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

Dissection Puzzles

The Infinite I

The Infinite I

This week the Puzzle Corner presents an open-ended, spatial-visualization activity that should both challenge and delight your students. The Infinite I is one of those delicious “put-together” puzzles that uses only a few pieces to form hundreds of interesting shapes. In this respect, it is similar to the popular tangram puzzle. Ironically, The Infinite I is a modification of… Continue Reading

Hatching the Egg

Hatching the Egg

This week’s Puzzle Corner activity challenges students to rearrange the nine pieces of a paper egg to produce a number of different shapes resembling birds. Doing this will exercise students’ spatial visualization abilities while building their problem-problem solving persistence. Hatching the Egg is patterned after the “Magic Egg” puzzle that appears in the Pieter van… Continue Reading

Penny Penning Puzzle

Penny Penning Puzzle

This week’s puzzle is a good one to use early in the school year. It is fairly easy and shouldn’t frustrate students too much in their early exposure to the puzzle-solving process. To do this puzzle, students need only the student sheet depicting the nine-penny arrays and a pencil. The puzzle challenges students to draw… Continue Reading

The Five-Piece Puzzle

The Five-Piece Puzzle

This week’s Puzzle Corner activity in one member of a family of challenging, multiple-solution, dissection puzzles. These puzzles are geometric in nature and many, like the one presented here, are modeled after tangrams, the best-known of the dissection puzzles. Like tangrams, students can put the five pieces of this puzzle together into a number of… Continue Reading

Shape Makers

Shape Makers

Shape Makers is one of a large family of dissection puzzles which challenge students to assemble a series of smaller shapes to form larger ones. Tangrams, which gained popularity in the early 1900s, are perhaps the most common kind of dissection puzzle. In Shape Makers, four squares and eight triangles must be reassembled to create… Continue Reading

Arranging Rectangles

My thanks to Richard Thiessen for this week’s puzzle. It consists of six pieces that can be put together to make rectangular regions (the regions can be solid or have openings in their interiors). Please download the Vee Diagram: A Guide to Problem Solving article, for ideas about how to use this puzzle with your… Continue Reading