bluuebunny/crossref_metadata_2025 huggingface dataset:
One Teacher's Story
Authors: Collins Anne M.
Published: December 2020

Follow the journey of a teacher who changed his practice to meet the needs of all students while maintaining high expectations for all.
Drawing a Regression Line between Spaghetti and Basketball
Authors: Özgün-Koca S. Asli , Edwards Thomas G.
Published: December 2020

Students make a slam dunk, first with spaghetti and a scatter plot, then with a graphing calculator.
Mathematical Exploration: All Shades Are the Right Shade
Authors: Reilly Stephanie S.
Published: December 2020

Students spend a lot of time in algebra 1 solving linear equations and systems of linear equations. These subtopics of algebra can be problematic and difficult for students to grasp. After months of finding the solution to a linear equation (a line) and finding the solution to a system of linear equations (generally, a point), students struggle with understanding the solution to a linear inequality or a system of linear inequalities (a shaded region). Students might think, Why do we shade at all, what does the shading mean, and why is an overlapping shaded region the solution in an inequalities systems graph?
Math for Real: Courting Your Mascot
Authors: Hill Crystal A.
Published: December 2020

Many schools place a decal of their school mascot at the center of their basketball court. Score Connects is a company that creates mascot decals for schools. To do so, the company needs to work within the size of a middle school basketball court, which is 74 feet × 42 feet. All courts have a center circle that is 12 feet in diameter.
Student Confidence and Student Involvement
Authors: Nebesniak Amy L. , Heaton Ruth M.
Published: December 2020

After getting over the hurdle of implementing cooperative learning, one teacher's action research revealed that her students were more engaged and more willing to tackle difficult problems.
The Important Thing about Teaching Problem Solving
Authors: Roberts Sally K.
Published: December 2020

I teach a content course in problem solving for middle school teachers. During the course, teacher candidates have the opportunity to confront their insecurities as they actively engage in solving math problems using a variety of strategies. As the semester progresses, they add new strategies to their problem-solving arsenal and explicitly reflect on teaching and learning practices that are conducive to this process.
One Lesson, Many Facets
Authors: Gómez Conrado L.
Published: December 2020

Manipulatives and technology can model the scaffolding of language acquisition while teaching algebra and geometry.
Mathematical Exploration: Keeping All the Trains on the Tracks
Authors: Moyer Todd O.
Published: December 2020

Many eighth-grade and algebra 1 textbooks explore the formula distance = rate × time. Problems involving this formula can help students learn to write expressions, solve equations, and make judgments as to the reasonableness of the answers found.
Math for Real: How to Check Digits
Authors: Hoslar Alyssa M.
Published: December 2020

When an account or product number is typed into a computer, there is often a quick way to check that the number had been entered correctly. One way is with a check digit, which is an extra digit at the end of the account number, representing the ones digit of the sum of the account digits, or some other formula.
Map the Race to the White House
Authors: Shore Felice S. , Cooper Linda L.
Published: December 2020

The 2008 presidential election is a great backdrop for analyzing graphs, learning about population distributions, and studying the effect on the electoral voting process.
Mathematical Exploration: Understanding the Value of Pi
Authors: Perry Christine , Cyrus Vivian
Published: December 2020

At times, we must ask our students to accept certain content without giving them a full explanation, because understanding the underlying mathematics would require knowledge beyond their current level. One good example of such a concept is the irrational number pi.
On My Mind: The Conceptual Chicken and the Procedural Egg
Authors: Roberts Sally K.
Published: December 2020

One lesson we learned early on in child psychology courses is that learning progresses from the concrete to the semiconcrete, or representational, and finally to the abstract or symbolic level. At first glance, this seems to be not only logical but also a given fact of life. This vision of learning is a linear progression. When applied to mathematics, this learning theory leads to the assumption that the use of manipulatives and hands-on learning experiences should precede procedural symbol manipulation. It also leads to the belief that using manipulatives can ensure understanding of more abstract representations.
Put the Right Spin on Student Work
Authors: Ely Robert E. , Cohen Jessica Strowbridge
Published: December 2020

A Compound Probability Task And Rich Classroom Discussion Promote High-Level Understanding.
van Hiele Revisited
Authors: Breyfogle M. Lynn , Lynch Courtney M.
Published: December 2020

To analyze students' geometric thinking, use both formative and summative assessments and move students along the van Hiele model of thought.
Math for Real: Mowing and Moving
Authors: Moreno Jerry
Published: December 2020

Chris mows lawns that are generally 100 feet × 50 feet. He is wondering how much exercise he gets from mowing a lawn and how much area he actually mows.
Informing Practice: Helping Students Develop Capacity for Transfer
Authors: Johanning Debra I.
Published: December 2020

Teachers often report the frustration of teaching new mathematical concepts to students who learn the concepts but are then unable to transfer that understanding to new situations. Perkins and Salomon (1988) describe a major educational goal shared among most teachers: to build students' performance in a way that they can use their knowledge outside of school. Although the goal is clear and widely shared, accomplishing it can be challenging.
Water Bottle Designs and Measures
Authors: Carmody Heather Gramberg
Published: December 2020

Open-ended projects will motivate your students to think at higher levels.
Dividing Fractions: What Is the Divisor's Role?
Authors: Coughlin Heather A.
Published: December 2020

Cut out misconceptions by tying in the repeated-subtraction process.
A Professional Collaboration Model
Authors: Jenkins Oliver F.
Published: December 2020

Team planning is explored in light of information drawn from professional learning communities.
Multiplication Fact Fluency Using Doubles
Authors: Flowers Judith M. , Rubenstein Rheta N.
Published: December 2020

A sequence of mental math problems using reasoning can boost students' understanding and confidence in performing multiplication.
Mathematical Exploration: A Geometric Approach to Solving Rate Problems
Authors: Sinn Robb , Spence Dianna J. , Poitevint Margaret
Published: December 2020

The proportional reasoning required to solve rate problems can cause difficulty for many students. However, understanding how to solve problems of this type is vital as students transition from arithmetic to algebra. A guided-discovery approach to modeling these problems using pattern blocks can help students appreciate the quantities involved and the relationships between them.
Quick Reads: Let's Cut a Square
Authors: Vinogradova Natalya
Published: December 2020

Geometry is one of the oldest branches of mathematics. Many important mathematical ideas and theorems are rooted in geometry and can be visualized using geometric interpretations. Students learn about shapes, their properties, and the methods of calculating perimeters and areas of basic shapes early in their school years. Geometry can and should be used to help students visualize and better understand a broad range of mathematical concepts. In the following activity, students use the concepts of area and length to help them understand an important algebraic idea.
Bring the Pythagorean Theorem “Full Circle”
Authors: Benson Christine C. , Malm Cheryl G.
Published: December 2020

Different representations for relationships help students visualize mathematical concepts rather than just memorize formulas.
Tell a Piecewise Story
Authors: Sinclair Nathalie , Armstrong Alayne
Published: December 2020

By focusing on slope and using dynamic software, students develop the ability to describe functions in a geometry context.
Virtual Data Collection for Real Understanding
Authors: Özgün-Koca S. Asli , Edwards Thomas G.
Published: December 2020

Extend a well-known circle-exploration activity using technology to connect geometry and algebra.
Taiwanese Arithmetic and Algebra
Authors: Lo Jane-Jane , Tsai Feng-Chiu
Published: December 2020

Developing problem solving and reasoning, deepening number and symbol sense, and promoting arithmetic and algebraic connections are tenets of Taiwan's Basic Competency Test.
Math For Real: Building Trades
Authors: Porath Jane , Porath Larry
Published: December 2020

When building home, it is critical for the walls to be at a 90° angle with the floor and with one another. Builders say the frame is square when these conditions are met. Otherwise, the structural integrity and safety of the house will be compromised. Builders use geometric properties to ensure that the walls and floor are square with one another.
Addressing Cultural Bias – Reflect and Discuss
Authors: Wilburne Jane M. , Marinak Barbara A. , Strickland Martha J.
Published: December 2020

A variety of approaches and strategies can help immigrant and English language learners understand and solve mathematical word problems.
Problem Solving around the Corner
Authors: Maida Michael , Maida Paula
Published: December 2020

A one-hour investment in game playing produces improvements in geometric reasoning and problem solving.
Integer Operations Using a Whiteboard
Authors: Andrews Delise R.
Published: December 2020

Integrating interactive technology enhances student engagement and understanding of a common middle school topic.
Math For Real: Hair Braiding
Authors: Williams Desha L.
Published: December 2020

Many students from various ethnic groups have memories of hair braiding. Braiders use geometric transformations, including dilations, rotations, slides, and translations, as well as reasoning to create the patterns in their designs.
Quick Reads: What Do You See?
Authors: Vinogradova Natalya
Published: December 2020

The idea of using multiple representations of mathematical concepts as a pedagogical strategy has received considerable attention (Cuoco and Curcio 2001). But, as stated by Zimmerman and Cunningham, it appears that “a concerted effort seems to be underway to bring visualization into the school and collegiate curriculum” (1991, p. 34).
Mathematical Explorations: A Different Perspective on the Multiplication Chart
Authors: Matteson Shirley M.
Published: December 2020

As an eductor of middle-level preservice teachers, I look for ways to introduce, explore, and assess students’ understandings of number concepts. I use manipulatives to model both instructional strategies and classroom management issues for these preservice teachers.
Math For Real: The Heat Index
Authors: Walton Jennifer
Published: December 2020

It’s 90° outside, so why does it feel like 100°? The temperature on the thermometer is not always the same as the temperature we perceive. This perceived temperature is called the heat index and is often reported along with the actual temperature. The heat index takes into account the relative humidity in the air.
Additional Information for Emerging Engineers Design a Paper Table
Authors: Enderson Mary C. , Grant Melva R.
Published: December 2020

The engineering design process challenges students to work together and communicate as they construct learning.
Works of Art
Authors: Kurz Terri L. , Bartholomew Barbara
Published: December 2020

To support mathematical investigations, use this framework to guide students in constructing art-based and technology-based literature.
The Status of Your Journal
Authors: McClain Kay
Published: December 2020

As the national council of teachers of Mathematics begins the third year of publishing Mathematics Teaching in the Middle School, the Editorial Panel thought it appropriate to highlight some of the changes that have occurred in the journal's short history. Although the intent of the journal is to target teaching in the middle grades, the variety of interests expressed by middlegrades teachers has prompted the inclusion of articles on a wide range of such issues as professional development and middle school mathematics education in other parts of the world. The journal was originally established with numerous departments to reflect readers' interests and to prompt the solicitation of manuscripts. However, the large number of unsolicited manuscripts being submitted and accepted for publication has allowed the balance of content to change so that the departments do not dictate the content of the journal but merely serve as overarching guides for themes that the Panel believes need to be addressed. These themes include assessment, technology, and professional development. Other features of the journal have remained because of their popularity with readers, such as the “Menu of Problems,” “Now & Then,” “Mathematics Detective,” “Cartoon Comer,” and “Window on Resources.”
Fraction Flags: Learning from Children to Help Children Learn
Authors: Kieren Tom , Davis Brent , Mason Ralph
Published: December 2020

Tanya and Ellen have made a “Fraction Flag” (fig. 1) by taking a half-sheet of paper and arranging smaller themselves how much of the whole sheet of paper is covered.
The Function Game
Authors: Rubenstein Rheta N.
Published: December 2020

When I began teaching in the late 1960s, we had no videotapes, commercial manipulatives, or calculators to create engaging learning activities for students. I recall spending a good part of my first year searching desperately for ways to motivate my seventh and eighth graders and help them learn mathematics. One activity that I stumbled across worked magically. I thought, “This is a gem,” and I continue to cherish it today. I call it the “function game,” but my students and others have called it the “input-output game,” “guess my rule,” or the “computer game.” I understand that the game first gained prominence in the “new math” era, but it must have been around in some form much earlier. Today, the game is available on many computer systems and is popular with students and teachers. The computer versions, however, lack many dimensions of the live version.
American and Canadian Indians—Mathematical Connectors
Authors: Hughes Barnabas , Anderson Kim A.
Published: December 2020

The names we attach to numbers act as quantifiers. They connect with the amount of a thing. American and Canadian Indians, who were successful at making these mathematical connections, created the first numeration systems used in the lands north of the Mexican border. Their widely differing ways of life caused them to create either simple or complex methods of counting and computing.
December's: Menu of Problems
Authors: Greer Cerry , Wantuck Larry
Published: December 2020

A light fare to whet your mathematical appetite.
Teacher to Teacher: Graphing and Social Studies: An Interdisciplinary Activity
Authors: Brehm Julia L.
Published: December 2020

Imagine mining for gold in california, drilling for oil in the Middle East, or locating forts on the western frontier. Students can fantasize about these activities while perfecting graphing skills by playing a form of the game Battleship. This variation is played on maps of various regions of the world, and instead of destroying targets, the students are trying to locate various natural resources and landmarks of a particular region. The only prerequisite is that students be familiar with graphing on the Cartesian coordinate system.
Toys ‘R’ Math
Authors: Tracy Dyanne M. , Hague Mary S.
Published: December 2020

Play is children's work: “… play, games and cognitive development are functionally related” (Sutton-Smith 1971, 258). Children eveywhere, in every time period, from every culture and economic class enjoy playing with toys. Toys are learning tools; whether handmade or commercially produced, they help children prepare for their adult lives. Children's toys are frequently small-scale representations of objects from the adult world.
Cartoon Corner
Authors: Fisher Julie
Published: December 2020

“Cartoon Corner” is designed to include cartoons that can be used to highlight mathematics in an interesting way. The questions accompanying the cartoons can be used as a large- or small-group activity, as homework, or as an extra-credit assignment. Students might want to create their own mathematics-related cartoons that demonstrate in a humorous way how mathematics is used and misused. Readers are encouraged to submit three copies of cartoons and classroom-tested questions, double-spaced, for review by the editor of this section. The Cartoons must include the date and the newspaper syndicate that holds the copyright.
Mathematics Detective: Close Shaves
Authors: Johnson Jerry
Published: December 2020

During an average lifetime, a man will remove about 27 1/2 feet of whiskers from his face through shaving.
January's Menu of Problems
Authors: Laughlin Connie , Georgeson Joseph
Published: December 2020

A light fare to whet your mathematical appetite.
The Thinking of Students: The Balance-Scale Problem
Authors: Greenwood Jay
Published: December 2020

A number of submissions were received from teachers who tried the problem with their students.
Professional Development: Toward a Cooperative Model of Mathematics Staff Development
Authors: Solomon Jesse , Martignette-Boswell Carol , Downes John , Crowe Josephine , Boyd Gail
Published: December 2020

Now is an exciting time to be a mathematics teacher. The field is constantly changing. Nothing is sacred—not materials, not methods, not forms of assessment. Such drastic change, however, necessitates serious and extensive time for teachers to reflect on their own teaching and to become comfortable with new ideas and approaches (Joyce and Showers 1981, 1982; Schon 1983; Stallings 1989).
Algebra: Real-Life Investigations in a Lab Setting
Authors: McCoy Leah P.
Published: December 2020

How will we make algebra accessible to all students? In the past, we have taught algebra as an abstract course involving manipulation of variables and numbers, which are symbolic representations. We have neglected to make a strong connection between the symbolic algebra and the underlying concrete relationships. Given the messages of the NCTM's Standards documents (1989, 1991), it is apparent that students need concrete experiences that enable them to experience algebra in the real world. In this manner, they will be able to construct an understanding of the concepts and connect the concrete with the abstract and their internal ideas.
Students' Construction of Formulas in Context
Authors: Van Reeuwijk Martin , Wijers Monica
Published: December 2020

The Mathematics in Contrat (MiC) project is an NSF-funded project carried out by the University of Wisconsin—Madison and the Freudenthal institute of Utrecht University in the Netherlands. The purpose of the MiC project is to create a comprehensive mathematics curriculum for grades 5 through 8 that reflects the content and pedagogy suggested by the NCTM's Curriculum amd Evaluation Standards for School Mathematics (1989). The materials being developed are based on the beliefs that mathematics should make sense to students and that mathematics is used to make sense of the world around us. The philosophy is based on the theory of Realistic Mathematics Education (RME), as developed at the Freudenthal Institute in the past decades, and on the belief that mathematics is fallible, changing, and, like any other body of knowledge, the product of human inventiveness. In the MiC project, the content is organized into four combined strands—number, algebra, geometry, and statistics and probability. Over forty instructionl units spread out over the four strands have been developed.
Teacher to Teacher: Building Algebraic Expressions: A Physical Model
Authors: Patterson Anne C.
Published: December 2020

Simple physical models can help middle school students move naturally from their limited world of numbers into the universe of algebraic thinking (NCTM 1989). According to Bruner (1995, 333), mathematics should feel like something a child already knows rather than something totally unfamiliar. He states that the end product of mathematics should not be formalism with a premature emphasis on mathematical language but the confidence a child gains from realizing that mathematics is something that he or she has been thinking right along. This two-part lesson, complete with a step-by-step student activity log, allows students to build on their elementary school experiences of measuring in nonstandard units—disguised here as variables—and thus draw their own blueprint of algebra.
February's: Menu of Problems
Authors: Laughlin Connie , Georgeson Joseph
Published: December 2020

A light fare to whet your mathematical appetite.
The Thinking of Students: Algebra Affinity
Authors: Berner Leslie , McLaughlin Patrick , Verzoni Kathryn A.
Published: December 2020

I regularly require my students to pose problems related to the mathematics that they are studying as in-school or at-home assignments. These problems were composed by seventh graders during their September study of algebraic ideas.
From Matching to Mapping: Connecting English and Mathematics
Authors: Anku Enyonam Sitsofe
Published: December 2020

One of the several NCTM recommendations on mathematical connections is that students “use and value connections between mathematics and other disciplines” (NCTM 1989, 146). In this article, I share with readers how my thirteen-year-old daughter, Dizzy, used her previous knowledge of matching words in English to construct her own understanding of mapping in mathematics.
Building Equations using M&M's
Authors: Borlaug Victoria
Published: December 2020

This activity uses M&M'S and is designed to be used in an algebra class after instruction in solving equations. It actively involves students in identifying the variable, formulating an equation, and then solving the equation.
Exploring Middle Graders' Mathematical Thinking through Journals
Authors: DiPillo Mary Lou , Sovchik Robert , Moss Barbara
Published: December 2020

Not so long ago, writing was considered to be the exclusive domain of the English teacher. However, the current emphasis on subject integration has made writing a cross-curricular affair. Middle grades' students no longer write just in English class; they may find themselves writing in science, social studies, or mathematics class. In fact, involving students in the act of writing about mathematics is gaining widespread acceptance among teachers (Kliman and Richards 1992; Wilde 1991).
March's Menu of Problems
Authors: Georgeson Joseph , Laughlin Connie
Published: December 2020

A light fare to whet your mathematical appetite.
April's Menu of Problems
Authors: Georgeson Joseph , Laughlin Connie
Published: December 2020

A light fare to whet your mathematical appetite.
Teacher to Teacher: Letting Your Students “Fly” in the Classroom
Authors: Adams Thomas
Published: December 2020

Teachers are always looking for new ways to help their students explore mathematical concepts. Many worthwhile activities use cooperative groups and hands-on learning, but few involve any real action. This article presents an activity for middle school students that really moves-in fact, it flies!
The Thinking of students: Creativity: A Key to Understanding
Authors: Lynch Diane
Published: December 2020

Recently, in a graduate course that I was taking at the University of Buffalo, we were discussing and presenting ways to implement the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). One of the suggestions made to encourage communication in mathematics was to have students write about mathematics. Using journals, which I have done with my students, was discussed. However, something I had not tried was also suggested, which was to ask students either to write a short story or joke or to create a cartoon about some aspect of mathematics.
Creating a Purchase Order: Using Spreadsheets
Authors: Indusi Joan
Published: December 2020

Computers have become such important and useful tools in our lives that we sometimes take them for granted. They can handle large amounts of data quickly and accurately, provide easy retrieval of information, compute the results of complex formulas and equations, allow fast and easy editing-and on and on. Young people today are growing up in a world that is becoming more dependent on computers. A familiarity with computer use, an ability to be an independent learner on the computer, and a recognition of the strengths and limitations of computers will be increasingly necessary for students as they enter college and the workplace. How can we as teachers apply this resource in our classrooms?
The Thinking of Students: A Nugget of Gold
Authors: Milou Eric
Published: December 2020

As treachers, we often assign the same problems every year without thinking twice. It is almost as if we were robots. However, every so often a little nugget of gold emerges as we discuss our students' solutions, even when their reasoning may be inaccurate. This article presents one such nugget from the annals of history that emerged in an undergraduate course in methods of teaching mathematics.
Cross-and-Turn Tile Patterns
Authors: Clason Robert G. , Ericksen Donna B. , Ericksen Craig S.
Published: December 2020

Assembling tile patterns using copies of polygons gives students opportunities to connect mathematics with graphic arts. When the polygons have been marked with geometric designs, potential exists for increased interest, creativity, and discovery. Such explorations are recommended for grades 5-8 in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). Using tile patterns, students can investigate angle measures, reflectional and rotational symmetry, and tessellations and can apply problemsolving skills in geometry while searching for visually appealing motifs and patterns.
Birthdays and the Binary System: A Magical Mixture
Authors: Karp Karen S. , Ronau Robert N.
Published: December 2020

Middle school students rank their birthday as being the most important day of the year for them and one that they eagerly anticipate, according to an informal poll. Teachers can capitalize on this interest by engaging them in the mathematical birth-date activities described in this article. Applications and tasks that are relevant to students' lives have been shown to motivate students at the middle school level, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).
Worthwhile Tasks: Exploring Mathematical Connections through Geometric Solids
Authors: Brahier Daniel J. , Speer William R.
Published: December 2020

After a full day of teaching, you take some time reflecting and planning lessons for the next several days. While paging through your course of study, you identify, among others, the following objectives that need to be developed with your middle school mathematics class:
Now & Then: Going Camping? Don't Forget to Pack Your Calculator: On the Trail of the Fur Traders
Authors: Greeley Nansee , Offerman Theresa Reardon
Published: December 2020

Now… Love the outdoors? Enjoy canoeing and fishing? Then the perfect business for you to own might be that of an outfitter. But if you think you will not need mathematics to be an outfitter, you are wrong, according to Pam Clark and Jim Clark.
Pythagorean Triples Served for Supper
Authors: Christensen Evelyn B.
Published: December 2020

After an enjoyable, but exhausting, week of teaching, my family-myself, my husband, Ralph; and our children, Martin and Susan- sits down to Friday supper with that “let go” sense of relief that the weekend has finally arrived. As the meal begins, our eighth grader casually, with almost studied indifference, remarks, “I figured out a new math idea at school today.” Martin is an inquisitive, motivated student, but he is definitely very reserved.
Assessment: Does the Task Truly Measure What Was Intended?
Authors: Santel-Parke Carol , Cai Jinfa
Published: December 2020

During a recent NCTM regional conference, a speaker addressed the significance of performance assessment in the mathematics classroom. Afterward, a mathematics teacher posed a question to the speaker: “I agree with you that performance assessment is very important in the classroom, and your sample tasks are very interesting. However, as a classroom teacher, how can I design these kinds of interesting tasks or modify existing tasks to ensure that they accurately measure my own students' performance throughout the year?” Although only one teacher voiced this concern during the session, many other teachers may have similar concerns. The purpose of this article is to share a few of our experiences in developing performance-assessment tasks. We hope that the examples will be helpful to teachers in designing their own performance tasks to measure students' higher-level thinking and reasoning skills in the classroom.
Turning Students into Problem Solvers
Authors: Verzoni Kathryn A.
Published: December 2020

Whether four or forty years old, people hope that what they learn in school will apply to their lives outside school. Unfortunately, these links do not occur as frequently as we would like. Too often, concepts and skills are learned with little apparent connection to their ultimate usefulness. Too often, students tolerate school learning in a disengaged fashion.
A Credit-Union Project
Authors: Schmidt Mary Ellen
Published: December 2020

I forgot my lunch money!” “I need a folder for math class today!” “Can I phone home and ask if I can stay after school to see the basketball game?” These types of authentic problems present opportunities to engage middle-grades students in meaningful mathematics. By establishing a classroom credit union, students can develop independence in solving real problems and model solutions used in the real world to solve similar problem. A classroom credit union also promotes the type of mathematics espoused in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) because it—

engages students in authentic mathematics;

promotes mathematical thinking, communication, and reasoning in solving problems;

constitutes an ongoing mathematics activity;

encourages students to verify solutions to problems;

involves students with technology; and

allows the teacher to be a facilitator of mathematics learning.
Teacher to Teacher: Creating a Mathematical Storybook
Authors: Wahlgren Genevieve F.
Published: December 2020

This year I tried having my sixth-grade students create mathematical storybooks on the basis of topics that they had learned during the year. They began by browsing and reading about how professional writers present mathematics in a simplified and enjoyable way. Excellent example of professional mathematics writing appear in the bibliography.
Mathematics Detective: Super-Jumbo Jet: An Airborne Village
Authors: Cave Linda
Published: December 2020

In four or five years, Boeing and Airbus may roll out the biggest airplanes ever made. The world's two biggest plane makers are each considering spending at least $10 billion to build jet airplanes that would seat 550 passengers-perhaps even 1,000 if an airline really packed them in. The largest models proposed by each company, the Boeing 747-600X and the Airbus A3XX-200, are much bigger than the largest passenger jet flying today, the Boeing 747-400….
The Thinking of Students: The Farmer's Dilemma Resolved
Authors: McClain Kay
Published: December 2020

The february 1997 “food for thought” department presented the following problem, which has been condensed, for readers to try with their students.
October's Menu of Problems
Authors: Georgeson Joseph , Laughlin Connie
Published: December 2020

A light fare to whet your mathematical appetite.
A Variation on “And the Winner Is …”
Authors: Johnson Iris DeLoach
Published: December 2020

Have you heard the one about an eccentric emperor who invites a number of guests to dinner, only to dump oatmeal onto the head of every other guest until only one remains dry? A variety of problems have solutions similar to the one for the problem posed by Harlos (1995). The version in our elementary-mathematics-methods textbook for preservice teachers (van de Walle 1994, 55) is called “The Emperor's Banquet Problem.”
Reflections on Practice: Understanding Students' Understanding of Graphs
Authors: Friel Susan N. , Bright George W. , Curcio Frances R.
Published: December 2020

Statistics has emerged as a major component of the school mathematics curriculum during the 1990 (NCTM 1989). We know that understanding the statistical-investigation process (Graham 1987) is central to working with statistics. A statistical investigation typically involve four components: (1) posing the question; (2) collecting data; (3) analyzing data; and (4) interpreting the results, in some order (Graham 1987). Kader and Perry (1994) suggest a fifth stage of a statistical investigation: communicating results.
Using the Telephone Book as a Source of Mathematical Activity
Authors: Small Marian S.
Published: December 2020

Are you a grade 6-9 teacher looking for easily accessible data to support your attempts to teach using a problem-solving approach? An old telephone book may be a good place to start. The ideas suggested in this article present some starting points for using the telephone book and telephone numbers at the middle school and junior high school level to develop a variety of mathematical concepts and skills.
Pennies from Heaven—Nickels from Where?
Authors: Kader Gary D. , Perry Mike
Published: December 2020

Major efforts to increase the attention that statistics receives in school mathematics have been under way since the appearance of NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The issue is what and how statistics should be integrated into the mathematics curriculum. The Standards promote the notion that students should be involved in all phases of statistical investigations and problem solving rather than focus on calculation and technique. Figure 1 proposes a model (Kader and Perry 1994) that displays the five components of the statistical problem-solving process.
Assessment: The STEM Model
Authors: Billstein Rick
Published: December 2020

The Six Through Eight Mathematics (STEM) project is one of the National Science Foundation's (NSF) funded middle school mathematics curriculum projects. The project received initial funding in 1992; the finished product is expected to be available in 1998. The STEM curriculum is organized in teaching units called modules. Each module is organized around a conceptual theme, such as “flight” or “wonders of the world.” The use of thematic modules promotes students' developing and applying mathematical concepts in broad contextual situations so that they do not view mathematics as a collection of separate and unrelated topics.
January's Menu of Problems
Authors: Georgeson joseph , Laughlin Connie
Published: December 2020

A light fare to whet your mathematical appetite.
Mathematics Detective: Calculations That Are Not Par for the Course
Authors: Spangler David B.
Published: December 2020

One way to warm up on a brisk winter day is to imagine yourself on a sun-drenched back green of a golf course in high summer. To aid the imagination, consider the following:
Teacher to Teacher: Implementing the NCTM's Evaluation Standards with House Plans
Authors: Boehm Elizabeth J.
Published: December 2020

Major changes in the instruction and evaluation of mathematics are called for in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). I dreaded trying to implement these changes in my classroom. I was afraid of the overwhelming amount of work that I thought would be involved. So instead of making big changes in my instruction, I started with small changes.
Reflections on Practice: Selecting and Creating Mathematical Tasks: From Research to Practice
Authors: Smith Margaret Schwan , Stein Mary Kay
Published: December 2020

What features of a mathematics classroom really make a difference in how students come to view mathematics and what they ultimately learn? Is it whether students are working in small groups? Is it whether students are using manipulalives? Is it the nature of the mathematical tasks that are given to students? Research conducted in the QUASAR project, a five-year study of mathematics education reform in urban middle schools (Silver and Stein 1996). offers some insight into these questions. From 1990 through 1995, data were collected about many aspects of reform teaching, including the use of small groups; the tool that were available for student use, for example, manipulatives and calculators; and the nature of the mathematics tasks. A major finding of this research to date, as described in the article by Stein and Smith in the January 1998 issue of Mathematics Teaching in the Middle School, is that the highest learning gains on a mathematicsperformance assessment were related to the extent to which tasks were et up and implemented in ways that engaged students in high levels of cognitive thinking and reasoning (Stein and Lane 1996). This finding supports the position that the nature of the tasks to which students are exposed detennines what students learn (NCTM 1991), and it also leads to many questions that should be considered by middle school teachers.
February's Menu of Problems
Authors: Vennebush Patrick , Demartini Thomas
Published: December 2020

A light fare to whet your mathematical appetite.
Teacher to Teacher: Calculator Poker
Authors: Trotter Terrel
Published: December 2020

Mathematical games are a popular element in any teacher's repertoire of motivational activities. This game promotes learning and fun at the same time by combining two unlikely allies: a deck of ordinary playing cards and a calculator. The material presented here uses a simple fourfunction calculator with a square-root key. With minor adjustments, the more powerful scientific models can be used.
Push-Penny: What Is Your Expected Score?
Authors: Kader Gary , Perry Mike
Published: December 2020

Probability is concerned with predicting the results of random phenomena. An understanding of randomness and its consequences is fundamental to the study of probability. Mathematics-education researchers have given considerable attention to the subjective understanding of probability concepts. The literature contains numerous articles that relate this type of research to the teaching of probability and statistics (see Shaughnessy and Bergman [1993] for a review of this literature).
By Way of Introduction Geometry
Authors: Collier C. Patrick
Published: December 2020

The editorial panel chose the topic of geometry for a focus issue because we wanted to promote an increase in the attention given to geometry and measurement for all students in all grades. We identify with the observation by Marjorie Senechal in her essay “Shape,” in which she notes that “the role of geometry is a perennial issue in mathematics education at all levels from elementary school to graduate school.” As she discusses some of these issues, she observes that “the teaching of geometry is defended on the grounds that it serves external purposes, rather than on the importance of the subject in its own right” (Senechal 1990).
A Plethora of Polyhedra
Authors: Sundberg Sue E.
Published: December 2020

So, just what is a polyhedron? we could say that a polyhedron is a simple closed surface in space whose boundary is composed of polygonal regions, but most middle school students would not understand this definition. Instead, involving students in an activity in which they actually create polyhedra enable them to understand the characteristics of different polyhedra and develop a clear definition for themselves. Once students gain a hands-on understanding of polyhedra, the shapes can be used to reveal a plethora of other geometric concepts.
Mathematics Detective: The Case of the Smash Hit
Authors: Spangler David B.
Published: December 2020

Detective Shirley Solvit is shopping for a new stom door. She knows that youngsters play baseball near her backyard-and that some of Them can really slam the ball. To reduce her chances of getting a broken window. she want to buy the door that will have the greatest chance of surviving these neighborhood sluggers.
Now & Then: Garden Designer: A Short History of Gardens
Authors: Greeley Nansee , Offerman Theresa Reardon
Published: December 2020

Now… From the angle of the sun as it moves across the sky to the structure of the containers that hold the plants, designing a garden requires mathematics because of its use of space and spatial relationships. Many people who design gardens focus on the plants rather than the space, but Martin Stern and Richard Meacock, partners and proprietors of Squire House Gardens in Afton, Minnesota, believe that quite the opposite is true. They think that the space in which they work is the basis of their garden designs and that the art of garden design is making the geometrical symmetry invisible to everyone but those who are searching for it. Martin extends this use of space to what he calls “the pyramid of space.” When designing a garden, he considers the ceiling, floor, and walls, regardless of their size. A background of shrubs might be the walls; the tallest trees, the ceiling; and the walkways or groundcover, the floor. To make the garden flow, all parts of the pyramid must be considered.
Sorting Activities for Polygons
Authors: Williams Carol G.
Published: December 2020

To encourage students to “identify, describe, compare, and classify geometric figures” (NCTM 1989, 112), I have developed materials and activities that involve sorting polygons. Although teachers can adapt these activities for students at various levels, they are particularly appropriate for the middle schooler. I have designed them for use in small groups, with whole-class discussion at the conclusion. Although geometric properties and definitions are the primary focus, various forms of the activities also encourage reasoning, communication, and measurement. These simple and inexpensive materials can be used for extensions involving probability and statistics as well.
Assessment: Another Perspective on Concept Maps: Empowering Students
Authors: Wilcox Sandra K. , Sahloff Marie
Published: December 2020

Two recent articles in this journal (bartels 1995; hanselman 1996) have promoted the use of concept maps and webs as instructional tools for helping students make connections and examine relationships among mathematical ideas. We present a use of concept maps as an assessment tool that is augmented by an additional activity. This elaboration of a concept map has the potential to give a teacher additional information about what students are coming to understand and to help the teacher decide the direction of future instruction. Further, it gives control to students to construct their own personal representation of what they know, how they know it, and what they are struggling with.
Reflections on Practice: Learning to See the Wind
Authors: Rachlin Sid
Published: December 2020

When I was at the university of hawaii, a colleague told me about an experience that he had had as a first grader growing up in Hawaii nearly forty years earlier. It was a simpler time, one in which a trip from one side of the island to the other was no small feat, since it involved traveling over a narrow mountain road called the Pali that stretched through a pass in the mountain range. At the top of the mountain, his family stopped to enjoy the view. As he watched from the windy edge of the mountain's lookout, he made a discovery that he deemed worthy of sharing at show-and-tell the next Monday. Contrary to what he had been taught in class, he could see the wind!
Teacher to Teacher: Tangrams and Area
Authors: Duke Charlotte
Published: December 2020

I would like to share an activity for demonstrating the area of five geometric figures-the square, rectangle, parallelogram, triangle, and trapezoid-that is based on a simple tangram puzzle.
Teacher to Teacher: Shopping Mall Assessment
Authors: Burns Julia C.
Published: December 2020

Students are assessed constantly in a typical classroom setting. assessment does not have to be a formal score in the grade book; it can be an informal process used by the teacher to direct the lesson. Many teachers assess students' progress by asking for a show of hands, by watching the students work a problem at the chalkboard, or simply by monitoring individual or group work.
State-ing the Facts: Exploring the United States
Authors: Bay Jennifer M. , Bledsoe Ann M. , Reys Robert E.
Published: December 2020

The diversity of our fifty states is known by most Americans; less acclaimed is the fact that the fifty states can form the background for our students to explore some important mathematics. The following progression of activities. includes such important mathematics topics as estimation, scaling, area of nonstandard shapes, algebraic thinking, and real-life situations for squaring and square roots. These activities allow the use of technology by employing such geometry software packages as The Geometer's Sketchpad (Jackiw 1995), Cabri (Texas Instruments 1997), and Geometric Supposer (Sunburst Communications 1997). For us, the activities offered an excellent integration of mathematics and social studies, one that our students enthusiastically enjoyed!
On My Mind: It's Time to Talk about Textbooks
Authors: Zucker Andrew A.
Published: December 2020

What do we know about mathematics textbooks used in the United States?
Teacher to Teacher: Building A Teenage Dance Club
Authors: Christina Mary Ann
Published: December 2020

As the nctm's curriculum and evaluation Standards for School Mathematics (1989) became more well known and I attended more workshops. I made a conscious decision to make algebra more closely tied to the outside world and show it importance in today's technological society. I started using the graphing calculator to eliminate some obsolete paper-and-pencil kill and started using relevant project that became an integral part of my course. I became involved in, and committed to, the philosophy of “Opening the Gate,” which is a series of activities developed in Florida to supplement the curriculum and to reform the teaching and learning of algebra. The idea is to make algebra more accessible, more dynamic, and more relevant to today's and tomorrow's society.
Wheel of Fortune for the Mathematics Classroom
Authors: Holbrook Edna L.
Published: December 2020

This mathematical wheel of fortune game is a classroom adaptation of the Wheel of Fortune television game show. The original players were seventh, eighth, and ninth graders enrolled in a precollege intervention program. To find solutions to the puzzles, the students had to solve first-degree equations in one variable.
September's Menu of Problems
Authors: Jamski William D. , Long Calvin T.
Published: December 2020

A light fare to whet your mathematical appetite.
Cartoon Corner
Authors: Fisher Julie A.
Published: December 2020

“Cartoon Corner” is designed to include cartoons that can be used to highlight mathematics in an interesting way. The qurstions accompanying the cartoons can be used as a large- or small-group activity, as homework, or as an extra-credit assignment. Students might want to create their own mathematics-related cartoons that demonstrate in a humorous way how mathematics is used and misused. Readers are encouraged to submit three copies of cartoons and classroom-tested questions, double-spaced, for review by the editor of this section. The cartoons must include the date and the newspaper syndicate that holds the copyright.