Inside a kindergarten classroom with Augustana students

## Shaping Understanding

So far our teacher has asked us to individually pull out one student at a time and work on certain skills that she has identified they have been struggling with. One of the skills that many students “need”, or as we have discovered “needed”, more practice with is identifying shapes. Many students, who have been targeted for not being able to identify their shapes, have proven to us that they certainly can. Since the records of the students are a bit outdated, we have decided to create a progressive chart of the student’s accomplishments and misunderstandings. We understanding that for a teacher in charge of 20+ students at once it can be very difficult to remember or record, no matter how organized one is, every benchmark the students reach when their understandings are so rapidly changing. We are certain that this progressive chart will help us and our cooperating teacher understand where the students are in their understandings and what categories of the students’ number sense needs to be addressed the most frequently.

One of the most impressive findings I came across when working with one of the students, which will definitely need to be noted on our new chart, was his ability to explain essential qualities of shapes, specifically with rectangles and squares. While working with a helpful shape book, where the student is shown a shape and has to verbally identify the shape by stating the name and then match a magnetic shape to each page, the only shape the student was unable to name was a rectangle. After guessing it was a triangle, a shape he clearly knew from previous assessments, I told him it was not a triangle and asked him, “Why is this shape not a triangle?”. I assumed I would get an answer of, “Because that is a triangle.”, as the student would point to the previous triangle page. However, this student went into great detail of the certain properties of the rectangle shape that made it different from all other shapes. He explained that it is similar to a square in that it has the same number of sides, except it [a rectangle] is like a stretched out square. He then added that the top and bottom sides were longer and the other sides were shorter. I then asked him why a square could not be a rectangle. He quickly replied that all of the sides of a square are the same [length] (he had troubles coming up with a word for distance or measurement, as would be expected).

At first, this student seemed to show a lack of ability in identifying a rectangle. However, he was able to demonstrate his understanding of what the shape was by using its properties, which concluded that this student was only unable to remember the name for that shape. Unlike most of his classmates, this student is much closer to the “analysis” level of van Hiele’s Geometric Thought diagram. This student furthered his demonstration of his level of understanding by drawing me multiple rectangles on a white board to show me how many different types of rectangles there can be. This student has mastered the “visualization” level and is ready to be challenged in his understanding of shapes.

As we work with students, we need to adjust our instructions to the small hints each individual student may demonstrate that can help us make sense of where the students are currently with their understandings. It is important to know why students think the way they do and for teachers to learn from their student’s development of their understandings or misunderstandings.

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