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Developing Cognitive Flexibility Satyawati Rawool

 P. V. D. T. College of Education for Women, Mumbai, India

To represent “content knowledge” in the textbook sim-ple looking, stereotyped, abridged forms are used. Theseknowledge representations are treated as the “ideal andonly correct one” by many teachers and learners. The

 way teachers learn the mathematics and the way they teach it to pupils lead them to believe that the math-ematical knowledge is rigid and rule bound. Conse-quently for most of the learners, mathematics learningends in remembering textbook representations. If learn-ers are assisted to make textbook representations mean-ingful for themselves then mathematics learning may not be drudgery for many of them. It is not possible forany educator to evolve a constructivist-learning envi-

ronment all of a sudden for helping learners of any level to change their attitude toward mathematics learn-ing. As a teacher one has to make deliberate efforts tocreate learning experiences that may bring in changein the mathematical activities in the classroom.

 Available research findings show that if learners areassisted to represent their thought processes and un-derstanding, using “different contexts”, “different me-

dia” and “different modes” the learning situation be-comes complex and challenges learners to be active.The situations thus evolved forces learners to work incollaboration for making textbook learning meaning-ful. The learners while revisiting their previous learn-ing are expected to liberate themselves from the way of understanding and create many ways of understand-ing mathematics The cognitive flexibility theory is

them to become expert performers. The critical fea-ture of this mode is that the teacher is not supposed toserve as effective or flawless model (with intention). Itis assumed that there is no idealized path for teaching

or learning. The learners in this situation are expectedto experience authentic way of doing mathematics.

This paper is based on my experiences with studentteachers. Our learners are student teachers aspiring tobecome mathematics educators. They equal ‘under-standing’ with ‘remembering procedures for gettingcorrect answers to the exercises that are given in thetextbook’. They expect pupils to use the writing proce-

dure that is given or rather dictated to them. Thoughclear instructions are given in the textbook for learn-ers and teachers that they should try to use all possiblemethods of getting answers to the exercises, most of them think it as needless work. Efforts are made tohelp them to get experiences in learning mathematicsas well as learning to design constructivist-learningenvironment. I expected to get answers to the follow-ing questions.

How far does a constructivist-learning environment helpstudent teachers to change their views about learningin general and mathematics learning in particular?

Do the cognitively flexible environment and the cogni-tive apprenticeship approach help them becomeepistemically motivated with respect to subject knowl-d d t iti t f l i ?

8/10/2019 Developing Cognitive Flexibility

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ties in the beginning as they feel that these are very 

complicated. They argue that they are in a position toanswer questions related to the logic, as they are gradu-ates but it is not possible with pupils. This opinion isconsistent with the opinion of many teacher educators.They forget the fact that learning takes place only whenthe situation challenges a person. My experience withschool children is different. Most of the school chil-dren enjoy this type of learning environment. Only fewlearners worry about important questions. If learner is

epistemically motivated then she or he might ask ques-tions related to the knowledge, the way it is repre-sented and its origin. Epistemically motivated learnersare ‘inquisitive’ and ‘curious’ about every experiencethey encounter. For example they may be asking ques-tions like how a particular way of representing differ-ent mathematical operations has evolved, how muchtime and effort a particular human culture required toevolve mathematical concepts, are there differentnumber systems with different logic, etc. My efforts asteacher educator did not motivate student teachers toask these types of questions.

This cognitive apprenticeship did help some studentteachers to change their view about learning of math-ematics and about mathematics as a subject to someextent. Now they don’t restrict their learning and teach-

ing to solving exercises given in the textbook. They are

motivated to learn more about subject but they are not yet empowered to question the authority of the text-book knowledge and fail to transfer this learning skillto the learning of other concepts. For example they didnot able to apply this learning for studying concept of division or other concepts of this type. Similarly they did not think along these lines with respect to learninggeometry. It appears that learners need more time toget attuned with this kind of learning approach. An-

other aspect was evident through reflective exercisesand their narratives about learning experiences. Stu-dent teachers did not think that they were learningmathematics and learning about teaching mathemat-ics simultaneously. Their stance was to learn to teachand not learning to learn and teach. Some studentsmentioned the fact that they don’t find any instance toask epistemological questions. Major hurdle in devel-oping cognitive flexibility is the attitude of teachereducators as well as student teachers. They think that we as teachers of mathematics are there to developconvergent thinking (certainty) and not divergent think-ing (uncertainty). Thus getting final correct answerusing a particular method or procedure is their soleaim of teaching mathematics.

Trends in Mathematics Education Research