Implementing the Assessment Standards for School Mathematics: Assessing Students' Performance on an Extended Problem–Solving Task: A Story from a Japanese Classroom

1997 ◽  
Vol 90 (8) ◽  
pp. 658-664
Author(s):  
Yoshinori Shimizu
Keyword(s):  
Problem Solving ◽  
Classroom Assessment ◽  
Secondary Level ◽  
School Mathematics ◽  
Assessment Task ◽  
Mathematics Educators ◽  
Extended Problem ◽  
Assessment Standards ◽  
Problem Solving Task

Japanese mathematics educators at the secondary level struggle with some of the same assessment issues that plague American educators. Yet in both cultures, teachers today are experimenting with alternative forms of classroom assessment. They want to encourage their students to think more deeply about the mathematics they are learning, and they want to improve their own teaching by finding out more about what their students know and can do. This article describes the use of an extended problem-solving assessment task with a Japanese secondary class.

The Wonder and Creativity in “Looking Back” at Problem Solutions

1988 ◽  
Vol 81 (6) ◽  
pp. 429-434
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Position Paper ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Competence ◽  
Mathematics Educators ◽  
Looking Back

Mathematics educators have always viewed problem solving as a preferential objective of mathematics instruction. It was not, however, until the National Council of Teachers of Mathematics published its position paper An Agenda for Action: Recommendations for School Mathematics of the 1980s that problem solving truly came of age. As its very first recommendation, the Council (1980) directed that “problem solving be the focus of school mathematics in the 1980s” and proclaimed that “performance in problem solving will measure the effectiveness of our personal and national possession of mathematical competence.”

Guiding Young Children in Successful Problem Solving

1982 ◽  
Vol 29 (5) ◽  
pp. 15-17
Author(s):  
Kil S. Lee
Keyword(s):  
Problem Solving ◽  
Young Children ◽  
Conference Report ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Skills ◽  
The Past ◽  
Mathematics Educators ◽  
Mathematics Curricula

In the past twenty years, problem solving has received much attention from mathematics educators. Inclusion of imaginative problems in school mathematics curricula was recommended in the 1963 Cambridge Conference report. Problem solving was the first of the ten basic mathematical skills identified by the National Council of Supervisors of Mathematics in 1976 and the position of the NCSM was endorsed by the National Council of Teachers of Mathematics in 1978. “That problem solving be the focus of school mathematics in the 1980s” is the first of eight recommendations expressed in An Agenda for Action: Recommendations for School Mathematics of the 1980s published by the NCTM.

Investigating the Mathematical Process with Nonlinear Asymptotes

2008 ◽  
Vol 101 (8) ◽  
pp. 574-580
Author(s):  
Michael J. Bossé ◽  
Karen A. DeUrquidi ◽  
David L. Edwards ◽  
N. R. Nandakumar
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Multiple Representations ◽  
School Mathematics ◽  
School Students ◽  
Mathematical Ideas ◽  
Mathematics Educators ◽  
Algebraic Concept ◽  
Mathematical Process

Principles and Standards for School Mathematics (NCTM 2000) emphasizes having students experience mathematics as mathematicians do and demonstrates that the Process Standards—Problem Solving, Reasoning and Proof, Communication, Connections, and Representation—are not simply means through which mathematics is learned and taught; they are also the manner through which mathematics is done. This article presents an abbreviated version of the musings and methodologies experienced by mathematics educators through a genuine problemsolving investigation. This account will investigate dimensions of an algebraic concept known to many high school students and show how these lead to an intuitive understanding of the limit in calculus. Readers will experience and come to a deeper understanding of the Process Standards as well as experience the necessity of using multiple representations to make and solve mathematical conjectures. To accomplish these multidimensional goals, the authors describe a chronological development of mathematical ideas among themselves and invite readers to reason along with them in their actual investigations.

The Football Coach's Dilemma: “Should We Go for 1 or 2 Points First?”

1995 ◽  
Vol 88 (9) ◽  
pp. 731-733
Author(s):  
Vincent P. Schielack
Keyword(s):  
Problem Solving ◽  
Mathematical Models ◽  
Real World ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Real World Problem ◽  
Mathematics Educators ◽  
Mathematical Techniques

Situations arise in many everyday endeavors that can be analyzed using various mathematical techniques. These situations give mathematics educators many opportunities to connect real-world problem-solving situations with appropriate mathematical models, as recommended in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The mathematics topic here involves applying elementary concepts of probability to a hotly debated question arising in football. h will be assumed throughout that a team values a win significantly more than a tie and also values a tie considerably more than a loss.

The Writing Process: A Strategy for Problem Solvers

1990 ◽  
Vol 38 (3) ◽  
pp. 35-38
Author(s):  
Margaret I. Ford
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Writing Process ◽  
School Mathematics ◽  
Problem Solver ◽  
Educational Progress ◽  
National Assessment ◽  
The Past ◽  
Mathematics Educators ◽  
Problem Solvers

Over the past decade, mathematics educators have promoted problem solving as the goal of school mathematics. Yet in 1987, the National Assessment of Educational Progress revealed that our nation's schoolchildren are still falling short of our goals for their problem solving abilities. Many students dislike word problems in mathematics, and many teachers report feeling frustration and discouragement in helping their students learn how to solve such problems (Ford 1988). What can teachers do to improve students' attitude toward problem solving and to realize the goal of helping students become better problem solver?

Implementing the Assessment Standards for School Mathematics: Teachers and Students Learning Together about Assessing Problem Solving

1997 ◽  
Vol 90 (6) ◽  
pp. 472-477
Author(s):  
Marge Petit ◽  
Judith S. Zawojewski
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Methods ◽  
School Mathematics ◽  
Written Responses ◽  
Teacher Understanding ◽  
Reasonable Solution ◽  
Teachers And Students ◽  
Curriculum Instruction ◽  
Assessment Standards

Enhancing problem-solving capabilities for all students is a goal that can be reached only when curriculum, instruction, and assessment are aligned toward the same goals, along with student and teacher understanding of the expectations associated with reaching these goals (NCTM 1995). The assessment of problem solving in particular is a difficult aspect, even when teachers have developed adequate resources and teaching methods to facilitate problem-solving activities. Pertinent questions regarding problem-solving assessment include the following: How can students' work be evaluated fairly when many reasonable solution paths exist? How can teachers assess students' responses to open-ended questions in a way that yields documentation useful for preparing progress reports? How can teachers help students understand what is expected in their written responses?

Using Bloom's Taxonomy as a Framework for Classroom Assessment

2003 ◽  
Vol 96 (6) ◽  
pp. 402-405 ◽  
Author(s):  
Signe E. Kastberg
Keyword(s):  
Mathematics Teacher ◽  
Classroom Assessment ◽  
Test Preparation ◽  
Opportunity To Learn ◽  
Bloom's Taxonomy ◽  
School Mathematics ◽  
Assessment Practices ◽  
Assessment Framework ◽  
Bloom’S Taxonomy ◽  
Assessment Standards

AS A MATHEMATICS TEACHER, I WANT MY CLASSroom tests to reflect what my students have had an opportunity to learn so that I can assess both their learning and my teaching. I find, however, that often I create tests haphazardly. As a result, the tests that I give accomplish only part of what I had intended them to do. In an attempt to discover ways to be more systematic in my test preparation, I read Assessment Standards for School Mathematics (NCTM 1995). That document contains a variety of helpful advice, including a description of an assessment framework. An assessment framework sounded like just what I needed to turn my classroom assessment practices from haphazard to systematic.

Scientific Problem Solving in a Virtual Laboratory: A Comparison Between Individuals and Pairs

2008 ◽  
Vol 67 (2) ◽  
pp. 71-83 ◽  
Author(s):  
Yolanda A. Métrailler ◽  
Ester Reijnen ◽  
Cornelia Kneser ◽  
Klaus Opwis
Keyword(s):  
Visual Search ◽  
Problem Solving ◽  
Process Data ◽  
Scientific Problem ◽  
Domain Specific ◽  
Scientific Problem Solving ◽  
Before And After ◽  
Verbal Data ◽  
Psychological Knowledge ◽  
Problem Solving Task

This study compared individuals with pairs in a scientific problem-solving task. Participants interacted with a virtual psychological laboratory called Virtue to reason about a visual search theory. To this end, they created hypotheses, designed experiments, and analyzed and interpreted the results of their experiments in order to discover which of five possible factors affected the visual search process. Before and after their interaction with Virtue, participants took a test measuring theoretical and methodological knowledge. In addition, process data reflecting participants’ experimental activities and verbal data were collected. The results showed a significant but equal increase in knowledge for both groups. We found differences between individuals and pairs in the evaluation of hypotheses in the process data, and in descriptive and explanatory statements in the verbal data. Interacting with Virtue helped all students improve their domain-specific and domain-general psychological knowledge.

Moving to Solution

2013 ◽  
Vol 60 (6) ◽  
pp. 403-409 ◽  
Author(s):  
K. Werner ◽  
M. Raab
Keyword(s):  
Problem Solving ◽  
Embodied Cognition ◽  
Cognitive Functions ◽  
Problem Space ◽  
Arm Swing ◽  
String Problem ◽  
Problem Solving Process ◽  
Problem Solving Task ◽  
Bodily Movements

Embodied cognition theories suggest a link between bodily movements and cognitive functions. Given such a link, it is assumed that movement influences the two main stages of problem solving: creating a problem space and creating solutions. This study explores how specific the link between bodily movements and the problem-solving process is. Seventy-two participants were tested with variations of the two-string problem (Experiment 1) and the water-jar problem (Experiment 2), allowing for two possible solutions. In Experiment 1 participants were primed with arm-swing movements (swing group) and step movements on a chair (step group). In Experiment 2 participants sat in front of three jars with glass marbles and had to sort these marbles from the outer jars to the middle one (plus group) or vice versa (minus group). Results showed more swing-like solutions in the swing group and more step-like solutions in the step group, and more addition solutions in the plus group and more subtraction solutions in the minus group. This specificity of the connection between movement and problem-solving task will allow further experiments to investigate how bodily movements influence the stages of problem solving.

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