Middle-Level Students Learn Mathematics Using the U.S. Map

2002 ◽  
Vol 8 (2) ◽  
pp. 86-90
Author(s):  
Hari P. Koirala ◽  
Phillip M. Goodwin
Keyword(s):  
Middle School ◽  
Mathematical Understanding ◽  
Middle Level ◽  
School Mathematics ◽  
Subject Areas ◽  
Principles And Standards ◽  
Middle Level Students ◽  
The U.S

Middle school educators have widely accepted the importance of interdisciplinary curricula (Cook and Martinello 1994), and Principles and Standards for School Mathematics argues that mathematics should be linked with other subject areas at all levels (NCTM 2000). According to Principles and Standards, “thinking mathematically involves looking for connections, and making connections builds mathematical understanding” (p. 274). Therefore, connecting mathematics to other disciplines has become particularly important.

scholarly journals Literacy-Based Instructional Techniques for the Middle School Mathematics Teacher

2020 ◽  
Vol 9 (2) ◽  
pp. 91
Author(s):  
Nicole Parker ◽  
Janet Breitenstein ◽  
Cindy Jones
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Mathematics Teacher ◽  
Middle School Mathematics ◽  
Mathematical Understanding ◽  
Disciplinary Literacy ◽  
School Mathematics ◽  
Instructional Techniques ◽  
Literacy Strategies ◽  
And Performance

Disciplinary literacy strategies in mathematics lessons are essential and may be embedded in three necessary parts of the lesson: before reading, during reading, and after reading. In this article, we highlight disciplinary literacy strategies that middle school mathematics teachers might implement to guide students to increased mathematical understanding and performance. 

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.

Developing Algebraic Thinking through Pattern Exploration

2006 ◽  
Vol 11 (9) ◽  
pp. 428-433 ◽  
Author(s):  
Lesley Lee ◽  
Viktor Freiman
Keyword(s):  
Middle School ◽  
Middle Grades ◽  
Algebraic Thinking ◽  
School Mathematics ◽  
Scientific Disciplines ◽  
Algebraic Language ◽  
Principles And Standards ◽  
Relationship Of ◽  
The Relationship ◽  
Repeating Patterns

Pattern exploration is A pivotal activity in all mathematics, indeed in all the scientific disciplines. Children who are attempting to express perceived patterns mathematically are in an excellent position to learn algebraic language and engage in algebraic activity. Principles and Standards for School Mathematics (NCTM 2000) acknowledges the relationship of pattern exploration and algebraic thinking by placing pattern work within the Algebra strand. Yet one can undertake considerable pattern exploration without engaging students in any algebraic thinking whatsoever and teachers may, themselves, be unclear about how patterns can be used to further algebraic thinking. Work with repeating patterns in the early grades, or teaching patterns as a “topic” in the middle grades, may not foster the development of algebraic thinking in students. In this article, we will address this question: How can teachers exploit pattern work to further algebraic thinking and introduce the formal study of algebra in middle school?

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.

Lollipop Statistics

2003 ◽  
Vol 9 (1) ◽  
pp. 12-15
Author(s):  
Dianne S. Goldsby
Keyword(s):  
High School ◽  
Middle School ◽  
High School Students ◽  
School Mathematics ◽  
Constructivist Approach ◽  
School Students ◽  
Area Of Interest ◽  
Approach To Teaching ◽  
The 1950S ◽  
Principles And Standards

AS NCTM'S Principles and Standards for School Mathematics (2000) points out, students should work directly with data to understand the fundamentals of statistical ideas. Teachers should also introduce statistics in a way that will capture the attention of students of varying abilities and interests. The constructivist approach to teaching emphasizes the idea that students work better when presented with tasks that are meaningful and relevant; in other words, they expend energy on topics that interest them (Brahier 2000). One way to harness that energy in the classroom is to teach with music, an area of interest for most middle school and high school students. This article describes the use of the 1950s hit “Lollipop” (Ross and Dixon 1986), heard in the movie Stand by Me, as a launching point to introduce ideas of counting, working with frequency tables, and graphing data.

Connecting Measurement and Architecture: Building an Inflatable

2007 ◽  
Vol 13 (3) ◽  
pp. 144-149
Author(s):  
Elizabeth D. Gray ◽  
Denise Tullier-Holly
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
School Mathematics ◽  
Classroom Experiences ◽  
School Students ◽  
The Real ◽  
Mathematical Connections ◽  
Principles And Standards

Middle school students need to see connections between mathematics and the real world. However, they often learn mathematics as a set of distinct topics or separate strands, because a majority of the available textbooks tends to present it that way, and teachers tend to follow the textbooks. According to Principles and Standards for School Mathematics (NCTM 2000), our students should be made aware of mathematical connections explicitly so that the manner in which topics are connected is obvious. McClain (1996) suggests that if teachers offer classroom experiences in which students can see connections, then “the vibrant discipline of mathematics actively engages students in their own learning” (p. 682).

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).

Geometric Conjectures: The Importance of Counterexamples

2003 ◽  
Vol 9 (4) ◽  
pp. 210-215
Author(s):  
Jeffery J. Boats ◽  
Nancy K. Dwyer ◽  
Sharon Laing ◽  
Mark P. Fratella
Keyword(s):  
Middle School ◽  
Pattern Recognition ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Mathematics Students ◽  
Reasoning Skills ◽  
Principles And Standards

TO DEVELOP STUDENTS' REASONING SKILLS, the NCTM's Principles and Standards for School Mathematics (2000) recommends that students make generalizations and evaluate conjectures. In particular, middle school mathematics students should be engaged in activities involving pattern recognition as a means of formulating such conjectures.

Proportional Reasoning: Lessons from Research in Data and Chance

2004 ◽  
Vol 10 (2) ◽  
pp. 104-109
Author(s):  
Jane Watson ◽  
J. Shaughnessy
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
Proportional Reasoning ◽  
School Mathematics ◽  
School Level ◽  
Principles And Standards ◽  
Middle School Level

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) places proportionality among the major concepts connecting different topics in the mathematics curriculum at the middle school level (p. 217). What concerns us about many of the problems presented to students, however, is that they are often posed purely as a ratio or proportion from the start. Often the statement of a problem is a giveaway that a proportion is involved. For example, the question “If 15 students out of 20 get a problem correct, how many students in a class of 28 would we expect to get the problem correct?” does not tap the depth of proportional reasoning that is required for meaningful problem solving.

Take Time For Action: The Number of Trials Does Matter

2002 ◽  
Vol 8 (2) ◽  
pp. 106-108
Author(s):  
Leslie Aspinwall ◽  
James Tarr
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
School Mathematics ◽  
School Students ◽  
Principles And Standards

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) calls for middle school students to develop and evaluate inferences that are based on data. Combining or “pooling” data from simulations reduces the likelihood of drawing incorrect inferences. But are your students aware that more accurate inferences can be drawn from larger sets of data and that smaller samples are more likely to produce unusual results?

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