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.

National Council of Teachers of Mathematics: The Council's drive to improve school mathematics

1963 ◽  
Vol 10 (6) ◽  
pp. 368-375
Author(s):  
Frank B. Allen
Keyword(s):  
School Mathematics ◽  
National Council ◽  
Local Organizations ◽  
Teaching Of Mathematics ◽  
High Degree

According to our Articles of Incorporation, the object of the National Council of Teachers of Mathematics is “To assist in promoting the interest of mathematics in America, especially in the elementary and secondary fields, by holding meetings for the presentation and discussion of papers, by conducting investigations for the purpose of improving the teaching of mathematics, by the publication of papers, journals, books, and reports: thus, to vitalize and coordinate the work of many local organizations of teachers of mathematics and to bring the interest of mathematics to the attention and consideration of the educational world.” I believe that any impartial review of our accomplishments will support the conclusion that we have achieved a high degree of success in the attainment of this objective.

Informing Learning Through the Clinical Interview

1991 ◽  
Vol 38 (6) ◽  
pp. 44-46
Author(s):  
Madeleine J. Long ◽  
Meir Ben-Hur
Keyword(s):  
Student Outcomes ◽  
Clinical Interview ◽  
School Mathematics ◽  
Assessment Tools ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Paper And Pencil ◽  
Primary Assessment

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Srandards for Teaching Mathematics (1989) endorse the view that assessment should be made an integral part of teaching. Although many of the student outcomes described in the Srandards cannot properly be assessed using paper-and-pencil tests, such tests remain the primary assessment tools in today's classroom.

Effective and Efficient Use of Math Writing Tasks

2018 ◽  
Vol 112 (2) ◽  
pp. 143-146 ◽  
Author(s):  
Matt M. Bixby
Keyword(s):  
School Mathematics ◽  
Clear Picture ◽  
Student Writing ◽  
National Council ◽  
Writing In Mathematics ◽  
Mathematics Class ◽  
Principles And Standards ◽  
The Many

Almost twenty years ago, the National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics (2000), which recommended that teachers should incorporate more writing into their math lessons, claiming that writing helps students “consolidate their thinking” (p. 402) by causing them to reflect on their work. In recent years, various studies point to the many benefits that can be gained by writing in mathematics class (e.g., O'Connell et al. 2005; Goldsby and Cozza 2002). Much research suggests that writing activities, if implemented effectively, can help students enjoy class more (Burns 2005) and can also help them deepen their understanding of the content (Baxter et al. 2002). In addition to benefiting students, student writing benefits teachers as well by providing a clear picture of what their students understand and even deepening understanding of the content for teachers themselves (Burns 2005; Pugalee 1997).

Technology Tips: When Is a Good Fit Not a Good Fit? Dynamic Regression with the TI-Nspire Graphing Calculator

2008 ◽  
Vol 102 (4) ◽  
pp. 300-305
Author(s):  
Michael Edwards ◽  
Michael Meagher ◽  
S. Asli Özgün-Koca
Keyword(s):  
Graphing Calculator ◽  
School Mathematics ◽  
Mathematical Education ◽  
National Council ◽  
Mathematics Textbooks ◽  
Multiple Points ◽  
Complex Concept ◽  
Mathematics Classrooms ◽  
Points Of View ◽  
Principles And Standards

In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) acknowledges the importance of exploring mathematical ideas from multiple points of view: “Different representations often illuminate different aspects of a complex concept or relationship…. The importance of using multiple representations should be emphasized throughout students' mathematical education” (2000, p. 68). In particular, NCTM notes that the introduction of technology in school mathematics classrooms provides new ways for teachers and their students to explore connections among representations: “Computers and calculators change what students can do with conventional representations and expand the set of representations with which they can work” (2000, p. 68). In this article, we discuss an interesting finding that our students made as they explored linear regression with a teacher-constructed TI-Nspire calculator document. The calculator's capability to link variables across two or more pages in the same document led students to findings that are important yet rarely discussed in school mathematics textbooks.

Activities for Students: Building Connections among Classes of Polynomial Functions

2000 ◽  
Vol 93 (7) ◽  
pp. 591-598
Author(s):  
Judy Curran Buck
Keyword(s):  
School Mathematics ◽  
Polynomial Functions ◽  
New Concepts ◽  
New Knowledge ◽  
Principles And Standards

A major thrust of Principles and Standards for School Mathematics is that teachers should help students see mathematics as an integrated whole rather than as a series of isolated topics. “Mathematics makes more sense and is easier to remember and apply when students can connect new knowledge to existing knowledge in meaningful ways” (NCTM 2000, p. 20). The document maintains that new concepts should be introduced, whenever possible, as extensions of familiar mathematics. The activity that follows emphasizes the commonalities among classes of polynomial functions and the themes that are transferred from one class to another.

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.

Writing About the Problem Solving Process to Improve Problem Solving Performance

2003 ◽  
Vol 96 (3) ◽  
pp. 185-187 ◽  
Author(s):  
Kenneth M. Williams
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
National Council ◽  
Instructional Programs ◽  
Principles And Standards ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the most important components of mathematics. In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics emphasized that instructional programs should enable all students in all grades to “build new mathematical knowledge through problem solving, solve problems that arise in mathematics and in other contexts, apply and adapt a variety of appropriate strategies to solve problems, and monitor and reflect on the process of mathematical problem solving” (NCTM 2000, p. 52). But how do students become competent and confident mathematical problem solvers?

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).

Delving Deeper: New Life for an Old Topic: Completing the Square Using Technology

2010 ◽  
Vol 104 (3) ◽  
pp. 230-236
Author(s):  
Steve Phelps ◽  
Michael Todd Edwards
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Structure ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
Teachers And Students ◽  
Principles And Standards

Mathematics teaching has always been a curious blend of the old and the new. As the use of technology becomes more commonplace in school classrooms, this blend becomes even more pronounced. When teachers and students revisit traditional topics using technology, they are afforded opportunities to connect mathematical ideas in powerful, previously unimagined ways. The National Council of Teachers of Mathematics (NCTM) captures the importance of connections clearly in its Principles and Standards for School Mathematics (2000): “The notion that mathematical ideas are connected should permeate the school Technologymathematics experience at all levels. As students progress through their school mathematics experience, their ability to see the same mathematical structure in seemingly different settings should increase” (p. 64).

Inquiry-Discourse Mathematics Instruction

2007 ◽  
Vol 101 (4) ◽  
pp. 290-300
Author(s):  
Azita Manouchehri
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Inquiry ◽  
Mathematical Structures ◽  
Approach To Teaching ◽  
Principles And Standards ◽  
Student Inquiry

Principles and Standards for School Mathematics (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaningmaking through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. Natural consequences of using an inquiry-based approach to teaching include the emergence of unexpected mathematical results and the articulation of novel and different strategies by students. Anticipating the potential for such occurrences, Professional Standards for Teaching Mathematics (NCTM 1991) urges all teachers to remain flexible and responsive to student ideas in their instruction: Help students make connections among various solutions, tie student ideas to important mathematical structures, and extend student inquiry by posing questions and tasks that challenge their initial interpretations of problems or their false generalizations.

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