
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 קולאץתקצירהידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ000,125 פריטים המתפרסמים בכ650 כתביעת מתמטיים למאגר המידע הביןלאומי 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?
AbstractShould 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
AbstractThe multiphase 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
AbstractIn 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 MathematicsNews 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 לאישהתקצירמדור 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 לרבמכר 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
AbstractThis 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 inservice 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
AbstractThis 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
K12 mathematics education in Israel: Issues and Innovations
AbstractThe 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 • K12 Mathematics Education in Israel
Introducing All High School Students to the True Nature of Contemporary Mathematics: Meeting the Challenge
AbstractThis chapter describes an ongoing 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 • K12 Mathematics Education in Israel
Mathematics Teachers Documenting, Sharing, and Improving Their Work Using a Newly Developed Software
AbstractThe increasing use of Wikipedia, social networks like Facebook, and databases with search engines such as Google, inspired us to consider a suitable computerbased 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 בישראלתקצירהידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ000,100 פריטים למאגר המידע הביןלאומי 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 טיולתקצירמדור 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 הביןלאומי המנוהל בידי החברה MathSciNet – AMS database of reviews, abstracts and :האמריקאית המתמטית info bibliographic הם מתפרסמים בכ1800 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
AbstractThis 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 חדשותתקצירהידעתם? בשנים האחרונות, בכל שנה מתווספים למעלה מ000,100 פריטים המתפרסמים בכ1800 כתביעת מתמטיים למאגר המידע הבינלאומי המנוהל עלידי 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 MathematicsTeachers’ CommunityofPractice
AbstractA 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?
AbstractAlthough mathematics is essential to mathematicseducation, and mathematicseducation is essential to mathematics, these claims do NOT imply that mathematics and mathematicseducation are the same. Actually, they are gradually growing apart. This chapter summarizes the views of its authors on the relationship between the mathematics and mathematicseducation communities… show more 
2014 • Book Chapter • The Life and Work of Leon Henkin
Tracing Back “Logic in Wonderland” to My Work with Leon Henkin
AbstractThe book Logic in Wonderland, I coauthored 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
AbstractFive 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 הפשוטתקצירמאמר 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
AbstractMathematics courses—pure or applied—and education courses, with pedagogical, didactic, and psychological contents are two groups of courses of which programs for training prospective highschool 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 PseudoProofs in Linear Algebra
AbstractIn an empirical study, the impact of exposing Linear Algebra students to a ‘Transparent PseudoProof’ (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 eLearning and Learning Objects
Nurturing a Community of Practice through a Collaborative Design of Lesson Plans on a Wiki System
AbstractEleven 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 HighSchool Mathematics
AbstractIntroduction: 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. MovshovitzHadar [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
AbstractLearning 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
AbstractThe 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
AbstractThis 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 pproof
AbstractThis paper is devoted to lessons about constructing Transparent PseudoProofs (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 3D Geometry
AbstractThis 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
AbstractThis 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 videotaped record… show more 
Feb 2003 • Journal Article • Visual Mathematics
Visualization Vs. Verbalization, Insight into the Morphology of Polyhedra
AbstractThe 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 3d 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
AbstractA 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
AbstractScience 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 MovshovitzHadar 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
על פיתולי נהרות והמודל המתמטי של תופעה זותקצירבמאמר 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 failureexperienced mathematics students: Can successpromoting assessment make a difference?
AbstractThe 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 failureexperienced 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 ManySplendored Thing
AbstractIn 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 האלגברהתקצירמתוך 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 יסודייםתקצירבמאמר 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
AbstractA 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
AbstractThe Fundamental Theorem of Algebra has always been considered beyond reach for high school and even college students, although 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
AbstractThis 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
AbstractThis 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
AbstractPresents evidence of knowledge fragility in connection with mathematical induction (MI) as observed while working with prospective teachers. Conflictresolution 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
AbstractThe 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 13. 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
AbstractSummary. 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
AbstractA 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
AbstractThis 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 studentteachers' 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
AbstractThis 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 studentteachers' 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
AbstractStudents (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
AbstractSpeaking 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
AbstractThree 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
AbstractA 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 decisionmaking 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
AbstractA contentoriented 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
AbstractThe 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 studentinvented 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
AbstractThe 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 4Weight Problem  A Pedagogical Account
AbstractThe 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 NumbersMagician's Approach
AbstractMagicians 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
AbstractIn 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
AbstractFor 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
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
AbstractWhen 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
AbstractThis 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 handson 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
AbstractThis 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
AbstractThis 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 fifthgrade 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 הפשוטתקצירמאמר המציג רציונל לרעיון העוסק בהצעה להסתפק בהיכרות ראשונית עם השברים הפשוטים, ולעבור אל ההצגה העשרונית של המספר הרציונלי לפני העמקה בשברים הפשוטים.