or learn something,” curiosity seems to be an important component of constructing new knowledge and, when joined with play, can create powerful learning experiences. Among the early math team, we are finding that it is often the simplest of materials that can elicit both of these characteristics. The Tubes and Cubes game, for example, has become a favorite of the children at the preschool site where we are working. This year we have the goal of working with all the teachers in all the classrooms, different from last year when we only worked with a select few children from each class. The growth in our outreach and the combined influx of new students makes Tubes and Cubes a relatively new experience for most of the children. We usually start by bringing out the tubes with a height of five or less cubes and placing a set of six cubes beside each one. Without needing instructions, the students usually start by picking up a tube, looking inside of it, and then start filling it up with blocks. Some notice the sleeve and make statements like, “Look, there are ten dots!” Or “I see fingers on here.” For each of these moments we help classroom teachers see the opportunity for a follow-up question. We ask, “How do you know there are ten?” Or “How many fingers do you see?” Students light up with purpose as they began counting on their own and find new ways of building and counting.
In the photo above you will see one student who has filled tubes that she is arranging by height. When she was finished she then aligned the tubes so she could see the dots on each sleeve and counted all the dots as one composite. She then lifted the tubes off revealing the towers of blocks and began to count how many blocks were in each tower.
In the second photo you will notice a student who has stacked the tubes. As she ventured to build up, she noticed that if the sleeve is pulled down it could form a connector, making the tower of tubes more stable. She began filling the tube with blocks as she counted, but then had trouble reaching for her blocks while she held the newly formed longer tube. She decided to move closer to the wall so she could lean the tube against it for more stability.
In the final photos below you will notice an interesting construction. The day before this occurred, one student seemed to noticed that if the tube was at an appropriate slope, the cube would slide out. He tried to make a way for the tube to be consistently positioned at this slant but did not have enough time to finish. The next time we were in the classroom he came over to the table and started building a wall. He first tried to stack the tube on the wall and noticed that the wall needed some reinforcing. He then doubled the wall construction but ran into another problem. The tube would slide off the wall when placed against it, so he decided to remove some of the cubes from the center and place the tube inside. This helped with the problem but did not solve it adequately because the tube kept sliding off. In noticing the playdough station at the adjacent table, I suggested to him, “What about a piece from there?” He seemed read my mind. He got a small amount of playdough and placed it directly under the portion of the tube that touched the table. He looked up and gave me a smile when it seemed to work. But that did not compare to the smile he gave me when he slid the first cube through his new creation.
Every day there is a dual learning experience. We learn from the students while seeing them exhibit curiosity in a playful way. We also strive to communicate to the teachers the potential of timely math questions and how moments like these can and should be more common for all children.
As my other colleagues have mentioned, it was a privilege to present to over 300 preschool teachers last month. Even though we each prepared our individual sessions, it was truly a collaborative effort. My specific presentation was on the topic of mathematical play, but I was also encouraged to share a portion of my own… Continue Reading
As I watched my children play at the park one day this summer, my attention quickly focused on a small voice saying, “one, two, three, four, five…” I looked over and observed a game of hide-and-seek in progress. Even my youngest is self-motivated to recite the number sequence more accurately when she is playing. This,… Continue Reading
My youngest daughter is 2 ½ years old and she has yet to discover just how much her mother loves mathematics. The other day, as she worked on a puzzle of shapes, she held up one of the shapes and said, “diamond.” I wrinkled my nose as I corrected her with the correct term, “rhombus.”… Continue Reading
In my learning of constructivism and the theories of Piaget, I often think of this quote: “No one but you can make your associations, and no one but you can isolate your sound-image and whatever you conceptualize in your experiential field.” (Von Glaserfield, 1995) This quote is from a chapter on language and meaning, but… Continue Reading
What is your math story? What comes to your mind when someone says the word math? Unfortunately in our society, math is unpopular. In fact, if you look at the amount of likes and retweets of the screen capture here, it would seem that the feelings shared are mutual to many. When I was a… Continue Reading
As the early math team moves forward on the work we are doing, the concept of practicality is an issue we are addressing. One-on-one interviews with the children have taught us a wealth of information about young children’s mathematics, but it is not a realistic structure that early childhood teachers have time to do in… Continue Reading
Did you know that the number thirteen is a frequently skipped number in a young child’s early number sequence? According to Karen Fuson’s research in “Children’s Counting and Concepts of Number,” the numbers 13, 14 and 15 are the most consistently omitted numbers. As we work with children at our partner school sites, we are… Continue Reading
Here at the AIMS Center, a central focus of our attention is the mathematical thinking of children. It should not be surprising that children do not think like adults. While as adults we agree in theory, our actions consistently seem to contradict this truth. The habitual act of laying our own mathematical thinking onto children… Continue Reading
Earlier this month my colleagues and I had the privilege of attending the National Association for the Education of Young Children Conference in Los Angeles. Professional learning is a wonderful opportunity where one can validate ideas, gain new insights, and network with others in the field. This was my first attendance at a preschool level… Continue Reading