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Pub Date: |
2013-08-00 |
Pub Type(s): |
Journal Articles; Reports - Evaluative |
Peer Reviewed: |
Yes |
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Descriptors:
Heuristics; Reaction Time; Misconceptions; Intervention; Graphs; Statistics; Mathematics Instruction; Cognitive Processes
Abstract:
Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this misinterpretation. Moreover, it was tested whether this heuristic reasoning was caused by the saliency of the area of the box. In a second study, the effect of an intervention aimed at improving students' interpretation of the box plot on their heuristic reasoning about box plots was investigated. The results suggest that this misinterpretation of box plots is indeed due to heuristic reasoning and is very difficult to overcome. (Contains 6 figures and 2 tables.)
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Pub Date: |
2013-10-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Goal Orientation; Student Attitudes; Foreign Countries; Feedback (Response); Educational Research; Written Language; Mathematics Instruction; Mathematics Achievement; Mastery Learning; Grade 9
Abstract:
Although feedback is a popular topic in educational research, the question of how and on what conditions feedback in mathematics affects learning seldom has been addressed. In this study, we investigated: (1) whether process-oriented feedback in mathematics leads to greater interest and higher achievement development compared to social-comparative feedback; (2) whether students' perception of feedback with regard to usefulness and competence support mediates these effects; and (3) whether the impact of feedback is moderated by students' mastery approach goal orientation. To answer these research questions, 146 ninth-grade intermediate school students in Germany were randomly assigned to both feedback conditions. Results of path analyses revealed (1) no significant total feedback effects on interest and achievement development, but (2) indirect effects on the development of interest via perceived competence support and usefulness, and on achievement development via perceived usefulness, as well as (3) a moderation effect of mastery approach goal orientation on the impact of feedback on perceived usefulness. (Contains 3 figures and 2 tables.)
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Disabilities; Mathematics Curriculum; Calculators; Mathematics Instruction; Problem Solving; Comparative Analysis; Mathematics Achievement; Grade 6; Grade 7; Standardized Tests; Learning Strategies; Educational Technology
Abstract:
This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional mathematics curriculum materials. Students solved multiple choice and open-ended problems based on items from the State's released previous assessments. A linear mixed model was conducted for each grade to analyze the factors impacting students' self-reported calculator use. Chi Square tests were also performed on both grade's data to determine the relationship between using a calculator and correctly solving problems. Results suggested only time as a main factor impacting calculator use and students who self-reported using a calculator were more likely to answer questions correctly. The results have implications for practice given the controversy over calculator use by students both with and without disabilities.
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Mathematics Education; Mathematical Concepts; Mathematics; Mathematics Instruction; Mathematical Logic; Mathematics Skills; Curriculum
Abstract:
In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners' bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic material, and we suggest a "pedagogy of the concept" that animates concepts as both logical and ontological. We draw on the philosopher of mathematics Gilles Chatelet in order to pursue this argument, elaborating on the way that mathematical concepts partake of the mobility of the virtual, while learners, in engaging with this mobility, enter a material process of becoming. We show how the concept of virtuality allows us to look at mathematical concepts in school curriculum in new ways.
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Rating Scales; Student Attitudes; Classroom Environment; Mathematics Instruction; Mathematics Anxiety; Correlation; Gender Differences; High School Students; Student Evaluation
Abstract:
We investigated relationships between the learning environment and students' mathematics anxiety, as well as differences between the sexes in perceptions of learning environment and anxiety. A sample of 745 high-school students in 34 different mathematics classrooms in four high schools in Southern California was used to cross-validate the What Is Happening In this Class? (WIHIC) learning environment instrument, together with an updated Revised Mathematics Anxiety Rating scale. Mathematics anxiety was found to have two factorially-distinct dimensions (namely, learning mathematics anxiety and mathematics evaluation anxiety) which yielded different patterns of results for sex differences and anxiety-environment associations. Relative to males, females perceived a more positive classroom environment and more anxiety about mathematics evaluation, but less anxiety about mathematics learning. Some statistically significant associations were found between anxiety and learning environment scales for learning mathematics anxiety but not for mathematics evaluation anxiety.
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Foreign Countries; Mathematics Instruction; Grade 1; Mathematics Teachers; Thinking Skills; Mathematical Logic; Grade 2; Academic Achievement; Mathematics; Interviews; Problem Solving
Abstract:
This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, "Human Development" 52:109-128, 2009) to understand students' mathematical thinking. This study challenged teachers' pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students' knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students' ideas and connect informal or invented strategies with classroom mathematics.
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Research |
Peer Reviewed: |
Yes |
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Descriptors:
Identification (Psychology); Academic Failure; Low Achievement; Mathematics Achievement; Mathematics Instruction; Mathematics Teachers; Teacher Attitudes; Grade 7; Teacher Student Relationship
Abstract:
Leaning on a communicational framework for studying social, affective, and cognitive aspects of learning, the present study offers a new look at the construction of an identity of failure in mathematics as it occurs through teaching-learning interactions. Using the case of Dana, an extremely low-achieving student in 7th grade mathematics, I attempt to unearth the mechanisms of interaction between Dana and myself, her teacher, that instead of advancing Dana, perpetuated her failure. Through examining the interactional routines followed by Dana and me, I show how Dana's deviations from normative routines resulted in my identification of Dana as "clueless" in mathematics. This identification, shared both by Dana and by me, was accompanied by adherence to ritual rule following that did not enable Dana's advancement in mathematical discourse. This case points to the need to re-examine permanent difficulties in mathematics in light of the reciprocal nature of such difficulties' (re)construction in teaching-and-learning interactions.
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Pub Date: |
2013-07-00 |
Pub Type(s): |
Journal Articles; Reports - Descriptive |
Peer Reviewed: |
Yes |
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Descriptors:
College Students; Mathematics Education; Mathematics Instruction; Higher Education; Mathematical Models; Mathematics
Abstract:
This paper describes university students' grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ' (x) = 0 as a necessary condition, (2) f ' (x) is not equal to 0 as a necessary condition, (3) f " (x) = 0 as a sufficient condition, and (4) the location of "a peak point, where the graph bends" as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval's frameworks to analyze students' errors that were rooted in mathematical and in real-life contexts.
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