NCTM Illuminations

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 in pre-kindergarten through grade 2. The three video clips shown illustrate the possible range in students’ understanding of numbers and number relationships during this grade band.

Gathering Evidence about Students’ Understanding of Volume

Teachers have many options for assessing mathematics learning. They 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. Students also need to be able to explain and communicate their thinking. These video segments illustrate a fraction activity as well as teacher/student dialogue in a fifth-grade mathematics class. They demonstrate the important role a teacher can play in facilitating and fostering communication so that students develop powerful mathematical understanding.

Interactive Geometry Dictionary: Areas in Geometry

Area is one of the most fundamental measurements in geometry. These JavaSketchpad applets can help you to understand and investigate how to find the area of the rectangle, parallelogram, and triangle.

	Gathering Evidence about Students’ Understanding of Volume Teachers have many options for assessing mathematics learning. They 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.
	Learning about Area, Perimeter, and Fractions with and from Peers Small groups provide a forum for students to communicate with their peers about mathematics. This Reflection activity’s video clips and accompanying questions help teachers consider students’ mathematical understanding as they learn with and from peers.
	Interactive Geometry Dictionary: Areas in Geometry Area is one of the most fundamental measurements in geometry. These JavaSketchpad applets can help you to understand and investigate how to find the area of the rectangle, parallelogram, and triangle.
	Determining the Impact of Applet-Based Instructional Materials on Teacher Knowledge of Content and Pedagogy, Instructional Planning, and Student Learning of Fractions - Report of Preliminary Research Findings (PDF file) This paper describes the preliminary findings of the first phase of a two-part study on the impact of NCTM E-Standards and Illuminations applets and support materials on teacher knowledge of mathematics content and pedagogy, instructional planning, and students’ learning of fractions. (Download Word document or PDF file.)

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.

Interactive Geometry Dictionary: Lines in Geometry

Lines, segments, and rays are among the most fundamental objects in geometry. These nine JavaSketchpad applets can help you to understand and investigate some of the many different lines that come up in geometry. Each line is defined and its important properties are illustrated with interactive applets.

Especially for Teachers. Put the Heart into Science and Mathematics Learning: Measuring Flow Rates Using Thermodilution

Michigan State University College of Natural Science Magazine
Fall 2001 (View images of the article below.)

	Improving Students’ Spatial Visualization Skills and Teachers’ Pedagogical Content Knowledge by using On-Line Curriculum-Embedded Applets: Overview of a Research and Development Project (PDF file) This paper outlines ongoing efforts to develop and evaluate curriculum-embedded applets for isometric drawings to develop students’ spatial visualization skills. (Download Word document or PDF file.)
	*Illuminating NCTM's Principles and Standards for School Mathematics* (PDF file)** School Science and Mathematics. Vol. 101, no. 6, (Oct 2001), pp. 292-304. (Download Word document or PDF file.)
	The NCTM Illuminations Web site Project: Changing the Vision of School Mathematics (PDF file) Paper presented at: ED-MEDIA 2001 World Conference on Educational Multimedia, Hypermedia, and Telecommunications, Tampere, Finland, June 2001 (Download Word document or PDF file.)
	What's the Big Idea We all want our students to acquire a deep understanding of big mathematical ideas. These big ideas grow over time and throughout the curriculum. On this hyper-linked page you will find Illuminations activities at different grade levels related to a variety of big mathematical ideas.