NCTM Illuminations


	Reflections on Teaching are activities designed to encourage thinking and discussion about teaching and learning mathematics. Most of these Reflection activities are centered around video vignettes of teachers teaching math or students learning math.

Understanding a Child's Development of Number Sense

Developing students' understanding of numbers, ways of representing numbers, relationships among numbers, and number systems are focus areas for grades Pre K- 2. The three video clips shown illustrate the possible range in students' understanding of numbers and their relationships during this grade band.

Gathering Evidence About Students' Understanding of Volume

There are many options available to teachers for assessing mathematics learning. Teachers can learn a great deal about their students' level of conceptual understanding and reasoning skills by monitoring small group and whole class discussions. This video example focuses on assessing students' knowledge as an ongoing part of instruction.

Teaching, Learning, and Communicating About Fractions

Learning about fractions is an important mathematical goal in grades 3-5. The teacher plays an important role in facilitating and fostering communication so that powerful mathematical understanding is developed. This video example focuses on one teacher's use of questioning in a fifth grade mathematics class.

Gathering Evidence About Students' Understanding of Volume

Learning about Area, Perimeter, and Fractions with and from Peers

When students work in small groups, they are given the opportunity to communicate with their peers about mathematics. The video clips and supporting questions in this Reflection activity support teachers as they reflect on mathematical understanding as students learn with and from peers.

Facilitating Communication about Measurement, Exponents, and Scientific Notation

Students need opportunities to communicate through reading, writing, listening, and speaking in mathematics classrooms. Multiple methods of communication can be used to help students reflect on their own ideas and the ideas of others. The video clips included in this example illustrate different methods and purposes of communication.