On the campus of

Building Understanding in Mathematics

Mexico House BuildingThis week I’m writing from Mexico. Every year, my church travels down to build houses for families in need. We work with local churches to supply building materials and manpower to build simple homes. The work could not occur without the help of local pastors, who help by identifying the families and local contacts we will be assisting. While engaged in this service, we often come to bond with those we help and work with in many ways. We also learn to be humble in our service. Even though we have some financial resources, we lack many other important pieces we need to complete the work. I think it is the same in any act of service. We serve better when we realize our limitations and are open to the wisdom of others to complement what we bring.

At the AIMS Center, I have been able to work with and learn from researchers who have knowledge of how students come to know math that I had not previously known. I have come to work with colleagues from the Center and in the field to make that research come alive and look for ways to use it to influence how I work with teachers to one day serve their classrooms.

An idea that has come from this work at the Center is to be willing to adjust what I believe is true about what a child knows and how to serve that child. For example, bridging the gap between manipulatives and the numeral. I have seen how what I thought would help is sometimes not sufficient. Another perspective that helped me was the idea that a student needs to depend on imagining the counters, how that looks in a small group setting, and how to engage students in tasks that might promote that thinking have also been enriched with research and collaboration.

Being open and willing to learn has helped to complete the homes we have built in Mexico and also informs the way we help students build new mathematical understanding.


Oh, The Places You’ll Go!

You have brains in your head. You have feet in your shoes. You can steer yourself any direction you choose. ― Dr. Seuss, Oh, The Places You’ll Go Every June, across the nation, thousands of people celebrate as relatives and friends graduate from high school. In July, parents start shopping for XL twin sheets, desk… Continue Reading

Yosemite Learning

My first visit to Yosemite National Park happened last weekend. I was absolutely wowed by the park as I marveled at the landscapes. Somewhat surprisingly, I also came away professionally inspired and energized. As I thought about the history of Yosemite, and the awesome natural environment I was in, I found myself making comparisons. I… Continue Reading


In the Common Core State Standards for Math, counting-on is considered “a strategy for finding the number of objects in a group without having to count every member of the group.” Counting-on is an efficient way to add and we want children to count-on. Yet, many young children begin by counting-all. For example: Teacher [placing… Continue Reading

Idea Generators

I just returned from two weeks of study at Michigan State University as part of my PhD program in Education. My study related to qualitative research purposes and methodologies. I gained experience in writing field notes, conducting interviews, collecting data, and describing and analyzing observations. Although much of this work requires taking notes, this is… Continue Reading

What Part Does Technology have to Play in the Future of Education? (Part I)

The major theme of the Jean Piaget Society annual conference in June was Technology and Human Development. Since attending the conference, I have been part of several fascinating discussions that I would like to explore concerning the future advance of technology within education. In his book Singularity, Ray Kurtzweil talks about how human beings are… Continue Reading

New Adventure

In my role as a Research Associate here at the AIMS Center, I have been asked many times how I would have changed my instruction in the classroom if I knew then what I know now. This is a question that I have asked myself as well. After teaching for over 11 years I know… 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