Multiple Strategies: Product of Reasoning and Communication

1993 ◽  
Vol 40 (7) ◽  
pp. 380-386
Author(s):  
Alice J. Gill
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Communication Skills ◽  
Business Community ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Multiple Strategies ◽  
Multiple Strategy

The NCTM's Curriculum and Evaluation Standards (1989) supports the idea that problems can be solved in more than one correct way. This multiple-strategy approach contains the seeds of motivation, success, and mind stretching. The curriculum standards that focus on reasoning and communication skills are integral to delivering mathematics education that generates the cre ative, problem-solving, divergent thinker that the business community would like to employ.

NCTM's Standards in Japanese Elementary Schools

1997 ◽  
Vol 4 (1) ◽  
pp. 20-23
Author(s):  
Daiyo Sawada
Keyword(s):  
Elementary Schools ◽  
Mathematics Education ◽  
Problem Solving ◽  
Mathematics Teaching ◽  
Observational Studies ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Standards Documents

In recent years, the NCTM's Standards (1989, 1991) and Asian mathematics education (Becker et al. 1990; Stevenson and Stigler 1992; Stedman 1994; and many others) have, each in its own right, received a great deal of attention. I believe, however, that to look at the connections between the two areas would greatly benefit teaching. In this article, five classroom situations taken from observational studies of mathematics teaching in Japanese elementary schools are described and interpreted from the perspective of the two Standards documents (1989, 1991). More specifically, the classroom situations are examined from the perspective ot the first four standards found in the Curriculum anil Evaluation Standards (1989): Mathematics as Problem Solving. Mathematics as Communication. Mathematics as Reasoning, and Mathematical Connections.

scholarly journals Exploring Multiple Strategic Problem Solving Behaviors in Educational Psychology Research by Using Mixture Cognitive Diagnosis Model

2021 ◽  
Vol 12 ◽  
Author(s):  
Jiwei Zhang ◽  
Jing Lu ◽  
Jing Yang ◽  
Zhaoyuan Zhang ◽  
Shanshan Sun
Keyword(s):  
Problem Solving ◽  
Diagnostic Testing ◽  
Cognitive Diagnosis ◽  
Mcmc Algorithm ◽  
Multiple Strategies ◽  
Dina Model ◽  
Single Strategy ◽  
Diagnosis Model ◽  
Multiple Strategy ◽  
Cognitive Diagnosis Model

A mixture cognitive diagnosis model (CDM), which is called mixture multiple strategy-Deterministic, Inputs, Noisy “and” Gate (MMS-DINA) model, is proposed to investigate individual differences in the selection of response categories in multiple-strategy items. The MMS-DINA model system is an effective psychometric and statistical approach consisting of multiple strategies for practical skills diagnostic testing, which not only allows for multiple strategies of problem solving, but also allows for different strategies to be associated with different levels of difficulty. A Markov chain Monte Carlo (MCMC) algorithm for parameter estimation is given to estimate model, and four simulation studies are presented to evaluate the performance of the MCMC algorithm. Based on the available MCMC outputs, two Bayesian model selection criteria are computed for guiding the choice of the single strategy DINA model and multiple strategy DINA models. An analysis of fraction subtraction data is provided as an illustration example.

Implementing the Standards: Developing Communication Skills in Mathematics for Students with Limited English Proficiency

1991 ◽  
Vol 84 (3) ◽  
pp. 186-189
Author(s):  
Gilbert J. Cuevas
Keyword(s):  
Problem Solving ◽  
Communication Skills ◽  
Limited English Proficiency ◽  
English Proficiency ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Listening And Speaking

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to “use language to communicate their mathematical ideas” (NCTM 1989, 78). Although these recommendations are valuable, teachers may find them difficult to implement with students who are not proficient in English.

News from the Net: Aunty Math's Challenges for Kids

1999 ◽  
Vol 5 (7) ◽  
pp. 420
Author(s):  
Beth Lazerick
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Web Site ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real ◽  
Problem Solving Strategies ◽  
The Web

Aunty Math, for students and their teachers, is a terrific site that emphasizes problem-solving strategies listed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The site is designed for children; the layout is easy to use, and the graphics are inviting. Aunty Math's problems, called “challenges,” are set in stories about Aunty Math's nephews and niece. The real Aunty Math behind the Web site is an experienced, awardwinning teacher who is very involved in mathematics education.

Pixy Stix Segments and the Midpoint Connection

1993 ◽  
Vol 86 (8) ◽  
pp. 668-675
Author(s):  
Ruth McClintock
Keyword(s):  
High School ◽  
Problem Solving ◽  
Cooperative Learning ◽  
Communication Skills ◽  
School Mathematics ◽  
Peter Pan ◽  
Evaluation Standards ◽  
High School Geometry ◽  
Mathematical Connections ◽  
School Geometry

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) offers a vision of mathematically empowered students embarking on exciting flights of discovery. This vision challenges teachers to look for ways to incorporate problem solving, cooperative learning, mathematical connections, reasoning, communication skills, and proofs into lesson plans. The Pixy Stix activities described in this article are not quite as magical as Peter Pan and Tinkerbell's prescription of sprinkling pixie dust over children who want to fly, but they do embody all the attributes mentioned above and may enable your high school geometry students to take off in some surprising directions.

Implementing The Standards: The Vision of Problem Solving in the Standards

1990 ◽  
Vol 37 (9) ◽  
pp. 14-17
Author(s):  
Patricia F. Campbell ◽  
Honi J. Bamberger
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Small Groups ◽  
Mathematical Knowledge ◽  
Curriculum And Instruction ◽  
Mathematics Curriculum ◽  
Focused Attention ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Widespread Acceptance

Problem solving has been espoused as a goal in mathematics education since the late 1970s, with focused attention ansmg from NCTM's An Agenda for Action (1980). But problem solving should be more than a slogan offered for its appeal and widespread acceptance. It should be a cornerstone of mathematics curriculum and instruction, fostering the development of mathematical knowledge and a chance to apply and connect previously constructed mathematical understandings. This perception of problem solving is presented in the Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989, 23, 75). See table 1. Indeed, as noted in the Standards, “students need to work on problems that may take hours, days, and even weeks to solve. Although some may be relatively simple exercises to be accompplished independently, others should involve small groups or an entire class working cooperatively” (NCTM 1989, 6).

Assessment: Describing Student Performance Qualitatively

1996 ◽  
Vol 1 (10) ◽  
pp. 828-835
Author(s):  
Jinfa Cai ◽  
Maria E. Magone ◽  
Ning Wang ◽  
Suzanne Lane
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Student Performance ◽  
Conceptual Understanding ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Reasoning Problem ◽  
Mathematics Educators

The issue of linking testing with instructional practice is not new. In recent years, mathematics educators have been redefining the goals of mathematics education to include increased attention to problem solving and reasoning. For example, the National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) and the National Research Council's Everybody Counts (1989) suggest an emphasis on reasoning, problem solving, conceptual understanding, and communicating mathematically.

Assessing Problem-Solving Thought

1999 ◽  
Vol 4 (5) ◽  
pp. 305-311
Author(s):  
Annette Ricks Leitze ◽  
Sue Tinsley Mau
Keyword(s):  
Critical Thinking ◽  
Problem Solving ◽  
Communication Skills ◽  
Risk Taking ◽  
Mathematics Curriculum ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Data Organization ◽  
Evaluation Standards ◽  
Recent Reform

Recent reform efforts that are based on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for an increase in problem solving as part of the mathematics curriculum for students at all levels. Teachers can use problemsolving activities for multiple purposes, such as developing critical-thinking skills, data-organization skills, communication skills, and a risk-taking attitude, as well as making connections among mathematical topics. Regardless of the curriculum goal, teachers face many challenges in finding suitable activities and then assessing the work that students do on these activities. Neither task is easy.

scholarly journals PENDIDIKAN MATEMATIKA REALISTIK: PENDEKATAN UNTUK MENINGKATKAN KEMAMPUAN KOMUNIKASI MATEMATIKA DAN PEMECAHAN MASALAH

2021 ◽  
Vol 9 (2) ◽  
pp. 197-210
Author(s):  
Rihlatis Sa'idah ◽  
Mukti Sintawati ◽  
Fitria Desi Nurhadiyani
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Data Collection ◽  
Communication Skills ◽  
Realistic Mathematics Education ◽  
Research Subjects ◽  
Mathematical Communication ◽  
Realistic Mathematics ◽  
Math Problems ◽  
Very High

This study aims to improve mathematics communication skills and problem solving through the application of realistic mathematics education. The type of research used is Classroom Action Research. The research subjects were 18 students of class V SD Muhammadiyah Notoprajan, while the object of this research was the mathematics communication skills and problem solving abilities. The data collection techniques used were tests and observations. The data collection instruments used were mathematical communication test questions and problem solving, and observation sheets. Mathematical communication data and problem solving abilities were analyzed descriptively. The results of the study indicate that there is an increase in mathematics communication skills and problem solving through the application of realistic mathematics education. This is indicated by the percentage of students with high and very high mathematics communication skills in the first cycle of 72.22% and an increase in the second cycle to 94%. The percentage of students with the ability to solve math problems in the high and very high category in the first cycle was 66.67%, an increase in the second cycle to 100%.

Apply the Curriculum Standards with Project Questions

1993 ◽  
Vol 86 (8) ◽  
pp. 686-689
Author(s):  
Richard T. Edgerton
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Organizing Principles

A goal of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is faci litating “mathematical power” in students. The curriculum standards use problem solving, communication, reasoning, and connections as organizing principles. One way to apply these principles in the classroom is with the use of “project questions.”

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