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Weber, Keith; Inglis, Matthew; Mejia-Ramos, Juan Pablo – Educational Psychologist, 2014

The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion…

Descriptors: Mathematics, Professional Personnel, Logical Thinking, Mathematical Logic

Weber, Keith; Mejia-Ramos, Juan Pablo – International Journal of Mathematical Education in Science and Technology, 2014

We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students' responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating…

Descriptors: Majors (Students), Mathematics Instruction, College Mathematics, Undergraduate Students

Weber, Keith; Mejia-Ramos, Juan Pablo – Educational Studies in Mathematics, 2011

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, "Journal for Research in Mathematics Education" 39:431-459,…

Descriptors: Mathematics Education, Mathematical Logic, Mathematics, Professional Personnel

Wasserman, Nicholas; Weber, Keith – For the Learning of Mathematics, 2017

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Teaching Methods

Zhen, Bo; Weber, Keith; Mejia-Ramos, Juan Pablo – International Journal of Research in Undergraduate Mathematics Education, 2016

In this paper, we investigate mathematics majors' perceptions of the admissibility of inferences based on graphical reasoning for calculus proofs. The main findings from our study is that the majority of mathematics majors did not think that graphical perceptual inferences (i.e., inferences based on the appearance of the graph) were permissible in…

Descriptors: Majors (Students), Mathematics Instruction, Inferences, Calculus

Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo – Journal for Research in Mathematics Education, 2017

This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

Descriptors: Notetaking, Mathematics Instruction, Advanced Courses, Undergraduate Students

Maher, Carolyn; Weber, Keith – AASA Journal of Scholarship & Practice, 2009

In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…

Descriptors: Elementary School Students, Elementary School Mathematics, Mathematics Education, Mathematical Concepts

Weber, Keith; Mejia-Ramos, Juan Pablo – For the Learning of Mathematics, 2015

Conviction is a central construct in mathematics education research on justification and proof. In this paper, we claim that it is important to distinguish between absolute conviction and relative conviction. We argue that researchers in mathematics education frequently have not done so and this has lead to researchers making unwarranted claims…

Descriptors: Mathematics Education, Educational Research, Mathematical Concepts, Mathematical Logic

Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron – Educational Studies in Mathematics, 2012

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

Descriptors: Reading Comprehension, Mathematics Education, Mathematical Logic, Number Concepts

Weber, Keith – International Journal of Research in Undergraduate Mathematics Education, 2015

In this paper, I identify five effective proof reading strategies that mathematics majors can use to comprehend proofs. This paper reports two studies. The first study is a qualitative study in which four successful mathematics majors were videotaped reading six proofs. These students used five proof reading strategies to foster comprehension: (i)…

Descriptors: Mathematical Logic, Reading Strategies, Majors (Students), Qualitative Research

Weber, Keith – Journal of Mathematical Behavior, 2009

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…

Descriptors: Concept Formation, Mathematical Concepts, Case Studies, Logical Thinking

Weber, Keith; Radu, Iuliana; Mueller, Mary; Powell, Arthur; Maher, Carolyn – Mathematics Education Research Journal, 2010

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications,…

Descriptors: School Activities, Mathematics Education, After School Programs, Problem Solving

Weber, Keith – For the Learning of Mathematics, 2010

Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…

Descriptors: Mathematical Concepts, Mathematics Instruction, Mathematics Education, Mathematical Logic

Iannone, Paola; Inglis, Matthew; Mejia-Ramos, Juan Pablo; Simpson, Adrian; Weber, Keith – Educational Studies in Mathematics, 2011

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or…

Descriptors: Undergraduate Students, Mathematics Education, Learning Strategies, Mathematical Concepts

Weber, Keith – Mathematical Thinking and Learning: An International Journal, 2010

In this paper, 28 mathematics majors who completed a transition-to-proof course were given 10 mathematical arguments. For each argument, they were asked to judge how convincing they found the argument and whether they thought the argument constituted a mathematical proof. The key findings from this data were (a) most participants did not find the…

Descriptors: Majors (Students), Mathematics Activities, Mathematical Logic, Validity

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