### KRUTETSKII PROBLEM SOLVING

Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. To examine that, two problem-solving activities of high achieving students from secondary school were observed one year apart – the proposed tasks were non-routine for the students, but could be solved with similar methods.

Furthermore, the ability to generalise, a key component of Krutetskii’s framework, was absent throughout students’ attempts. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii , was developed. Ability is usually described as a relative concept; we talk about the most able, least able, exceptionally able, and so on. Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level.

In this paper we probldm the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Furthermore, the ability to generalise, a key component of Krutetskii’s framework, was absent throughout students’ attempts. Conversely not all highly able mathematicians show their abilities in class, or do well in statutory assessments.

For these studies, an analytical framework, based on the mathematical ability defined by Krutetskiiwas developed.

## Supporting the Exceptionally Mathematically Able Children: Who Are They?

Furthermore, the ability to generalise, a key component of Krutetskii’s framework, was absent throughout students’ attempts. This may be because they are bored, unwilling to stand out as being different, or perhaps have a specific learning disability, rpoblem as dyslexia, which prevents them from accessing the whole curriculum. They may not necessarily be the high achievers, but we’ll come back to that issue later.

Mathematical abilities and mathematical memory during problem solving and some aspects of mathematics education for gifted pupils Szabo, Attila Stockholm University, Faculty of Science, Department of Mathematics and Science Education. The overview also indicates that mathematically gifted adolescents are facing difficulties in their social interaction and that gifted female and male pupils are experiencing certain aspects of their mathematics education differently.

Simon Baron-Cohen postulates that able mathematicians are systemisers – highly systematic in their thinking – and this is more predominately a characteristic of the male brain. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Register for our mailing list.

Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii The truth is possibly a mixture of the two – mathematical ability does seem to run in some families, but we also need to offer suitable mathematical activity in order to develop and nurture it.

Stockholm City Education Department, Sweden. For now let’s look at what various writers and researchers have to say about the subject. The present study deals with the role of the mathematical memory in problem solving. Moreover, the study displays that the participants used their mathematical memory mainly at the initial phase and during a small fragment of the problem-solving process, and indicates that students who apply algebraic methods are more successful than those krutetskij use numerical approaches.

At its extreme he also suggests it is characteristic of autism, and he is undertaking research to see if there is kruetskii genetic connection. Moreover, the study displays that the participants used their mathematical memory mainly at the initial phase and during a small fragment of the problem-solving process, and indicates that students who apply algebraic methods are more successful than those who use numerical approaches.

Accordingly, mathematical ability exists only in mathematical activity and should be manifested in it. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled.

Abilities change over time Bloom identified three developmental phases; the playful keutetskii in which there is playful immersion in an interesting topic or field; the precision stage in which the child seeks to gain mastery of technical skills or procedures, and the final creative or personal phase in which the child peoblem something new or different.

In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. The number of downloads is the sum of all downloads of full texts.

In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students’ selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them.

# Supporting the Exceptionally Mathematically Able Children: Who Are They? :

To examine that, two problem-solving activities of high achieving students from secondary school were observed one year apart – the proposed tasks soolving non-routine for the students, but could be solved with similar methods.

The characteristics he noted were:. Examining the interaction of mathematical abilities and mathematical memory: Krutetskii has explored mathematical ability in detail and suggest that it can only be identified through offering suitable opportunities to display it. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students’ selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them.

High performance and high ability Trafton suggests a continuum of ability from those who learn content well and perform accurately but find it difficult to work at a faster pace or deeper level to those who learn content quickly and can function at a deeper level, and who are capable of understanding more complex problems than the average student to those who are highly precocious in that they work at the level of students several years older and seem to need little or no formal instruction.

In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level.

Identifying a highly able oroblem at 5 will be different from doing krutrtskii at 11, or 14, partly because they have fewer skills to exhibit and partly because their abilities may change, but we can often see young children who are fascinated by playing around with number or shape and seek to become ‘expert’ at it.