Integrating Mathematical, Technologic, and Pedgogical Knowledge in Teacher Preparation

2011 ◽  
Vol 104 (8) ◽  
pp. 608-613
Author(s):  
Kady Schneiter ◽  
Brynja R. Kohler ◽  
Brandon J. Watts
Keyword(s):  
Teacher Preparation ◽  
Teaching Strategies ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Classroom Learning ◽  
High Quality ◽  
Mathematical Content ◽  
Integrate Technology ◽  
Principles And Standards

In Principles and Standards for School Mathematics (NCTM 2000), the authors describe a vision for school mathematics in which “all students have access to high-quality, engaging mathematics instruction” (p. 3). Students deserve teachers who are knowledgeable about mathematical content, who understand and use a variety of teaching strategies appropriately, who can effectively integrate technology into classroom learning, and who continually progress as professionals. But what kinds of experiences lead to such professionalism?

Helping Students Become Mathematically Powerful

2002 ◽  
Vol 9 (2) ◽  
pp. 91-95
Author(s):  
Robin Ittigson
Keyword(s):  
Mathematics Instruction ◽  
School Mathematics ◽  
High Quality ◽  
Principles And Standards ◽  
Problem Solvers

Principles and Standards for School Mathematics asks us to imagine a classroom scenario in which all students become engaged in high-quality mathematics instruction (NCTM 2000, p. 13). Students approach problems from different perspectives and represent their thinking and solutions in many different ways. The students involved in this activity are flexible and resourceful problem solvers who communicate ideas and results effectively, both orally and in writing. These students are mathematically powerful because they possess a range of viable approaches, the arguments to support their thinking, and the ability to tell others about their work.

On My Mind: Not All Manipulatives and Models Are Created Equal

2007 ◽  
Vol 13 (1) ◽  
pp. 6-9
Author(s):  
Sally K. Roberts
Keyword(s):  
Mathematics Instruction ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Knowledge ◽  
Proof Techniques ◽  
Reasoning And Proof ◽  
Principles And Standards

The vision of the mathematics curriculum articulated in Principles and Standards for School Mathematics (NCTM 2000) calls for students to construct their own understanding of mathematical ideas by making, refining, and exploring conjectures based on evidence and use of a variety of reasoning and proof techniques (p. 3). For many of us who struggled to learn mathematics through a chalk-and-talk, do-it-my-way approach to mathematics instruction, the notion of using models and manipulatives to help the learner construct mathematics knowledge is both refreshing and exciting.

Mythmatics

2005 ◽  
Vol 12 (3) ◽  
pp. 136-143
Author(s):  
Larry E. Buschman
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Solution Method ◽  
Computational Algorithm ◽  
School Mathematics ◽  
Story Problems ◽  
Mathematical Question ◽  
Principles And Standards ◽  
Genuine Problem ◽  
Answering Questions

Principles and Standards for School Mathematics (NCTM 2000) recommends that classroom mathematics instruction be more problem- centered—children need to be given the opportunity to engage in genuine problem solving by answering questions to which the answer is not apparent or the solution method is not known in advance (Charles and Lester 1982; NCTM 2000). Traditionally, problem solving has been associated with routine word, or story, problems. However, almost any mathematical question can be a problem; even computational exercises can be problematic if the answer is not apparent and children have not been taught a solution method, such as a computational algorithm.

Mathematics in the Preschool

2001 ◽  
Vol 7 (5) ◽  
pp. 270-275
Author(s):  
Douglas Clements
Keyword(s):  
Young Children ◽  
Mathematics Instruction ◽  
Basic Skills ◽  
New Age ◽  
School Mathematics ◽  
Principles And Standards ◽  
First Time

Anyone who is pushing arithmetic onto preschoolers is wrong. Do not hurry children. No math in preschool!” “What else is preschool for if teachers do not get children ready for school? They should teach the children basic skills and how to sit and listen.” Principles and Standards for School Mathematics identifies a new age band that includes preschoolers for the first time (NCTM 2000). What mathematics instruction is appropriate for these young children? The two speakers have different opinions. I think that each is a little bit right and a little bit wrong.

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.

Math through the Mind's Eye

2005 ◽  
Vol 99 (4) ◽  
pp. 246-250 ◽  
Author(s):  
Sara P. Fisher ◽  
Christopher Hartmann
Keyword(s):  
Mathematics Teachers ◽  
Visually Impaired ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Principles And Standards ◽  
New Perspective ◽  
Mind's Eye

This paper considers recommendations from the Principles and Standards for School Mathematics (PSSM) in relation to pedagogy for the visually impaired. The authors present three examples of ways that mathematics instruction for blind learners can employ representations in ways that are consistent with PSSM. In reflecting on these examples, the authors identify lessons for all mathematics teachers. The nature of these accommodations provide a new perspective on the recommendations in the PSSM.

Principles and Standards (2002): February 2002

2002 ◽  
Vol 8 (6) ◽  
pp. 380-383
Author(s):  
Wendy Rich ◽  
Jeane Joyner
Keyword(s):  
Teaching And Learning ◽  
Instructional Program ◽  
School Mathematics ◽  
Internet Technology ◽  
High Quality ◽  
Integrating Technology ◽  
Principles And Standards

Few would argue that computers and Internet technology can positively influence teaching and learning. Unfortunately, teachers face many hurdles when integrating technology with a high-quality mathematics instructional program. Several resources are available through NCTM that support Principles and Standards for School Mathematics (NCTM 2000) and assist teachers with this dilemma.

Early Childhood Corner: Hidden Mathematics in the Preschool Classroom

2005 ◽  
Vol 11 (6) ◽  
pp. 345-347
Author(s):  
Mileen McGee
Keyword(s):  
Early Childhood ◽  
Early Childhood Education ◽  
Young Children ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
Preschool Classroom ◽  
Childhood Education ◽  
The Past ◽  
Principles And Standards

With increased attention being focused on the youngest children in our schools, changes in mathematics instruction that have occurred over the past decade are most evident in early childhood education. This emphasis is especially true since the April 2000 release by NCTM of Principles and Standards for School Mathematics, in which mathematics for the prekindergarten child is included as part of the pre-K–2 grade band. By including three- and four-year-olds in its recommendations, NCTM recognizes and emphasizes the importance and value of mathematics instruction for young children. Subsequently, in drafting their own standards, many states are also recognizing the need for early childhood standards.

Selecting High-Quality Mathematics Textbooks

2006 ◽  
Vol 12 (1) ◽  
pp. 50-54
Author(s):  
James E. Tarr ◽  
Barbara J. Reys ◽  
David D. Barker ◽  
Rick Billstein
Keyword(s):  
Mathematics Learning ◽  
High Stakes Testing ◽  
School Personnel ◽  
Learning Opportunities ◽  
School Mathematics ◽  
High Quality ◽  
High Stakes ◽  
Principles And Standards ◽  
Curricular Materials ◽  
Silver Bullet

In this era of high-stakes testing and public accountability, school personnel are scrambling for ways to improve mathematics learning opportunities for all students. Although there is no single silver-bullet solution, Principles and Standards for School Mathematics (NCTM 2000) provides guidelines for designing high-quality school mathematics programs. One avenue for strengthening programs is through selecting and implementing high-quality curricular materials (textbooks).

Reader Reflections: January 2000

2000 ◽  
Vol 93 (1) ◽  
pp. 4-59
Keyword(s):  
Mathematics Education ◽  
Board Of Directors ◽  
School Mathematics ◽  
High Quality ◽  
The Board Of Directors ◽  
Principles And Standards

The coming years will be exciting as NCTM's updated Standards document, Principles and Standards for School Mathematics, makes its debut in 2000. The coming years will also be challenging as we try to achieve our mission of a high-quality mathematics education for every child. Next year, NCTM members will elect their next president and four members of the Board of Directors.

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