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.

Spotlight on the Principles: Creating an Environment for Learning with Understanding: The Learning Principle

2005 ◽  
Vol 11 (1) ◽  
pp. 35-39
Author(s):  
Emily Fagan
Keyword(s):  
Prior Knowledge ◽  
Conceptual Understanding ◽  
School Mathematics ◽  
Factual Knowledge ◽  
Procedural Fluency ◽  
New Knowledge ◽  
Principles And Standards ◽  
Knowledge Learning

The learning principle in NCTM'S Principles and Standards for School Mathematics (2000) states: “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” Learning with understanding is defined as “being able to apply procedures, concepts, and processes” (NCTM 2000, p. 20). This view of learning represents a departure from a view that emphasizes a student's factual knowledge and ability to apply procedures. Although facts and procedures are important, they will not, in and of themselves, result in learning with understanding. Instead, factual understanding, procedural fluency, and conceptual understanding must coexist so that students reach learning with understanding. The extent to which a student can apply his or her learning to a new problem or situation is often an indicator of this understanding.

Links to Literature: May 2001

2001 ◽  
Vol 7 (9) ◽  
pp. 538-541
Author(s):  
Jorie Borden ◽  
Elsa Geskus
Keyword(s):  
Children's Literature ◽  
Problem Solving ◽  
Real World ◽  
Children’S Literature ◽  
School Mathematics ◽  
Teaching Skills ◽  
The Real ◽  
New Knowledge ◽  
Principles And Standards

The phenomenal resurgence of children's literature in the marketplace has allowed teachers to help their students construct new knowledge by fostering the love of literature while teaching skills and knowledge. Principles and Standards for School Mathematics (NCTM 2000) recommends connecting mathematics with the real-world experiences of children. The authors chose Cook-a-Doodle-Doo! (Stevens and Crummel 1999) to provide students with opportunities for problem solving, estimating, predictive reading, and enjoyable eating.

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.

Maps and Algebra

2003 ◽  
Vol 8 (6) ◽  
pp. 300-302
Author(s):  
William Gratzer
Keyword(s):  
Middle School ◽  
Prior Knowledge ◽  
Mathematics Teacher ◽  
Life Experiences ◽  
Linear Equations ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
New Knowledge ◽  
Principles And Standards ◽  
And Algebra

The learning principle from principles and Standards for School Mathematics (NCTM 2000) states, “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge” (p. 20). How to help students develop such understanding is a question that confronts every middle school mathematics teacher. The method described in this article helps students use their life experiences to develop mathematical understanding by illustrating that linear equations can be solved using ideas with which they are already familiar.

scholarly journals II BRAZILIAN CONSENSUS ON GASTRIC CANCER BY THE BRAZILIAN GASTRIC CANCER ASSOCIATION

2020 ◽  
Vol 33 (2) ◽  
Author(s):  
Leandro Cardoso BARCHI ◽  
Marcus Fernando Kodama Pertille RAMOS ◽  
André Roncon DIAS ◽  
Nelson Adami ANDREOLLO ◽  
Antônio Carlos WESTON ◽  
...  
Keyword(s):  
Gastric Cancer ◽  
Literature Review ◽  
Cancer Treatment ◽  
New Concepts ◽  
New Knowledge ◽  
Gastric Cancer Treatment

ABSTRACT Background: Since the publication of the first Brazilian Consensus on Gastric Cancer (GC) in 2012 carried out by the Brazilian Gastric Cancer Association, new concepts on diagnosis, staging, treatment and follow-up have been incorporated. Aim: This new consensus is to promote an update to professionals working in the fight against GC and to provide guidelines for the management of patients with this condition. Methods: Fifty-nine experts answered 67 statements regarding the diagnosis, staging, treatment and prognosis of GC with five possible alternatives: 1) fully agree; 2) partially agree; 3) undecided; 4) disagree and 5) strongly disagree A consensus was adopted when at least 80% of the sum of the answers “fully agree” and “partially agree” was reached. This article presents only the responses of the participating experts. Comments on each statement, as well as a literature review, will be presented in future publications. Results: Of the 67 statements, there was consensus in 50 (74%). In 10 declarations, there was 100% agreement. Conclusion: The gastric cancer treatment has evolved considerably in recent years. This consensus gathers consolidated principles in the last decades, new knowledge acquired recently, as well as promising perspectives on the management of this disease.

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?

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.

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