Division by a Fraction: Assessing Understanding through Problem Writing

2008 ◽  
Vol 13 (6) ◽  
pp. 326-332
Author(s):  
Angela T. Barlow ◽  
Jill Mizzell Drake
Keyword(s):  
Mathematical Understanding ◽  
School Mathematics ◽  
Assessment Practices ◽  
Teacher Accountability ◽  
Classroom Assessments ◽  
Assessment Standards ◽  
Principles And Standards

As performance-based curricula and teacher accountability gain greater emphasis, teachers need avenues to ensure that their students are learning the mathematics content being delivered. According to the NCTM's Assessment Standards for School Mathematics (1995), assessment practices should enable teachers to assess students' performance in a manner that reflects what students know and can do. Unfortunately, the typical classroom assessments, such as chapter tests, homework assignments, and the like, rarely accurately reflect the depth of mathematical understanding expected to meet performancebased standards like those found in NCTM's Principles and Standards for School Mathematics (2000).

Teaching Sensible Mathematics in Sense-Making Ways with the CPMP

1995 ◽  
Vol 88 (8) ◽  
pp. 694-700 ◽  
Author(s):  
Christian R. Hirsch ◽  
Arthur F. Coxford ◽  
James T. Fey ◽  
Harold L. Schoen
Keyword(s):  
School Districts ◽  
School Mathematics ◽  
Sense Making ◽  
Teaching Mathematics ◽  
Assessment Practices ◽  
Classroom Teachers ◽  
Current Policy ◽  
Evaluation Standards ◽  
American Schools ◽  
Assessment Standards

Current policy reports addressing mathematics education in American schools, such as Everybody Counts (NRC 1989), Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), Professional Standards for Teaching Mathematics (NCTM 1991), and Assessment Standards for School Mathematics (NCTM 1995), call for sweeping reform in curricular, instructional, and assessment practices. Implementing the proposed reforms poses new opportunities and challenges for school districts, mathematics departments, and classroom teachers.

By Way of Introduction: Learning Environments That Support Mathematical Understanding

2008 ◽  
Vol 15 (3) ◽  
pp. 132-133
Keyword(s):  
Learning Environment ◽  
Learning Environments ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Learning Tools ◽  
Student Comprehension ◽  
Principles And Standards ◽  
The Ideal ◽  
Nctm Process Standards

The first chapter of Principles and Standards for School Mathematics (NCTM 2000) presents a vision of the ideal learning environment for all mathematics learners—one that supports student acquisition of knowledge, incorporates learning tools that promote student comprehension, engages students in mathematical tasks that provide opportunities to make sense of mathematics concepts and procedures, and incorporates all the NCTM Process Standards.

Implementing the Assessment Standards for School Mathematics

1998 ◽  
Vol 91 (9) ◽  
pp. 786-793
Author(s):  
Denisse R. Thompson ◽  
Sharon L. Senk
Keyword(s):  
School Mathematics ◽  
Assessment Practices ◽  
Specific Task ◽  
Evaluation Standards ◽  
Know How ◽  
Solution Strategies ◽  
Assessment Standards ◽  
Choice Tasks ◽  
Broad Outline ◽  
Insight Into

Recommendations in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and in the Assessment Standards for School Mathematics (NCTM 1995) encourage teachers to incorporate into their curriculum and assessment practices more tasks that require students to construct their own responses, as opposed to primarily using tasks for which a response is provided, such as true-orfalse or multiple-choice tasks. Constructed responses enable students to demonstrate their depth of understanding of mathematics and give teachers greater insight into their students' knowledge of concepts. But when students are required to write about mathematics or explain their solution strategies, teachers want to know how to score such responses. Teachers have therefore become more interested in issues related to rubrics. A rubric is a set of guidelines for evaluating students' responses to one or more tasks. A general rubric is a broad outline that indicates vatious levels of performance and the factors that teachers should consider when specifying performance levels; a task-specific rubric interprets the general rubric for a specific task and specifies the particular mathematical aspects of the task that determine each level of performance (NCTM 1995; California Mathematics Council 1993).

A Little-Used Art of Teaching: The Case of Storytelling

2006 ◽  
Vol 100 (1) ◽  
pp. 64-68
Author(s):  
David E. Meel ◽  
Deborah Gyurko ◽  
Michelle Gaspar
Keyword(s):  
Mathematical Understanding ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
National Council ◽  
Working Through ◽  
New Concepts ◽  
Teaching Of Mathematics ◽  
Art Of Teaching ◽  
Principles And Standards ◽  
Math Teacher

How many students would agree with the statement “My math teacher fails in the area of creativity” when asked if their teachers try to enliven their classroom? So, where is the fun in our teaching of mathematics? In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics clearly recognizes the need for lively classrooms by stating, “Teaching mathematics well involves creating, enriching, maintaining, and adapting instruction to move toward mathematical goals, capture and sustain interest, and engage students in building mathematical understanding” (NCTM 2000, p. 18). We suggest incorporating storytelling as a means of introducing students to new concepts and working through the solution of several problems before the students even know they are investigating them.

Middle-Level Students Learn Mathematics Using the U.S. Map

2002 ◽  
Vol 8 (2) ◽  
pp. 86-90
Author(s):  
Hari P. Koirala ◽  
Phillip M. Goodwin
Keyword(s):  
Middle School ◽  
Mathematical Understanding ◽  
Middle Level ◽  
School Mathematics ◽  
Subject Areas ◽  
Principles And Standards ◽  
Middle Level Students ◽  
The U.S

Middle school educators have widely accepted the importance of interdisciplinary curricula (Cook and Martinello 1994), and Principles and Standards for School Mathematics argues that mathematics should be linked with other subject areas at all levels (NCTM 2000). According to Principles and Standards, “thinking mathematically involves looking for connections, and making connections builds mathematical understanding” (p. 274). Therefore, connecting mathematics to other disciplines has become particularly important.

Implementing the “Assessment Standards for School Mathematics”: Using Students' Portfolios to Assess Mathematical Understanding

1994 ◽  
Vol 87 (9) ◽  
pp. 698-701
Author(s):  
Harold Asturias
Keyword(s):  
Mathematical Understanding ◽  
School Mathematics ◽  
Professional Standards ◽  
Assessment Tools ◽  
Teaching Mathematics ◽  
Pedagogical Issues ◽  
Evaluation Standards ◽  
Assessment Standards ◽  
Link Assessment

In 1989, NCTM published the Curriculum and Evaluation Standards for School Mathematics, which presented the mathematics profession with a broad view of the important mathematics that should be taught in schools. Two years later, the Professional Standards for Teaching Mathematics gave teachers the opportunity to address the pedagogical issues inherent in teaching a broad-based, thinking curriculum as described in the curriculum standards. The next link, assessment, though part of the first document, required specific attention. Assessment Standards for School Mathematics, currently in progress, will present the criteria for judging the appropriateness and quality of assessment tools and systems.

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.

Improving Classroom Tests as a Means of Improving Assessment

1997 ◽  
Vol 90 (1) ◽  
pp. 58-64
Author(s):  
Denisse R. Thompson ◽  
Charlene E. Beckmann ◽  
Sharon L. Senk
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Assessment Practices ◽  
Education Community ◽  
Assessment Standards

Cunently much discussion is occurring within the mathematics-education community regarding assessment. In attempting to develop the mathematical power of students, the Assessment Standards for School Mathematics (NCTM 1995, 29) encourages teachers to make several changes in their assessment practices. Among these are the following:

What influence will the new Principles and Standards for School Mathematics (2000) have?

2000 ◽  
Vol 31 (4) ◽  
pp. 394-395
Author(s):  
Judith T. Sowder
Keyword(s):  
Annual Meeting ◽  
Research Community ◽  
School Mathematics ◽  
The Public ◽  
Principles And Standards

The new NCTM Principles and Standards for School Mathematics (2000) were presented to the public with great fanfare at the NCTM Annual Meeting in Chicago in April of this year. The mood was celebratory, perhaps even more so than when the 1989 Standards were presented. How will these new Principles and Standards be accepted? What influence will they have? Are there messages here to which the research community ought to be attending?

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