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Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Exploring ratios

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

Support fall-readiness for students as your student prepares to enter the next grade in mathematics

We extend an earlier study on the role of memorising in learning science with three case studies on mathematicians' experiences as learners of mathematics and their views on memorising in students' learning. Each report reflects a different view of memorising--from a minimal role in learning mathematics, to a "stepping stone" role to memorising as a key learning strategy. The mathematicians' views about memorising in their students' learning appears consistent with their reports on memorising in their own learning. Our data leads to the conjecture that personal experiences of memorising underpin attitudes to memorising in teaching mathematics and that further investigation is warranted on this little researched aspect of "coming to know" mathematics. [For complete proceedings, see ED496848.]

The present study examined the significance of the Mathematics Laboratory for Mathematics teaching in Schools, Colleges & Teacher Training Institutes in India. Researchers present the overview of Math-Lab for effective mathematics teaching and discuss the important roles of the mathematics laboratory for mathematics learning. The mathematics laboratory classroom solves this problem by combining these environments. Laptop computers address the needs of software and networking but there are fewer pro levels that help maintain a more balanced classroom environment. In the teaching and learning of mathematics, the mathematics laboratory, with the support and companionship of both the student-teachers, can play a significant role and can have a significant impact on the progress of the students in mathematics. The main objective of the present study is to find out the major factors of Mathematics Laboratory in Mathematics-Education. This study discusses the concepts of mathematics in the classroom, the mathematics laboratory and its importance, and how to use the mathematics laboratory for trained teachers, from beginning to elementary level mathematics education. The methodology of the study is a mixed type involving an interpretative approach where qualitative data were collected and study secondary sources, like books, articles, journals, thesis, university news, expert opinion, and websites, etc. Finally, meaningful suggestions are offered. Kaushik Das 2020. Significant of Mathematics Laboratory Activities for Teaching and Learning. International Journal on Integrated Education. 2, 5 (Mar. 2020), 19-25. DOI:https://doi.org/10.31149/ijie.v2i5.138. Pdf Url : https://journals.researchparks.org/index.php/IJIE/article/view/138/135 Paper Url : https://journals.researchparks.org/index.php/IJIE/article/view/138

In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.

This document contains 15 case studies developed by the group teachers during a teaching experiment. Background information on each second grader, behavior and achievement characteristics, and analyses of the evaluation interviews are presented. (MS)

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The system first administers a diagnostic test in arithmetic which locates the individual's weaknesses and prescribes modules directed at them; students pass through the modules and are post-tested on each. The process is repeated for algebra. Each module consists of a learning packet with: a description of the material to be learned a pre-test with answers, learning objectives and activities to reach them, a video-taped lecture, notes and supplementary materials, and a post-test. Since the tapes are on call, the student can schedule himself, proceed at his own pace, repeat material when necessary, and concentrate on his weakness. Instructors are freed from classroom lectures, and are able to provide individual attention to students. In addition, the learning packets are easily developed and can be made available to other institutions. Due to these advantages, this mode of instruction should be widely adopted. (PB)

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The system first administers a diagnostic test in arithmetic which locates the individual's weaknesses and prescribes modules directed at them; students pass through the modules and are post-tested on each. The process is repeated for algebra. Each module consists of a learning packet with: a description of the material to be learned a pre-test with answers, learning objectives and activities to reach them, a video-taped lecture, notes and supplementary materials, and a post-test. Since the tapes are on call, the student can schedule himself, proceed at his own pace, repeat material when necessary, and concentrate on his weakness. Instructors are freed from classroom lectures, and are able to provide individual attention to students. In addition, the learning packets are easily developed and can be made available to other institutions. Due to these advantages, this mode of instruction should be widely adopted. (PB)

Findings from five related studies carried out in Tasmania, Australia in 1979-80 are summarized. The first study attempted to determine the memory capacity of a cross-sectional population of children aged 4-7, while the second study was designed to portray differences on a variety of mathematically related developmental tasks for the same population. Data from these two studies were used to form six groups differing in cognitive capacity, and the remaining three studies each used a sample of students from these groups. The third study examined the performance and strategies used to solve a structured set of verbal addition and subtraction problems. The fourth study involved repeated assessment of performance on a set of items measuring objectives related to addition and subtraction. In the last study, the children and their teachers were observed to see how addition and subtraction were taught and whether instruction varied because of the children's cognitive capacity. Differences in capacity were reflected in performance, but instruction did not vary. The capacity of children for processing information, the procedures students have invented to solve a variety of problems, and the way in which instruction is carried out in schools did not appear to be related to each other. (Author/MNS)

The principal focus of this brief report is on findings and observations from relatively recent research on the learning of mathematics. The distinction between learning and the concepts of curriculum and instruction is first reviewed. Then Piaget's theory of intellectual development is discussed, with the conclusion that it does not provide a basis for determining readiness for mathematics instruction. The contribution of information processing theory is then noted. Four additional observations from contemporary research concern the following: the focus on individuals (versus groups), behavioral objectives, invention or construction of knowledge by young children, and metacognition. A list of references is included. (MNS)

The textbook remains a central resource for teaching and learning mathematics in many secondary classrooms, however, its effectiveness is open to question. In this article, the author argues three things: (1) that there can be a substantial disjunction between the assumptions and content of mathematics textbooks and the knowledge and experiences which students draw on in engaging with those texts; (2) that this disjunction applies particularly to those students who are unsuccessful with this form of learning; and (3) that an alternative approach, extending the work of Lave and Wenger (1991) and Wenger (1998) on communities of practice, offers a more inclusive and effective means of promoting mathematical understanding for such students. Forty-three young people took part individually in 20-30 minute semi-structured interviews. The students provided accounts of their experiences of learning mathematics in school and TAFE. Selected excerpts are utilised to demonstrate that shaping of an identity of participation for some students is influenced by the practice of using textbooks in classrooms. Results show that students chose not to participate in their learning because of personal learning difficulties. While this may be the case, a close analysis suggests that these students may never win. That is, despite their efforts to try, learning mathematics from a text, with little or no support from the teacher, just became too difficult. Such taken for granted practices contribute to the maintenance of unequal relations in some mathematics classrooms. In consequence, when students contest or challenge these relations they are either coerced or eliminated from the classroom. In some instances, this exclusion may contribute to students leaving school early. Through this process, students are blamed for their inability to learn, when in fact the opposite may be the case: the taken for granted practice of using textbooks for all learners positions students as have learning difficulties or who are problems in the classroom.

The textbook remains a central resource for teaching and learning mathematics in many secondary classrooms, however, its effectiveness is open to question. In this article, the author argues three things: (1) that there can be a substantial disjunction between the assumptions and content of mathematics textbooks and the knowledge and experiences which students draw on in engaging with those texts; (2) that this disjunction applies particularly to those students who are unsuccessful with this form of learning; and (3) that an alternative approach, extending the work of Lave and Wenger (1991) and Wenger (1998) on communities of practice, offers a more inclusive and effective means of promoting mathematical understanding for such students. Forty-three young people took part individually in 20-30 minute semi-structured interviews. The students provided accounts of their experiences of learning mathematics in school and TAFE. Selected excerpts are utilised to demonstrate that shaping of an identity of participation for some students is influenced by the practice of using textbooks in classrooms. Results show that students chose not to participate in their learning because of personal learning difficulties. While this may be the case, a close analysis suggests that these students may never win. That is, despite their efforts to try, learning mathematics from a text, with little or no support from the teacher, just became too difficult. Such taken for granted practices contribute to the maintenance of unequal relations in some mathematics classrooms. In consequence, when students contest or challenge these relations they are either coerced or eliminated from the classroom. In some instances, this exclusion may contribute to students leaving school early. Through this process, students are blamed for their inability to learn, when in fact the opposite may be the case: the taken for granted practice of using textbooks for all learners positions students as have learning difficulties or who are problems in the classroom.

The textbook remains a central resource for teaching and learning mathematics in many secondary classrooms, however, its effectiveness is open to question. In this article, the author argues three things: (1) that there can be a substantial disjunction between the assumptions and content of mathematics textbooks and the knowledge and experiences which students draw on in engaging with those texts; (2) that this disjunction applies particularly to those students who are unsuccessful with this form of learning; and (3) that an alternative approach, extending the work of Lave and Wenger (1991) and Wenger (1998) on communities of practice, offers a more inclusive and effective means of promoting mathematical understanding for such students. Forty-three young people took part individually in 20-30 minute semi-structured interviews. The students provided accounts of their experiences of learning mathematics in school and TAFE. Selected excerpts are utilised to demonstrate that shaping of an identity of participation for some students is influenced by the practice of using textbooks in classrooms. Results show that students chose not to participate in their learning because of personal learning difficulties. While this may be the case, a close analysis suggests that these students may never win. That is, despite their efforts to try, learning mathematics from a text, with little or no support from the teacher, just became too difficult. Such taken for granted practices contribute to the maintenance of unequal relations in some mathematics classrooms. In consequence, when students contest or challenge these relations they are either coerced or eliminated from the classroom. In some instances, this exclusion may contribute to students leaving school early. Through this process, students are blamed for their inability to learn, when in fact the opposite may be the case: the taken for granted practice of using textbooks for all learners positions students as have learning difficulties or who are problems in the classroom.

The textbook remains a central resource for teaching and learning mathematics in many secondary classrooms, however, its effectiveness is open to question. In this article, the author argues three things: (1) that there can be a substantial disjunction between the assumptions and content of mathematics textbooks and the knowledge and experiences which students draw on in engaging with those texts; (2) that this disjunction applies particularly to those students who are unsuccessful with this form of learning; and (3) that an alternative approach, extending the work of Lave and Wenger (1991) and Wenger (1998) on communities of practice, offers a more inclusive and effective means of promoting mathematical understanding for such students. Forty-three young people took part individually in 20-30 minute semi-structured interviews. The students provided accounts of their experiences of learning mathematics in school and TAFE. Selected excerpts are utilised to demonstrate that shaping of an identity of participation for some students is influenced by the practice of using textbooks in classrooms. Results show that students chose not to participate in their learning because of personal learning difficulties. While this may be the case, a close analysis suggests that these students may never win. That is, despite their efforts to try, learning mathematics from a text, with little or no support from the teacher, just became too difficult. Such taken for granted practices contribute to the maintenance of unequal relations in some mathematics classrooms. In consequence, when students contest or challenge these relations they are either coerced or eliminated from the classroom. In some instances, this exclusion may contribute to students leaving school early. Through this process, students are blamed for their inability to learn, when in fact the opposite may be the case: the taken for granted practice of using textbooks for all learners positions students as have learning difficulties or who are problems in the classroom.

The District of Columbia Public Schools has adopted new learning standards for core subjects, including reading/English language arts, mathematics, science, and social studies. The new standards show what students should know and be able to do: (1) in each subject; (2) at each grade level; and (3) in every school. This publication guides parents in how to talk to their children's teachers in Reading/Language Arts, Mathematics, Science, and Social Studies about the new standards and about how well their children are doing in these subjects in prekindergarten through second grade.

NO LIMIT! (New Outcomes: Learning Improvement in Mathematics Integrating Technology) in Washington state was a six-year initiative originally designed to enhance mathematics teaching and learning in the middle grades through integration of technology, alignment of pedagogical practice with NCTM standards, and strong mentorship of teachers. The focus of the NO LIMIT! project was to develop classroom models in which students experienced standards-based instruction, with the goal of improving student achievement in mathematics. This age span was extended in later years to include elementary and high school students, diluting the original clearer focus. The success of the NO LIMIT! project depended upon the negotiation of many elements that continue to command keen interest in the education community. The project combined high stakes professional development and consequent teacher change, successful implementation of national and state standards in mathematics, with appropriate infusion of technology to improve student learning. It originally was a very ambitious project. The NO LIMIT! program was funded in Year One as a federal Technology Literacy Challenge Fund (TLCF) project and in later years through the Enhancing Education Through Technology (EETT) program. In Phase I (years one and two, 2001-2003), more than 200 teachers received technology hardware and software, mentor support, training, and opportunities to collaborate across grade levels. In Phase II (2003-2005), approximately 250 new teachers were involved. Though program funding was reduced (by 28%), approximately 325 teachers were involved in the first year of Phase III (2005-2006); though that number dropped back to 250 teachers in the second year of Phase III (2006-2007) after a further budget cut of 50%. In Phases I and II, this was a relatively modest program, with each teacher receiving approximately $10,000 for equipment and software purchases over a two-year period. A crucial component was the mentorship provided (the equivalent of $10,000 per teacher per year in Phases I and II). In Phases I and II, each Educational Service District (ESD) maintained technology and mathematics specialists (MISs), who spent approximately 80% of their time in the classroom with teachers and students. In Phase III, program funding was drastically reduced, resulting in the elimination of many MIS positions in the ESDs, and in a severe reduction in technology purchases ($1500 per teacher in Year 5, and no funding for technology whatsoever in Year 6). The following five appendixes are included: (1) Bibliography; (2) Sample Teacher Log (including NLC [Networked Learning Community] section at end); (3) Year Five RFP for School Districts; (4) Year Five Teacher Participants; and (5) Year Six Teacher Participants. (Contains 2 tables and 1 figure.) [This report was written with Oddmund Myhre and prepared for the Office of the Superintendent of Public Instruction, Olympia, Washington.]

The prime objective of this research was to investigate whether the Montessori method of learning helped kindergarten pupils improve their mathematical proficiency, critical thinking and problem-solving skills, besides training them to be responsible learners. Quantitative, qualitative, and observational methods were employed in the investigation. The sample for the study comprised 180 kindergarten pupils from "TadikaBestari Al-Hidayah," located in Bandar Seri Damansara, Malaysia. The instruments for collecting data were questionnaires, interviews, and field observations. Results from a pre-test and a post-test showed that pupils who used the Montessori method, i.e. the experimental group, outperformed (72.2% passed) their peers who were not ex- posed to the Montessori method (39% passed). The findings indicated that the Montessori method indeed helped learners to improve their mathematical proficiency. This research offers guidelines to future researchers on alternative learning methods, especially for very young children. The findings of this empirical research could be prototyped for learning other subjects.

This paper describes a field experiment with a pretest-posttest-control group design in which the potential of reading picture books to children for supporting their mathematical understanding was investigated. The study involved 384 children from eighteen kindergarten classes in eighteen schools in the Netherlands. Data analyses revealed that the experimental group showed a significantly larger increase than the control group in their mathematics performance in a project test containing items on a variety of mathematical topics including arithmetic, measurement, and geometry. [For the complete proceedings, see ED597799.]

Mathematical achievement is an early predictor of students' academic outcomes, and mathematics achievement continues to be important throughout life. Thus, it is essential to examine instructional methods that enhance mathematical learning. One method that may impact mathematical learning is the use of gestures, yet a comprehensive methodical review of the data has not been conducted. The current study examined the impact that gestures have on student learning when educators use gestures during mathematical instruction and educators' perception of student mathematical knowledge when students use gestures. A systematic search was conducted to assemble research studies that evaluated the use of gestures in mathematical instruction with students in preschool to 12th grade. Empirical data from 35 research articles indicate that gestures used by students or educators that enhance verbal instruction can increase student mathematical performance and memory. Furthermore, it is practical to teach students and educators to use gestures effectively during mathematical learning. [This paper was published in "Gesture" v17 n3 p375-416 2018.]

This paper presents an account of a new place-based education initiative using both the mathematical construct of hypothetical learning trajectory and the 3D printing technology or Projection Augmented Landscape Models (PALM), as a tool for learning. The goal of the pilot study is to create bridges between Aboriginal and Western ways of knowing and learning to enable academic success in the challenging area of mathematics. The project explores powerful ways to construct cultural learning trajectory in which Tiwi preservice teachers can apply their prior traditional knowledge to their learning and teaching of Western mathematical constructs, within the Australian curriculum strand of geometry/measurement. The outcomes of this unique Tiwi project are significant because it is an applied research project using 3D PALM technology for educational purposes, particularly knowledge exchange in Aboriginal contexts. This application is unique as such technology to date has been used largely in applications related to land management.

This report presents results from the first cycle of the Program for International Student Assessment (PISA). PISA is a new international assessment of 15-year-olds in reading, mathematics, and science literacy. The United States has joined with 27 other member countries of the Organization for Economic Cooperation and Development (OECD) and 4 non-OECD countries to assess their students performance against international benchmarks through PISA. PISA content is not drawn strictly from school curricula, but rather from a framework agreed to nationally on what reading, mathematics, and science literacy mean. After the year 2000, PISA results are scheduled to be available every 3 years so that progress for each of the subjects can be tracked over time. As a first step toward measurement of cross-curricular competencies, in PISA 2000, student questionnaires sought information about student attitudes toward reading and learning strategies. This information, in conjunction with achievement data, provide baseline information for later PISA studies. Four appendixes contain technical notes, descriptions of the international studies in subject areas, supporting statistical data, and the released items from the PISA 2000 assessments. (Contains 38 tables, 26 figures, and 41 references.) (SLD)

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

This occcasional paper is a dialog in the form of two separate papers about mathematics education: "Reaching Out to Colleagues and the Public:" A University Mathematician Engages School Mathematics Reform by Reid Davis, and "A Response to 'Reaching Out to Colleagues and the Public'" by Jeff Connor. Their differing views are illustrative of the ongoing debate in mathematics education reform. The discussion centers around the National Council of Teacher of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Many of the differences of perspective are endemic to the operation of all Centers for Learning and Teaching commissioned by the National Science Foundation where mathematics is a concern. The reason for this tension is that the Foundation requires the collaboration of mathematicians and mathematics educators, and prominent representatives of the two groups often take differing positions on the desiderata of mathematics education.

This paper describes findings from a blocked randomized design (BRD) field study conducted to examine the "Next Generation Preschool Math" (NGPM) program's implementation in preschool classrooms and promise in improving young children's mathematic learning. NGPM integrates traditional preschool activities with developmentally appropriate technology to support teaching and learning. During development, an evidence-based curriculum design framework and iterative development processes were employed (i.e. design-based research). Research questions guiding this research include: (1) Does experiencing NGPM impact young children's mastery of subitizing and equipartitioning?; (2) Can the NGPM units feasibly be implemented in preschool classrooms?; (3) Does experiencing the NGPM unit 1 impact young children's mastery of subitizing?; (4) Does experiencing the NGPM unit 2 impact young children's mastery of equipartitioning?; and (5) Does experiencing the NGPM intervention improve general mathematics knowledge? The study took place in early childhood education centers in the New York City and San Francisco metropolitan areas. A sample of 16 teachers from different early childhood education centers that serve low-income children participated in the study. Approximately 8-10 children (169 children total) were randomly selected from each classroom to participate in the mathematics assessments. A set of research-based activities were developed to introduce and help young children learn the important, but rarely taught, topics of subitizing and equipartitioning. These activities included both physical manipulatives and innovative tablet-based games that complemented each other. Study results provide preliminary evidence that NGPM: (1) improves preschool children's understanding of unit-specific mathematics content; (2) was feasible to implement in preschool classrooms; and (3) left teachers wanting additional units. A table is appended.

Teachers of inquiry mathematics face many challenges as understandings of how children learn in this environment are still developing. Children learn as they hold onto the moment of not knowing what to do. This paper operationalises learning for a small group of Year Three students exploring the usefulness of maps. As part of a PhD study using Design Research, the teacher-as-researcher identified perturbations generated by the students in her class and applied an operational definition of learning to track student development of mathematical knowledge.

A current issue in initial teacher education (ITE) in Aotearoa, New Zealand is how students can best be supported to use digital technologies for mathematics teaching. While many ITE students are familiar with digital technologies for personal use, they are less likely to know how to incorporate them into the mathematics learning process. Supporting ITE students to become more critical, knowledgeable, skilled, and confident about using digital technologies was the main aim of the study. Forty second-year ITE students were surveyed about the Digital Learning Objects promoted by the Ministry of Education that they would choose to use to teach area measurement. Several different reasons were reported.

Thirty primary classroom teachers quantified perceived changes in their practice and knowledge attributed to their school leaders' participation in a six-day course focused on leaders designing and implementing a whole-school reform of mathematics teaching and learning, and the school-based professional learning that followed. The project and framework underpinning the reform are outlined, and the teachers' reported changes in pedagogical practices are described. Teachers identified many changes in pedagogy and growth in knowledge. Not surprisingly, changes in pedagogical practices were even greater for specialist mathematics teachers who had also participated in a separate six-day course.

This study aims to investigate 10th grade students' agency and authority in a mathematics problem-based learning (PBL) classroom. The participants were 40 Grade 10 students. The data were collected during January-February of 2019 from twelve PBL lesson plans, Agency and Authority Observation Forms, Teacher's Notes, Students' Reflections and Students' In-Depth Interview Forms. The Agency and Authority Observation Forms were adapted from Schoenfeld and Floden (2014). The researchers found that all of the students' agency and authority dimensions in all steps of the PBL process were observable. The overall level of each dimension was at a high level.

In response to the call for research on integrating best general practices in teaching with those that promote equity and access, we present a two-part study focused on instructional strategies that may remove learning barriers for English Language Learners. We theoretical developed and empirically explored supplemental components for traditional quality of instruction measures (MQI, Hill, 2014, Math Habits Tool, Melhuish & Thanheiser, 2017). We share results from a quantitative study empirically verifying the effect of suggested ELL-focused instructional strategies (Chval & Chávez, 2011) on ELL learning via the creation of an additional MQI dimension. Based on these results, we then provide theoretical operationalizations of these strategies to integrate into the student-and-teacher interaction tool: the Math Habits Tool (Melhuish & Thanheiser, 2017) as means to concretize these strategies for researchers and practitioners. [For the complete proceedings, see ED606556.]

The study reported here was conceptualised using a theoretical framework that included three dimensions of engagement; emotional, behavioural, and cognitive, and these were used to structure the data collection and analysis vis-à-vis learning mathematics outdoors. This comparative case study involved 34 students from two Year 6 classes at a Queensland state primary school. The findings indicate that the students were engaged in their mathematics learning in the outdoor context. However, there was no compelling evidence that suggested the outdoor environment was any more emotionally, behaviourally, or cognitively engaging than the indoor context.

This book gives a definitive theoretical account of radical constructivism., a theory of knowing that provides a pragmatic approach to questions about reality, truth, language and human understanding. The chapter are: (1) "Growing up Constructivist: Languages and Thoughtful People," (2) "Unpopular Philosophical Ideas: A History in Quotations," (3) "Piaget's Constructivist Theory of Knowing," (4) "The Construction of Concepts," (5) "Reflection and Abstraction," (6) "Constructing Agents: The Self and Others," (7) "On Language, Meaning, and Communication," (8) "The Cybernetic Connection," (9) "Units, Plurality and Number," and (10) "To Encourage Students' Conceptual Constructing." Each chapter contains notes. (Contains 218 references.) (MKR)

It is widely recognized that developing a successful teaching practice, one that is grounded in the principles that guide the current effort to reform mathematics education, requires a qualitatively different and significantly richer understanding of mathematics that most teachers in the 1990s possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K-6 teachers' mathematical investigations--inquiry into mathematics itself and inquiry into children's mathematical thinking--and illustrates how they arise in elementary teaching situations and how they can be explored in a professional development setting. Contains 43 references. (Author)

This meta-analysis synthesizes experimental and quasi-experimental research on instruction that enhances the mathematics performance of K-12 students with learning disabilities. It reports the findings from this synthesis, discusses the implications for practice, and suggests next steps for research and professional development efforts in this field. Appended are: (1) Design Variables of Studies Included in Math Meta-analysis; (2) Post-tests, Maintenance Tests and Transfer Tests of Studies Included in the Meta-analysis; and (3) Worked Example. (Contains 15 tables, 3 figures and 1 footnote.) [This publication was created by Instructional Research Group. For the "Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics: A Guide for Teachers", see ED521882.]

This report describes a program for increasing class achievement by raising the motivational level of adolescents. The targeted population consisted of high school mathematics students from a metropolitan area located in central Illinois. The problem of low motivation level found in the targeted students was documented by student surveys. Evidence of this problem was also reflected in a high dropout rate as noted in the school's report card. The analysis of probable causes revealed that the students' lack of motivation was possibly caused by poor past performances, boredom, and a missing sense of ownership and responsibility. The attitudes of both students and parents continued to contribute to this problem. The presentation of inappropriate levels of task difficulty and a non-stimulating classroom environment has also fostered low motivation. Possible solution strategies involved a threefold approach. The first intervention targeted the students in an attempt to raise their level of intrinsic motivation and to increase their sense of ownership and responsibility. This treatment plan included student journals and surveys. The second intervention targeted the interest level of the students in the classroom. Collaborative groups and the use of multiple intelligence activities increased the motivational atmosphere. The third intervention targeted the classroom presentation by incorporating strategies such as writing through mathematics and solving real-life applications. The teachers' personal reflective journals indicated that progress was made in this area. Post intervention data indicated that cooperative learning and Multiple Intelligences (MI) activities did enhance the students' motivation for learning mathematics. Teacher and student journal reflections added a metacognitive element to this intervention. Appendices include the student survey and classroom materials. (Contains 73 references.) (Author/WRM)

The effects of mastery learning strategies, interactive video mathematics (IVM), individualized instruction (IND), and the lecture method on mathematics achievement of community college students was studied. Interactions among instructional methods, gender, and age were examined; and the grade success rate was determined for each instructional method. The IND and IVM methods were characterized by mastery learning principles. Pretest and posttest components determined the mathematics achievement of college freshmen. Of 377 students enrolled in basic skills mathematics courses at an urban multicampus two-year community college for whom pretest results were available, complete data were obtained for 137 adults aged over 22 years and 82 traditional students aged 17 to 22 years. The efficacy of the methods was compared, and a final grade success rate was determined for each group using chi-square for testing significant differences. IVM and IND methods had a positive educational influence on students' achievement on mathematics basic skills posttest scores, but, because many of these students did not complete the course in 10 weeks, grade success rate was significantly lower for these methods than for the lecture method. No significant difference was found for gender on the main effects, but a significant difference for simple effects shows that males favor the IVM method. Those over 22 years old had higher achievement than did those in the traditional college age group. Six tables present study data. (SLD)

This paper looks at the ideas of R. Skemp which emphasize fostering "intelligent learning" in the teaching of mathematics. Skemp posits that schematic learning takes place when new concepts are constructed by the learner. Three modes of building such internal schema are proposed. Teachers are urged to ensure that at every stage the new concepts to be learned can be assimilated by the children's available schemas. Suggested teaching strategies include: (1) sequencing new material schematically, (2) using structured practical activities, and (3) beginning with a do-and-say approach followed by written work only when the connections between thoughts and verbal symbols are well established. (DB)