AN INVESTIGATION ON CHINESE TEACHERS�� REALISTIC PROBLEM POSING AND PROBLEM SOLVING ABILITY AND BELIEFS

In the present study, which is a part of a research project about realistic word problem solving and problem posing in Chinese elementary schools, a problem solving and a problem posing test were administered to 128 pre-service and in-service elementary school teachers from Tianjin City in China, wherein the teachers were asked to solve 3 contextually challenging division-with-remainder (DWR) word problems and pose word problems according to 3 symbolic expressions. Afterwards, they were also given 2 questionnaires wherein they had to evaluate 3 different pupil reactions to, respectively, 1 problem solving item and 1 problem posing item about DWR. First, our results revealed that teachers behaved quite ‘realistically’ not only when solving and posing DWR problems themselves but also when evaluating elementary school pupils’ DWR problem solving and problem posing performance. Second, we found a correspondence between teachers’ own performance on the tests and their evaluations of pupils’ reactions. Third, the present study provides some further insight into the role of one of the instructional factors that is generally considered responsible for the strong and worldwide tendency among elementary school children to neglect real-world knowledge and realistic considerations in their endeavours to solve and pose mathematical word problems, namely the teachers’ conceptions and beliefs about this topic.     

ON A PROBLEM OF N.SALINAS

This paper presents a discussion on a problem suggested by N.Salinas(J.Operator Theory,Vol.10,1983),i.e.,if T=(T_1,T_2,…,T_n)is a commuting n-tuple ofhyponormal operators on a complex Hilbert space,do we have(1)(2)δ(T-μ)=dist(μ,σ_l(T)),μ∈C~n?It is proved that the problems(1)and(2)are both true for some commuting n-tuples ofsemihyponormal operators.In general case,problem(1)has a negative answer.As an ap-plication,we point out that there exists a commuting n-tuple of hyponormal operatorsT(n≥2),such that|λ|<,where σ_T(T)denotes J.L.Taylor'sjoint spectra of T,even if the condition of Taylor's joint spectra of T is given.     

APPENDIX A： ALTERNATIVE WAY OF OBTAINING THE LEAST-SQUARES PROBLEM

It is worth to mention that Eq.（19） can be found alternatively first by describing the boundary conditions at each of the sampling points to obtain a set of linear equations with respect to the modal coefficients Then, determining the number of sampling points in order that the number of linear equations be twice the number of unknowns     

EMERGENCY SUPPLY FOR MULTI-DEPOT PROBLEM IN CERTAIN AND UNCERTAIN CIRCUMSTANCES

ＩＮＴＲＯＤＵＣＴＩＯＮＥｍｅｒｇｅｎｃｙｓｅｒｖｉｃｅｓ,ｓｕｃｈａｓｅｍｅｒｇｅｎｃｙｉｎ ｖｅｎｔｏｒｙｓｕｐｐｌｙ ,ｅｍｅｒｇｅｎｃｙｍｅｄｉｃａｌｓｅｒｖｉｃｅａｎｄｆｉｒｅｒｅｓｃｕｅｃｏｍｐｒｉｓｅａｍａｊｏｒｃｏｎｃｅｒｎｏｆｅｍｅｒｇｅｎ ｃｙｐｌａｎｎｅｒｓ.Ｔｈｅｓｔｒａｔｅｇｉｃｐｒｏｂｌｅｍｏｆｗｈｅｒｅｔｏｌｏｃａｔｅｅｍｅｒｇｅｎｃｙｓｅｒｖｉｃｅｓｓｔａｔｉｏｎｓ (ｄｅｐｏｔｓ)ａｎｄｔｈｅｓｔｒａｔｅｇｉｃｐｒｏｂｌｅｍｏｆｔｈｅｑｕａｎｔｉｔｙｏｆｅｍｅｒｇｅｎ ｃ…     

A UNIFIED FRAMEWORK OF FUNCTIONAL METHODS FOR ELECTROMAGNETIC BOUNDARY VALUE PROBLEM

IntroductionFor a practical clectromagnetic boundary value problem(BVP),there are three impor-tant steps in theoretical research:**Formulation of the mathematical models,*Choice and operation of solving method,*Mathematical skill process,where the second step always makes one difficult,since so many miscellancous methodsappear in various publications,they were proposed and developed by different persons ofdifferent affiliations in different ages,and under different backgrounds of professional ap-plication.     

THE RESPONSE OF OLDER WOMEN TO A CREATIVE PROBLEM‐SOLVING PROGRAM

Little work has been done in the development of creativity in older adults. The limited research seems to support the notion that older people are not as creative as younger people.

The purpose of the study was to investigate whether or not creative behavior as measured by Torrance Tests of Creative Thinking can be increased in older adult women through a creative problem‐solving program. The major hypothesis under investigation was: The use of a specific problem‐solving program designed to increase certain creative thinking abilities will increase those abilities at a significant level in older adult women. Forty women volunteers, ranging in age from 60 to 82, participated in the six‐week program.

Experimental subjects did not score significantly higher on the Torrance tests than the control subjects who had not participated in the program. However, information collected via the teacher's log and a questionnaire given to the subjects at the end of the class showed that the experience was unusually positive and creatively beneficial.

It is concluded that the program was not of sufficient intensity and that in order to measure change in creative thinking with older people, a more creative approach in testing may need to be developed.     

ORTHOGONAL PROJECllON OF THE DOMAIN BORNDARY OPERATOR FOR ELLIPITIC PROBLEM BY DOMAIN DECOMPLSITION

ＯＲＴＨＯＧＯＮＡＬ ＰＲＯＪＥＣｌｌＯＮ ＯＦＴＨＥ ＤＯＭＡＩＮＢＯＲＮＤＡＲＹＯＰＥＲＡＴＯＲＦＯＲＥＬＬＩＰＩＴＩＣＰＲＯＢＬＥＭＢＹＤＯＭＡＩＮＤＥＣＯＭＰＬＳＩＴＩＯＮ（石佩虎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｎｉａｔｉｃｓａｎｄＭｅｃ?..     

‘METHOD‐REVERSION’: THE PROBLEM OF SUSTAINING CHANGES IN TEACHER‐BEHAVIOUR

The NFER research into comprehensive education reported that around one‐third of pupils in the schools studied took no part in extra‐curricular activities, and that level of involvement was lower among certain groups. This study examines whether the interests of these pupils were being met by their schools and finds that low participation cannot be explained‐‐directly at least‐‐by school failure in providing desired activities. Nearly two‐thirds of all non‐participant pupils indicated that there was no activity which they would like to see introduced. Detailed study in three schools suggests that the ‘traditional’ school activities, though gathering a large number of participants, may be poor integrators of pupils of different abilities and that smaller activities are more successful in this respect.     

A MODIFIED CRANK－NICOLSON SCHEME FOR THE INITIAL－BOUNDARY VALUE PROBLEM OF SUPERTHERMAL ELECTRON TRANSPORT EQUATION

ＡＭＯＤＩＦＩＥＤＣＲＡＮＫ－ＮＩＣＯＬＳＯＮＳＣＨＥＭＥＦＯＲＴＨＥＩＮＩＴＩＡＬ－ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＳＵＰＥＲＴＨＥＲＭＡＬＥＬＥＣＴＲＯＮＴＲＡＮＳＰＯＲＴＥＱＵＡＴＩＯＮＳｕｎＺｈｉｚｈｏｎｇ（孙志忠）（Ｄｅｐａｒｔ...