# 3-5

### Taking Apart and Putting Together Cubes

In earlier posts I’ve mentioned Friedrich Froebel and his geometric gifts. The third of his geometric gifts was a box containing eight cubes. Instead of the students simply opening the lid and dumping the cubes on the table, he would have the students place the box with the lid down on the table, slide the… Continue Reading

### One Object Three Shapes: The Solution

In an earlier post, One Object Three Shapes, we posed the problem of finding an object that would appear to be a triangle when viewed in one way, a square when viewed in another way, and a circle when viewed in yet a third way. The challenge was to create an object that would fit… Continue Reading

### One Object Three Shapes: Circle Square Triangle

Front and back, top and bottom, and left and right are ideas that we use to describe objects in our three-dimensional world. Young children learn these positional words in Kindergarten. In fact, learning the meaning of these words is one of the Common Core Kindergarten geometry standards. In reality these are big ideas that are… Continue Reading

### Month, Day, Year: A Number Sequence

Daily journaling is one of the constants in my life. Over many years, I don’t believe there has been a single day when I did not make at least half a dozen entries in my journal. Each entry is dated, so on any given day I will write the date at least half a dozen… Continue Reading

### Do Algorithms Sometimes Get In The Way Of Mathematical Thinking?

As a professor of mathematics education at Fresno Pacific University, I often have the opportunity to work with K-6 teachers in their schools. One such visit sticks out in my mind. A lesson study team comprised of myself, another university math educator, a district math specialist, and four fourth grade teachers had planned a lesson… Continue Reading

### Moving Beyond the Answer

As a student, I received good grades and loved following all the procedures. As a teacher and coach, I wanted all students to be successful: the students needed to be able to understand, not just follow the procedures. There are only a small percentage of us that only follow rules and are successful. I have… Continue Reading

### Frank Lloyd Wright, Froebel Geometric Gifts, and Hands-On Learning

This post is a continuation of the story of Froebel’s geometric gifts that was introduced in my previous post. I ended with a promise to tell a story about the famous architect, Frank Lloyd Wright. In 1876, when Wright was eight or nine years old, his mother attended the Philadelphia Centennial Exposition. Wright describes in… Continue Reading

### Dimension, On the Shoulders of Giants

I’ve spent forty years teaching mathematics to undergraduate and graduate students in mathematics education. Through all these years, it was geometry that I most enjoyed teaching. I still have a passion for geometry, and it is this passion and some of the things I’ve learned and continue to learn that I hope to share in… Continue Reading