The nature of preservice mathematics teachers’ knowledge of students

Kılıç, Hülya

doi:10.1016/j.sbspro.2010.12.292

Cited by 19 publications

(13 citation statements)

References 9 publications

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“…A study of 70 secondary mathematics pre-service teachers from two universities found significant content weaknesses (Wilburne and Long 2010), and other research found content knowledge to generally be lacking in conceptual depth (Bryan 2011). Research has documented the struggle of pre-service teachers to identify the source of students' misconceptions and the challenge of finding ways other than the recitation of rules or procedures to eliminate errors and misconceptions (Kilic 2011). This is consistent with research on inservice teacher knowledge of probability, which was found to be often limited to procedural of formula-based knowledge and to lack conceptual depth.…”

Section: • Proportional Thinkingsupporting

confidence: 59%

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Brase

Martinie

Castillo-Garsow

2014

Advances in Mathematics Education

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The idea of probabilities has been described as a "Janus-faced" concept, which can be thought of either in terms of frequencies or in terms of subjective confidence. This dualism contributes to debates about the nature of human rationality, and therefore the pedagogical assumptions and goals of education. For this reason, the present chapter explores the evidence regarding how quantitative information is intuitively understood in the human mind over the course of elementary school education. Are particular interpretations of probability equally weighted or does one interpretation predominate as mathematical concepts are being acquired? We find multiple, converging lines of evidence that indicate a frequency interpretation of probabilistic information is developmentally primary and privileged. This has implications for mathematics education, even before the introduction of actual probabilities, in areas such as learning fractions and decimals. Educational practices should work to bootstrap from these privileged representations (rather than fight them) and built towards a more inclusive and comprehensive model of probability knowledge. We conclude that a fundamental issue is not just whether students think about probabilities as a frequentist or as a subjectivist, but rather how they recognize when to be one versus the other.

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Section: • Proportional Thinkingsupporting

confidence: 59%

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Brase

Martinie

Castillo-Garsow

2014

Advances in Mathematics Education

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“…The mistake made it difficult for pre-service teachers to detect misconceptions that occur in the students, so prospective teachers are wrong in providing strategies to improve the misconception. Kilic's finding supports this discourse, that prospective teachers have difficulty in identifying the source of student misconceptions so that mistakes in producing an effective way to eliminate these misconceptions [2].…”

Section: Introductionmentioning

confidence: 65%

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Susandi¹,

Sa’dijah²,

As’ari³

et al. 2018

Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)

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Mathematical critical thinking is an essential ability for prospective teachers. The prospective teachers must be able to use the ability to think critically well so that students who are taught can also have good mathematical critical thinking skills. However, sometimes prospective teachers have a mistake in solving the problem of critical mathematical thinking skills. The present paper aims to analyze the mistakes of prospective teachers in solving the problem of critical mathematical thinking skills. The type of research method is descriptive with the qualitative approach. The subject in this research is one student of semester VI. The methods used in this research include test method amounting to one essay question, interview method, and triangulation method. The findings show that the prospective teacher on the focus indicator can be completed well whereas the indicators of reason, inference, situation, clarity, and overview, the teacher cannot solve well. Causes of the teacher error based on APOS theory are (1) error in distinguishing between commutative and addition characteristic of multiplication on matrix, (2) error in multiplication operation on the matrix, (3) error inequality of two matrices, and (4) error in the concept of inverse equation matrix.

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“…On the other hand, mathematics teachers' understanding of quadratic functions is critical to students' success in mathematics, and there seems to be agreement that, for many high school students, solving and understanding quadratic functions can be conceptually challenging because of the need to make connections between various representations of the function, as well as the connections between the various ways in which the quadratic equation can be expressed (Didis, Bas, & Erbas, 2011;Kilic, 2011).…”

Section: Quadratic Functionmentioning

confidence: 99%

Solving Problem Types Contextualized to the Quadratic Function and Error Analysis: A Case Study

Díaz¹,

Aravena²,

Flores³

2020

EURASIA J Math Sci Tech Ed

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The article aims to determine the academic performance and errors in the resolution of types of problems of application of the quadratic function, of high school students from the Los Lagos Region and Los Rios Region in Chile. The approach is qualitative and descriptive with case studies. A math test with open response problems and an opinion questionnaire were developed and applied. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context and fantasist context, but with difficulty in the resolution of non-routine problems. In addition, errors originating in affective and emotional attitudes associated with blockages at the time of initiating the resolution, forgetfulness at the time of posing the quadratic function, prevail over cognitive errors originating in an obstacle and errors originating in the absence of meaning.

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The nature of preservice mathematics teachers’ knowledge of students

Cited by 19 publications

References 9 publications

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Intuitive Conceptions of Probability and the Development of Basic Math Skills

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Solving Problem Types Contextualized to the Quadratic Function and Error Analysis: A Case Study

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