bluuebunny/crossref_metadata_2025 huggingface dataset:
Achievement Tests in Primary Mathematics: Perpetuating Lower-Order Thinking
Authors: Kamii Constance , Lewis Barbara Ann
Published: October 2020

The Curriculum and Evaluation Standards (NCTM 1989) states that if we want to improve the nation's mathematics education, it is necessary to change the current method of evaluation that depends on standardized achievement tests. The National Research Council (1989) is even more explicit about the harmful effects of achievement testing.
Calculators and Word Problems in the Primary Grades
Authors: Willson Katherine J.
Published: October 2020

One teaching strategy for problem solving that appears to be highly successful is to have pupils write their own word problems. This process involves pupils in a teaching method that combines reading, critical thinking, and examining data (Fennell and Ammon 1985). Some pupils, however, may write problems containing numbers that require computation beyond their capabilities. This situation requires that students use calculators to solve problems.
Research into Practice: The Problem of Fractions in the Elementary School
Authors: Steffe Leslie P. , Olive John
Published: October 2020

Researchers in Finland have warned for some years that children learn mathematics too mechanically in our comprehensive school. They learn rules and tricks. but not mathematical thinking. It is rote learning without meaning. I think this is what happens often with the fraction concept.
ONE POINT OF VIEW: We Must Have “Designated Math Leaders” in the Elementary School!
Authors: Bruni James V.
Published: October 2020

NCTM's development of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and the recent companion document, Professional Standards for Teaching Mathematics (NCTM 1991), is an extraordinary achievement. At a time when many agree that we urgently need change in mathematics education, these sets of standards project an exciting vision of what mathematics learning can be and how all students can develop “mathematical power.” They establish a broad framework to guide reform efforts and challenge everyone interested in the quality of school mathematics programs to work collaboratively to use them as a basis for change. How will we meet this challenge? The Editorial Panel believes that translating that vision into reality at the elementary school level will be possible only if elementary school teachers are involved in taking leadership roles as agents of change.
Kindergarten Mathematics: Teaching or Controlling?
Authors: Hegland Susan M.
Published: October 2020

Ryan was working to identify sets of from six to ten elements on a mathematics worksheet. While he was busily coloring the last of ten apples in a row, his teacher commented, “Ryan, see the ‘nine’ here? You were supposed to color nine apple in that row, not all the apples.” Ryan responded sheepishly, “I forgot.”
Area Models—Spanning the Mathematics of Grades 3-9
Authors: Schultz James E.
Published: October 2020

Educators have advocated the use of various models for basic operations of arithmetic, including set models (using concrete objects or representations for objects), length models (using rods or numberlines), and area model (using tiles or pictures).
Multiplication of Fractions: Teaching for Understanding
Authors: Cramer Kathleen , Bezuk Nadine
Published: October 2020

Multiplication of fractions is a deceptively easy skill for students to learn. In a large school district in Minnesota, fifth-grade students identified as being in the lower quartile on the district's mathematics competency test had great difficulty with all the fraction items except multiplication of fractions. Although only 18 percent of these students could find the sum of 1/2 and 1/8, 75 percent could find the product of 2/3 and 4/7. Students can successfully multiply, for example, 2/3 and 4/7, using their whole-number ideas. The answer. 8/21, can be calculated without considering the meaning of either of the fractions or of the answer.
Problem Solving in the Preservice Classroom
Authors: Woodward Ernest
Published: October 2020

My experience has been that teachers will not become teachers of problem solving until they first become problem solvers themselves. From that perspective, those of us who are responsible for the preparation of teachers need to ensure they get appropriate problem-solving experiences. Like many other colleges and universities across the country, Austin Peay State University has a one-year mathematics requirement for prospective elementary school teachers. Problem solving is emphasized in the three required courses. The initial course begins with a unit on the problem-solving process. Various problem-solving strategies—such as look for a pattern, build a table, draw a picture, use trial and error, write an equation, work backward, and solve a simpler problem—are introduced and illustrated. Throughout the year, problem-solving situations are presented within the framework of the specific mathematics topic being studied. Students are encouraged to employ the strategies that were learned in the first unit.
Readers' Dialogue
Authors: Friend Hope , Draznin Sharon
Published: October 2020

“Animated numbers” is the classroom game of choice for my intermediate school Students. It is also an entertaining and exciting way to encourage mental computation.
Real-Life Business Math at Enterprise Village
Authors: Zepp Raymond A.
Published: October 2020

The question of relevance is central to mathematics education. Links must be found between the classroom and the real world if education is to be meaningful to students.
One Point of View: The Standards? We Did Them Last Fall
Authors: Reys Robert E.
Published: October 2020

I recently witnessed the following exchange during an evening Parent Teacher Organization meeting. In addition to all the teachers in the school, probably over two hundred parents were in attendance. During the large-group question-and-answer session, one of the parents said, “I have heard about some standards prepared by the National Council of Teachers of Mathematics and was wondering what our school is doing in response to them.” Without hesitation the principal said, “Yes, we know about the Standards and we did them last fall.”
A Dynamic Way to Teach Angle and Angle Measure
Authors: Wilson Patricia S. , Adams Verna M.
Published: October 2020

These quotation reflect the properties of rectangles that students thought were important when they were directed, “In your own words, define a rectangle.”
IDEAS
Authors: Nevin Mary Lou , Fennell Francis (Skip)
Published: October 2020

The “IDEAS” section for this month focuses on patterning using geometric figures. The sequentially planned activities help students discover the attributes—segments and angles—of various figures and how the figures can be combined to make a pattern; they then apply this information to the everyday world in such activities as making quilts and tessellations (tiling patterns). With the teacher's guidance, students develop the language needed to talk about their discoveries (definitions of less familiar terms are furnished in the Glossary): thus they will be able to communicate mathematically about geometric figures and patterning. The parent-child activity reinforces the school activity. Parents are invited to help students look for patterns in their community and share their findings with their child's class.
Teaching Mathematics with Technology: How to Win People and Influence Friends: Calculators in the Primary Grades
Authors: Thompson Virginia
Published: October 2020

Administrators want the best educational program for their schools, and they want parents to support that program. Parents want the very best for their children in everything, including mathematics education. They remember arithmetic as the mainstay of elementary school mathematics and want their children to acquire the computational skills that they see as necessary for everyday life and future work.
Ideas
Authors: Sammons Kay B. , Kobett Beth , Fennell Francis (Skip)
Published: October 2020

The IDEAS section for this month emphasizes number sense. Number sense is an important component of any contemporary mathematics program. Number sense is the basic skill of the decade. It is the intuition for knowing when an answer is close or correct. Number sense involves the development of number meaning, a feel for magnitude of numbers, and operation sense. Students with number sense also use estimation and mental mathematics with proficiency. This month's kite theme allows students to use their number sense as they involve comparison and ordering, magnitude of numbers, and operation sense in completing the IDEAS activities. The first activity sheet suggests games that parents and their children can play at home to develop number sense.
Research into Practice: Spatial Sense and the Construction of Abstract Units in Tiling
Authors: Wheatley Grayson H.
Published: October 2020

Although tiling has been a supplementary topic in elementary school mathematics for many years, its value has not been fully appreciated. This article dicusses a variation on tiling that offers rich opportunities for the construction of fundamental mathematical relationships. In particular, unitizing as a mental operation is identified as a basis for much mathematical activity in both geometric and numerical settings.
Making Mathematical Connections
Authors: Welchman-Tischler Rosamond
Published: October 2020

Mathematically literate students should view mathematics as a way of looking at their environment that aids understanding and adds insight This attitude toward mathe matics can be fostered in the daily routines of the classroom. Mathematical experiences need not be restricted to the “math period” but can be incorporated throughout the school day. The importance of making mathematical connections, both within mathematics and between mathematics and other curriculum areas, is emphasized by the inclusion of “mathematical connection” as one of the curriculum standards for school mathematics (NCTM 1989). This article how how a simple manipulative device useful for taking attendance can be used to exercise mathematical thinking processes in a variety of contexts at different grade levels throughout elementary school.
Numbers and Codes in Ancient Peru: The Quipu
Authors: Zepp Raymond A.
Published: October 2020

Students should be aware of the contributions their cultures have made to mathematics. This view led Zaslavsky (1973) to travel to Africa to collect examples of African mathematics and to write her well-known book Africa Counts. She then used her material in American schools to instill in her students the notion that black African culture had created quite sophisticated mathematical inventions.
Meanings in Division
Authors: Christofferson H. C.
Published: October 2020

Whenever one word has several meanings there is danger of misunderstanding. The boy who thought slide rule was spelled “sly drool,” could be expected to have some difficulty.
How Effective Is the Meaning Method? A Report of the Los Angeles Study
Authors: Miller G. H.
Published: October 2020

How effective is the meaning method in teaching arithmetic? The answer to this perplexing question still remains uncertain. It is apparent that despite the great amount of literature written on the benefits to be derived from the use of the meaning method by the students, little research has been initiated to justify the great emphasis upon this approach. Most theorists on methods of teaching arithmetic appear to be united in stressing the meaning method. However, are their recommendations on the instruction of arithmetic based upon experimental evidence or are they mere postulation?
Arithmetic Can Be Fun
Authors: Harmon Norene
Published: October 2020

To some six-and seven-year olds, arithmetic is a dull and fearful subject, to others fun and frolic. This is how one class made it fun and frolic.
Estimating the Quotient in Division: A Critical Analysis of Research
Authors: Hartung Maurice L.
Published: October 2020

There are several reasons why the process of division in arithmetic is more difficult to learn than the other processes. One of these reasons stems from the fact that division is not a direct process. It is an inverse process in which it is frequently necessary to estimate in finding the quotient. In the past, two methods of estimating the quotient have been in common use. One of these is generally called the “apparent quotient” method and the other is called the “increase-byone” method. There has been considerable research directed toward determining whieh of these methods is to be preferred for instructional purposes. The present article is not only a summary and critique of this research but also includes numerous comments upon aspects of the issue which have hitherto been largely neglected.
Keep Score on the Abacus
Authors: Armstrong Elizabeth
Published: October 2020

In many games found in the elementary classroom, there is the need for keeping score. Each one of us, regardless of age, likes to see the “little marks” showing to tell how many times we won the game or how many times our team scored.
Shall We Expose Our Pupils to Errors?
Authors: Aftreth Orville B.
Published: October 2020

WILL EXPOSING PUPILS TO ERRORS generally made in the addition and subtraction of fractions result in a lower level of achievement than if conventional procedures are followed? Certain studies in typewriting, spelling, language, punctuation, and speech have claimed that an exposure to errors will either result in adverse effect on the achievement level or will result in a higher level of achievement. As no rigorous studies related to this problem in the area of arithmetic have been reported in the literature, the author in a doctoral dissertation1 determined to what extent the identification and correction of typical errors embedded in practice exercises in addition and subtraction of fractions affected learning of these processes.
From Cake to Cancellation
Authors: Lansdown Brenda C.
Published: October 2020

Concrete materials can be an aid to mathematical discoveries for children of all levels of ability. Materials have often been referred to as “crutches” to be relegated to the mentally lame. If we use instead, the analogy of the toddler's “walker,” to represent a stage of intellectual growth, and leave the crutch for “remedial” work, then both take on a new meaning: throwing away the aid before the individual is ready may leave him permanently crippled. And who but a disturbed person hangs onto crutches and walkers when these are no longer needed?
Fraction Concepts Held by Young Children
Authors: Gunderson Agnes G. , Gunderson Ethel
Published: October 2020

What can we do to help children gain a better understanding of what fractions are and what they mean? How can we give the child a longer acquaintance period with fractions before he is required to work with the written symbols?
Opening the Eyes of a New Teacher
Authors: Flemming Suzanne
Published: October 2020

Sometimes we teachers feel SO buffeted about by the sea of change that surrounds education that we close our ears to all suggestions—both good and bad. Methods of teaching have been altered so much in the past twenty years that even the best informed teacher has difficulty in selecting just what will be helpful in her own situation. Surrounded as we are by this constant aura of change many of us have clung to the ivy-covered methods of the past in the hope that, after all, that which is old is best.
Reduction of Fractions
Authors: Geary Catherine
Published: October 2020

Children to whom fractions have been presented in a meaningful manner, know that certain fractions equal, or are the same size as, other fractions. This knowledge has been acquired by the actual division of objects, by using blackboard drawings or the flannel board, by studying fraction charts, and by counting fractional parts. Later, when pupils add simple fractions (like ¼ and ¼) mentally, someone will always give the answer as ¼ This provides the teacher, or another pupil, with the opportunity to state that “2/4 equals, or is the same as, ¼” Therefore, when the class is ready for reduction of fractions, a previous knowledge of equal fractions forms the basis for the new concept.
The Forgotten Level: Semi-Concrete Materials—A Valuable Bridge
Authors: Drasin Lillian Packer
Published: October 2020

Most teachers are aware of the aspects to be considered in the teaching of arithmetic, namely, the logical, social, and psychological. Both the logical steps and the social understandings are defined to a greater or a lesser extent in guides, manuals, and other curriculum sources. When the psychological phase is examined, however, the emphasis is upon technique rather than upon content. Here the teacher's skill, insight, and sympathy toward the learner, his problems and the hurdles he must overcome are of paramount importance.
Milwaukee's In-Service Arithmetic Education Program
Authors: Paukner Lillian C.
Published: October 2020

As a part of the in-service education program in the Milwaukee Public Schools, designed to encourage professional study and instructional improvement, a course in the teaching of arithmetic will be offered to intermediate grade teachers. Emphasis will be placed on the sequential program for these grades, teaching techniques, provisions for individual differences, use of manipulative materials, and the evaluation of pupil growth. This will be a workshop type of course, giving teachers opportunities to share successful practices in the teaching of arithmetic and the laboratory experience of trying out these practices in their own classrooms.
Why Invert the Divisor?
Authors: Hannon Herbert
Published: October 2020

Certain operations in the fundamental processes seem to present difficulties to students which are often either inadequately removed by the teacher of arithmetic or are left completely unexplained. This would appear to be particularly true in the case of explaining the process used in division of fractions. A survey of the students in my teacher training classes in arithmetic usually shows that the students have had little if any explanation as to why the inverting of the divisor in division of fractions is justified.
Alignment of Tests with The Standards
Authors: Romberg Thomas A. , Wilson Linda D.
Published: October 2020

At all levels of schooling in the United Stare. resting is an increasingly common experience in the life of students. The push for “accountability” in the schools has led to a constant increase in mandated testing. For at least two reasons, it is important that teacher learn more about the standardized tests their students are taking. The first rea on is validity, and the second is the influence te ting has on teaching practice.
Ideas
Authors: Hopkins Martha H. (Marty) , Gard Diane M. , Speer William R.
Published: October 2020

The “IDEAS” section for this month focuses on connections between mathematics and exploration, from exploring a community to exploring space. The activities are designed to reflect and support the vision of the Curriculum and Evaluation Standards (NCTM 1989) and the Professional Teaching Standards (NCTM 1991). Although each “IDEAS” section this year focuses on mathematical connections, mathematics as communication, mathematics as reasoning, and problem solving, this issue highlights the following curriculum standards: Measurement, Geometry and Spatial Sense. Patterns and Relationships. Algebra, and Computation and Estimation. At each activity level, students analyze data presented on charts or maps while attempting to solve problems and draw conclusions. The reproducible sheet for the “IDEAS” section are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet that involves parents in the child's exploration. A teacher may want to reproduce and use several of the activities from this month's selection.
Multiplication of Fractions Through Paper Folding
Authors: Sinicrope Rose , Mick Harold W.
Published: October 2020

“One of the most well established facts in all mathematics education literature is that performance on fraction is undesirably low” (Hope and Owens 1987, 37). One example of that performance is that less than half of the seventh graders tested in the 1986 National Assessment of Educational Progress recognized that 5 1/4 equals 5 + 1/4 (Kouba et al. 1988)! We keep trying to comprehend why so many students and intelligent adults don't understand fractions.
“Silent Teacher” and Mathematics as Reasoning
Authors: Schwartz James E.
Published: October 2020

The teacher begins class by silently and mysteriously drawing a vertical line down the middle of the transparency. He then proceeds to write numerals first on one side of the line, then on the other. On the left he places the number 2; on the right he places the number 4. Without a word he pauses and looks expectantly at his students. Then he places the number 3 under the 2 in the left column. He places the number 6 under the 4. Again he pauses for effect before placing the number 5 under the 3.
The Patchwork Quilt: A Context for Problem Solving
Authors: Carey Deborah A.
Published: October 2020

A mathematics curriculum that focuses on problem solving needs relevant, challenging problems for students to solve. The most engaging problems initially emerge from real-world contexts and offer opportunities for extensions that are limited only by the problem-solving abilities of the students. As suggested by the NCfM's Curriculum and Evaluation Standards for School Mathematics (1989), students learn new concepts and skills through problem-solving experiences. Therefore, selecting appropriate contexts that offer opportunities for problem solving and from which students can generate problems is critical. This article discusses how one piece of children's Literature be used to develop appropriate problem solving tasks.
Folded Fashions: Symmetry in Clothing Design
Authors: Evered Lisa J.
Published: October 2020

Recent reports supported by research indicate the need to encourage girls as well as boys to continue the study of mathematics. Two reasons often given for the lack of females' interest in mathematics are its perception as a male domain and the scarcity of female role models. These influences appear to be active early in the mathematics curriculum. Despite the efforts of concerned teachers and textbook publishers, the majority of classroom applications of mathematics are oriented more toward males than females. Further, historical references to such female mathematicians such as Hypatia, Kovalevsky, and Noether do little toencouragetoday's young women who may not wish to become mathematicians to choose vocations in which mathematics is important
Have a Problem? Make the Writing-Mathematics Connection!
Authors: Wadlington Elizabeth , Bitner Joe , Partridge Elizabeth , Austin Sue
Published: October 2020

Get out our journals? I don't get it. We just had English!” This is the initial reaction of most elementary school students when asked to keep daily mathematics journals. However, the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) indicates that mathematics should emphasize the meaningful communication of mathematics. Talking, listening, reading, and writing about mathematical concepts help
Preparing Elementary Mathematics-Science Teaching Specialists
Authors: Miller L. Diane
Published: October 2020

The Curriculum and Evaluation Standards for School Mathematics “expresses the consensus of professionals in the mathematical sciences for the direction of school mathematics in the next decade” (NCTM 1989, vi). It represents a response to the call for reform in the teaching and learning of mathematics. As one familiar with the preparation of elementary school teachers examines the Curriculum and Evaluation Standards, a sense of doom pervades the otherwise enthusiastic attitude toward the reform represented by the document. Many practicing and prospective teachers are not adequately prepared to meet the challenge of implementing the curriculum standards.
A “Handy” Database Activity for the Middle School Classroom
Authors: Browning Christine A. , Channell Dwayne E.
Published: October 2020

An examination of middle school mathematics textbooks published prior to the 1990s reveals that the statistics component consists mainly of computing averages and drawing simple bar, line, and circle graphs. Although finding centers or averages of data sets or conducting surveys and graphing the results are certainly appropriate activities. they usually involve only collecting and organizing data and do not focus on understanding or interpreting the data
The Mathematics-Children's-Literature Connection
Authors: Gailey Stavroula K.
Published: October 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) promotes mathematical power for all students so that they can function a informed citizens in a rapidly changing and technologically complex society. A way of working toward this goal is by investigating connections within mathematics and between mathematics and other instructional areas. The mathematic— children's-literature connection is examined in this article.
Looking at the World from a Mathematical Perspective
Authors: Whitin David J.
Published: October 2020

I the nhis recentbook titled Beyond Nwneracy John Paulos describes a car ride he took into New York City. As he looks out his window, he frames what he sees from a mathematical perspective. For instance, he use the concepts of equivalence and inequality to de te rmine if the kindness ex hibited by one moto ri s t he lping another is greater than the aggravation caused by their interrupting the flow of traffic for every-Experience one else. He use the concept of probability to consider the I ikelihood of his becoming a famous writer or the chances that the cables of the bridge might snap as he drivesacross it. He thinks about the concept of time and distance when he devises a strategy for nabbing speeding motorists by stamping the time they emer and exit a toll road and thereby determining their speed.
Fostering Communication In Mathematics Using Children's Literature
Authors: Lewis Barbara A. , Long Roberta , Mackay Martha
Published: October 2020

The Cmerpillar and Alice looked at each other for some time in silence: at last the Caterpillar took the hookah out of its mouth. and addressed her in a languid. sleepy voice.
Fractions: in Search of Meaning
Authors: Witherspoon Mary Lou
Published: October 2020

Results of the National Assessment of Educational Progress indicate that “although most students could perform simple whole-number calculations, many evidenced little knowledge of the most fundamental concepts of fractions, decimals, or percents” (Carpenteret at. 1988, 40). This statement proved quite accurate during a project to compile a videotape to help preservice teachers team how elementary school students think about fractions. Students who had completed the fifth grade struggled—and often failed—to give appropriate pictorial representations of such “simple” situations as one-third of a pie and one-fourth of a set of eight marbles. (For convenience. the word fraction is used to mean a fractional number.)
International Update: a National Australian Statement on Mathematics
Authors: Bobis Janette
Published: October 2020

A National Statement on Mathematics for Australian Schools (Australian Education Council and the Curriculum Corporation 1991) wa released in July 1991. This document is the result of a collaborative project whose recommendations are to be implemented by the State and Territory Government education systems in Australia. It does not prescribe a panicularcurriculum but supplies a framework around which system and schools in the proces of planning can structure their mathematic curriculum.
Ideas
Authors: Hopkins Martha H. (Marty) , Brahier Daniel J.
Published: October 2020

The “IDEAS” section for this month focuses on connections between mathematics and children's literature. Five piece of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages. The reproducible sheets in “IDEAS” are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet for parents use. A teacher may want to reproduce and use everal sheets.
Ideas
Authors: Shaw Jean M. , Firkins John
Published: October 2020

The “IDEAS” section for this month focuses on connections between mathematics and environmental concerns. The activities were designed to make students aware of various materials that people ordinarily use and discard, to increase their knowledge of the numbers of materials that people use, and to make plans to use marerials more conservatively. Plans may include reducing materials used, reusing materials, or recycling them. Each activity includes gathering, graphing, and interpreting data, thus extending opportunities for communicating, reasoning, and problem solving. Each activity features ideas to share with classmates or family members. These activities' investigative approaches are recommended in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Discussing the environment connects school life to everyday life. Most students want to make a difference in saving the earth, and the activities in “IDEAS” can help them get a start or extend their efforts in this appealing and important area.
Implementing the “Professional Standards For Teaching Mathematics”: Questioning in the Mathematics Classroom
Authors: Vacc Nancy Nesbitt
Published: October 2020

For many of us, implementing the Professional Standards for Teaching Mathematics (NCTM 1991) in our classrooms makes great sense. It is clearly reasonable that if students are to develop an understanding of and an ability to use mathematical applications in a variety of contexts (NCTM 1989). they should have meaningful and relevant experiences that will actively engage them in constructing their own knowledge. Also, that active engagement needs to be accompanied by opportunities for students to talk about what they already know and don't know and what they are doing as they strive to extend or change their current level of understanding. For many teachers, however. offering this type of instruction means changing their beliefs about mathematics instruction. After all, most of us are products of elementary and secondary school classrooms in which the teachers told us what we needed to know or do and we listened to and did what they told us to do. What we were thinking about during this interaction often did not matter, and we were unaware that it should. This same type of discourse existed in many of our methods courses. The instructor spent most of the class telling us what we needed to know so that we could tell our future students what they needed to know. Fortunately, we have come to the realization that this style of teaching is not as effective as once thought, and consequently we need to change what we are doing. However, how we go about making needed changes in our teaching is unclear.
Promising Research, Programs, and Projects: Safemap
Authors: Pagni David
Published: October 2020

Safemap is an acronym for the Santa Ana/Fullerton Elementary Mathematics Project, a partnership between the Santa Ana Unified School District and California State University at Fullerton and is cofunded with the National Science Foundation. Teachers of grades K–5 meet on weekends once a month to study mathematics content, complete homework assignments, and prepare to implement lessons in their classrooms, all of which are shared and discussed at the next monthly meeting. Regularly scheduled monthly meetings allow for networking and bonding among teachers that have not previously been evident in summer institute. Every participant in SAFEMAP is also trained in Family Math courses and conducts six Family Math sessions for students and their parents.
Ideas
Authors: Channel Marea W. , Firkins John
Published: October 2020

The “IDEAS” ection for this month focuses on mathematics as communication. Each investigation in geometry begins with an open-ended question that challenges students to become actively involved in mathematical experiments, ideas, discussions, manipulative materials, tools, and techniques.
Implementing The K–4 Mathematics Standards in Kentucky
Authors: Bush William S.
Published: October 2020

The state motto of Kentucky is “United We Stand—Divided We Fall.” Never has this creed been so evident than through the recent statewide mathematics education reform efforts in grades K–4. Over the past two years, university faculty, classroom teachers, school administrators, public policymakers, the Kentucky Department of Education, and corporations have developed partnerships to initiate systemic changes in the mathematics education of students in grades K–4. These groups banded together to enact for Kentucky the vision set forth by the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).
One Point of View: Gender and Mathematics Contests
Authors: Nichols Rosalie S. , Kurtz V. Ray
Published: October 2020

Local, regional, state and provincial, and national contests in mathematics certainly generate enthusiasm for mathematics. Thousands of students are experiencing the excitement of comparing their mathematical skills with those of other student their age. Even though reasons for the current popularity of the contest movement are uncertain, this interest does appear to be contributing lO the promotion of mathematics. The movement is even contributing to the growth of local, state, and provincial mathematics education organizations.
Teacher to Teacher: Use Color to Assess Mathematics Problem Solving
Authors: Biggerstaff Margaret , Halloran Barb , Serrano Carolyn
Published: October 2020

Authentic assessment aligned with the curriculum is changing expectations of students' work in mathematics. The move away from one right answer to multiple solutions and multiple strategies in mathematics problem solving requires a way to increase students' awareness about expectations and increase their competence. Students need to know the criteria that will be used to measure their mathematics problem-solving work. Equitable mathematics instruction includes ensuring that all students understand the purposes, standards, and processes of assessment.
Ideas
Authors: Brumfield Emalou
Published: October 2020

The “IDEAS” section for this month focuses on student organization, preparation, and presentation of some simple foods as a way to apply various mathematical concepts, with problem-solving techniques being central to almost all the activities. The applications can be developed and extended depending on the teacher's creativity and the students' maturity and interest. These activities should help develop problem-solving techniques and increase number sense among students.
Reflect… for Better Problem Solving and Reasoning
Authors: Krulik Stephen , Rudnick Jesse A.
Published: October 2020

During the past decade, many articles have been written and many speeches have been delivered about using the heuristic method in the mathematics classroom to improve the problem-solving skills of students. Pólya's plan for problem solving, whether in its original four-step model or in one of the modified versions found in contemporary textbooks, has proved to be an effective pedagogical way to improve students' problem-solving performance (Pólya 1980).
Teacher to Teacher: A Number Line with Character
Authors: Fitzgerald William M. , Boyd Jane U.
Published: October 2020

Vince and Sarah are playing the Factor Game, a two-person game in which me first player selects a number from 1 to 30 (see game board in fig. 1). The second player then selects all the divisors of the first number that are less than that number. If Vince begins the game by choosing 13, Sarah would select 1 because the divisors of 13 are 1 and 13 and Vince has already elected 13. The score is then 13 to 1 in favor of Vince. During the second round of play it is Sarah's turn to go first. She chooses 24 and has a total of 1 + 24 = 25 points. However, next Vince can select 2, 3, 4, 6, 8, and 12 (the remaining divisors of 24), which, added to his previous score of 13. will give a total of 48 point. Once a number is chosen, it is out of play and can be marked off or covered up. A play is legal only if a divisor remains on the board for the opponent to select. A player making an illegal move gets to keep the number chosen, but loses his or her next turn. The game ends when no more legal moves are possible. The highest sum wins. The Factor Game is the first activity in Factors and Multiples, a unit of the Middle Grades Mathematics Project (Fitzgerald et al. 1986).
Research into Practice: Calculators and Computers: Tools for Mathematical Exploration and Empowerment
Authors: Battista Michael T.
Published: October 2020

Over the last decade, major advances in technology have brought new and exciting possibilities to mathematics education. The universal availability of calculators—both as stand-alones and as built-ins for such devices as cash registers—is having a profound impact on what should be taught in mathematics curricula. Computers are furnishing increasingly more powerful learning environments for students. Both devices require and support enhanced development of students' mathematical reasoning. This article discusses a number of ways that calculators and computers can be used as tools for exploration and empowerment in school mathematics.
Reviewing and Viewing
Authors: Whitin David J. , Bauman-Boatman Janet
Published: October 2020

In the old days, the Richest Man in the World was, of course, the Fattest Man in the World. He lived in the Biggest House in the World, all alone except for 100 cooks and 3 vice presidents. Four weeks before his fortieth birthday he instructs these cooks and vice presidents to bake him the Biggest Birthday Cake in the World.
Research into Practice: Concrete Materials and Teaching for Mathematical Understanding
Authors: Thompson Patrick W. , Lambdin Diana
Published: October 2020

Today we find common agreement that effective mathematics instruction in the elementary grades incorporates liberal use of concrete materials. Articles in the Arithmetic Teacher no longer exhort us to use concrete materials, nor does the Professional Standards for Teaching Mathematics (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.
Horizontally, Vertically, and Deeper Work for the Fast-Moving Class
Authors: Dick Hillman Gertrude
Published: October 2020

FOR SEVERAL YEARS at the Mill Plain School in Fairfield, Connecticut, we have had an interesting grouping program. One of the big areas of disagreement in the philosophy of this grouping as related to the mathematics classes was whether to enrich at a horizontal level or whether to move vertically toward more advanced work. While this issue was still unsettled, Dr. John Clark at a conference held in November 1955 at the University of Connecticut compounded it further by telling the assembled group to do neither, but to “dig deeper”!
Report of the Nominating Committee
Authors: Bell Clifford , Adkins Jackson , Foster Mary , Gager William , Pingry Robert , Sauble Irene , Schult Veryl , Wilcox Marie , Wren Lynwood
Published: October 2020

The Committee on Nominations and Elections presents its slate of nominees for offices to be filled in the 1958 election. The term of office for the president and the two vice-presidents is two years. Three directors are to be elected for terms of three years.
New Membership and Subscription Dues
Authors: Ahrendt M. H.
Published: October 2020

BECAUSE of the increased cost of printing … ” — these were the words with which an announcement began in the April 1947 issue of the Mathematics Teacher giving notice of an increase in dues from S2.00 to $3.00 per year.
To Tell—or Not to Tell
Authors: Hatton Clark Caroline
Published: October 2020

If the Pupil is to get optimum benefit from his arithmetic instruction, it is essential that the teacher distinguish between what elements of a topic the child learns by being told and what elements he learns by being guided to analyze, to discover, to deduce. This paper presents 15 items that enter into the over-all development of the number six. (Similar items would apply in the development of any other onedigit number.) The reader is invited to classify each of thee items. When the reader encircles the “D” placed after an item, it will mean that he considers this to be a phase of learning he would help the child arrive at mainly by DEDUCTION. On the other hand, if he considers a learning item to be one that is dictated by cultural usage, is arbitrary, and one that the learner cannot deduce, the reader can so indicate by encircling the “T” for TOLD after the item. Some items may rate both a “D” and a “T”.
Casting Out Nines and Other Numbers
Authors: Driscoll Lucy E.
Published: October 2020

Today, Perhaps More Than ever before, we at least pay lip service to teaching for understanding in arithmetic. Too often, however, this “ understanding” still implies mere knowledge of how to perform a mechanical process. Checking any one of the four processes of arithmetic by casting out of nines is a good illustration of this fact; though, occasionally some wide awake boy or girl in junior high school arithmetic challenges the teacher by asking such questions as: “Why does it work?” “Will it work with any other number?” These are good, intelligent questions, but questions which many teachers who feel rather secure in teaching most of the arithmetic find difficulty in answering. And yet, at least partial answers are understandable, interesting and challenging to pupils.
Kindergartners Learn Arithmetic
Authors: Campbell Dorothy
Published: October 2020

It has been said that “kindergarten is the bridge between home and school.” The fact that learning is a continuous process that is based on all previous experience makes this statement a very significant one for the kindergarten teacher. When children enter kindergarten, they come with their specific backgrounds of concepts, of language and of skills. For all children, this includes mathematical experiencing. Children have been surrounded by quantitative relationships from their earliest experiencing. In kindergarten the concepts already learned can be further amplified and new understandings developed to form a firm foundation for mathematical experiencing throughout the school years and beyond.
Arithmetic Problems: Cause and Solution
Authors: Taylor W. R.
Published: October 2020

There is considerable confusion among teachers and administrators about the steps that should be taken to meet the demands for more—and better—arithmetic instruction coming from industry, government, science and the general public.
Fish and Arithmetic
Authors: Amsden Dorothy , Szado Edward
Published: October 2020

When the north elementary school in Williamsville recently acquired an acquarium for a second grade classroom, few people realized the effects of this on the total curriculum of the classroom. The aquarium was purchased primarily to bolster the science program. As it turned out perhaps the most marked interests of the students were of a mathematical nature though they may not have realized it. Becoming cognizant of the opportunity to correlate science and arithmetic we began planning numerous activities which enriched both programs to a marked degree.
“1” and “1” is “11”
Authors: Wolf Frank L.
Published: October 2020

Second and third graders and even older students are intrigued by riddles. We much older folk in our sophistication may not find humor or inspiration in some of the riddles they find amusing, but perhaps we can find enlightenment. Please consider the following examples.
One Classroon, with Arithmetic and Justice for All
Authors: Phillips Jo McKeeby
Published: October 2020

AN EMINENT AND ARTICULATE BRITISH scientist, J. Bronowski, has written an article called “Planning for the Year 2000.”1 Because hls predictions agree perfectly with those of other scientists, in our own country and in other countries, and because he is disposed to consider the social implications of the scientific advances in many fields, I should like to call attention to them here.
Quantitative Thinking in Today's World
Authors: Collier Calhoun C.
Published: October 2020

Twentieth century man, living in a constantly changing scientific and technological world, is called upon every day to form judgments, make decisions, and take actions concerning problems relative to some quantitative aspect of his environment.
Zero and Infinity
Authors: Pfreim Raymond C.
Published: October 2020

Zero, for most youngsters, has but one meaning. To them zero means “nothing.” Phrases such as “five to nothing” heard at the ball park to indicate a score of 5 runs to 0 runs helps to substa ntiate this common belief. In subtracting six apples from six apples, one is naturally led to believe that the answer zero means that nothing is left. Although this reasoning is correct in as far as we have gone, it is not entirely without fault. A student entering junior high school must learn that the concept of zero has a broader meaning. If a student does not learn to accept a broad point of view, he will experience great difficulty in future mathematics courses.
Arithmetic in Verse
Authors: Dessart Donald J. , Brown John A.
Published: October 2020

“LET'S MAKE MATHEMATICS EASY ” is often times given as the solution to the difficulties experienced in acquiring this discipline. We need only pick up a Sunday newspaper to read an advertisement for a simplified method of learning some phase of mathematics. Back in the 1840's a clever, enterprising man named George Van Waters felt he had found a solution to the difficulties in acquiring arithmetic.
A Method of Front-End Arithmetic
Authors: DeBethune Andre J.
Published: October 2020

As a teacher of chemistry, I use arithmetic as a work tool every single day, and so do my students. There is hardly a problem in chemistry whose solution does not call for at least one, if not many, arithmetical operations. The routine handling of large volumes of arithmetical work is an accepted occupational hazard of the chemist's. It is a tribute to our schools that our chemistry students come to us well prepared in this regard. Our budding chemists do know how to add, subtract, multiply and divide, and they can do so without hesitation or dismay.
“Sets” Aid in Adding Fractions
Authors: Hannan Herbert
Published: October 2020

Some of the concepts developed in modern mathematics can find immediate application in elementary arithmetic. Perhaps the most usable is the concept of a set. For the purposes of this discussion a set will be defined as a collection of objects which have one or more characteristics in common. It is of course on the basis of this characteristic (or characteristics) that any set is different from other sets as a whole.
Help in Problem Solving
Authors: Geary Catherine
Published: October 2020

When children do problems mentally (figuring them out without writing them down), it is well to ask them to tell what they thought in order to get the answer. This shows that problems may be done in different ways, it helps other children to understand difficult problems, and talking about a problem helps to fix a method of doing a certain kind of problem in the mind of the person who discusses it. It is well to remember that a child may tell the correct answer and yet may write it incorrectly. For instance, in the problem, “If one pencil costs 5¢ how much would 6 pencils cost?”, the child may answer correctly, 30¢. However, if he is asked to write it, he may omit the cents' sign (¢). In that case the problem would be considered incorrect. For this reason, writing problems on the board helps the child to see that sometimes a word or a sign must be included in order to have a totally correct answer.
Distinguishing Between Basic and Superficial Ideas in Arithmetic Instruction
Authors: Hartung Maurice L.
Published: October 2020

Critics of our schools complain that not enough arithmetic is learned by children in general, or, at least, that some children fail to learn enough. I believe these views are well-founded. Most children can and probably should learn much more arithmetic than they do.