Central Bucks Schools Teaching Authentic Mathematics in the 21st Century

There is considerable student-student interaction. The interaction is sustained so that it promotes coherent and shared understanding. Disagreement and debate are encouraged, and students respectfully respond directly to others' ideas using academic language. For written work, students demonstrate an elaborated, coherent account that draws conclusions or makes generalizations and supports them with examples, summaries, illustrations, details, or reasons. Almost all students are clearly engaged.

The majority of students are engaged in extended discussion with each other. In writing, students consider alternative perspectives, solutions, or strategies.

Lectures and other forms of didactic instruction, or drill and practice, dominate the lesson, but some students engage in substantive communication (written or oral) for a part of the lesson. Conversation entails at least three interchanges (a statement by one person and a response by another). Responses do not build upon ideas expressed by others. Written work entails explanations or arguments such that students construct some new knowledge rather than recall or report information.

Student responses, if any, are fill-in-the-blank or short answer. Responses are low level recall or reporting. Lectures score a "1" on substantive conversation.

These activities enable students to recognize the connection between classroom knowledge and situations outside the classroom, as they explore these connections in ways that create personal meaning and significance. The teacher creates instructional experiences that enable students to become involved in efforts to affect or influence a larger audience beyond their classroom. These instructional strategies enable students to communicate knowledge to others (including within the school), advocating solutions to social problems, providing assistance to people, or creating performances or products with utilitarian or aesthetic value.

These instructional experiences enable students to study or work on a topic, problem, or issue that they clearly see as connected to their personal experiences or actual contemporary public situations. They explore these connections in ways that create personal meaning and significance for the knowledge. There is no effort to influence a larger audience.

As a result, students recognize some connection between classroom knowledge and personal experiences or situations outside the classroom, but they do not explore the implications of these connections. The teacher may inform students of potential value of the subject matter but for the students, connections are superficial, abstract, or hypothetical.

As a result, there are no justifications for learning the lesson's material, or the subject matter is deemed important for success only in school (now or later). Student work has no impact on others and serves only to certify their level of competence or compliance with the requirements of formal schooling.

As a result, the class is characterized by high expectations, challenging work, strong effort, mutual respect, and assistance in achievement for all students. Teachers AND students communicate the expectation that all members of the class should try hard and can learn important knowledge and skills. Struggling students are clearly accepted and assisted in their learning. The class is a "community of learners."

As a result, comments and behaviors by the teacher and many students encourage effort and value risk-taking by all students. A climate of mutual respect contributes to achievement for most students. The teacher attempts to support struggling students using a variety of methods.

Evidence may be mainly in the form of verbal approval from the teacher for student effort and work. However, such support tends to be given to those who are most engaged in the lesson but not to those who are reluctant participants or less articulate or skilled in the subject.

Social support is mixed or negative. While some positive actions may be evident, the overall classroom climate is not mutually supportive for students. Teacher or student behavior, comments, and actions tend to discourage effort, participation, and taking risks to learn.

As a result, the class is characterized by high levels (almost all students, almost all of the time, successfully) of the following: self-direction, initiative, and autonomy by students (individually or in groups); students critical reflection and review of their own and others' work; collaborative work on a complex project; understanding, valuing, and acceptance of traditions, beliefs, knowledge, language, and practices of diverse social groups; effective use of current technologies to enhance learning, communication, and real-world connections.

As a result, the class incorporates some of the following for most students to successful levels: self-direction, initiative, and autonomy by students (individually or in groups); students critical reflection and review of their own and others' work; collaborative work on a complex project; understanding, valuing, and acceptance of traditions, beliefs, knowledge, language, and practices of diverse social groups; use of current technologies to enhance learning, communication, and real-world connections.

As a result, students are provided few opportunities to do any of the following and students show only minimal competence: self-direction, initiative, and autonomy by students (individually or in groups); students critical reflection and review of their own and others' work; collaborative work on a complex project; understanding, valuing, and acceptance of traditions, beliefs, knowledge, language, and practices of diverse social groups; use of current technologies to enhance learning, communication, and real-world connections.

As a result, students have no, or only minimal, opportunities to develop 21st century skills and to use technology to enhance learning. Learning activities are not collaborative, diversity is not recognized or valued, and technology is not used effectively to evoke higher level thinking.