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Descriptors:
Academic Achievement; Mathematics Achievement; Geometry; Experimental Groups; Early Childhood Education; Grade 1; Elementary School Students; Gifted; Measurement; Mathematical Concepts; Statistical Analysis; Comparative Analysis; Measures (Individuals)

Abstract:
The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of Basic Skills (ITBS) mathematics concepts subtest and an open-response assessment. Using HLM, as expected there were no statistical differences between the experimental (n = 186) and comparison (n = 174) groups on the ITBS (91% of the items focused on number). Statistically significant differences (p less than 0.001) favoring the experimental group were found on the open-response assessment with a large effect size (d = 1.88). Thus the experimental group exhibited a deeper understanding of geometry and measurement concepts on the open-response assessment while performing as well on a traditional measure that covered all Grade 1 mathematics. (Contains 7 tables and 4 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Social Environment; Problem Solving; Financial Support; Administrator Attitudes; Childhood Attitudes; Parent Attitudes; Clergy; Participation; Observation; Interviews; Mathematical Applications; Mathematical Aptitude; Mathematical Concepts; Religion Studies; Number Concepts; Number Systems; Numeracy; Influences; Theory of Mind; Beliefs; Spiritual Development; Role of Religion

Abstract:
The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem solving was related to the social context of tithing. I introduce the direct influence model to describe components of the practice itself and to identify supports and constraints that exist related to children's opportunities to engage in problem solving that varied by participation frequency and mathematical complexity. (Contains 2 figures and 1 footnote.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Preservice Teachers; Elementary School Teachers; Multiplication; Elementary School Mathematics; Mathematical Concepts; Knowledge Base for Teaching; Visual Aids; Word Problems (Mathematics); Misconceptions; Textbooks

Abstract:
This study examines preservice elementary teachers' (PTs) knowledge for teaching the associative property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to illustrate AP of multiplication conceptually, particularly due to a fragile understanding of the meaning of multiplication. The study also revealed that the textbooks used by PTs at both the university and elementary levels do not provide conceptual support for teaching AP of multiplication. Implications of findings are discussed. (Contains 4 tables and 7 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Foreign Countries; Canada Natives; Mathematics Education; Mathematical Concepts; American Indian Education; American Indian Students; Elementary Secondary Education; Mathematics Instruction; Teaching Methods; American Indian Languages

Abstract:
As part of a larger project focused on decolonising mathematics education for Aboriginal students in Atlantic Canada, this article reports on the role of the Mi'kmaw language in mathematics teaching. By exploring how mathematical concepts are talked about (or not talked about) in the Mi'kmaw language, teachers and researchers can gain insight into how Mi'kmaw children think about mathematical concepts. It is argued that much can be learned by asking questions such as "What's the word for... ?" or "Is there a word for... ?" Numerous examples of such conversations are presented. It is argued that particular complexities arise when words such as "flat" and "middle" are taken-for-granted as shared, but in fact do not have common use in the Mi'kmaw language. By understanding these complexities and being aware of the potential challenges for Mi'kmaw learners, teachers can better meet the needs of these students. It is argued that understanding Aboriginal languages can provide valuable insight to support Aboriginal learners in mathematics. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Foreign Countries; Indigenous Populations; Multiple Regression Analysis; Oral Language; Language Role; Language Tests; Mathematics Instruction; Language Patterns; Learner Engagement; Early Childhood Education; Mathematical Concepts; Mathematical Aptitude; Program Implementation; Program Effectiveness; Outcome Measures; Pretests Posttests; Predictor Variables; Mathematics Achievement; Mathematics Tests

Abstract:
This paper explores the outcomes of the first year of the implementation of a mathematics program ("Representations, oral language and engagement in Mathematics": RoleM) which is framed upon research relating to effectively supporting young Indigenous students' learning. The sample comprised 230 Indigenous students (average age 5.76 years) from 15 schools located across Queensland. The pre-test and post-test results from purposely developed language and mathematics tests indicate that young Indigenous Australian students are very capable learners of mathematics. The results of a multiple regression analysis denoted that their ability to ascertain the structure of patterns and to understand mathematical language were both strong predictors of their success in mathematics, with the latter making the larger contribution. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Curriculum; Foreign Countries; Community Schools; Rural Areas; Indigenous Populations; Mathematics Skills; Interviews; Mathematical Concepts; Knowledge Level

Abstract:
It is widely accepted that mathematical learning builds upon students' prior knowledge and understandings, and their identities. In this study, this phenomenon is explored with indigenous students in remote community schools in outback Australia. Through one-on-one task-based interviews, it was found that these students had some clear understandings of the measurement concepts involved, although these understandings were often idiosyncratic to these students in this context. The task-based one-on-one interview gave better insights into students' knowledge than the written form of the National Assessment Program-Literacy and Numeracy assessment. Nevertheless, the students' conceptions provide a useful basis upon which to build subsequent knowledge, understanding and skills in the forms required by the formal mathematics curriculum. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Individualized Instruction; Private Schools; Grade 11; Mathematics Instruction; Secondary School Mathematics; Mathematical Concepts; Mathematical Aptitude; Equations (Mathematics); Mathematics Teachers; Instructional Materials; Teaching Methods; Peer Teaching

Abstract:
Teachers of mathematics recognize the difficulty of reaching every student when the range of student abilities puts a considerable strain on the classroom discussion and time. In a response to the problem, students are grouped so that those with greater mathematical aptitude help those who have difficulties. While this approach is to be appreciated, it tends to mean that the more able students have less opportunity to explore further their own initiatives in mathematics, while those who have more difficulties find themselves on the receiving end with little opportunity to be in the role of enriching the mathematics experience for everyone, including themselves. A "multiple-centres" approach is designed to overcome these problems. In this variation of differentiated instruction, all students get the chance to engage the material from a vantage point and at a level they find interesting and challenging as a consequence of their selecting extensions of the teacher's initial focus problem. This article will present some findings of 11th year (roughly Fifth Form) average mathematics students at a US Independent School in transforming the standard quadratic equation to represent fountain parabolic trajectories, which was the teacher's focus problem, along with some multiple-centre investigations they chose. A further set of opportunities with commentaries providing additional centres for student inquiry are included. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Instruction; Mathematical Concepts; Instructional Materials; Teaching Methods; Misconceptions; Definitions; English

Abstract:
As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of "if" and "or" from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students' mistakes. To fill this gap, this article presents three studies for the classroom that engage students in confronting the differences between mathematical and everyday meaning in statements of implication and statements of disjunction. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Undergraduate Students; Mathematics Instruction; Mathematical Concepts; Teaching Methods; Statistical Distributions; Class Activities; College Instruction; College Mathematics

Abstract:
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and subsequent investigation, a wealth of mathematical and statistical material is covered. We go on to discuss the educational benefits of carrying out activities such as the one suggested here. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Teaching Methods; Grade 6; Grade 7; Algebra; Mathematical Concepts; Mathematics; Cognitive Structures; Mathematics Achievement; Middle School Students

Abstract:
Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students' development of advanced fractional knowledge and algebraic reasoning. Steffe (2010) has hypothesized that students construct splitting through the unification of partitioning and iterating operations contained within the partitive unit fraction scheme. We used written assessments of 49 students, across sixth and seventh grades, to test this hypothesis. Our results show that students who have constructed a partitive unit fraction scheme go on to construct splitting within a relatively short period of time. Conversely, students who have not constructed a partitive unit fraction scheme generally do not construct splitting. We discuss these results and their implications for designing instruction and curricula that support students' development of algebraic reasoning. (Contains 10 figures, 5 tables and 1 footnote.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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