The Mathematics that Every Secondary School Math Teacher Needs to Know

Sultan, Alan; Artzt, Alice F.

doi:10.4324/9781315391908

Cited by 8 publications

(10 citation statements)

References 3 publications

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“…Note that RQ1 is a theoretical research question, asking for specific links between a school mathematical notion ("infinite decimals") and appropriate undergraduate mathematics, thus it is about the knowledge to be taught to future teachers. RQ1 is in general answered by several classical and newer texts (e.g., Sultan & Artzt, 2018), and we summarize one answer at the beginning of the next section. We address RQ2 by investigating students' work on a concrete assignment, also presented in the next section.…”

Section: Theoretical Framework and Research Questionsmentioning

confidence: 99%

“…We mainly consider nonnegative infinite decimals here, as a negative infinite decimal can be defined as the additive inverse of a positive one. We use a part of chapter 8 in the book The mathematics that every secondary school math teacher needs to know (Sultan & Artzt, 2018) to outline a possible answer to RQ1.…”

Section: Mathematical Context Real Numbers Represented As Infinite De...mentioning

confidence: 99%

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Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Huo

2023

EUR J SCI MATH ED

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In our investigation of university students’ knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was carried out in the context of a course for university students who aim to become mathematics teachers in high schools. The main data consists of students’ written responses to an assignment of the course and interviews to clarify students’ perspectives in relation to the responses. The analysis of students’ work is based on the anthropological theory of the didactic (ATD). Our results indicate that simple CAS-routines have a potential to help university students (future teachers) to apply their university knowledge on certain problems related to the decimal representation of real number which are typically encountered but not well explained in high school.

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Section: Theoretical Framework and Research Questionsmentioning

confidence: 99%

Section: Mathematical Context Real Numbers Represented As Infinite De...mentioning

confidence: 99%

Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Huo

2023

EUR J SCI MATH ED

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“…After pointing out the existence of such ambiguous graph titles, it has been emphasized in [1] that each of those ambiguous graph titles should be replaced by the unambiguous ones in a manner as has been proposed in [1] to enhance the quality of graphing. Furthermore, it has been found that the traditional procedure employed for drawing enlarged graph by making use of two different scales along the two axes of coordinates is flawed on account of the fact that such a procedure of drawing an enlarged graph violates the fundamental concept of "Enlargement" in Transformation geometry [2]. A further discovery in the said context along with a procedure of drawing an enlarged graph without violating the fundamental concept of "Enlargement" in Transformation geometry has been reported in [3].…”

Section: Introductionmentioning

confidence: 99%

Discovery of Ambiguity in the Traditional Norms of Specifying Physical Quantities along the Axes of Coordinates in Drawing Data Based Graphs

Bhattacharjee¹

2022

ujpa

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This paper (falling within the purview of Physics Education Research in particular, and Science Education Research in general) deals with a very significant issue related to labeling of the physical quantities along the axes of coordinates in graphing. It has been discovered that the traditional norms of specification of physical quantities along the axes in graph drawing are ambiguous. Such norms of specification totally ignore the inherent nature of a physical quantity. Furthermore, as a result of such a specification, each coordinate of a point lying on the graph assumes a numerical value along with a unit tagged with it, thereby violating the most fundamental concept of Cartesian coordinate geometry according to which the coordinates of a point in two-dimensional real space should be an ordered pair of real numbers. To get rid of such an ambiguity, an unambiguous procedure of specifying the physical quantities along the axes of coordinates in graph drawing has been finally proposed. The issue raised in the paper along with the relevant solution offered are both original and novel, never considered by any one earlier and hence the present scheme could not be placed into context to other existing works on the same issue. However, the present work has been compared with two other earlier works reported by the author in relation to graphing to judge its novelty and originality.

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“…According to Xiayan probability is a branch of mathematics which utilizes the principles of addition and multiplication (combinatorial mathematics principle) to do pure digit arithmetic during the calculation process [1]. Besides, Sultan and Artzt stated that the study of probability is the study of proportion that makes claims about likelihood or chance of certain events occurring and this why probability is often defined as the study of chance [2]. Therefore, it can be concluded that probability is branch of mathematics which is about proportion to make claims about chance of certain events by using addition and multiplication principles.…”

Section: Introductionmentioning

confidence: 99%

The Analysis of Students' Difficulties in Solving Problems of Probability for 8th Grade

Anggraini¹,

Kusrini²

2018

Proceedings of the University of Muhammadiyah Malang's 1st International Conference of Mathematics Education (INCOMED 2017)

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Probability is one part of mathematics material that is learned in school. In Indonesia, probability is learned from Junior High School level and is continued in Senior High School level. Hence, understanding of probability's concept in Junior High School level is very important. The aim of this research is to analyze students' difficulties of 8 th Grade of SMPN 1 Prambanan Klaten in solving problems of probability. The method used in this research is descriptive method. Data collection was done based on students' work through essay test. The result shows that the difficulties which are experienced by the students in solving pobability's problem are the difficulty in understanding proportional reasoning and the difficulty in resolving misconceptions or misperceptions in probability. The misconceptions are representativeness, probability cannot be measured mathematically, misuse or extend conclusions inappropriately, inappropriate reasons, beliefs, equi-probability bias, and possible means certain.

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The Mathematics that Every Secondary School Math Teacher Needs to Know

Cited by 8 publications

References 3 publications

Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Discovery of Ambiguity in the Traditional Norms of Specifying Physical Quantities along the Axes of Coordinates in Drawing Data Based Graphs

The Analysis of Students' Difficulties in Solving Problems of Probability for 8th Grade

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