bluuebunny/crossref_metadata_2025 huggingface dataset:
Evaluation of Cardiopulmonary Resuscitation and Underlying Medical Conditions in Hospitalized Patients
Authors: Moezzi Meisam , Alavi Mostafa , Afshari Golshan , Fatemi Nasrin
Published: December 2020

Background: A critical, therapeutic interference that develops the opportunity of survival is cardiopulmonary resuscitation (CPR). One of the practical factors resulting from resuscitation is the presence or absence of underlying disorders in patients. Objectives: This experiment aims to evaluate the primary disease and success rate of resuscitation. Methods: This study was an observational retrospective study; the therapeutic histories of all patients who sustained CPR were collected. A total of 587 patient case histories, who were supported with in Hospital CPR within two years from January 2017 to June 2018, were enrolled in the current investigation. The association of CPR success rate with underlying disease, the first cardiac rhythm observed after monitoring, and the use of cardiac defibrillator was investigated. Results: Overall, the success valuation of CPR in this investigation was 26.3%. There was no notable correlation between the success rate of CPR, and the early detection of cardiac rhythm after monitoring and using a cardiac defibrillator. Past medical histories reported a difference among the success rates of CPR in patients with hypertension, diabetes, and cardiac and renal disease. Conclusions: The current study revealed a significant difference in past medical histories and CPR outcomes.
The Impact of Radiofrequency Waves on Male Infertility: A Systematic Review
Authors: Darvish Leili , Amraee Azadeh , Akhavan Amjadi Marjan , Atarodi Kashani Zahra , Ghazanfarpour Masoumeh , Roozbeh Nasibeh , Abdi Fatemeh
Published: December 2020

Context: As the use of cellphones and other electronic devices increases, concerns about the possible effect of radiofrequency waves on health are growing. Long-term use of the cellphone may have negative effects on sperm quality. Objectives: The purpose of this research was to examine men's infertility due to the effect of radiofrequency waves. Methods: In this systematic review, language restrictions were not considered in searching the databases. Cochrane Library, Google Scholar, PubMed, EMBASE, ProQuest, CINAHL, Science Direct, MEDLINE, and Scopus were used to obtain the data from them. All data were scanned from the year 2000 until 2019. Papers selected for retrieval were evaluated by the Newcastle-Ottawa and CONSORT scales. Results: A total of 14 articles that met the inclusion criteria were ultimately assessed. Motile sperm, sperm vitality and membrane integrity, morphology, volume, total sperm count, sperm concentration, and sperm fertility were found to be influenced by radiofrequency waves. Conclusions: The results showed that RF has detrimental effects on semen parameters and due to an increase in RF wave use currently and its role in male infertility, giving information to men about adverse complications of RF is necessary. Further studies are needed to design the less harmful devices.
From the Chair
Authors: Kellam Lynda
Published: December 2020

Dear GODORT Members,I am excited to serve as the chair of GODORT for this year. And what a year to serve! For those unfamiliar with me, I am the senior data librarian at the Cornell Institute for Social and Economic Research, where I’ve been since July 2019. Before that, I was the data and government information librarian at the University of North Carolina at Greensboro (UNCG) for fourteen years. At UNCG I was the Federal Library Depository Program selective depository coordinator and, while I no longer work directly with documents, I remain committed to the use, preservation, and continuity of access to government information.
Problematic Global Metrics
Authors: Church Jim
Published: December 2020

An added benefit of doing library instruction is you learn things from students and faculty. This knowledge informs both collection development and research consultations. It is especially interesting when a new faculty member arrives and issues a revised syllabus for a popular course. One such class at UC Berkeley is in the Global Poverty and Practice (GPP) minor, founded by Professor Ananya Roy ten years ago. Her book, Poverty Capital: Microfinance and the Making of Development, makes the uncomfortable point that people and institutions profit from poverty: it is a lucrative business. But there are also those who attempt to create and influence “poverty knowledge.” The 1998 subtitle of the World Bank’s flagship publication, the World Development Report, was “Knowledge for Development.” In 2017 the World Bank wrote a feature news article (about itself) as a “knowledge institution.” There are articles that trace the history of the World Bank’s vision of itself as a “knowledge bank,” a term I find both amusing (do they charge “interest”?) and problematic. Yet a library is also a knowledge institution, and what we purchase or recommend influences the thinking and research of students and scholars.
Food Loss Waste in the United States Food Supply Chain: An Analysis of Its Functions, Oversight, and Recent Impacts from the Coronavirus Pandemic
Authors: Price Anna L.
Published: December 2020

Government oversight of the food supply chain consists of a complicated regulatory framework involving multiple executive branch agencies, congressional committees, and state governments. The agencies primarily involved with food safety issues are the Food and Drug Administration (FDA), the Food Safety and Inspection Service (FSIS), the US Department of Agriculture (USDA), the Environmental Protection Agency (EPA), and the National Marine Fisheries Service (NMFS). Although the above entities divide responsibility for different aspects of food safety and quality, according to a 2019 Government Accountability Office (GAO) report, the patchwork of statutes and regulations has led to “inconsistent oversight, ineffective coordination, and inefficient use of resources.”
Claim-Rule-Connection: A Strategy for Justifying Reasoning
Authors: Ervin-Kassab Lara , Roddick Cheryl , Vickery, Alison , Tapper Juliana
Published: December 2020

Develop middle school students' ability to defend their thinking with this engaging tactic.
Exploring Exponential Growth in Elementary School
Authors: Russo James , Russo, Toby , Kalogeropoulos Penelope
Published: December 2020

Four task-design principles show the value of earlier exposure to this powerful concept.
Children’s Games and Games for Children
Authors: Banting Nat , Williams Chad
Published: December 2020

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.
Cultural Connections: Exploring the Mathematics of Qatayef
Authors: Naanou Paul , Rhodes Sam
Published: December 2020

Students grapple with the problem of finding the volume of two different folds of a traditional Levantine dessert using either geometry or calculus.
This Journal is Yours
Authors: Greenwood Jay
Published: December 2020

NCTM Proudly Announces the Arrival of its newest journal, Mathematics Teaching in the Middle School. In so doing, we have increased the already impressive lineup of professional mathematics publications dedicated to the CTM's principles and standards. Aspects that make this journal so exciting are its focus and emphasis on the middle school teacher and student. The Editorial Panel has worked hard to address the interests and needs of the many classroom teachers who have offered their feedback, both as a result of several surveys and as a result of the “Call for Manuscripts” announcement that appeared in both the Arithmetic Teacher and the Mathematics Teacher.
Power On! Promoting Classroom Dialogue: Using Calculators to Discover Patterns in Dividing Decimals
Authors: Williams Susan E. , Copley Juanita V.
Published: December 2020

The three questions that seem the most difficult for mathematics teachers to answer satisfactorily for themselve about the use of calculators in the classroom are as follows:
Fractions of Ancient Egypt in the Contemporary Classroom
Authors: Michalowicz Karen Dee
Published: December 2020

It is quite remarkable that so much is known about arithmetic in ancient Egypt. The major source of our knowledge is the Rhind Mathematical Papyrus, circa 1600 B.C., named after A. Henry Rhind. Sir Henry purchased the papyrus in 1858 after it had been discovered in Thebes in the ruins of a small structure. No other document presents such extensive information about early Egyptian mathematics. The papyrus can be viewed in London at the British Museum, which received it as a legacy of the Rhind estate.
Now & Then: From Manager to Meteorologist From Heavenly Bodies to Barometers
Authors: Barnes Sue , Michalowicz Karen Dee , Womack Melanie A.
Published: December 2020

Now… Shreveport is a large town in Northwest Louisiana. A state that is classified as a severe-weather area. Northern Louisiana is often hit by thunderstorms and tornadoes. Southern Louisiana, on the Gulf of Mexico, is susceptible to hurricanes during late summer. When the manager of television station KSLA in Shreveport began looking for a person to fill the weather-news slot a few years ago, he did not want someone who could just point to a weather map. He wanted a good meteorologist. In regions that have invariant weather, those people who give the weather are usually actors or actresses who read the predictions prepared by someone else. The study of weather, however, is called meteorology, and a professional meteorologist is someone who has a degree in weather study. Even in area with severeweather conditions, some television stations do not hire a professional meteorologist but hire a broadcast meteorologist instead. A broadcast meteorologist is a journalist who has taken general courses in meteorology while studying for a communications or journalism degree.
The “Mangoes Problem”
Authors: Stonewater Jerry K.
Published: December 2020

Look at the mangoes problem in Figure 1 and work on a solution before reading the rest of this article. Pay particular attention to how you go about solving the problem. Look for alternative solution strategies if you get stuck.
Now & Then: Diana Lee, Actuary
Authors: Barnes Sue , Michalowicz Karen Dee
Published: December 2020

Now … what do diana lee from des plaines, illinois, and merlin the Magician have in common? Both of them try to see into the future. Merlin concocts potions, waves his magic wand, and wears a pointed hat Diana uses mathematics. Merlin is a mythical figure from King Arthur's Court. Diana is a modern business executive with the National Association of Independent Insurers (NAII), an organization that furnishes research and technical support and lobbying services in insurance legislation and regulation to 570 insurance companies across the United States.
“Real People”: A Fifth-Grade Class Investigates the Lives of Mathematicians
Authors: Morrow Jean , Schrock Connie , Buchman Debbie
Published: December 2020

By the end of the twentieth century, only 15 percent of the people entering the work force in the United States will be white males. Today, white and Asian males make up 95 percent of the recipients of college degrees in mathematics, science, and engineering (National Research Council 1989). Consequently, we must prepare females and minorities to fill this coming void. One way to encourage young women and minority students is to offer them role models who have been successful in mathematics. As the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 5) states, “Students should have numerous and varied experiences related to the cultural, historical, and scientific evolution of mathematics so that they can appreciate the role of mathematics in the development of our contemporary society.…”
What is the Whole?
Authors: Wentworth Nancy M. , Monroe Eula Ewing
Published: December 2020

Defining the unit or “the whole” in fraction examples is often confusing to students, not only because of the particular example being considered but often because of the representations teachers use as they help students construct meanings. This article begins with a brief summary of constructivist mathematics education along with a situation in which a teacher misunderstood the meaning of an answer constructed by two students. Then three examples of representations of common fractions and ways that teachers can encourage students to construct useful meanings of the fractional unit will be considered.
The Thinking of Students: Students Travel “The Road Not Taken”
Authors: Oldman Michele
Published: December 2020

Here is a glimpse at seventh- and eighthgrade mathematics students' responses to Robert Frost's poem:
National Council of Teachers of Mathematics: Selling and Buying Reform: If We Build It, Will They Come?
Authors: Price Jack
Published: December 2020

The original title of the talk on which this article is based was “Mathematics Reform: Field of Dreams or Waiting for Godot?” In the film, Ray Kinsella's “field of dreams” brings thousands of people. He built it and they came. In Waiting for Godot, two people talk to each other throughout the entire play, waiting for someone who never comes. A logical comparison consists of these questions: Will we bring thousands of people to join us in building a betler mathematics education for all students, or are we talking to each other while wailing for the change that never comes?
Implementing Data Analysis in a Sixth-Grade Classroom
Authors: Brosnan Patricia A.
Published: December 2020

A middle school mathematics classroom is an exciting place to be. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) presents for grades 5-8 many curricular idea that have generated much enthusiasm by incorporating teaching strategies that promote active student learning. Middle school teachers have taken great strides toward implementing ideas that are both innovative and instructive. This article explains how one teacher is converting her traditional mathematics classroom into one that more closely reflects the standards document. These result could not have happened as quickly without the cooperative efforts of school and university personnel.
Now & Then: Counting On the Air: Time through the Age
Authors: Bennett Betsy K.
Published: December 2020

Now … “I play music. I sing. I talk, but mostly I do math,” Kenny Curtis replies when asked about his work as a disc jockey. “Mostly math” is probably not what his audience expects this twenty-six-year-old entertainer to say, but when he describes the careful counting, adding, and subtracting of times essential to live radio broadcasting, his description of his work during his time on the air seems accurate. The preparation for his radio show includes selecting music, taping segments, gathering information from a variety of sources, and organizing them all into a show that will entertain and inform his audience. Once on the air, he is a disc jockey, actor, public speaker, comedian, director, and manager of the radio's stage. While presenting the content of the show, he constantly checks his computer clocks showing the current time and the times for airing pretaped commercials, adds and subtracts the exact times of songs and taped reports, and adjusts his live segments so that the time required for the material and the time available between commercials match exactly. His accurate arithmetic in units of minutes and seconds is extremely important because he has only a ten-second window of time during which he must act on the computer's directions to play a commercial. He is a talented entertainer who uses both his college training in theater and mass communication and his basic mathematics skills during every minute of the five hours each day that he is on the air.
January's Menu of Problems
Authors: Greer Gerry , Wantuck Larry
Published: December 2020

A light fare to whet your mathematical appetite.
Covering the Plane with Rep-Tiles
Authors: Fosnaugh Linda S. , Harrell Marvin E.
Published: December 2020

Because of its beauty and applicability in ancient as well as modern times, the art of tiling has interested humankind for centuries. Roman mosaics and Moslem religious buildings are among some of the oldest examples of tiling. More modern examples of tiling as an art form can be found in the works of the Dutch artist M. C. Escher. Senechal (1990) notes that the study of tilings is important in mathematics education because the study of shape “draws on and contributes to not only mathematics but also the sciences and the arts.” Some common uses of tilings include the covering of walls, floors, ceilings, streets, sidewalks, and patios.
On My Mind: Conceptual Understanding and Computational Skill in School Mathematics
Authors: Scavo Thomas R. , Conroy Nora K.
Published: December 2020

Evaluation standard 9 of the NCTM's curriculum and Evaluation Standards for School Mathematics (1989) addresses the issue of mathematical procedures including, but not limited to, computational methods and algorithms. The standards document relates that.
The Arcs of Archaeology
Authors: Spence Bonnie S.
Published: December 2020

For the past several years, i have sought out opportunities outside mathematics for personal enrichment and enjoyment. These experiences have caused me to become more aware of the connections between mathematics and other areas. As a result, I have begun developing lessons to show my students how mathematics is used in the real world. One summer I joined another teacher and twelve middle school students and decided to brave the eighteen-hour drive from Oklahoma to the Crow Canyon Archaeological Center in Co1tez, Colorado. The mathematical lesson discussed in this article emerged from one week of learning about the Anasazi culture and experiencing hands-on archaeology. Throughout the years, this lesson has been revised and expanded as both students and experience have given me new ideas.
Assessment: Assessing Mathematical Processes: The English Experience
Authors: Swan Malcolm
Published: December 2020

Historically, assessment has been concerned with measuring how completely students have mastered knowledge and skills. More recently, however, increasing attention is being placed on how effectively students can tackle unstructured problems and investigate novel, open-ended situations. Here, the focus of assessment is on how well students have acquired those processes or strategies that guide the choice of appropriate skills and enable students to explore unfamiliar situations. In short, we are becoming more aware of the need to assess how well students perform as mathematicians in addition to how well they have learned mathematics.
Now & Then: Livestock Production by the Numbers: Taking the Measure of Things
Authors: Hilgart Faye
Published: December 2020

Now … when marlin subra graduated from high school, he knew that he wanted to continue working on the family dairy farm in westcentral Wisconsin. He had prepared well by taking all the high school awicultural classes available and by actively participating in the 4-H and Future Farmers of America (FFA) organizations. He loved working with animals, and he enjoyed the hard work required of a dairy farmer. In addition to maintaining a dairy herd, Marlin also raised registered Suffolk sheep. However, after sixteen years of farming, the rapidly evolving agticultural scene and a changing farm economy meant that modifications were needed to stay competitive.
Teacher to Teacher: Harry Potter in the Mathematics Classroom
Authors: Beaton Tisha
Published: December 2020

Inspired by my students' enthusiasm for Harry Potter and the Sorcerer's Stone, I developed a multidisciplinary thematic unit. It started with the novel that the class was reading aloud for language arts and evolved into a mathematics problem that formed the foundation of the unit. The context of the problem linked literature to mathematics, provided a world about which most children could understand, and produced mathematics problems that are relevant to daily life. The students were keen to try the problems, and the familiar context helped them to feel self-confident.
Two Students' Constructed Strategies to Divide Fractions
Authors: Perlwitz Marcela
Published: December 2020

Students need opportunities to make connections among different concepts in mathematics throughout their mathematics education (NCTM 2000). For example, research has shown that students build their knowledge of fractions from their knowledge of whole numbers (Saenz-Ludlow 1990; Greer 1994).
Adding á La Gauss
Authors: Martinez-Cruz Armando M. , Barger Ellen C.
Published: December 2020

Carl Friedrich Gauss (1777–1855), considered the greatest mathematician of modern times, was born to a poor family in Brunswick, Germany. Although his father worked several unprofitable jobs to earn a meager living and assumed that Carl would follow in his footsteps, his mother insisted that her son receive an appropriate education. Young Gauss demonstrated amazing intellect at an early age. He was just three years old when he corrected a mistake in his father's weekly payroll computation. By the time he was nine, his schoolmasters admitted, “There was nothing more they could teach the boy” (Burton 2003, p. 509).
How Much Water Is in the Skating Rink?
Authors: Ameis Jerry
Published: December 2020

The transition from direct measurement to the use of formulas for determining perimeter, area, and volume can be difficult for students. This article concerns easing that transition for a grade-6 student with respect to the formula for the volume of a rectangular prism (a box, in the eyes of some grade-6 students).
Comparing Kisses
Authors: Haller Susan , Richardson Mary
Published: December 2020

Middle grades students should be given ample opportunities to explore probability and statistics topics. In particular, students should be encouraged to collect, organize, and describe data; construct appropriate charts and graphs to summarize the data; make predictions and conclusions based on the data; and test these predictions and conclusions (NCTM 1989, 2000). In this article, we describe three activities, all of which involve materials that students are certain to enjoy—Hershey's Kisses candies.
Families Ask: What Does Algebraic Thinking Look Like?
Authors: Bay-Williams Jennifer , Martinie Sherri
Published: December 2020

A lgebraic thinking is a critical skill for all students. Algebra is the study of patterns, and patterns span the curriculum. Algebraic thinking can support students' learning of many topics. For example, if students collect data on the radius, diameter, and circumference of various-sized circles and look for patterns in their data, they will discover the formula for the circumference of a circle. Similarly, if students explore patterns in problems like 3 ÷ 1/2 (how many 1/2s are in 3?), 4 ÷ 1/4, and 2 ÷ 1/5, they will begin to develop a strategy for the division of fractions (multiply by the denominator). Algebraic equations are used to describe real-world phenomena and can then be used to predict new phenomena. For example, if you know that you can walk 3 miles in an hour, then you can determine a distance for any amount of time (d = 3t), or how much time it will take to cover any distance (t = d/3).
Exploring Measurement Concepts through Literature: Natural Links across Disciplines
Authors: Austin Richard A. , Thompson Denisse R. , Beckmann Charlene E.
Published: December 2020

Literature Provides a Natural OPPortunity to motivate middle school students in their mathematics study. Stories are not only a springboard into measurement activities but are also a bridge between the mathematics of measurement and other curricular areas. As middle school teachers increasingly team with teachers of other disciplines, literature offers an opportunity to coordinate lesson content across a variety of fields. The authors' experiences in middle school classrooms have convinced them that middle school students respond positively to stories and to mathematical investigations that are based on the story presentation (Austin and Thompson 1997; Thompson, Austin, and Beckmann 2002).
Using Humor to Gain Mathematical Insight
Authors: Gadanidis George , Gadanidis Janette M. , Huang Alyssa Y.
Published: December 2020

Sometimes Missing in Mathematics classrooms is mathematical humor, which might alleviate the tension that many students experience. Also needed are opportunities for mathematical insight, through which students might sense the pleasure of doing mathematics. Humor and insight have many similarities. Both are creative acts. Both emerge from our predisposition to explore and take pleasure in novel ways of seeing and understanding our world. We are drawn to apparent dissonance, to seek to understand complexity, and to make ourselves more complex; these elements often produce positive feelings and all can be a part of both humor and insight.
Dividing Fractions: Reconciling Self-Generated Solutions with Algorithmic Answers
Authors: Perlwitz Marcela D.
Published: December 2020

In this Article, I Discuss Some Key Episodes that occurred in one of my mathematics classes on basic arithmetic notions. The core concepts of the course included place-value numeration, whole numbers and operations, fractions and operations, and foundations of number theory.
A Look at Some Numbers of Old: Perfect, Deficient, and Abundant
Authors: Adams Thomasenia , Murphy Katherine
Published: December 2020

No One Knows Just When Number theory, the study of numbers (integers) and their properties, evolved, but “the origins of the study of number properties go back probably almost as far as counting and the arithmetic operations” (Ore 1988, p. 25). Carl Friedrich Gauss (1777–1855), one of the greatest of all mathematicians, stated that “mathematics is the queen of the sciences, but number theory is the queen of mathematics” (Long 1965, p. 1).
By Way of Introduction: Connecting Mathematics and Literature in the Middle Grades
Authors: Sherard Hamp
Published: December 2020

Why Should We Use Literature to Teach Mathematics to Students in the Middle grades? There are compelling reasons for doing so. Literature can provide meaningful contexts in which students make sense of mathematics and construct their understandings of mathematical concepts. Well-chosen literature sparks interest and curiosity in students and increases their willingness to do mathematics; it also builds positive attitudes toward mathematics. The use of literature encourages communication and makes connections to other subjects as well as to topics within mathematics. Literature helps make mathematics relevant to students.
The Power of Two: Linking Mathematics and Literature
Authors: Zambo Ron
Published: December 2020

One of my interests as a mathematics educator is helping teachers learn how to integrate mathematics instruction with other content areas. I like to demonstrate how an interesting story can be used as the focal point for a series of mathematics explorations. In that context, I have read A Grain of Rice (Pittman 1986) over the last several years to many undergraduate and graduate education majors, teachers at middle schools and elementary schools, and groups at mathematics conferences. Each time, I have enjoyed reading the story, the audience has enjoyed hearing the story, and they have been interested in the related mathematics activities.
You Read Me a Story, I Will Read You a Pattern
Authors: Pace Charyl L.
Published: December 2020

Have You Ever Wondered how to use children's literature in a middle school mathematics classroom? In today's standards-driven environment, aligning activities to various standards is important. Children's books can be the perfect introduction to a unit or lesson. Paying careful attention to the elements in the story and using a little imagination, creativity, and a working knowledge of the mathematics Standards are all the items needed to begin.
Children's Literature: A Motivating Context to Explore Functions
Authors: Billings Esther M. H. , Beckmann Charlene E.
Published: December 2020

Most students love a good story! When we use children's literature as a context to explore functional relationships, our students are more motivated to learn. In this article, we share how we use children's literature in courses for prospective middle-grades teachers to explore and deepen these teachers' understanding of functions. We expect prospective teachers to teach functions to their future middle-grades students with understanding; therefore, we use literature to help them develop a personal understanding of functions that is connected and comprehensive.
Questioning Our Patterns of Questioning
Authors: Herbel-Eisenmann Beth A. , Breyfogle M. Lynn
Published: December 2020

Teachers pose a variety of questions to their students every day. As teachers, we recognize that some questions promote deeper mathematical thinking than others (for more information about levels of questions, see Martens 1999, Rowan and Robles 1998, and Vacc 1993). For example, when asking, “Is there another way to represent or explain what you are saying?” students are given the chance to justify their thinking in multiple ways. The question “What did you do next?” focuses only on the procedures that students followed to obtain an answer. Thinking about the questions we ask is important, but equally important is thinking about the patterns of questions that are asked.
Spotlight on the Principles: Creating an Environment for Learning with Understanding: The Learning Principle
Authors: Fagan Emily
Published: December 2020

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.
Using Schemas to Develop Algebraic Thinking
Authors: Steele Diana F.
Published: December 2020

To prepare students to meaningfully understand algebraic concepts, they need early and continuous opportunities to think algebraically. But what is algebraic thinking? Although it may include variables and expressions, algebraic thinking has a broader and different connotation than the term algebra. Kieran (1996) defined the term algebraic thinking as “the use of any of a variety of representations that handle quantitative situations in a relational way” (pp. 4–5). Smith (2003) characterized algebraic thinking as the ability to extend patterns by examining them and finding the relationship between the variables in the patterns—how the patterns grow. In a teaching experiment that I conducted in a seventh-grade prealgebra class, I used these definitions to guide my instruction.
Using Student Work to Develop Teachers' Knowledge of Algebra
Authors: Herbel-Eisenmann Beth A. , Phillips Elizabeth Difanis
Published: December 2020

Recent literature has shown that having teachers examine student work can enhance teachers' thinking about what constitutes mathematical understanding (Crespo 2000; Crockett 2001). There is also evidence that teachers need to experience unconventional mathematics problems to see the value of using them in their own classrooms (Ball 1988; Crespo 2003).
Mathematics Detective: The Case of the Culinary Counting Clues and Conditions
Authors: Campbell Larry
Published: December 2020

Before we go any further, what do you think? Do you think there are 81 different meal combinations possible from those listed?
Solve It!: Elizabeth's Long Walk
Authors: Kersaint Gladis
Published: December 2020

The editorial panel is presenting the following problem to stimulate submissions to “The Thinking of Students” department. We encourage teachers to try this problem with students and analyze the different strategies that they use to solve it.
Take Time for Action: Investigating Students' Thinking about Nets
Authors: Wiest Lynda R.
Published: December 2020

Can students articulate how they reason about a spatial task? Can they integrate visual and analytic reasoning to make the best use of both types of thinking when working on a single task? Are “integrated” thinkers more successful than those who draw mainly on one side of their brain?
Families Ask: Rules or Understanding?
Authors: Martinie Sherri
Published: December 2020

The role of understanding in learning mathematics has been referred to in textbooks from the 1800s and has been supported throughout the 1900s by psychologists, philosophers, and educators. Despite its persistent appearance, the importance of understanding continues to be questioned for several reasons. First, many adults view school mathematics as something separate from the mathematics needed in everyday life. The mathematics they learned in school was dominated by isolated facts, skills, rules, and procedures to be memorized and practiced. It has been reported that the mathematics curriculum is shallow, undemanding, and covers too many topics superficially (Kilpatrick, Swafford, and Findell 2001).
Spatial Visualization: What Happens When You Turn It?
Authors: Chavez Óscar , Reys Robert , Jones Dusty
Published: December 2020

Spatial Visualization Is An Important Skill that deserves instructional attention. Strong evidence supports the claim that “measures of mathematical ability tend to be strongly correlated with spatial ability” (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will have additional benefits for their mathematical growth, perhaps even going so far as to improve test performance.
Keeping It Real: The Rationale for Using Manipulatives in the Middle Grades
Authors: Weiss Dana M. Freer
Published: December 2020

Mathematics skills are critical to functioning in today's world. These skills are not just useful in middle school mathematics classes; they are important in our daily lives. To become competent adults, students must learn basic mathematics concepts and how to apply them to reasoning and problem solving (Cass, Cates, Smith, and Jackson 2003; Goldsmith and Mark 1999). With 32 percent of United States eighth graders falling below the basic proficiency level for mathematics, and 61 percent of Blacks performing at a substandard level, the United States has been woefully unsuccessful in its preparation of citizens for a productive life (NCTM 2004). Our educational system is clearly failing to teach important skills to a significant number of students. This article will examine research on one teaching method—the use of manipulatives—that if used in the middle grades may help remedy this problem. The question explored will be whether or not the use of manipulatives is an effective tool in teaching mathematics concepts and reasoning to middle- grades students.
Creating Multiple Representations in Algebra: All Chocolate, No Change
Authors: Hyde Arthur , George Katie , Mynard Suzanne , Hull Christina , Watson Sharon , Watson Patrick
Published: December 2020

As teachers of mathematics in the middle grades, we were excited to find an approach to teaching algebra concepts that could be readily modified to be successful with all our students.
Developing Algebraic Thinking: An Academy Model for Professional Development
Authors: Langham Belinda , Sundberg Sue , Goodman Terry
Published: December 2020

To think algebraically, one must be able to understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts, according to Navigating through Algebra (NCTM 2001). Many teachers, however, often view algebra as a set of isolated skills and procedures.
The A-Maizing Corn Lab: A Geneticist's Biography Leads a Mathematics Exploration
Authors: Cwikla Julie , Patterson Marcelle
Published: December 2020

Literature can offer a meaningful context for discussing and learning mathematics. Books allow students to view mathematics in a variety of contexts, which can provide a forum for both verbal and written mathematics communication. “Students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically” (NCTM 2000, p. 60).
Teacher to Teacher: Dialogue: A Route to ACT-ive Learning
Authors: Bennett Curtis D. , DeYoung Mary J. , Rutledge James J. , Young Elaine
Published: December 2020

Engaging students is an important part of planning for daily class lessons. The two-person skit discussed in this article was adapted from an idea by a master biology teacher who had developed this novel teaching/ learning strategy to allow for more student participation in larger class settings. The format is deceptively simple and straightforward; pairs of students perform the two roles in the skit during simultaneous classroom performances. The resulting “noise” is actually the sound of students engaging with the subject at hand. The inclusion of appropriate gestures and staging commands heightens the interest level for a lot of students, and most respond with enthusiasm.
Selecting High-Quality Mathematics Textbooks
Authors: Tarr James E. , Reys Barbara J. , Barker David D. , Billstein Rick
Published: December 2020

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).
Fantasy Football and Mathematics Score Touchdowns with Students
Authors: Flockhart Daniel J.
Published: December 2020

In the 1990s, I combined two of my passions— mathematics and Fantasy Football— into a meaningful, powerful assignment that engaged students in grades 5–8 who lacked motivation in mathematics. Fantasy Football is a game played nationwide by an estimated 15 million adolescents and adults (Fantasy Sports Trade Association 2003). Between 16 percent to 20 percent of all participants are female (Beason 2005). Students create fantasy teams by purchasing National Football League (NFL) players and compete by earning points based on the real-life statistics of the players. Each week, students locate the names of their players in box scores (statistical summaries of games) to compute the points scored by their players. Weekly points are accumulated throughout the entire season, and the student with the highest cumulative points is the winner.
Solve It!: State Fair
Authors: Kersaint Gladis , Mooney Edward
Published: December 2020

The editorial panel is presenting the following problem to stimulate submissions to “The Thinking of Students” department. We encourage teachers to try this problem with students and analyze the different approaches they use to solve it. feel free to photocopy this problem for use in your classroom. Please send the following if students generate unique strategies:
How Come? What If? So What? Reading in the Mathematics Classroom
Authors: Wallace Faith H. , Clark Karen K. , Cherry Mary L.
Published: December 2020

When You Think About Students reading in the mathematics classroom, what immediately comes to mind? What text sources do students generally read in a mathematics classroom? Are you picturing students reading a textbook or a workbook? do you see students reading problems and checking their answers? In many classrooms across the united states, this textbook work is exactly what reading in the mathematics classroom entails (Alvermann and moore 1991; bean 2000; Hiebert et al. 2003), particularly since the textbook has a profound influence on both what is taught and what is learned (Koehler and grouws 1992).
Hitting the Bull's-Eye: A Dart Game Simulation Using Graphing Calculator Technology
Authors: Mittag Kathleen Cage , Taylor Sharon E.
Published: December 2020

What do plotting points, making decimal representations, graphing circles, using a random number generator on a calculator, calculating the Pythagorean theorem, studying probability, and throwing darts have in common? We did not know the answer to that question either until we accidentally discovered an activity that incorporates all these elements.
Curriculum Focal Points for Pre-K–Grade 8 Mathematics: A Quest for Coherence
Authors: (Skip) Fennell Francis
Published: December 2020

On April 24, 2006, the National Council of Teachers of Mathematics (NCTM) Board of Directors approved “Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence.” The Curriculum Focal Points are specifically designed to provide leadership in the discussion about important mathematical topics at the pre- K–8 level. This introduction will define, identify the need for, and place in perspective the use of the focal points.
Solve It!: Number Golf
Authors: Mooney Edward S.
Published: December 2020

The editorial panel is presenting the following problem to stimulate submissions to “The Thinking of Students” department. We encourage teachers to try this problem with students and analyze the different approaches they use to solve it. Feel free to photocopy this problem for use in your classroom.
International Perspective: Beyond Su Doku
Authors: Sharp John
Published: December 2020

The current craze for su doku puzzles, which seem to be in most UK newspapers as well as numerous puzzle books, is a small subset of a much more interesting puzzle with a long history in recreational mathematics. What I find puzzling about Su Doku is why, with so many further possibilities, the puzzles seem so stuck in a rut. At least with crosswords there are many interesting variations on the clues. In looking at the history of the puzzle, I hope someone will devise new, more cunning ones.
Solve It! The Two-Digit Game
Authors: Mooney Edward S.
Published: December 2020

The Editorial Panel is presenting the following problem to stimulate submissions to “The Thinking of Students” department. We encourage teachers to try this problem with students and analyze the different ways that students solve it. Feel free to photocopy this problem for use in your classroom.
Math Roots: The Beginnings of the Metric System
Authors: Johnson Art , Norris Kit
Published: December 2020

The metric system is slowly but surely becoming an integral part of American society. Two-liter bottles of soda, 100- meter dashes, and milligrams of medicine are now commonplace. It is more important than ever that students have a working knowledge of the metric system. When students study metrics in mathematics class, it can be beneficial for them to learn something about its origins. The historical underpinnings of the metric system can be instructive and entertaining for students in the middle grades.
Finding Areas on Dot Paper
Authors: Pagni David L.
Published: December 2020

Finding The Areas Of Rectangles, TrIangles, parallelograms, and trapezoids through formulas are part of most state mathematics standards and are included in middle school mathematics textbooks. Students are expected to know these formulas and apply them to find the areas of figures shown in textbooks. But as the TIMSS 1995 video study pointed out, students in the united States are seldom given the opportunity to discover the formulas for themselves (Stigler and Hiebert 2004). This article provides activities that prompt students to investigate and discover the formulas, with a teacher's guidance. Finally, students work with a nonstandard unit of area measure, an equilateral triangle, to investigate area formulas using this unit.
Using Prediction to Promote Mathematical Reasoning
Authors: Kim Ok-Kyeong , Kasmer Lisa
Published: December 2020

Mathematical reasoning is fundamental to the learning of mathematics. when reasoning is effectively and routinely promoted and fostered in the classroom through justifying solutions, developing ideas, predicting results, or making sense of observed phenomena, students can develop a deeper understanding of mathematical ideas.
Math Roots: A Dozen Ways to Celebrate Mathematician of the Month
Authors: Fugitt Jamie
Published: December 2020

“Mathematics is one of the greatest cultural and intellectual achievements of humankind, and citizens should develop an appreciation and understanding of that achievement, including its aesthetic and even recreational aspects.” (NCTM 2000, p. 4)
Some Thoughts about Fractions
Authors: Usiskin Zalman P.
Published: December 2020

The writing of “The future of fractions” in 1978 was motivated by a single incident, the quote that begins the article. That quote—indicating that fractions would become obsolete—is from an editorial essay in the Virginia Mathematics Teacher by Lucien Hall. Hall was an active, responsible, and knowledgeable member of the mathematics education community, and when I saw what he had written, I knew that his statement represented the beliefs of many other mathematics teachers and educators. I felt that his statement and this broader view of the impending demise of fractions had to be addressed.
Solve It!: Christie's Cake
Authors: Mooney Edward S.
Published: December 2020

The editorial panel is presenting the following problem to stimulate submissions to “The Thinking of Students” departinent. We encourage teachers to try this problem with students and analyze the different ways that students solve it. Feel free to photocopy this problem for use it.
Integer Target: Using a Game to Model Integer Addition and Subtraction
Authors: Burkhart Jerry
Published: December 2020

Imagine a classroom where students are gathered in small groups, working with number lines and cards marked with integers. The students have chosen a “target number” on the number line and are deep in discussion, trying to find ways to make the sum of the integers on their cards match this number. There is a deck from which they draw, discard, or exchange cards. They also give, take, or trade cards with one another.
Mathematics, Art, Research, Collaboration, and Storytelling: The High M.A.R.C.S. Project
Authors: Reilly Edel M. , Pagnucci Gian S.
Published: December 2020

The deadening effect the separate-subject approach has on the lives of young people cannot be overestimated. (Beane 2000, p. 229)
Building an Online Discussion Group for Teachers
Authors: Groth Randall E. , Bergner Jennifer A.
Published: December 2020

Conversations with colleagues can be valuable in thinking through the logistics of implementing the NCTM's (2000) recommendations for teaching mathematics.
Focal Points—What's Next for You?
Authors: Fennell Francis
Published: December 2020

NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence was published in 2006. Change, or reform, has been something we in mathematics education have been involved with for decades—some would say since Sputnik, or for half a century. The intent of Curriculum Focal Points is to begin a dialogue relative to curricular reform at the pre-K–8 level, paying particular attention to state and local school district curricular frameworks. Some state frameworks contain over 100 outcomes at each grade level. What's a teacher to do? What's really important at these grade levels?