Curriculum Focal Points for Pre-K–Grade 8 Mathematics: A Quest for Coherence

2006 ◽  
Vol 100 (3) ◽  
pp. 179
Keyword(s):  
School Mathematics ◽  
Focal Points ◽  
Principles And Standards ◽  
Grade 8

An introduction to the topic of the NCTM's “Curriculum Focal Points for Prekindergraten through Grade 8 Mathematics: A Quest for Coherence,” including the need for the focal points, what they are, how they should be used, and how they are related to the Principles and Standards for School Mathematics. The purpose for the Curriculum Focal Points is to provide leadership in the discussion about important mathematical topics at the pre-K-8 level.

A Look at the Development of Data Representation and Analysis in Curriculum Focal Points: A Quest for Coherence

2007 ◽  
Vol 13 (4) ◽  
pp. 208-210
Author(s):  
Jane F. Schielack ◽  
Cathy Seeley
Keyword(s):  
Data Analysis ◽  
Grade Level ◽  
Focal Point ◽  
Data Representation ◽  
School Mathematics ◽  
Descriptive Statistics ◽  
Focal Points ◽  
Principles And Standards ◽  
Grade 8 ◽  
Developing Knowledge

One of the questions often raised with regard to NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence is, “Where are data representation and analysis?” In this month's Focal Points feature, we take a look at an area of content—data representation and analysis—that is important enough to warrant a separate strand in Principles and Standards for School Mathematics (NCTM 2000) but that does not appear in the title of a content Focal Point until Grade 8. However, in the Appendix of Curriculum Focal Points, in comparison with Principles and Standards, it is clear that the content of the Data Analysis strand presented in each of the pre- K–2, 3–5, and 6–8 grade bands in the Standards is included in the specific grade-level descriptions in Curriculum Focal Points. Skills for data representation begin in prekindergarten and appear throughout later grades and are presented as connections to the concepts and skills involved in the Geometry and Measurement Focal Points. In Kindergarten through Grade 7, data representation and analysis in the Connections to the Focal Points sections also provide meaningful contexts as students apply their developing knowledge of number and operations. In Grade 8, the analysis of data through descriptive statistics becomes a Focal Point in itself.

Implementation of the NCTM Curriculum Focal Points: Concept versus Content

2007 ◽  
Vol 13 (2) ◽  
pp. 78-80
Author(s):  
Jane F. Schielack ◽  
Cathy Seeley
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Focal Points ◽  
Major Step ◽  
Versus Content ◽  
P 16 ◽  
Principles And Standards ◽  
Coherent Curriculum ◽  
Grade 8

On September 12, 2006, the NCTM released a new lens through which to view the content presented in Principles and Standards for School Mathematics (NCTM 2000). In Principles and Standards, the Curriculum Principle calls for a mathematics curriculum to be coherent, focused on important mathematics, and well articulated across the grades. This means that an effective curriculum “gives teachers guidance regarding important ideas or major themes, which receive special attention at different points in time. It also gives guidance about the depth of study warranted at particular times and when closure is expected for particular skills or concepts” (NCTM 2000, p. 16). With the publication of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, NCTM has taken a major step toward defining the mathematics that every student should know and be able to do. Where the Principles and Standards presented content across multiple grade bands, this new publication applies the Curriculum Principle to create a specific example of a focused and coherent curriculum, prekindergarten through grade 8.

A Look at the Development of Ratios, Rates, and Proportionality

2007 ◽  
Vol 13 (3) ◽  
pp. 140-142
Author(s):  
Cathy Seeley ◽  
Jane F. Schielack
Keyword(s):  
Middle School ◽  
Building Block ◽  
Secondary Mathematics ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Linear Functions ◽  
Focal Points ◽  
Rates Of Change ◽  
Future Success ◽  
Grade 8

One of the most significant features of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence is that the document highlights the coherent development across the grades of important ideas and the connections among these ideas. In this month's Focal Points article, we will take a look at one of the most important ideas in middle school mathematics: proportionality. The ability to recognize, understand, and work with ratios, rates, and proportional relationships is crucial to future success in algebra. When students are able to describe situations involving constant rates of change and discuss how two quantities are related proportionally, they will be prepared to understand linear functions. This understanding is a critical building block to the study of topics found in secondary mathematics.

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.

Let's Talk: Promoting Mathematical Discourse in the Classroom

2007 ◽  
Vol 101 (4) ◽  
pp. 285-289 ◽  
Author(s):  
Catherine A. Stein
Keyword(s):  
Mathematical Discourse ◽  
School Mathematics ◽  
Mathematical Concepts ◽  
Student Discourse ◽  
Principles And Standards

As part of reform-based mathematics, much discussion and research has focused on the idea that mathematics should be taught in a way that mirrors the nature of the discipline (Lampert 1990)—that is, have students use mathematical discourse to make conjectures, talk, question, and agree or disagree about problems in order to discover important mathematical concepts. In fact, communication, of which student discourse is a part, is so important that it is one of the Standards set forth in Principles and Standards for School Mathematics (NCTM 2000).

Internal Rate of Return

2005 ◽  
Vol 98 (8) ◽  
pp. 531-533
Author(s):  
Harris S. Shultz
Keyword(s):  
Real Life ◽  
School Mathematics ◽  
Rate Of Return ◽  
Opportunities To Learn ◽  
Internal Rate Of Return ◽  
Daily Lives ◽  
Internal Rate ◽  
Subject Areas ◽  
Principles And Standards

The Principles and Standards for School Mathematics (NCTM 2000, pp. 65–66) states, “School mathematics experiences at all levels should include opportunities to learn about mathematics by working on problems arising in contexts outside of mathematics. These connections can be to other subject areas and disciplines as well as to students' daily lives.” In this article we shall see that the discipline of finance can provide rich real–life applications of mathematics.

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