Search results for: Mathematical concepts
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An Investigation of Prospective Secondary Mathematics Teachers’ Conceptual Knowledge of and Attitudes towards Statistics
This study explored prospective secondary mathematics teachers’ conceptual understanding of statistics, attitudes towards statistics and the relationship between attitudes and conceptual understanding. The findings reveal that prospective mathematics teachers in this study had all taken modules in linear algebra and calculus at university and higher-level mathematics at secondary school. Despite being very mathematically able and confident, these self-selecting prospective mathematics teachers do no better in the assessment than the students from other disciplines. In addition, the results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn, but these positive attitudes are not strongly correlated with their conceptual understanding of statistics.
Updated: Sep. 07, 2016
The present article reports on the results of three different investigations into pre-service teachers’ understanding of the mathematical concepts of area and perimeter. The results indicated that many pre-service teachers across the cohorts had a procedural understanding of area and perimeter, displayed similar misconceptions to their student counterparts, and were limited in their ability to demonstrate examples of the mathematics knowledge required to teach these topics.
Updated: Jul. 03, 2016
Prospective Mathematics Teachers’ Sense Making of Polynomial Multiplication and Factorization Modeled with Algebra Tiles
This study examines prospective secondary mathematics teachers’ understanding and sense making of representational quantities generated by algebra tiles, the quantitative units inherent in the nature of these quantities, and the quantitative addition and multiplication operations—referent preserving versus referent transforming compositions—acting on these quantities. Two student–teachers constantly relied on an additive interpretation of the context, whereas three others were able to distinguish between and when to rely on an additive or a multiplicative interpretation of the context. The results indicate that the identification and coordination of the representational quantities and their units at different categories are critical aspects of quantitative reasoning and need to be emphasized in the teaching–learning process.
Updated: Jan. 26, 2016
This study describes changes in secondary mathematics teachers’ mathematical knowledge for teaching function through their engagement in a mathematics methods course teaching experiment. The participants in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the connections they could make between function representations, and to consider the role of definition in mathematics and the K-12 classroom. The course focused on function which supports work in the classroom; by focusing on one topic, teachers experience the sequencing of tasks and topics in ways that build a conceptual understanding, much in the way that they might design a curricular sequence in their own classroom.Furthermore, the course activities provided teachers with opportunities to refine and elaborate those initial understandings.
Updated: Jan. 05, 2016
In this study, the authors examined primary school teacher candidates’ ability to use their existing pedagogical and mathematical knowledge to incorporate social justice into the content of mathematics lessons. The findings revealed that Grades 1-6 elementary Teacher candidates had foremost trouble articulating their understandings of social justice, its role in mathematics education, and its meaning in mathematics classrooms. They were unable to provide explicit and relevant examples of social justice teaching in the context of mathematics classroom, nor were they able to incorporate social justice into the mathematics lesson.
Updated: Sep. 08, 2015
Exploring the Mathematical Knowledge for Teaching Geometry and Measurement through the Design and Use of Rich Assessment Tasks
In this article, the author describes the development of a series of tasks designed to investigate and measure teachers’ mathematical knowledge for teaching geometry and measurement. The author presents three design features for rich, open-response items that assess mathematical knowledge for teaching. The set of six two-dimensional geometry and measurement tasks embody these design features and illustrate the ways in which the tasks are grounded in the context of teaching, capture nuanced teacher performance, and measure common and specialized content knowledge. The examples of teacher performance on these tasks illustrate the ways in which the tasks can differentiate teacher performance.
Updated: Aug. 20, 2014
This article examines prospective elementary teachers’ difficulties and growth with language for defining the whole. Thirty-three prospective teachers participated in a semester-long classroom teaching experiment conducted in a content course focusing on mathematics for teaching elementary school. The results of this study indicate that three mathematical ideas became taken-as-shared as prospective elementary teachers developed an understanding of language use for defining the whole. The first was that fractional solutions depend on a group or whole. The second included defining an of what. The third was developing language in terms of what the denominator represents.
Updated: May. 20, 2014
The goal of this study is two-fold: 1) to examine the role content knowledge plays in prospective teachers’ (PSTs) ability to recognize children’s conceptual understanding of mathematics, and, 2) to examine examined PSTs' ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. The results of this study suggest that content knowledge is necessary but insufficient in supporting PSTs’ ability to recognize evidence of children’s conceptual understanding of mathematics.
Updated: May. 11, 2014
Making Sense of Double Number Lines in Professional Development: Exploring Teachers’ Understandings of Proportional Relationships
This study aims to understand how teachers used their existing knowledge about proportions to make sense of a representation that was new to them and the ways in which their existing knowledge proved to be helpful or unhelpful. The authors identified two knowledge components that were important to the participants’ sense-making activities. The first necessary component of knowledge for making sense of the DNL was coordination. Partitioning was the second critical concept for reasoning with the DNL. They also identified three components that impeded sense-making with the DNL representation. The authors also found three knowledge components participants invoked in these tasks that prohibited effective reasoning with the DNLs.
Updated: Apr. 23, 2014
Mathematically Based and Practically Based Explanations in the Elementary School: Teachers’ Preferences
This paper focuses on elementary school teachers’ preferences for mathematically based and practically based explanations. Using the context of even and odd numbers, the article examines the types of explanations teachers generate on their own as well as the types of explanations they prefer after reviewing various explanations. The article also explores the basis for these preferences.
Updated: May. 26, 2011