• Feb 2021 Journal Article The Israel Journal of research in mathematics education

    Mathematics news section

    מדור חדשות מתמטיות: בעיית הסוף הטוב, התקדמות בהוכחת הערת התאומים, גלגוליה של בעיית ABC, מספר הצבעים המינימלי הנדרש לצביעת מכפלה טנזורית של שני גרפים נתונים, זהות הקושרת בין וקטורים עצמיים של מטריצה לערכים עצמיים של מטריצה, והשערת קולאץ
    תקציר
    הידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ-000,125 פריטים המתפרסמים בכ-650 כתבי-עת מתמטיים למאגר המידע הבין-לאומי המנוהל בידי החברה המתמטית MathSciNet: AMS database of reviews, abstracts האמריקאית info bibliographic and .רוב הפריטים מכילים תוצאות חדשות בענפי המתמטיקה השונים. מדור החדשות בגיליון זה מכיל הפעם חדשות על התקדמות משמעותית לקראת פתרונן של שלוש בעיות, על… show more
  • Oct 2020 Journal Article OnCore, The AATM journal

    Is it our responsibility to introduce high school students to contemporary mathematics?

    Abstract
    Should high school mathematics teachers give their students a taste of contemporary mathematics? In this article, obstacles and a suggested solution are provided to enable teachers to incorporate contemporary mathematics into their programs.
  • Feb 2020 Conference Paper ICMI Study25: Teachers of Mathematics Working and Learning in Collaborative Groups

    RAMZOR–a Digital Environment That Constitutes Opportunities for Mathematics Teachers Collaboration

    Abstract
    The multi-phase study described in this paper is a part of an R&D project aimed at examining the development and the implementation of a digital environment named RAMZOR for constituting opportunities for professional collaboration among mathematics teachers and supporting their efforts to plan and realize their complex daily tasks. The results of the study indicate… show more
  • Aug 2019 Conference Paper the International Conference on Theory and Practice: An Interface or A Great Divide?

    Bridging between School Mathematics and Contemporary Mathematics: Turning a Dream into Reality

    Abstract
    In many countries, school mathematics curriculum does not go beyond the 18th century mathematics. Any solution for bridging this gap must consider students’ limited background, as well as teachers’ time constrains. Our ‘bridge’ consists of periodically interweaving Mathematics-News Snapshots (MNSs), i.e., short descriptive presentations of recent mathematical results… show more
  • Jul 2019 Journal Article The Israel Journal of research in mathematics education

    Mathematics news section

    מדור חדשות מתמטיות: הספרות של פאי "משגעות" את כולם; תחום מתמטי חדש: המתמטיקה של האהבה; פרס אבל 2019 לראשונה לאישה
    תקציר
    מדור החדשות בגיליון זה מכיל שתי חדשות, אחת על המספר π המוכר לכולנו, שהחתירה למצוא את ערכו בדיוק גדול ככל האפשר גורמת למהפך לאחרונה, ועוד אחת על מתמטיקאית צעירה )ויפה...( שכתבה בשלוש השנים האחרונות שלושה ספרים שהראשון בהם הפך לרב-מכר ושמו "המתמטיקה של האהבה", לא פחות ולא יותר.
  • 1 Jul 2018 Book

    Logic in Wonderland: An Introduction to Logic through Reading Alice in Wonderland — Teacher's Guidebook

    Abstract
    This guidebook is for college instructors who teach a course in Introduction to Logic at a teachers college or provide a workshop in this subject for in-service mathematics teachers. It can also be used by high school mathematics teachers for teaching students who are capable and interested in Logic. Learning is based on reading Alice's Adventures in Wonderland, and… show more
  • 1 Jul 2018 Book

    Logic in Wonderland: An Introduction to Logic through Reading Alice in Wonderland — Student's Workbook

    Abstract
    This is a student's workbook that accompanies the teacher's guidebook of the same title. It is for students who take a course in Introduction to Logic at a teachers college, whose instructor decides to provide students with a learning environment based on reading Alice's Adventures in Wonderland, and discussing quotes from that book as a trigger for developing basic… show more
  • Apr 2018 Edited Volume

    K-12 mathematics education in Israel: Issues and Innovations

    Abstract
    The book provides the reader with a multifaceted picture of mathematics education in Israel, put into an international perspective where relevant. It is intended to give an overview of a wide range of topics covering issues such as raising and maintaining motivation, search for excellence, treatment of difficulties, teacher education, language issues, minorities issues… show more
  • Apr 2018 Book Chapter K-12 Mathematics Education in Israel

    Introducing All High School Students to the True Nature of Contemporary Mathematics: Meeting the Challenge

    Abstract
    This chapter describes an on-going attempt at decreasing the gap between the ordinary school mathematics curriculum and contemporary mathematics, in order to give all high school students a taste of what contemporary mathematics is about.
  • Apr 2018 Book Chapter K-12 Mathematics Education in Israel

    Mathematics Teachers Documenting, Sharing, and Improving Their Work Using a Newly Developed Software

    Abstract
    The increasing use of Wikipedia, social networks like Facebook, and databases with search engines such as Google, inspired us to consider a suitable computer-based platform for preserving, accumulating, and continuously improving mathematics teachers’ practice, through collaborative efforts, aiming at empowering the mathematics teachers’ community of practice. This… show more
  • Mar 2018 Journal Article The Israel Journal of research in mathematics education

    Mathematics news section –Three news from 2017

    מדור חדשות מתמטיות: פרס אָבֶל לשנת 2017 על תורת הגלונים, לראשונה בהיסטוריה - הזוכה במדליית פילדס לשנת 2014 היא אישה, על הספר על החינוך המתמטי בישראל
    תקציר
    הידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ-000,100 פריטים למאגר המידע הבין-לאומי שמנהלת החברה המתמטית האמריקאית:  and abstracts, reviews of database AMS – MathSciNet info bibliographic רוב הפריטים מכילים תוצאות חדשות המעשירות את ענפי המתמטיקה השונים. לציון ההישגים הכבירים האלה, שכולם הם בזכות היצירתיות המפליגה של המתמטיקאים בני זמננו, הונהגו בעת האחרונה פרסים… show more
  • May 2017 Journal Article The Israel Journal of research in mathematics education

    Mathematics news section –Three news from 2016

    מדור חדשות מתמטיות: מה מיוחד למספר 7,825, ראשוניים ללא הספרה 7 ותכנון טיול
    תקציר
    מדור החדשות בגיליון זה מכיל שלוש חדשות משנת 2016 המסתיימת בעת כתיבת שורות אלו. חדשות אלו הן כמובן רק חלק פעוט של המתרחש במתמטיקה השכם והערב. בשנים האחרונות מתווספים מעל 000,100 פריטים בכל שנה למאגר המידע המתמטי הבין-לאומי המנוהל בידי החברה MathSciNet – AMS database of reviews, abstracts and :האמריקאית המתמטית info bibliographic הם מתפרסמים בכ-1800 כתבי עת מתמטיים. רובם… show more
  • 12 Jan 2017 Journal Article The IfColog Journal of Logics and their Applications

    Leon Henkin: A Logician's View on Mathematics Education

    Abstract
    This paper is divided into two parts. In the first one reasons are given for strongly recommending reading some of Henkin’s expository papers. The second one describes Leon Henkin’s work as a social activist in the field of mathematics education, as he invested a large portion of his career to increase the number of women and underrepresented minorities in the upper… show more
  • Nov 2016 Journal Article The Israel Journal of research in mathematics education

    Mathematics news section –Pentagonal tiling and more news

    מדור חדשות מתמטיות: ריצוף חדש במחומשים ועוד חדשות
    תקציר
    הידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ-000,100 פריטים המתפרסמים בכ-1800 כתבי-עת מתמטיים למאגר המידע הבינלאומי המנוהל על-ידי החברה המתמטית האמריקאית:  מכילים הפריטים רוב MathSciNet – AMS database of reviews, abstracts and bibliographic info תוצאות חדשות בענפי המתמטיקה השונים. מדור החדשות בגיליון זה מכיל ארבע חדשות מהשנה הנוכחית )2016 ,)שהן כמובן רק חלק… show more
  • 11 Feb 2015 Conference Paper The Proceedings of the 12th International Congress on Mathematical Education

    The Evolution of Mathematics-Teachers’ Community-of-Practice

    Abstract
    A successful implementation of educational change depends on teachers’ professional development, and their ability to translate innovative ideas into practice. Although teaching, by its very nature, is a complex practice, most teachers work in isolation, making their own planning and decisions, and solve pedagogical problems having limited consultation with and feedback… show more
  • Jan 2014 Book Chapter Mathematics & Mathematics Education: Searching for Common Ground

    Reflections on Policy: What Should We Do, and Who Decides?

    Abstract
    Although mathematics is essential to mathematics-education, and mathematics-education is essential to mathematics, these claims do NOT imply that mathematics and mathematics-education are the same. Actually, they are gradually growing apart. This chapter summarizes the views of its authors on the relationship between the mathematics and mathematics-education communities… show more
  • 2014 Book Chapter The Life and Work of Leon Henkin

    Tracing Back “Logic in Wonderland” to My Work with Leon Henkin

    Abstract
    The book Logic in Wonderland, I co-authored with Atara Shriki, was published in early 2013, about 40 years after I started my Ph.D. thesis with Leon Henkin. The time gap did not diminish his influence. A few anecdotes from my early days with Leon and two sample tasks from the book recently published illustrate it.
  • 2014 Book Chapter The Life and Work of Leon Henkin

    Pairing Logical and Pedagogical Foundations for the Theory of Positive Rational Numbers—Henkin’s Unfinished Work

    Abstract
    Five different ways of “founding” the mathematical theory of positive rational numbers for further logical development are presented as Leon Henkin outlined in 1979 in the form of notes for a future paper, suggesting that pairing them up with five representation models could possibly yield further pedagogical development. In turn, he thought that this would indicate a… show more
  • Jun 2013 Journal Article Mispar Chazak 2000 – The Israel Elementary Mathematics Teachers Journal

    Can we do without fractions? – No, but…A proposal to teach the decimals prior to teaching the fractions

    האם אפשר בלי שברים פשוטים? – לא, אבל ... חלק ב: הצעה להקדמת ההוראה של המספר העשרוני לפני השבר הפשוט
    תקציר
    מאמר המציג את האפשרות להסתפק בהיכרות ראשונית עם השברים הפשוטים, ולעבור אל ההצגה העשרונית של המספר הרציונלי לפני העמקה בשברים הפשוטים.
  • 2013 Journal Article DAPIM Academic Journal
  • 12 Apr 2011 Book Chapter Constructing Knowledge for Teaching Secondary Mathematics

    Bridging Between Mathematics and Education Courses: Strategy Games as Generators of Problem Solving and Proving Tasks

    Abstract
    Mathematics courses—pure or applied—and education courses, with pedagogical, didactic, and psychological contents are two groups of courses of which programs for training prospective high-school mathematics teachers commonly consist. They often are given in separate departments, with very little, if any, coordination among the instructors. Four independent problem… show more
  • 18 Feb 2011 Journal Article Research in Mathematics Education

    The effect of using Transparent Pseudo-Proofs in Linear Algebra

    Abstract
    In an empirical study, the impact of exposing Linear Algebra students to a ‘Transparent Pseudo-Proof’ (TPP) of theorems was compared to that of exposing a comparable group of students to the formal proof of the same theorems. Following an analysis of the quantitative data collected in 36 sessions, this paper suggests a distinction between the benefit from employing TPPs… show more
  • 1 Jan 2011 Journal Article Interdisciplinary Journal of e-Learning and Learning Objects

    Nurturing a Community of Practice through a Collaborative Design of Lesson Plans on a Wiki System

    Abstract
    Eleven graduate students, experienced mathematics teachers, participated in a semester long activity in which they collaboratively designed and developed lesson plans on a Media Wiki system. The described study examined the processes involved in this collaborative effort and its contribution to the development of mathematics teachers' community of practice. Data were… show more
  • 1 Jan 2011 Book Chapter Recent Developments on Introducing a Historical Dimension in Mathematics Education:

    Exposure to Mathematics in the Making: Interweaving Math News Snapshots in the Teaching of High-School Mathematics

    Abstract
    Introduction: The Ever Growing Nature of Mathematics Beyond its glorious past, mathematics has a vivid present and a promising future. New results are published on a regular basis in the professional journals; new problems are created and added to a plethora of yet unsolved problems, which challenge mathematicians and occupy their minds. Movshovitz-Hadar [13] suggested… show more
  • Jan 2009 Book Chapter The Professional Education and Development of Teachers of Mathematics

    Studying Student Teachers' Voices and Their Beliefs and Attitudes

    Stephen Lerman, S A Amato, N Bednarz, M David, Viviane Durand-Guerrier, G Gadanis, P Huckstep, P Moreira, F Morselli, Nitsa Movshovitz-Hadar, Immaculate Kizito Namukasa, J Proulx, Tim Rowland, A Thwaites, Carl Winsløw
    Abstract
    Learning to teach mathematics is a complex undertaking, and in the last twenty years there has been a great deal of research looking at aspects of the process. There are many ways one might structure an analysis of research on learning to teach mathematics. It is clear, though, from all the research on learners in all kinds of situations that what student teachers bring… show more
  • 2009 Book Chapter Tasks in Primary Mathematics Teacher Education

    Logic in Wonderland: Alice's Adventures in Wonderland as the Context of a Course in Logic for Future Elementary Teachers

    Abstract
    The teaching experiment described in this chapter assumes at the outset that children's literature can be a useful context for teaching elementary ideas of logic while bridging the gap between the abstractness of formal logic and its expression in a real world context. Alice's Adventures in Wonderland, by Lewis Carroll (a unique combination of a logician and a story… show more
  • 1 Jan 2009 Book Chapter Creativity in Mathematics and the Education of Gifted Students

    Intellectual Courage and Mathematical Creativity

    Abstract
    This paper considers examples from the history of mathematics in which intellectual courage played an important role in mathematical creativity. In many cases social courage is also involved. Lessons are drawn about the education of mathematically gifted students.
  • 2009 Conference Paper ICMI Study 19

    The art of constructing a transparent p-proof

    Abstract
    This paper is devoted to lessons about constructing Transparent Pseudo-Proofs (abbr. TPPs) drawn from an empirical study of the impact of undergraduate students' exposition to TPPs of theorems in Linear Algebra. The following issues are discussed: (i) an appropriate formal proof that the TPP will reflect; (ii) an adequate value for the particular case that will become… show more
  • 1 Jan 2005 Conference Paper Renaissance Banff: Mathematics, Music, Art, Culture

    A Computerized Environment for Learning and Teaching 3-D Geometry

    Abstract
    This is a presentation of a project in progress at Technion – Israel Institute of Technology. The ultimate goal of this project is a computerized environment integrated in a program for learning and teaching 3D Geometry in high schools, focusing on the morphology of solids. 3D Geometry is an area of mathematics that most country's curricula almost totally neglect, yet… show more
  • Nov 2004 Journal Article International Journal of Mathematical Education in Science and Technology

    How to Present It? On the Rhetoric of an Outstanding Lecturer

    Abstract
    This paper analyses a lecture by an excellent teaching award winner professor of mathematics, given to high school mathematics teachers. The analysis is based upon two sources: (i) the lecture plan, as expressed in a series of 29 transparencies, prepared by the lecturer in advance; (ii) the actual implementation of the lecture, as transcribed from its video-taped record… show more
  • Feb 2003 Journal Article Visual Mathematics

    Visualization Vs. Verbalization, Insight into the Morphology of Polyhedra

    Abstract
    The impact of visual representations on understanding, and even more so, on actively doing mathematics, has been intensively researched and is widely recognized. This is particularly true for the study of 3-d geometry. What about the role of verbal descriptions - - Are they necessarily needed? Simply redundant? Or are they inappropriate, may be even disturbing??? In… show more
  • Jan 2001 Book Chapter Encyclopedia of Mathematics Education

    The Notion of Proof

    Abstract
    A proof in mathematics, much like a proof in any other area, is an argument one gives in order to convince others (and often one's self) of the correctness of one's assertion. The need to prove an assertion stems from doubts about its truth. In mathematics, unlike in many other areas, the standards of proof demand that every assertion can be given a conclusive proof… show more
  • Oct 2000 Journal Article Museum International

    Science in the service of society: the Israel National Museum of Science

    Abstract
    Science as a cornerstone of nation building is a guiding principle of the Israel National Museum of Science, which caters to a culturally diverse public of all ages. Nitsa Movshovitz-Hadar is director of the museum and professor at the Technion–Israel Institute of Technology and former head of its Department of Education in Technology and Science. Since 1986, she has… show more
  • 2000 Journal Article Aleh – The Israel Journal for High School Mathematics Teachers

    The Mathematics of River Meanders

    Nitsa Movshovitz-Hadar, Alla Shmukler
    על פיתולי נהרות והמודל המתמטי של תופעה זו
    תקציר
    במאמר מוצג מודל מתמטי של ניבוי וחיזוי של מסלול ההתפתלות של נחלים ונהרות. המחברות מראות כיצד ניתן להגיע לאותו מודל בשתי גישות שונות: הגישה הדטרמיניסטית והגישה ההסתברותית.
  • 1 Jan 1998 Journal Article Studies in Educational Evaluation

    Curricular change agenda for failure-experienced mathematics students: Can success-promoting assessment make a difference?

    Abstract
    The study reported in this paper addressed the question: Can a success promoting assessment schema (SPAS) be designed so as to have a positive impact on mathematics learning of failure-experienced students? Addressing the problem of the study is important because assessment of students' mathematics learning greatly impacts the way mathematics is taught and learned in… show more
  • Jun 1997 Journal Article The Mathematical Intelligencer

    Proof: A Many-Splendored Thing

    Abstract
    In a 1993 article, Jaffe and Quinn, concerned that “today in certain areas there is again a trend toward basing mathematics on intuitive reasoning without proof” (Bull Am Math Soc 29:1–13, 1993), have suggested a framework for dealing with the issue which includes attaching labels to “speculative and intuitive” work. The article has engendered a fascinating debate within… show more
  • 1995 Journal Article 16

    An intuitive basis for the fundamental theorem of algebra

    בסיס אינטואיטיבי למשפט היסודי של האלגברה
    תקציר
    מתוך הכרה בחשיבות במשפט היסודי של האלגברה ומתוך מודעות לעובדה שכל ההוכחות של המשפט דורשות ידע מתמטי שאינו נלמד בבית הספר העל יסודי, מתעוררת השאלה כיצד ניתן להביא תלמידים לידי הכרות ראשונה עם המשפט וליצור בכך מסגרת מתאימה לדיון בפתרון משוואות פולינומיאליות? במאמר מוצג רקע הסטורי ומתמטי של המשפט היסודי של האלגברה, סקירה של דרכי טיפול בהוכחות המשפט המוצעות ע"י חוקרים אחרים… show more
  • 1995 Journal Article Aleh – The Israel Journal for High School Mathematics Teachers

    A survey of the use of computers for mathematics

    סקר על השימוש במחשבים להוראת מתמטיקה בבתי ספר על יסודיים
    תקציר
    במאמר מוצג סקר הבא לספק תמונת מצב על השימוש במחשבים בהוראת המתמטיקה. מטרת הסקר היא לעזור במציאת מענה לשאלות  אירגוניות וקונספטואליות. המסקנה היא שהתמונה הכללית בתחום שילוב מחשב בהוראת המתמטיקה היא דלה מאד וכי על מנת לשנות את המצב יש להשקיע מאמצים בהכשרת מורים למתמטיקה ובהנחייתם בתחום השימוש במחשב בהוראת המקצוע.
  • Dec 1994 Journal Article American Mathematical Monthly

    The Role of Paradoxes in the Evolution of Mathematics

    Abstract
    A paradox has been described as a truth standing on its head to attract attention. Undoubtedly, paradoxes captivate. They also cajole, provoke, amuse, exasperate, and seduce. More importantly, they arouse curiosity, stimulate, and motivate. In this paper we present examples of paradoxes from the history of mathematics which have inspired the clarification of basic… show more
  • 21 Mar 1994 Journal Article Journal of Computers in Mathematics and Science Teaching Archive

    Facilitating an intuitive basis for the fundamental theorem of algebra through graphical technologies

    Abstract
    The Fundamental Theorem of Algebra has always been considered beyond reach for high school and even college students, al-though it is, indeed, a fundamental and significant component of mathematics culture. With the aid of graphical technologies, it is now possible to create a qualitative intuitive basis for understanding the underlying ideas and concepts of this… show more
  • Dec 1993 Journal Article School Science and Mathematics

    Mathematical Induction: A Focus on the Conceptual Framework

    Abstract
    This paper presents ten tasks with the opportunity to focus on various conceptual aspects of Mathematical Induction. Many of the tasks involve debugging in the process of their solution. Some of the "bugs" reside in the cognitive image of mathematical induction, which students bear in their minds. Others are simply false inductions which need to be resolved. Incorporating… show more
  • Oct 1993 Journal Article School Science and Mathematics

    A Constructive Transition From Linear To Quadratic Functions

    Abstract
    This paper presents a didactical phenomenology of the mathematics of quadratic functions, which shows how they evolve from linear functions. Aided by computer graphics, we look at quadratic functions from two points of view: (a) as the product of two linear functions g(x) = ax + b and t(x) = cx + d ; and (b) as the sum of three simple monomial functions, namely, p(x)… show more
  • 1 Sep 1993 Journal Article The Journal of Mathematical Behavior

    The False Coin Problem, Mathematical Induction and Knowledge Fragility

    Abstract
    Presents evidence of knowledge fragility in connection with mathematical induction (MI) as observed while working with prospective teachers. Conflict-resolution activity and teacher education, the place of MI in the curriculum, and participating students' MI competency are considered. An attempt is made to explain the observations based on an analysis of the logic… show more
  • May 1992 Journal Article The College Mathematics Journal

    Infinitely Many Different Quartic Polynomial Curves

    Nitsa Movshovitz-Hadar, Alla Shmukler
    Abstract
    The graph of every polynomial of first degree is an inclined straight line. The graph of every polynomial of second degree is a parabola. Such uniformity of shape does not hold for the graphs of all polynomials of third degree, as we can see in Figures 1-3. How many distinct shapes are there to the graphs of cubic polynomials? What about the quartics? And polynomials… show more
  • Feb 1992 Journal Article British Journal of Educational Psychology

    Is More Always Better? The Separate and Combined Effects of a Computer and Video Programme on Mathematics Learning

    Abstract
    Summary. This study was designed to assess the combined and separate effects of instruction via a computer and video programme on students' learning processes, intrinsic motivation, and achievement in geometry. A 2times2 (Computer by Video) factorial design was employed. Participants were 268 fifth grade students who studied the same content for the same duration of… show more
  • 1 Jul 1991 Journal Article International Journal of Mathematical Education in Science and Technology

    A qualitative study of polynomials in high school

    Nitsa Movshovitz-Hadar, Alla Shmukler
    Abstract
    A method is suggested for getting students acquainted with polynomials of degree higher than 2. The goal is to develop students’ intuition for polynomials as a basis for further algebraic and analytical study of polynomials. In particular, existence, number and type of real and complex roots of polynomials of a given degree n >2 are under consideration. Polynomials… show more
  • Jan 1991 Journal Article Teaching and Teacher Education

    More about mathematical paradoxes in preservice teacher education

    Nitsa Movshovitz-Hadar, Rina Hadass
    Abstract
    This is a third report on a naturalistic study in Israel of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; and (b) raising their pedagogical awareness of the constructive role of fallacious… show more
  • Jun 1990 Journal Article Educational Studies in Mathematics

    Preservice Education of Math Teachers Using Paradoxes

    Nitsa Movshovitz-Hadar, Rina Hadass
    Abstract
    This is a report on a naturalistic study of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; (b) raising their pedagogical awareness of the constructive role of fallacious reasoning in the… show more
  • Mar 1990 Journal Article Interchange

    Aspects of the pluralistic nature of mathematics

    Abstract
    Students (and not only students) usually think of mathematics as monolithic and fixed for all time, and of mathematicians (if they give any thought to the creators of the subject they are dealing with) as in total agreement on mathematical means and ends. How many of them realize that not only the methods and results of mathematics but also its basic concepts are… show more
  • Feb 1989 Book Review Educational Studies in Mathematics

    Speaking Mathematically: Communication in Mathematics Classrooms by David Pimm

    Abstract
    Speaking Mathematically is an examination of the mathematics classroom from a linguistic point of view. It illuminates aspects of mathematics and of its teaching which may have not been that apparent previously. The author, David Pimm, a mathematics educator at the Open University in Britain, analyses the nature of speaking and of writing the language of mathematics… show more
  • May 1988 Journal Article International Journal of Mathematical Education in Science and Technology

    Inductive problem‐sequences for independent study of linear algebra

    Abstract
    Three chapters of the syllabus of a basic mathematics course for engineering students at the Technion† were adapted for the student's independent development of mathematical knowledge by means of solving a chain of inductive problem‐sequences: (i) vectors and scalars in the plane; (ii) vectors in the three‐dimensional space; (iii) planes and lines in the 3‐dimensional… show more
  • 1988 Journal Article For the Learning of Mathematics

    Stimulating Presentation of Theorems Followed by Responsive Proofs

    Abstract
    A mathematics teacher's task is often to convey a certain theorem In practice, this task usually comprises two parts: a presentation of the theorem followed by a presentation of a proof Planning how to do this is a decision-making process of selecting the method by means of which each part of the presentation should take place, and the sequential path connecting the… show more
  • Mar 1987 Journal Article Mathematics Teacher: Learning and Teaching PK–12

    Sometimes Students' Errors Are Our Fault

    Abstract
    “The root of students' frustration with mathematics is that they are so frequently wrong” (Wood 1982). We accept this thesis, along with the fact that taking a written test is not a relaxing experience. Therefore, as teat designers, we must make an effort to minimize the amount of irrelevant obstacles students face when taking a test.
  • Jan 1987 Journal Article Journal for Research in Mathematics Education

    An Empirical Classification Model for Errors in High School Mathematics

    Abstract
    A content-oriented analysis of written solutions to test items in Israeli high school graduation examinations in mathematics yielded a system of six error categories: misused data, misinterpreted language, logically invalid inference, distorted theorem or definition, unverifed solution, and technical error. This system enabled most of the documented errors to be classified… show more
  • Jan 1986 Journal Article Focus on Learning Problems in Mathematics

    Students’ distortions of theorems

    Abstract
    The high school mathematics curriculum is loaded with theorems that students are expected to be able to recall and to apply in order to solve problems. in this study of solutions to high school matriculation exams in mathematics, the authors were astonished by the multiplicity of student-invented variations of theorems. The collection of distortions presented in this… show more
  • Jan 1986 Journal Article Undergraduate Mathematics and Its Applications Journal

    Independent learning of college mathematics: An inductive approach

    Abstract
    The current mode of instruction at the Technion, as at many schools of engineering, universities, and colleges, is based largely on frontal presentations, sometimes for audiences of several hundreds. In these circumstances the lecturer is in a state of continual activity and maximum concentration, while the class audience is condemned to function as passive listeners… show more
  • Nov 1982 Journal Article Mathematics in School

    The 4-Weight Problem -- A Pedagogical Account

    Nitsa Movshovitz-Hadar, Rina Hadass
    Abstract
    The Weight Problem of Bachet de Meziriac is described, which looks for four integral weights to measure every amount between one and forty kilograms. Discussed are generalizations of the problem and analogous problems, solutions of particular cases, and a solution of the general problem.
  • May 1982 Journal Article Mathematics Teacher: Learning and Teaching PK–12

    Odd and Even Numbers--Magician's Approach

    Abstract
    Magicians somehow manage to produce a “question mark look” on the faces of their audience. Their audiences whisper, “Wow. I wonder how that happened?” “I wish I knew how it works.” They would try to understand the magic trick and to learn how to perform it if the magicians were ready to reveal the secrets.
  • Nov 1981 Journal Article Educational Studies in Mathematics

    The Road to Solving a Combinatorial Problem is Strewn with Pitfalls

    Nitsa Movshovitz-Hadar, Rina Hadass
    Abstract
    In this paper we examine typical difficulties involved in solving a combinatorial problem, and demonstrate them throughout the solution of the “Problem of the misaddressed letters”. We focus on difficulties of two sorts: Those which stem from the fact that a combinatorial problem is usually an infinite set of problems, and others which are involved in finding a systematic… show more
  • Sep 1981 Journal Article International Journal of Mathematical Education in Science and Technology

    Between associativity and commutativity

    Abstract
    For any binary operation, four alternatives exist. It could be (i) both commutative and associative; (ii) neither commutative nor associative; (iii) commutative but not associative; (iv) associative but not commutative. The basic arithmetical operations provide examples for the first two possibilities. This paper presents elementary examples for the last two possibilities… show more
  • Jan 1981 Journal Article International Journal of Mathematical Education in Science and Technology

    An analysis of teaching moves in the teaching of the Sine Theorem via guided discovery

    Nitsa Movshovitz-Hadar, Rina Hadass
    Abstract
    “Is there a common (algebraic) property to all triangles inscribed in a given circle?"—this is the key motive to students' independent study intended to lead them to a discovery of the Sine Theorem. A detailed transcript of a lesson based upon this trigger is analysed in the paper. For the analysis, fourteen teaching moves are specified. Each move appears in two versions… show more
  • 1 Dec 1979 Journal Article Mathematics Teaching

    Division by Zero

    Abstract
    When children first meet ideas about division, they are concerned only with division of whole numbers. In fact, often it is arranged that to begin with quotients are exact, and remainders come later. After some time comes 'long' division, and then division involving fractions, written as rational numbers or as decimals. The problem of division by zero comes much later… show more
  • Feb 1978 Journal Article Educational Studies in Mathematics

    Children's Conditional Reasoning Part III: A Design for Research on Children's Learning of Conditional Reasoning and Research Findings

    Abstract
    This is the third in a sequence of papers describing an experimental study in which fifth grade students were introduced to the distinction between valid and fallacious inferences drawn from conditional premises. The previous two papers in this sequence described the hands-on learning materials used throughout the experiment, and the measuring instrument used to assess… show more
  • Feb 1978 Journal Article Educational Studies in Mathematics

    Children's Conditional Reasoning Part II: Towards a Reliable Test of Conditional Reasoning Ability

    Abstract
    This is the second in a sequence of three papers describing an investigation of fifth graders' ability to learn to distinguish between valid and fallacious inferences from simple conditional premises. The first paper presented the experimental materials. The present paper discusses the measuring instrument used to assess the effect of the experimental materials. This… show more
  • Dec 1977 Journal Article Educational Studies in Mathematics

    Children's conditional reasoning

    Abstract
    This study stemmed from a desire to redress the distorted view of mathematics in the elementary curriculum, created by the current imbalanced emphasis on computational rules and some applications, but very little logical analysis. The study is intended to show that fifth-grade students can significantly improve their use of logical analysis through a suitable instructional… show more
  • *** DATE MISSING *** Journal Article Mispar Chazak 2000 – The Israel Elementary Mathematics Teachers Journal

    Can we do without fractions? – No, but… The decimals as a road to understanding fractions

    האם אפשר בלי שברים פשוטים? – לא, אבל ... חלק א: העשרוניים כנתיב להבנת השבר הפשוט
    תקציר
    מאמר המציג רציונל לרעיון העוסק בהצעה להסתפק בהיכרות ראשונית עם השברים הפשוטים, ולעבור אל ההצגה העשרונית של המספר הרציונלי לפני העמקה בשברים הפשוטים.