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1、ALTERNATIVE MODES FOR TEACHING SCHOOL MATHEMATICS: A SYNOPSIS_HOWARD A. PEELLEUniversity of Massachusetts, Amherst, MA 01003hapeelleeduc.umass.eduA variety of modes are profferred as alternatives for teaching mathematics in schools. Each mode is described briefly, along with general purposes, advant
2、ages and disadvantages. Combinations of modes are suggested, general issues identified, recommendations offered, and feedback from teachers summarized.IntroductionMathematics teacher educators can provide prospective and in-service teachers with a repertoire of teaching modes to help them develop st
3、udents mathematical abilities. (Here, the term mode refers to a way of structuring students learning environment for teaching purposes and is used to distinguish modes of teaching from methods of doing mathematics and strategies for problem solving.) While the National Council of Teachers of Mathema
4、tics principles and standards acknowledge that there is no one right way to teach, its vision does not specify alternatives to traditional instruction other than teaching students alone or in groups 1. This paper outlines various modes for teaching mathematics, listed in increasing order of student
5、group size and roughly from student-centered to teacher-centered: EXPLORATIONPAIRED COACHING INDIVIDUAL THINK ALOUDBRAINSTORMINGPROBLEM POSINGINTERVIEWFAMILYINCUBATIONGAMINGLARGE GROUPCOMPUTERSMALL GROUPSPRESENTATION General PurposesCommon to all these modes are a dozen general purposes, seen from t
6、he teachers perspective and linked to NCTMs principles and process standards 1:(1) Practical Purpose: To teach mathematics in a suitable setting within constraints of time, space, and resources. T Note: All modes are intended primarily for use in the classroom unless indicated otherwise.(2) Technolo
7、gical Purpose: To use appropriate technology for enhancing teaching and learning. K(3) Pedagogical Purpose: To engage students in actively studying the curriculum. T,C(4) Problem-Solving Purpose: To motivate students to apply their skills and knowledge to solving mathematical problems. PS(5) Cogniti
8、ve Purposes: To stimulate students to think about mathematics; to instill careful reasoning; and to help them understand relevant concepts and methods. RP(6) Affective Purposes: To build students positive attitude toward mathematics; to reduce math anxiety; and to nurture the joy of problem solving.
9、 (7) Interactive Purpose: To encourage students to communicate in mathematical terms.CM(8) Learning Purposes: To engage students in active learning; and to develop their skills and knowledge. L(9) Metacognitive Purpose: To develop students ability to monitor, control, and reflect on their cognitive
10、processes. L,A(10) Cultural Purposes: To respect students individual differences, heritage, values, and beliefs about mathematics; to include social, economic, and historical perspectives; and to promote equity in math education. CN,E (11) Assessment Purposes: To record students efforts; to assess t
11、heir progress; and to uphold school, state, and national standards. RN,A Note: All modes require individual student reports.(12) Real-world Purposes: To develop students appreciation for life skills involved in mathematics education; and to acknowledge relevant application areas and career opportuni
12、ties. CNNCTM Principles:NCTM Process Standards:E = EquityPS = Problem SolvingC = CurriculumRP = Reasoning and ProofT = TeachingCM = CommunicationL = LearningCN = ConnectionsA = AssessmentRN = RepresentationK = TechnologyModesIn order to help teachers choose a particular mode, each mode is described
13、below in a synopsis, along with salient advantages and disadvantages (using the same numbering as for the purposes above). Full descriptions of all modes, including recommended grade/level, time frame, special purposes and detailed operational guidelines for students and teacher, are given in 2.EXPL
14、ORATION MODESynopsis: Each student selects a mathematical topic or problem or puzzle to explore, discovers as much as possible about it, and prepares a map of what s/he finds. (This map is a guide to its important features.) Students share their maps with each other and then with the teacher, who co
15、nfirms what actually needs to be learned.Note: This may also be called Investigation or Discovery mode and can be structured with specific activities for students to follow in stages.Advantages and Disadvantages: (1) Students may work in their own chosen space - library, computer lab, or home. Yet its easy to lose focus and to lose track of time. (2) Students can seek related information using browsers and search engines via Internet, a virtually unlimited resource. Yet they may
