Answer1

=Characteristics of Significant Mathematical Tasks =
 * present realistic mathematics
 * open-ended
 * have multiple entry points
 * activate existing/prior knowledge
 * contain true mathematical rigor
 * address core/generative/enduring mathematical topics/concepts
 * address multiple standards (national and/or state)
 * align to national standards, //Curriculum Focal Points//, //Focus in High School Mathematics//, and //Guiding Principles for Mathematics Curriculum and Assessment//
 * are brief
 * are a means to an end, not an end in and of itself
 * are appropriate for the class's level of ability and interests
 * draw on motives actually present in the learner

The **National Council of Teachers of Mathematics** (NCTM) has defined worthwhile mathematical tasks as those that: (Source: NCTM, //Professional Standards for Teaching Mathematics//, 1991, p. 25)
 * Are based on sound and significant mathematics
 * <span style="font-family: Verdana, Geneva, sans-serif;">Use knowledge of students' understandings, interests, and experiences
 * <span style="font-family: Verdana, Geneva, sans-serif;">Develop students' mathematical understandings and skills
 * <span style="font-family: Verdana, Geneva, sans-serif;">Stimulate students to make connections and develop a coherent framework for mathematical ideas
 * <span style="font-family: Verdana, Geneva, sans-serif;">Promote communication about mathematics
 * <span style="font-family: Verdana, Geneva, sans-serif;">Promote the development of all students' dispositions to do mathematics.

NCTM released, //Guiding Principles for Mathematics Curriculum and Assessment// on June 1, 2009. This document has been released to help guide current and future efforts to develop pre-K-12 mathematics curricula and corresponding assessments. The following link will provide the full text document: [|Guiding Principles for Mathematics Curriculum and Assessment.pdf]

The teacher of mathematics should pose tasks that are based on- and that (Source: National Council of Teachers of Mathematics. (1991). //Professional standards for teaching mathematics//, pp. 25, 35, 45, 52, 57, 63. Reston, VA: NCTM.)
 * [|Worthwhile Mathematical Tasks.pdf]**
 * sound and significant mathematics;
 * knowledge of students' understandings, interests, and experiences;
 * knowledge of the range of ways that diverse students learn mathematics;
 * engage students' intellect;
 * develop students' mathematical understandings and skills;
 * stimulate students to make connections and develop a coherent framework for mathematical ideas;
 * call for problem formulation, problem solving, and mathematical reasoning;
 * promote communication about mathematics;
 * represent mathematics as an ongoing human activity;
 * display sensitivity to, and draw on, students' diverse background experiences and dispositions;
 * promote the development of all students' dispositions to do mathematics.

Summary and Dimensions of Core Features of //**Mathematics Classrooms that Promote Understanding**// (Hiebert et al., 1997) Nature of Classroom Tasks


 * Make mathematics problematic
 * Connect with where students are
 * Leave behind something of mathematical value