icem 3 values, tradition, and daily practice in math class: the cultural clash between new...
TRANSCRIPT
ICEM 3
Values, Tradition, and Daily Practice in Math Class:
The Cultural Clash between New Immigrant Teachers from the FSU and Israeli Teachers
Miriam Amit, Israel
LomonosovLomonosov
The quote “ Why do we learn mathematics? Because it organizes our mind” is attributed to the famous eighteenth century Russian mathematician, scientist, poet and linguistics reformer, Mikhail Lomonosov
(1711-1765)
Lena, who Immigrated to Israel in 1995, recalls wistfully, yet with pride, that she yearns for order, clarity, and a
sense of belonging .
Order in lifeOrder in life
Lomonosov’s inspiring message resounds far beyond mathematics.
The importance of “order” in life as stemming from
mathematics is part of an ongoing cultural legacy.
This maxim, however, runs counter to the view of mathematics held by “old timers” math teachers in Israel who see their discipline as a vehicle for developing critical and creative thinking.
When Lena and many other Soviet immigrants arrived
in Israel, they suddenly found themselves in a strange
culture based on an entirely different value systems.
immigrants
What is this lecture aboutWhat is this lecture about??
This lecture deals with the cultural encounter in
mathematics education, as experienced by
mathematics teachers, all recent immigrants from
the FSU, who integrated into the Israeli
educational system.
The research goalThe research goal
Our research goal has been to identify the
differences between two mathematics
education cultures - that of the FSU until the
early 90’s, and that of Israel from the 1990’s to
2005 - as perceived by new immigrant math
teachers.
Sources of dataSources of data
Data is based on personal interviews with immigrant and veteran Israeli teachers, video taped sessions and open discussions.
Culture, Values and MathematicsCulture, Values and Mathematics
The international research community of
mathematics educators has long claimed that an
inseparable link exists between mathematics
education and values, culture, and society.
(Bishop, 1988; Amit, 2000)
Certainly the main theme of this conference –
-testifies to this view .
Neutral mathematicsNeutral mathematics
However in society at large math is perceived as a neutral discipline, void of cultural affinity.
Therefore, it is commonly thought that mathematics can easily be transferred from one country or culture to another, without undue crisis or conflict.
This perception was found to be far from the truth.
Mathematics education Mathematics education in societies undergoing transition in societies undergoing transition . .
We do not claim to cover every facet of this cultural encounter, but the following may reflect with considerable accuracy the phenomenon of mathematics education in societies undergoing transition.
A wave of mathematics teachersA wave of mathematics teachers
During the 1990’s nearly 900,000 immigrants from the FSU came to Israel – a 15% percent addition to the country’s population of 6 million.
Many of the new arrivals had academic degrees in science, engineering, medicine, and music.
On the assumption that math was “a neutral, non-
ideological discipline, that is, a field of study that
lacked values or cultural affinity,” thousands of
immigrant teachers, as well as engineers, got a
certificate provided they knew some Hebrew, and
joined the school system.
math is “neutral”
Confidence and adjustmentsConfidence and adjustments
The halo surrounding Soviet mathematicians contributed to the immigrant teachers’ self-confidence and the expectation that their adjustment into the system would be immediate.
This presumption proved to be mistaken.
A waste of timeA waste of time!?!? Tamara (22 years of experience, Ph.D. in
mathematics) said about the teacher training course:
“… At first I thought that the course had nothing to offer me . . . I thought that with my experience as a teacher I could just go to work. [I was sure] that the course would be a waste of time, a mere formality, and that I’d sit there for a year, and begin work the following year
- Was I ever wrong !
“…. I was sure I would be able to step into a
classroom and begin teaching math. [I thought
that] while people’s natures are naturally
somewhat different, traditional mathematics is
the same everywhere, and there is no need to
go to an absorption center.
Taiti- I was wrong”
crackscracks
In the absorption process, a great dissonance exists between FSU teachers’ confidence in their undeniably successful pedagogical heritage, and their ability to prove the same success in their new country .
This dissonance has created cracks not only in the immigrant culture, but also in Israel’s mathematical-educational culture.
The dilema of immigrant The dilema of immigrant teachersteachers
Almost no literature.
In an enculturation system, the teacher is, by definition, the guardian of the culture and the disseminator of values.
Herein lies the dramatic dilemma: which culture and which values should they transmit –
the old ones that they were brought up on, lived by and respected, or the new ones from which they feel somewhat alienated?
Analysis processAnalysis process
In the first stage of the interviews we asked general fact-finding questions in order to obtain a clear picture of the structure and principles on which the Soviet Union’s education system had been built.
Based on this information we tried to critically dissect the general concept of ‘cultural differences,’ and understand the ‘day-to-day’ reality from which the teacher came, and compare it with the Israeli reality.
Attitudes towards educationAttitudes towards education
“First of all the attitude (towards education) was extremely positive, granting it enormous prestige. Education was considered a goal in its own right, as well as a key to a better way of life, higher social position, and larger income. This was the Soviet view.
In Israel there are other paths to success, such as opening a business.”
VospitanieVospitanie
The Soviet government placed mathematics on the highest pedestal.
Teachers and educators regarded math and science as vital tools in developing “upbringing” (vospitanie - in Russian, éducation – in French, Erziehung – in German) (Muckle, 1988), and saw themselves as agents of the mathematics culture in the Soviet Union.
IsraelUnionThe Soviet
Teacher's status
and conduct
1.Teaching is a low status profession. Math teachers have a higher status than others.
2.There is no "welcoming ceremony" when a teacher enters a classroom.
3.Teachers must be treated with respect, but the teacher is required to treat the pupils in a like manner.
4. The teacher is not allowed to make any personal remarks regarding discipline or achievement in a way that might be considered humiliating by the student.
1.Teaching is a high status profession. Math teachers have a higher status than others.
2.Students rise when teachers enter the classroom and welcome them.
3.The teacher must be treated with a large degree of respect, but not vice versa.
4.A teacher is allowed to make personal remarks to students in front of the class regarding their abilities. There were no discipline problems.
Teacher’s StatusTeacher’s Status
IsraelThe Soviet Union
Professional resources
1. Time: 4-6 (6 is rare) math lessons per week; scheduled according to the convenience of the timetable.
2. In most schools, students study all their subjects in the “home room class.” No special resources exist in the classroom. "Math classrooms" in high schools are rare.
1. Time: throughout all the years of schooling, math lessons are given at the beginning of the day, every day. Six hours a week minimum; 8-10 hours a week maximum.
2. In most schools, math classrooms are very well equipped and maintained (formula board, large mobile boards, books, etc.).
Professional resourcesProfessional resources
curriculum and curriculum contents
1. Compulsory national curriculum set by the Ministry of Education.
2. The main emphasis in high school was on algebra and calculus. Other math subjects include: geometry (two and three dimensional), trigonometry (taught in 10th or 11th grade), statistics and probability.
1. Compulsory national curriculum set by the Ministry of Education.
2. The main emphasis in high school was on algebra, geometry, and trigonometry (including sketching skills). Almost no emphasis on was placed on calculus. Statistics and probability were not taught since "math is deterministic."
IsraelThe Soviet Union
CurriculumCurriculum
IsraelThe Soviet Union
Examinations and evaluations
1. No element of testing during the lessons.
2. During the 1990’s, national written exams were given only at the end of high school. No oral exams in math.
.3. All exams include an
element of choice.
1. Every study session contains an element of testing in which pupils come to the board and receive a grade for their performance.
2. At the end of every school year an oral exam is given by external testers and a written external test is taken.
3. The exams contain no element of choice.
EvaluationEvaluation
What happened in the culture What happened in the culture encounterencounter??
From the immigrant teachers’ view of mathematics education:
Two mathematics education cultures exist, each basically different from the other.
Both reflect the general culture and educational-pedagogical perception of math instruction in each country – FSU and Israel.
In the FSUIn the FSU
In the immigrants’ country of origin, everyday life was highly centralized, especially in the educational system - from the state level, via the school, down to the classroom.
The approach was rigid and authoritarian. It strove toward uniformity, to the point of relinquishing choice, while emphasizing order, discipline, strict supervision and consistent follow-up:
"We knew exactly what was permitted and forbidden. There was a sense of order”.
The teaching profession was held in respect,
especially teachers of math and the sciences.
The state and society gave math, science, and
technology the highest priority, and provided enough
resources to attain this goal.
Competitiveness and achievement-oriented
approaches were encouraged.
Israel in the FSU’s teachers’ viewIsrael in the FSU’s teachers’ view
FSU immigrant math teachers view their new culture as:
Overly flexible and lacking centralization.
Pupils are given too many choices;
Individuality and autonomy are overstressed;
An exaggerated inclination toward cooperation, rather than competitiveness, prevails in the learning environment.
The Israeli education system seems to be bent on providing equal opportunity to all, instead of enhancing talented pupils.
Although officials and agents of culture in Israel ballyhoo the priority of math and science studies, when it comes to the practical realization of this statement, Israel lags far behind the FSU.
Centralization versus “free marketCentralization versus “free market””
In the FSU, the state decides all aspects of the educational curriculum (books, scope, pace, sequence) whereas in Israel the approach resembles a “free market” to a certain extend.
Running in many directionsRunning in many directions
As for learning materials and pedagogical
approaches, in Israel the choices and tendencies
run in many directions. This poses a difficulty for
immigrant teachers who were accustomed to an
authoritarian culture.
Freeing the teacher from being freeFreeing the teacher from being free
The USSR Academy of Pedagogical Sciences (APN) explicitly stated:
“Research …. frees teachers from repeated trial and error, from discovering what science already knows, and applying ideas that are unrealistic for the ordinary school.”
(Autotov,P.R. Babansky,Yu.K. in Dunston, J. Suddaby, 1992. p.9)
In other words, the system “freed the teacher” from
the need to be liberated, ambitious, and independent.
Against the constructivist theoryAgainst the constructivist theory
Another obstacle that teachers who came from a centralized authoritative culture faced was the difficultly in accepting autonomy, the investigative approach, and the constructivist theory, that were widespread in Israel during the 1990’s.
Big mathematicians said…
What is wrong with a good explanationWhat is wrong with a good explanation??
“There [in FSU] we knew how to teach properly and we succeeded at it; we knew what was best
for them [the students] . . . Student cannot discover math rules on their own . . Why should they have to? We can teach them the
correct ones. . . The students’ role is to learn in any situation; they must practice continuously, become organized,
then their minds will be orderly . . .
What is wrong with a good explanation”?
Criticism = humiliationCriticism = humiliation
Immigrant teachers found it hard and sometimes even humiliating, to accept the involvement in and occasional criticism of their teaching performance by parents and students, as is common in Western countries.
I can see your mistake, professor!
Math is not Literature
These differences were strongly rooted in the values and pragmatic reality
At the ethical level:
1 .Hard work was an important value in the Soviet regime.
“ Soviets hold that complex calculations inculcate good habits of
hard work, while British (and others in the West) feel that mathematics
is a subject [that teaches that] by hard thinking it is possible to
avoid hard work”.
)Muckle, J.Y., 1988, p. 58(
Hard work vs. hard thinkingHard work vs. hard thinking
Algebraic techniques
Simplify :
.
פשט:
221222
122
212
))3432()3412()1(3
(
aaaaaa
a
a
)1(9
342
2
a
a
Answer:
Algebraic techniques
Algebraic techniques is a mathematical topic that serves as a major point of contention between immigrant teachers from the FSU and experienced Israeli teachers.
Thinking or Doing
Tamara describes her first visit to an Israeli school:
“ There, [In the FSU] enormous emphasis was placed on algebraic technique… here, this has no influence on “mathematical thinking” even though it. should. The first time I arrived at a school with a solid reputation I had been asked to prepare a sample lesson. Of course I wanted the job so I chose the most interesting problems for the class. During the lesson, when we found how to solve a problem we realized that the solution required a quadratic equation (or equations) system. I said: well, from here you do it by yourself…. Eventually one pupil came up to me and said that I had explained ‘the easy things but not the hard stuff.’ For him and many others the ‘thinking part’ was easy but the equations were hard. (
Later, after I began teaching, I realized that the problem
[with the Israeli system] is that it emphasizes
“mathematical thinking” but ignores “technique.” In this
way the pupils are like engineers who know how to design
a building, but not how to actually build it. I think this is
really the basic difference between mathematics teaching
in Israel and the FSU”.
Process vs. Product
Is it enough to design the buildingIs it enough to design the building??
The goals of algebra study, see, Muckle, J.Y., A Guide to the Soviet
Curriculum; What the Russian Child is Taught in School, (1988).
The meta-goal of algebra teaching in the Former Soviet
Union is to raise the level of the pupils
“calculatory culture.“
calculatory culturecalculatory culture
Gershon – an experienced Israeli teacher, believes that:
o The development of critical thinking in mathematics
serves as a tool for critical thinking in life, and needs to
be inculcated at an early age when the child’s thinking
patterns are being shaped.
o That critical understanding and thinking are not the
exclusive birthrights of the intellectual elite, but belong
to everyone. The quest for equality influences the
perception of mathematics teaching.
Gershon – an Israeli point of view Gershon – an Israeli point of view
The transformation immigrant The transformation immigrant teachers undergoteachers undergo
The final question was: had your teaching
experience in Israel changed your views
on the aims of mathematics education
and the ways of teaching it? Replies
varied.
Leonid claimed that no change had taken place in his
personal views on math, but, he had
trouble defining the goals of math teaching.
Olga , who came from the “top of the mathematics
education pyramid” in the FSU, assured us that no
changes had occurred in her personal view on
mathematics education.
The transformation immigrant teachersThe transformation immigrant teachers undergoundergo
Lena experienced a genuine conceptual change. She was
confused about her views of society’s attitude toward mathematics: “It seems to me now that what went on [in the FSU] was a bit exaggerated. A child who failed to make the grade in math was considered worthless . . .” Lena’s pervious certitude in the social importance of mathematics has begun to crack.
Irena was the only interviewee who claimed that her outlook had
swung around “180 degrees.” She now sees the purpose of math instruction as the opportunity to provide a useful, accessible tool for everyone. She is looking for methods that simplify mathematics .
Tamara.. almost gave up manipulations…
The transformation immigrant teachersThe transformation immigrant teachers undergoundergo
Berry’s modelBerry’s model
Berry’s model (1990, 2005) deals with immigrant social absorption. He coined the term
acculturation strategies.
He divides acculturation strategies into four
categories according to:
the attitude toward the target culture and
the attitude to the culture of origin
Integration (+,+)
Assimilation (-,+)
Marginalization(-,-(
Separation (+,-)
New cultureNew culture
Old cultureOld culture
The fire keepers…
AssimilationAssimilation
Acceptance of the target culture, rejection of the culture of origin
Teacher’s statement: “There we were forbidden to budge from the study program. Even if they [the authorities] admitted that our suggestions were good, they said that it made no difference. ‘This [the official way] is how we expect things to be done!’ In Israel teachers have more
leeway to realize their creative capacity.”
Olga’s math class
SeparationSeparationRejection of the target culture along with attachment to the
culture of origin .
A teacher who taught a medium-low ability class gave the best pupils a grade of 75 (out of 100). When asked how it was possible that this was the highest grade she answered: “This is a group of weak pupils !”.
For her, one absolute scale existed for
achievement evaluation.
MarginalizationMarginalization
Rejection of the target culture and the culture of origin
A teacher who retreats into “a bubble” in the field of mathematics.
A teacher who claims that there is no difference between the two cultures of mathematics education.
IntegrationIntegration
Acceptance of the target culture along with retention of theculture of origin
A teacher spent many lessons “pounding” the algebra’stechnical skill into the pupils’ heads according to theSoviet method, then returned to the problems and dealtwith them at a deeper, more complex cognitive level.
… her pupils often complained that she wasn’t teaching them the material that they would be tested on in the
matriculation exams.
IntegrationIntegration
Integration is not always clear-cut. It is an ongoing cyclic process (Berger, 2003) .
In some cases integration was merely
“ fence straddling” - claiming there was a value and advantage to both approaches .
The influence of immigrant teachers on the The influence of immigrant teachers on the mathematics education culture in Israelmathematics education culture in Israel
Most of FSU math teachers were absorbed
into the Israeli educational system !!
““Math speakersMath speakers””
Another welcome influence has been the legitimization of the striving for excellence.
In many schools groups of “math speakers” have been set up under the experienced tutelage of FSU immigrant teachers.
““KidumaticaKidumatica””
Israel’s most successful “promoting excellence” program to date has been a math club called “Kidumatica – For the Advancement of Mathematics Excellence in the Negev.”
“Kidumatica” was established at the Ben-Gurion University of the Negev on the initiative of one of this study’s authors. The program is designed for young students with a high cognitive potential, many of whom come from lower socio-economic strata.
Most of “Kidumatica’s” teachers are immigrant mathematicians who derive immense satisfaction from this work, claiming that it’s “like breathing here with the oxygen-rich air from there.”
““Oxygen – rich airOxygen – rich air””
Conclusions and Closing RemarksConclusions and Closing Remarks
The purpose of this study was to identify differences between two mathematics education cultures .
FSU teachers left a society based on hierarchy, uniformity and discipline to one that encourages equality, diversity, choice, and autonomy.
Conclusions and Closing RemarksConclusions and Closing Remarks
They left a culture with a
centralized educational system
that promotes the teacher’s status,
individual excellence and competitiveness They came to a culture that permits a generous degree of autonomy;
appreciates diversity in teaching methods;
Negotiating new codesNegotiating new codes
From a retrospective view of the absorption process
(Berger, 2003), we see that the teachers in this
study now understand the codes of Israel’s
educational culture. They are able to evaluate and,
to a certain degree, internalize them.
These teachers have not really “fit in”. They are,
negotiating new codes and creating a math-
education sub-culture.
Understanding cultural codes
Evaluating
Internalizing
NOT fitting in. Negotiating new codes
A two directional process of refinement
A dynamic model of integrationA dynamic model of integration
What fits me? What fits my pupils?
Causes a change of behavior
Develops “new lances”, influences back on the former stages
With migrating populations Israel may be a case study and
a model for mathematics education in a multi-cultural,
immigrant-filled society. Principles for the model are:
o respect for differences and diversity.
o a desire to expand cooperation and
responsibility.
o an interest in cross-cultural dialogue;
o and the willingness to create mutual
systematic patterns for positive cultural
encounters.
A model for successful A model for successful integration /absorptionintegration /absorption
When the absorbing group is dominant, the less dominant group should have the opportunity to present and explain its values, so that a profitable synthesis between the two cultures may ensue.
A synthesis between cultureA synthesis between culture
The cultural encounter has been challenging for the absorbing population and has forced “us” to:
o reexamine our value system
o reevaluate basic axioms in our mathematics education system
o and take an honest and critical look at our educational “truths” in light of those that the immigrant teachers have brought with them.
Reexamine truthsReexamine truths
Reexamine truthsReexamine truths
o Then, we had to candidly, courageously, and without favor decide which “truths” were pertinent and viable, and where changes would have to be introduced.
Teachers of mathematics and science may further reduce
authoritarianism and dogmatism by:
adopting a humanistic approach toward teaching
educating toward openness and conceptual flexibility
and by developing human rationalism and critical reasoning.
The role of Mathematics EducationThe role of Mathematics Education
These aspirations have been the motivating factors behind this study and the
justifications for further research on the absorption of immigrant mathematics
teachers.
Thank you and SHALOM.
Big mathematicians said…
Order!
Olga’s math class
Math is not Literature
What do they really thinkWhat do they really think? ?
According to Tamara: “Students [in the Soviet Union or FSU] did not say what they thought or felt, [certainly] not in the realm of mathematics. …It was standard practice to think one thing and say something else . . . Here people say what’s on their mind and they do not always say good things . . ."
Absorption sequenceAbsorption sequence
“A large part of the immigrants’ difficulties lies in their ignorance of local cultural codes”
Berger, (2003) .
Absorption includes four sequential and one-directional phases:
understanding evaluation internalization fitting in
NoneNone sequential processsequential process
We challenge this view, since it becomes apparent in our study that a
non-sequential, interactive, and bi-directional, absorption process occurred in the case of FSU immigrant teachers.
Understanding cultural codes
Evaluating
Internalizing
Integration Fitting in
A two directional process of refinement
Zooming in” to Berger’s theoryZooming in” to Berger’s theory""
What fits me? What fits my pupils?
Causes a change of behavior
Develops “new lances”, influences back on the former stages