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.

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.

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.

News from the Net: Mrs. Glosser's Math Goodies

2003 ◽  
Vol 9 (7) ◽  
pp. 407
Author(s):  
Barbara L. Clanton
Keyword(s):  
Prior Knowledge ◽  
Classroom Environment ◽  
Mathematics Classroom ◽  
Learning Opportunities ◽  
School Mathematics ◽  
National Council ◽  
Link Type ◽  
New Knowledge ◽  
Good Resource

The National Council of Teachers of Mathematics (NCTM) lists the Learning Principle as one of its six principles for school mathematics. The Learning Principle suggests that students learn by actively building new knowledge from prior knowledge. In doing so, they will become autonomous learners. NCTM promotes a mathematics classroom environment in which students feel comfortable making mistakes that can lead to learning opportunities. Mrs. Glosser's Math Goodies, located at www.mathgoodies.com, can support teachers' implementation of these two recommendations and is a good resource for students in grades 4–9 as well as parents.

Extending the Regular Curriculum Through Creative Problem Solving

1993 ◽  
Vol 41 (2) ◽  
pp. 83-87
Author(s):  
Harry Bohan ◽  
Susan Bohan
Keyword(s):  
Problem Solving ◽  
Learning Environment ◽  
Prior Knowledge ◽  
School Mathematics ◽  
Creative Problem Solving ◽  
New Knowledge ◽  
Creative Problem

Increased attention in school mathematics is also being given to creating a learning environment in which students can use prior knowledge and experiences to construct new knowledge for themselves.

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.

Build Your Own Fraction Computer!

2002 ◽  
Vol 8 (4) ◽  
pp. 204-208
Author(s):  
Peter L. Glidden
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Addition And Subtraction ◽  
Principles And Standards ◽  
Fraction Addition

The NCTM's Curriculum and Evaluation Standards (1989) called for increased emphasis on promoting students' conceptual understanding of fractions and fraction operations; this call was reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). Currently, many manipulatives, including pattern blocks, fraction circles, fraction squares, geodot paper, and fraction strips, are available to help teachers promote this understanding. This article describes another manipulative, the fraction computer, that I have found helpful for teaching fraction addition and subtraction.

Sorting Symbol Strings

2005 ◽  
Vol 10 (7) ◽  
pp. 334-338
Author(s):  
Jodie D. Novak ◽  
Judith E. Jacobs
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Skilled Performance ◽  
Principles And Standards

Atheme Throughout All Grade Bands of the Algebra Standard of the NCTM's Principles and Standards for School Mathematics is the ability of students to “represent and analyze mathematical situations and structures using algebraic symbols” (p. 222). In the band for grades 6–8, this theme is further articulated as asking students to “develop an initial conceptual understanding of different uses of variables” (p. 222). Although variables sometimes occur alone, more often they occur in expressions, equations, and inequalities. We will refer to letters and numbers combined in equations, inequalities, and expressions as “symbol strings” as do Chazan and Yerushalmy (2003). The role of the variable is often determined by the symbol string in which it occurs; therefore, if students understand the different kinds of symbol strings, they will understand the roles that variables play. We have developed activities that ask students to identify, describe, compare, and classify symbol strings—in other words, to develop a feel for symbol strings. Chazan and Yerushalmy (2003) discuss it in this way: “Skilled performance [in school algebra] involves developing a feel for symbol strings … that indicates what sorts of creatures they are and what should be done with them.”

Multiplication by 10 base-5: Making Sense of Place Value Structure Through an Alternate Base

2015 ◽  
Vol 3 (2) ◽  
pp. 83-98
Author(s):  
Jodi Fasteen ◽  
Kathleen Melhuish ◽  
Eva Thanheiser
Keyword(s):  
Preservice Teachers ◽  
Conceptual Understanding ◽  
Sense Of Place ◽  
Number System ◽  
Place Value ◽  
Mathematical Activity ◽  
Making Sense ◽  
Procedural Fluency ◽  
Whole Number

Prior research has shown that preservice teachers (PSTs) are able to demonstrate procedural fluency with whole number rules and operations, but struggle to explain why these procedures work. Alternate bases provide a context for building conceptual understanding for overly routine rules. In this study, we analyze how PSTs are able to make sense of multiplication by 10five in base five. PSTs' mathematical activity shifted from a procedurally based concatenated digits approach to an explanation based on the structure of the place value number system.

scholarly journals Developing The Mathematics Conceptual Understanding and Procedural Fluency through Didactical Anticipatory Approach Equipped with Teaching AIDS

2018 ◽  
Vol 3 (2) ◽  
pp. 367
Author(s):  
Asmida Asmida ◽  
Sugiatno Sugiatno ◽  
Agung Hartoyo
Keyword(s):  
Conceptual Understanding ◽  
Junior High School ◽  
Mathematics Learning ◽  
Posttest Score ◽  
Mathematics Textbook ◽  
Teaching Aids ◽  
Procedural Fluency ◽  
Mathematical Problems ◽  
Epistemological Obstacles ◽  
And Mathematics

The students’ conceptual understanding and procedural fluency have not been yet integrated into the mathematics learning as the teachers’ common mathematics textbook has not explicitly explained the conceptual understanding and procedural fluency in solving the mathematical problems that the teachers have not yet connected it to the mathematics learning. The interview result shows that the students only memorize the procedures without understanding. If the procedure is continuously applied, it is predicted that the students may face the epistemological obstacles in solving the mathematical problems. This research aims at developing the students' mathematics conceptual understanding and procedural fluency through the Didactic Anticipatory Approach equipped with the teaching aids in learning the operations of integer multiplication at Junior High School in Grade VIII. This pedagogical action research involves 14 students. The research data are collected using tests, interviews, voice recorders and cameras. The result shows that learning mathematics through the Didactic Anticipatory Approach equipped with teaching aids may develop the students' conceptual understanding and mathematics procedural fluency marked by the reduced students’ epistemological obstacles. However, they are not yet been completely resolved. The students' conceptual understanding and mathematics procedural fluency also supported with the average posttest score higher than that of the pretest score.

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