Journal articles on the topic 'Views, Mathematics Curriculum'

<span lang="EN-US">Progressivism is one of the streams that can contribute and require problem solving in mathematics learning. Progressivism supports changes for the better that prioritize students and develop various student abilities in the implementation of learning. Educational programs that prioritize students in the progressivism view of the curriculum. The 2013 curriculum is a learning system renewal that is expected to further develop the potential of students. The 2013 curriculum requires students who are passive to be active in order to solve problems in learning mathematics. The implementation of the 2013 curriculum changes previous learning activities towards a learning system more advanced so that students' ability to solve math problems can develop. This article aims to determine the relationship between progressivism views and the 2013 curriculum on mathematics learning. This article uses a literature study method. This data is obtained from some of the research results contained in books, journals, and proceedings that are related to the title of the article. The results show that the viewpoint of progressivism is interrelated with the 2013 curriculum in mathematics learning. Progressivism can make a major contribution to the development and progress in the implementation of the 2013 curriculum, it can be seen from the relationship between the two wanting a change in the learning process so that it focuses more on students. </span>

This study examines preservice teachers’ perspectives of creativity and character education in mathematics through a university-based teacher education program. We developed a curricular unit on creative character education in a mathematics methods course and investigated participants’ (n = 56) emerging perspectives of teaching creativity and character by the integration of content and process in mathematics. Data were collected through pre- and post-questionnaires and transcribed course discussion and presentation sessions. A quantitative analysis of the questionnaires through a t-test confirmed key changes in participants’ perspectives, while the qualitative context of data illustrates the participants’ emergent views on creative character education in mathematics. Overall, findings suggest that a mathematics teacher education curriculum integrating mathematical creativity and character education has the potential to prepare future educators to implement pedagogy that bridges between process and content in school mathematics for the next generation of learners.

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) presents a view of precollege mathematics t hat stresses the development of mathematical power. Framed within the context of students' needs, societal expectations, and engaging teaching, the Standards proposes to define the mathematical content of school mathematics. It responds to the crisis in mathematics education described in Everybody Counts: A Report to the Nation on the Future of Mathematics Education (National Research Council 1989), A Nation at Risk (National Commission on Excellence in Education 1983), and Educating Americans for the 21st Century (National Science Board Commission on Precollege Education in Mathematics, Science, and Technology 1983). Although representing a consensus of mathematics educators, the Standards does not present a research basis for its recommendations (NCTM 1988) and thus at times stands at odds with the descriptive accounts of current mathematics teaching practices found in The Underachieving Curriculum (McKnight et al. 1987) and The Mathematics Report Card (Dossey, Mullis, Lindquist, and Chambers 1988). This article examines implications for teaching of explicit and implicit assumptions in the Standards and compares them with other views in the literature.

This research is an exploration of the implementation of learning geometry mathematics through discourse and aims to get a model of theaching materials as adevelopment of those used by lecturers so far. The research was carried out through questionnaires, direct observation, and discussion of critical discourse analysis and was linked to important needs in mathematicals literacy. Exploration is constructed through theoretical reviews, synthesis from previous research, and examples of development though discourse. The contens of the questionnaire follow the natural discourse of the presentation of theacing materials on the dispotitions of lecturers and students. In particular, the exploration of theaching materials as part of the means of disseminating a culture of mathematics, an aesthetic description of mathematics, and dominant aspecs of lecturers and students. Development road maps are done through centralized examination of discourse, where data tajen from oral and written delivery and from texts that extend views on mathematics and by opening the choice of lectures and students. The result showed the depth of the description of teaching materials without the assumption that curriculum were sufficient to obtain the effectiveness of mathematical literacy and as a more contextual product.Keywords: theaching material, curriculum, continuity of the discourse of mathematics

The following commentary on the direction and substance of the curriculum reviewprocess currently happening in Singapore was included because of its interest toreaders from other countries. However, the views expressed here are those of theauthor, a respected and experienced Asian mathematics educator, and do notnecessarily reflect those of the editors or the international advisory panel.

Picture a school-board meeting or a meeting of a school district's elementary curriculum committee. Raise the issue of integrating microcomputers into the elementary school's mathematics curriculum, and a debate will ensue. Focus the discussion on the use of microcomputers in the primary classroom, and the remarks will become intense and passionate. Although the diversity of comments prompted by such a discussion cannot be anticipated, two views will probably be voiced. Seeking the promise of a supposed competitive edge, one faction will favor microcomputer use while questioning whether the calculator threatens children's learning of the basics, that is, arithmetic. Citing the added danger of producing socially isolated children who are obsessed with the lure of microcomputers, another group will reject any form of technology in the primary classroom.

Teachers&rsquo; views on the nature of maths have a crucial effect on their interactions with children, their choice of method and technique to be used while preparing the curriculum, their decision on the type and frequency of activities to be applied, their behaviors in the classroom, children&rsquo;s attitudes towards maths and their achievement. With this research, it is aimed to examine teacher candidates&rsquo; philosophical views on the nature of maths. The research is in relational scanning model. &ldquo;The Scale of Philosophical Thoughts on the Nature of Mathematics&rdquo; was implemented to 141 pre-school teacher candidates studying in 2019-2020, which constitute the sample of the study. As a result of the analysis, it has been found that 52.5% of teacher candidates have an absolutist view, the views of female and male teacher candidates support each other and there is a significant difference between the grade level in they study.

Since the release of the timss results, a call has been issued to emulate the curriculum, if not the educational practices, of Asian countries that have done well on the TIMSS. California has even stated that its “new” mathematics curriculum will be fashioned after the “rigorous” Singapore mathematics curriculum. Before endorsing such views, it would be instructive to look at some possible reasons that Singapore's eighth graders performed so well in the TIMSS and some possible implications. I list five possible reasons for Singapore students' success in the eighth-grade TIMSS and ask the reader to reflect on the implications to mathematics teaching and learning in the United States under “Questions to ponder.”

Indonesian students’ poor performance in the mathematics test of PISA 2015 prompted the decision by the Ministry of Education of Indonesia to pay more attention to the integration of higher-order thinking (HOT) in the curricula starting in 2018. This new regulation emphasizes the need to have a shared understanding of HOT in mathematics on many levels, such as curriculum, pedagogy, and assessment, and among students, teachers and policy makers. This study aims to examine HOT in Indonesian lower secondary mathematics classrooms by assessing students’ ability to demonstrate HOT skills through an open-ended mathematics problem, and by exploring teachers’ views of HOT skills through semi-structured interviews. It involved 372 ninth-grade students and six mathematics teachers from six lower secondary schools in Jakarta and Palembang. The findings show that most students could construct the mathematical model but experienced difficulty in transferring knowledge into new contexts, in applying creative thinking, and with information literacy skills. Besides, some of the teachers were familiar with the concept of HOT, but some viewed HOT as skills for talented students, or HOT problems having a high level of difficulty and long storylines. The knowledge of existing teaching strategies, familiarity with HOT problems, and colleague-support are needed to improve the development of HOT skills in the mathematics classroom.

The need for students to be effective problem solvers is a primary concern of today's mathematics educators. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) views problem solving as “a process that should permeate the entire program and provide the context in which concepts and skills can be learned”(p.23). The recognition of the critical role of problem solving in today's mathematics classroom challenges teachers to develop creative and effective ways to bolster students' problem-solving skills. At Hollywood Elementary School in College Park, Maryland, a program titled” Math Pairs—Parents as Partners” was developed in an attempt to tap available resources to meet the challlenge of teaching problem solving in mathematic.

The teaching of culture and heritage studies is the flagship of Great Zimbabwe University. This present study is investigating preliminary views and conceptions of in-service teachers on culture and mathematics education. Data was collected through a questionnaire survey on all 27 teachers who majored in mathematics education. The group was considered small enough to render sampling unnecessary. It was observed that a good part of students were aware of the significance of the role of culture on mathematics education whilst some were not very sure how culture played a role in the field of mathematics. We recommend the school curriculum to implement culture-oriented mathematics education that ensures the survival of African culture.Â

As always, I enjoy and learn from the thoughtful analyses and well-argued comments about educational practices by my colleague Michael Apple. In reading his often flattering, yet critical, analysis of NCTM's Curriculum and Evaluation Standards/or School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991), I must admit he is right on several counts. The lens through which he views the world is not one familiar to most mathematics educators. Relating any message about schooling to the patterns of differential economic, political, and cultural power is not common in our field. Furthermore. the five issues he raises—the financial crisis in education, the nature of inequality in schools, the role of mathematical knowledge as a filter that maintains those inequalities. the possibilities and limitations of a curriculum grounded in problem situations, and the complex realities of teachers' lives—are critical issues facing all educators interested in changing the current system. Clearly. the Standards documents by themselves are not well situated with respect to these broader ideological and political issues. In fact, none of the five issues, although considered, were the driving forces behind the NCTM's reform documents.

This study aims to describe Mathematical Problem-Based Learning with a scientific approach on educators class XI MIPA in SMA Negeri 7 Makassar. The result of the research shows that: 1) In developing RPP, mathematics teacher of XI MIPA class in SMA Negeri 7 Makassar is still arranged in collaboration, the reason is still lack of understanding about RPP development mechanism in accordance with Permendikbud Number 22 year 2016. 2) Problem Based Implementation Process mathematics with a scientific approach in the class XI MIPA in SMA Negeri 7 Makassar has not run optimally. This is seen in the indicators at each stage of the core activity on the aspect of the educator applying the scientific approach, and on the application aspects of Problem Based Learning has not been fulfilled. The constraints faced by educators are the difficulty of changing the views of educators who are still a little carried away with the curriculum before the Curriculum 2013, the lack of knowledge and the ability of educators in facilitating the process of Problem Based Learning with scientific approach, and time management in implementing the process of Problem Based Learning Implementation with scientific approach.

Multiple American educational organizations such as the National Education Association, Association for Supervision and Curriculum Development, and the Council of Chief State School Officers have advocated for globalizing the K-12 curriculum. The National Science Teaching Association (NSTA) in a position statement on international education and the Next Generation Science Standards have produced goals and standards for internationalizing the science curriculum by addressing topics such as climate change, environment, and disease that cross borders. In contrast to those pronouncements on the curriculum, this article views global science education through an instructional lens that focuses on a students’ global interdependence in science continuum allowing researchers and casual observers to classify science classroom activities into one of five stages based on the interdependence during instruction of students in two or more countries. At the continuum’s lowest stage labeled isolated, instruction is contained within a classroom with students having no interaction with students in another country. At the highest end called collaborate, students in two or more countries are working jointly to co-create a solution to the task before them. This science education continuum can also be used to categorize technology and engineering activities and could be adapted for use in other curricular areas including mathematics, language arts, and social studies, used as a tool to complement scholarship about a range of education topics from social justice to curriculum to student motivation, or inform pre- and in-service teacher education.

For more than a decade, government primary-school teachers in many parts of India have been using mathematics textbooks based on National Curriculum Framework 2005 (NCF 2005). While curriculum and textbook development is often debated, teachers’ use of textbooks does not receive enough attention in policy and research. This article, drawing from a multiple-case study of 10 teachers, using classroom observations and teacher interviews, explores different ways in which teachers use the Math-Magic mathematics textbook in Delhi’s government primary schools. The findings demonstrate heterogeneity in the ways in which teachers use textbooks, which are the dominant teaching resource in these schools. Teachers use different degrees of agency in textbook use—from avoiding the textbooks to designing their lessons. These are influenced by their views about the textbooks, as well as their institutional realities. Finally, this heterogeneity offers a useful approach to understanding textbooks, and their relevance to teaching beyond being viewed as teaching scripts.

<p>In a country where there is a consistent loud outcry about school achievement of youth<br />in the final school examination in Grade 12, attention has recently shifted to children in<br />the primary school. The very founding of this journal was motivated by a deep concern<br />about research in childhood education and children’s lives. Questions were being asked<br />about what happens in the first years of schooling, about the suitability of the national<br />curriculum for such a diverse population, about specialised research in the field of<br />learning in the early years, and about teaching with care and with insight, knowing<br />who the children of this nation are.<br />The journal took an early stand when, at its launch in 2010, the editor noted that the<br />notion of a national foundation phase curriculum assumes the existence of a ‘national’<br />Grade 1 learner. In South Africa there are children who come to school, well prepared<br />for the demands of school – and there are others who come with only their survival<br />records in homes of extreme poverty, of absent parents and of families broken by the<br />effects of the history of the nation and the effects of disease. Much as we would like<br />to see a standard of performance expected from the ‘national’ young learner, we need<br />to see the layers of diversity too. Can such a stratified population, socially fractured<br />in many ways, truly enact a differentiated curriculum for children who have so much<br />and for children who have so little at the same time and at the same pace? Can our<br />foundation phase classes be truly inclusive?<br />It remains a vexing question. Much research is needed to even try to give a robust<br />response. In recent years, in the research of the Centre for Education Practice Research<br />at my home institution, we have encountered more than 3000 children between five<br />and seven years old in an extensive interview test of mathematical cognition. In the<br />process we found children who had never encountered a print drawing and children<br />who did not know that a page can be turned. However, the very same children had<br />a perfectly normal idea of approximate number and size. We regard this as evidence<br />that they have the core knowledge of number that has to be developed by systematic<br />instruction and caring apprenticeship in classrooms. But for that they would need<br />teachers who know them as well as they know the latest curriculum and its suggested<br />tools of teaching.<br />This is but one example of how important teacher education is and how important<br />it is that we should investigate both learners and teachers, but also teacher education<br />and teacher educators. Teachers and their educators at universities have their own<br />view of children, of learning and of childhood. Much as we may all agree that the<br />core activity of schools is for the young to learn the three Rs and the subject areas of<br />the curriculum, there are researchers who are opposed to a developmental view of<br />learning. The journal’s stance is that, in the Vygotskian tradition (Kozulin, 1990), the<br />young learn and are initiated – and thus develop – in the work of school (and society).<br />SAJCE– December 2014<br />ii<br />In the SAJCE we welcome different views on child learning and celebrate South<br />Africa’s researchers who argue that “pedagogical ‘know-how’ and views of child and<br />childhood constitute the subject knowledge that is foundational in the foundation<br />phase curriculum” – as Murris and Verbeek do in this issue. Add to that knowledge<br />of how children the world over have core knowledge systems, as argued by cognitive<br />developmental psychologists and neuroscientists, and we have a composite picture<br />of what the object of teacher education is – to know 1) the learner and 2) the subject<br />content, but also 3) the self as teacher.<br />This ‘didactical triangle’, was already proposed as view of teaching in the 17th century<br />in Comenius’s major work, Didactica Magna (Comenius, 1632/1967). In the 20th century,<br />for some reason, the English- speaking world used the term ‘didactic’ to denote<br />teacher-centred learning, while Comenius proposed what can arguably nowadays be<br />termed pedagogical content knowledge (PCK). Jari Lavonen, the chair of the teacher<br />education department at the University of Helsinki, recently noted that PCK is the<br />transformation of subject content knowledge by infusing it with knowledge of the<br />learner and of the self as teacher. In Finland they refer to PCK simply as Didactics, while<br />taking full cognisance of Shulman’s model (Shulman 1986).<br />But, views on teaching become more complicated when teachers are faced<br />with children who enter Grade 1, but who are not ready to embrace the way of life<br />at school. Bruwer and her co-authors report in this issue on teachers’ views on the<br />predicament they face when children need to cross the liminality boundary – when<br />they are still ‘betwixt and between’ life as an informal learner and life in school, where<br />they have to be inducted into life as a formal learner in a national curriculum. In the<br />same vein, Condy and Blease argue that a “one-size-fits-all curriculum cannot address<br />the issues that rural multigrade teachers and learners face”. Seldom do educational<br />researchers contemplate this very real issue. I was in the same class in Grade 1 as my<br />brother, who was then in Grade 8, in a little farm school. I recall vividly how we young<br />ones spent much time making clay oxen while they were doing indecipherable maths<br />on the writing board.<br />When more than one language is used, or required to be used, in a single classroom<br />communication set-up, a teacher is faced with yet another dimension. Ankiah-Gangadeen<br />and Samuel write about a narrative inquiry that was conducted in Mauritius, noting<br />that the “narrative inquiry methodology offered rich possibilities to foray into these<br />[teachers’] experiences, including the manifestations of negotiating their classroom<br />pedagogy in relation to their own personal historical biographies of language teaching<br />and learning”.<br />Added to the multilayered types of knowledge around which a teacher needs to<br />negotiate her way in a foundation phase classroom, are knowledge and understanding<br />of children’s transition from one grade to the next. Nieuwenhuizen and co-authors<br />found that the move from Grade 2 to Grade 3 is notably more difficult for children than<br />earlier grade transitions. I wish to add that it is also a grade transition that requires<br />much more of the learning child in volume and in pace of learning; the transition<br />Editorial<br />requires a ‘mature’ young learner who has worked through the curriculum of the<br />earlier grades effectively.<br />Kanjee and Moloi not only present information about ANA results, but show how<br />teachers utilise these in their teaching. To that, the editorial team adds: what is the<br />national testing ritual really doing for teachers? Are there many unforeseen and even<br />unintended effects? Many teachers may say that it alerts them to gaps in their own<br />knowledge and pedagogy and, especially, we would think, the way in which they<br />assess children’s learning effectively. While Kanjee and Moloi invoke local national<br />tests, Fritz and her co-authors from Germany, Switzerland and South Africa show<br />how a mathematics competence and diagnostic test for school beginners found<br />its way from Europe to South Africa. They point to the challenges of translating an<br />interview-based test and of validating it in a local context in four languages. With the<br />promise that the test will be normed in this country, the foundation phase education<br />as well as the educational psychology community may stand to benefit from such a<br />test, which is theoretically grounded in children’s conceptual development.<br />The matter of teaching with formative assessment as pedagogical tool comes to<br />mind whenever one discusses assessment. In an article by Long and Dunne, one reads<br />about their investigation into teaching of mathematics with a very specific angle – how<br />to “map and manage the omissions implicit in the current unfolding of the Curriculum<br />and Assessment Policy Statement (CAPS) for mathematics”. In a very dense and fast<br />paced curriculum it is not possible to fill all the gaps. Who knows what the effect may<br />be for future learning of children who move through a curriculum quite rapidly?<br />Staying in the early grade classroom, Sibanda explores the readability of two<br />textbooks for natural science learning for Grade 4 learners. She touches on one of<br />the sensitive nerves of South African school education, namely the English language.<br />In her analysis of two textbooks, using a range of methods of text analysis, she<br />comes to the conclusion that the books are simply too difficult to read. She argues<br />that the authors have not taken into account that both vocabulary and syntax have<br />to be taught systematically in order for Grade 4 children to be able to read texts in a<br />language they do not know well, for one, and in a discourse of science writing that is<br />new for them as well.<br />Ragpot narrates the story of how an instructional film, #Taximaths: how children<br />make their world mathematical, was conceptualised, scripted and produced with<br />senior undergraduate students at UJ. This artefact serves not only as higher education<br />material in teacher education, but is also used as material for teacher development.1<br />This issue of the journal is rounded off by an important contribution about the<br />ethics of research on children. Pillay explains how experts in ethics have advised him<br />in the work they do in the National Research Foundation South African Research<br />Chair he holds in ‘Education and Care in Childhood’ at the University of Johannesburg.<br />The reader is reminded that care of vulnerable children and the protection of their<br />rights should be high on the list of educational practice and its research.<br />iii<br />SAJCE– December 2014<br />The next issue of SAJCE is a special one. It is edited by Nadine Petersen and Sarah<br />Gravett and it celebrates a programme of research and development of the South<br />African Department of Higher Education and Training, with funding support from the<br />EU. The Strengthening Foundation Phase Teacher Education Programme started in<br />2011 and included most of the universities in the country. The issue promises to be a<br />milestone publication on teacher education for the primary school.<br />Editorial greetings<br />Elizabeth Henning</p>

The purpose of this study was to reveal the challenges and advantages of the implementation of the lesson studymodel in Turkish middle schools. This study was a case study and the participants of the study was 11 middle schoolmathematics teachers in three different school in a city at central Anatolia region of Turkey. Three lesson studycycles were carried out at one month. The data were collected with field notes, focus group interviews and anopen-ended questionnaire. Data were analysed by using content analysis. Moreover, direct quotations from teachers’views were also included. Findings indicated that teachers had prejudice that the lesson study implementations wouldnot help their professional development. However, their prejudices were positively changed and they began to showinterest when they attended the implementations of lesson study. Implementation of the lesson study model enabledthe teachers to share experiences, to focus on students’ thinking / understanding, it also enabled teachers to be moreactive, to examine the curriculum and resources related to instructional materials in depth. On the other hand,challenges in the process of lesson study implementation were as follows: time problem, teachers' ego and fear ofbeing observed, adaptation of students in research lessons, differences between researcher and teachers’ views aboutmathematics teaching, the intensity of the curriculum and the pressure of the central exam.

In this article, three different descriptions of curricula for scientific literacy (SL) are summarized, compared, and critically reviewed from the point of view of their suitability for all citizens. Science for All Americans, a publication of the American Association for the Advancement of Science, envisages giving every citizen a thorough exposure to the world of science, technology, and mathematics; the report Towards Scientific Literacy, published by the International Institute for Adult Literacy Methods, recommends a phenomenological approach to science designed to make science useful for people in their daily lives; and a similar curriculum, Minimum Science for Everybody, published by a voluntary organization in India, provides a detailed alternative conceptual framework for SL in which community traditions and knowledge systems are interfaced with science. The three reports are seen to differ from one another not only in respect of the contents of the curricula recommended, but also in their approaches, and the world views underlying these different approaches are brought out. It is suggested that SL curricula in both “developed” and “developing” countries be reviewed in the light of the ideas contained in all three reports in accordance with the needs and circumstances of the people. The article argues for the need to review the nature of science from the perspective of the common citizen.

The purpose of this research is to examine the views of middle school mathematics teachers about the usability of VUstat and TinkerPlots software in data processing learning in the Curriculum of Mathematics Teaching in Middle School (5th, 6th, 7th and 8th grades). In the study, the phenomenology design from qualitative research patterns was employed. The study group was determined by maximum variation sampling method of purposeful sampling methods. The number of middle school mathematics teachers in the study group is 14. Pre-Interview Form, Activity Forms, Software Evaluation Forms and Focus Group Interview Form were used as the data collection tool in the research. The analysis and interpretation of the data was done by content analysis. The results of the research show that teachers have some problems regarding the use of technology in teaching mathematics and that VUstat and TinkerPlots software can be used in statistical teaching even though they have certain deficiencies. Some suggestions were made according to the results of the research.

The past few years have seen the emergence of five mathematics curricula developed with support by the National Science Foundation for the middle grades: Mathematics in Context (MIC) (National Center for Research in Mathematical Sciences Education and Freudenthal Institute 2001), Math Thematics (Billstein and Williamson 1999), Connected Mathematics (CMP) (Lappan et al. 1998), MathScape, a View of the World from a Mathematical Perspective (Education Development Center 1998), and Pathways to Algebra and Geometry (Institute for Research on Learning 1997). One striking similarity that characterizes these middle school curricula, as well as their reform counterparts at the elementary and secondary school levels, is the pervasive use of context. Using a definition suggested by Borasi (1986), context is “the situation in which [a] problem is embedded” (p. 129). Context is usually supplied by the text of the problem, but it can also be contained in pictures, diagrams, or tables. A quick review of any of the curricula mentioned above shows that context is plentiful and varied. This abundance of context is in marked contrast with traditional textbooks, in which context appears only in brief introductions or end-of-section story problems.

Changing curricula in mathematics is more difficult than moving an old graveyard in January. Nevertheless, cries for changing our mathematics programs are coming from many directions as ideas for a forward-looking, futuristic mathematics curriculum are offered. Although calls for specific curricular changes are varied, all seem to agree on one thing: mathematics programs must give significantly more attention to the development of skills in mental computation and estimation and much less attention to traditional written algorithms for computation.

“Many academics turn from church or synagogue sometime in early adolescence, and their image of religion remains what they learned in fourth grade Sunday School. It is as if one assumed that the curriculum of a college mathematics department culminated in long division, or that biological research consisted exclusively in gathering the leaves from different species of trees and pressing them flat under three volumes of the World Book Encyclopedia. If those no longer involved with churches want to update their views of religion, they sometimes turn their television dials to the cable evangelists and find most of their prejudices confirmed.”

Profile: Lisa Hansel is the director of communications for the Core Knowledge Foundation, a nonprofit dedicated to the idea that every child should learn a core of content that spans language arts and literature, history and geography, mathematics, science, music, and the visual arts. Prior to joining the Foundation in 2013, she was the editor of American Educator, the quarterly journal of educational research and ideas published by the American Federation of Teachers. In that role, she often published articles jointly with E. D. Hirsch Jr., and Daniel T. Willingham that explained why reading comprehension, critical thinking, and problem solving depend on relevant prior knowledge—and why, as a result, all students need a rigorous, coherent, grade-by-grade curriculum that builds broad knowledge. Lisa has a B. S. in Psychology from Washington and Lee University and an Ed. D. in Education Policy from George Washington University, where she was also an adjunct Professor and the writer and editor for the National Clearinghouse for Comprehensive School Reform. To learn more about Core Knowledge, please see www.coreknowledge.org and blog.coreknowledge.org. She expressed her views regarding the Core Knowledge and Common Core Curriculum.

Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

This study focused on educators’ beliefs about implementing a large-scale curriculum called Common Core State Standards (CCSS), or as they are identified in one state, College- and Career- Readiness Standards. Building–level educators in the state of West Virginia were surveyed using a modified Stages of Concern instrument that measures attitudes toward an innovation at a given point in its implementation (Hall et al, 1977). The research questions for the study were: (1) What is the comfort level of educators with new curriculum standards four years after adoption? and (2) What are the relationships among gender, grade level taught, the highest degree earned, and age on educators’ comfort level and concern toward a new curriculum set of standards? For research question one, the data showed that mathematics and English language arts teachers held a high awareness of the standards and were not overly concerned about the standards regarding time management. For research question two, simple regression results revealed significant relations between five of the seven stages of concern and some demographic variables: awareness with grade level taught and gender, informational with the highest degree obtained, personal with age, management with grade level taught, and collaboration with age. In general, educators who had more years of teaching, higher educational credentials, and were older were more likely to know where and how to obtain additional resources as well as get assistance, possibly as a result of their experiences and sociocultural capital gained over the years on the job. Administrators’ views were in alignment with teachers regarding their awareness of the standards and time management, and administrators were slightly more concerned with the consequences of the new standards and with teacher collaboration.

Abstract. In this opinion paper, we review recent literature related to data and modeling driven instruction in hydrology, and present our findings from surveying the hydrology education community in the United States. This paper presents an argument that that data and modeling driven geoscience cybereducation (DMDGC) approaches are essential for teaching the conceptual and applied aspects of hydrology, as a part of the broader effort to improve science, technology, engineering, and mathematics (STEM) education at the university level. The authors have undertaken a series of surveys and a workshop involving university hydrology educators to determine the state of the practice of DMDGC approaches to hydrology. We identify the most common tools and approaches currently utilized, quantify the extent of the adoption of DMDGC approaches in the university hydrology classroom, and explain the community's views on the challenges and barriers preventing DMDGC approaches from wider use. DMDGC approaches are currently emphasized at the graduate level of the curriculum, and only the most basic modeling and visualization tools are in widespread use. The community identifies the greatest barriers to greater adoption as a lack of access to easily adoptable curriculum materials and a lack of time and training to learn constantly changing tools and methods. The community's current consensus is that DMDGC approaches should emphasize conceptual learning, and should be used to complement rather than replace lecture-based pedagogies. Inadequate online material publication and sharing systems, and a lack of incentives for faculty to develop and publish materials via such systems, is also identified as a challenge. Based on these findings, we suggest that a number of steps should be taken by the community to develop the potential of DMDGC in university hydrology education, including formal development and assessment of curriculum materials, integrating lecture-format and DMDGC approaches, incentivizing the publication by faculty of excellent DMDGC curriculum materials, and implementing the publication and dissemination cyberinfrastructure necessary to support the unique DMDGC digital curriculum materials.

Abstract. In this opinion paper, we review recent literature related to data and modeling driven instruction in hydrology, and present our findings from surveying the hydrology education community in the United States. This paper presents an argument that that Data and Modeling Driven Geoscience Cybereducation (DMDGC) approaches are valuable for teaching the conceptual and applied aspects of hydrology, as a part of the broader effort to improve Science, Technology, Engineering, and Mathematics (STEM) education at the university level. The authors have undertaken a series of surveys and a workshop involving the community of university hydrology educators to determine the state of the practice of DMDGC approaches to hydrology. We identify the most common tools and approaches currently utilized, quantify the extent of the adoption of DMDGC approaches in the university hydrology classroom, and explain the community's views on the challenges and barriers preventing DMDGC approaches from wider use. DMDGC approaches are currently emphasized at the graduate level of the curriculum, and only the most basic modeling and visualization tools are in widespread use. The community identifies the greatest barriers to greater adoption as a lack of access to easily adoptable curriculum materials and a lack of time and training to learn constantly changing tools and methods. The community's current consensus is that DMDGC approaches should emphasize conceptual learning, and should be used to complement rather than replace lecture-based pedagogies. Inadequate online material-publication and sharing systems, and a lack of incentives for faculty to develop and publish materials via such systems, is also identified as a challenge. Based on these findings, we suggest that a number of steps should be taken by the community to develop the potential of DMDGC in university hydrology education, including formal development and assessment of curriculum materials integrating lecture-format and DMDGC approaches, incentivizing the publication by faculty of excellent DMDGC curriculum materials, and implementing the publication and dissemination cyberinfrastructure necessary to support the unique DMDGC digital curriculum materials.

A curriculum with goals for students of valuing mathematics, being confident in their abilities, making mathematical connections, becoming mathematical problem solvers, and learning to reason and communicate mathematically is a call for classrooms in which students are actively involved in learning. It is a call for teachers to establish environments that encourage the use of manipulatives to assist students in attaining these goals proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989). A major difficulty, however, is how to manage the materials efficiently.

Integrating mathematics, science, language arts, and social studies within the middle school curriculum can be an important and worthwhile endeavor. With integration, students realize that, at least in the real world, disciplines do not exist in perfect isolation and that the separations so often seen in school are arbitrary and, at times, unnecessary. Although any one of these disciplines can be the center of the integration, mathematics may be the most natural choice, especially when we focus on mathematical models, descriptions of real-world phenomena through mathematics. The Connections strand of Principles and Standards for School Mathematics states that students across grade levels should be able to “recognize and apply mathematics in contexts outside of mathematics” (NCTM 2000, p. 64). Students can naturally make connections when the mathematics they are learning is presented through problems emanating from other disciplines, particularly in science. In turn, students may grasp underlying concepts of the other disciplines better when they view them through a mathematical lens.

Kuwait, has participated in international TIMSS test for many years, however, there has been little systematic effort to compile and assess changes between genders. This study attempts to look at the results of Kuwaiti students on the TIMSS mathematics assessments in general and according to gender in particular and the views of supervisors on the relatively low performance of Kuwaiti students. The study employed a mixed method approach in which data analysis of test results, IEA-issued documents, and statistics and official reports were used. Two focus group interviews were conducted with a convenience sample of nine educational supervisors from mathematics and science. The results show that the performance of Kuwaiti students in both the fourth and eighth grades was extremely low on the TIMSS mathematics assessments in general and in content areas in particular, since the first participation in 1995, even though the performance of eighth graders showed a slight improvement in 2015 in all areas. The TIMSS results also show that the higher the level of thinking that was assessed, the lower the performance of Kuwaiti students was. The data indicate that throughout all years, Kuwaiti girls outperformed boys, considering the slight improvement especially in 2015, yet both performances lagged behind international norms. Focus group transcript analysis reveals that supervisors perceived that students’ low performance on the TIMSS assessment test is related to a number of reasons as lack of interest in TIMSS test, unfamiliarity with TIMSS questions, and students’ weakness in the Arabic language. The paper concludes the need to systematically evaluate the TIMSS results, and develop interventions and a competent national curriculum in Kuwait.

Algebra's “Gatekeeper” status has prompted several in the mathematics education research community (e.g., Davis 1985; Kaput 1998; Olive, Izsak, and Blanton 2002) to urge educators to view algebra not as an isolated course but as a continuous K–12 strand that is present throughout the entire mathematics curriculum. Central to the transition from arithmetic to algebraic reasoning is the concept of variable (Schoenfeld and Arcavi 1988). Schoenfeld and Arcavi argue that despite its importance, most mathematics curricula offer little to assist students in developing ideas about this concept. They assert that instead of providing students opportunities to practice manipulating terms and solving for unknowns, teachers should encourage students to view variables as shorthand tools for expressing already-understood ideas about varying quantities. This article describes a mathematical problem that can encourage students to view variables in this way while confronting a common misconception.

Implementing the NCTM's curriculum and evaluation standards will require a change in the beliefs of many mathematics teachers and widespread acceptance of a fundamental premise of the Standards: that “appropriate calculators should be available to all students at all times” (Commission on Standards for School Mathematics of the NCTM 1989. 8). It will require widespread acceptance of the use of calculators in testing, for as the Standards observes, “until tests provide for the appropriate use of calculators, many teachers will continue to prohibit their use in the classroom. Without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change.”

Mathematics education research has established itself a a viable, identifiable discipline. Publications in the area are readily available, presentation on mathematic education research are expected to be part of national and regional programs, and mathematic education positions at the university level often include an expectation of efforts in research. Why then doe the en e linger that the research remains great theory, with little or no clas room impact? Perhap the truth is somewhere between this extreme and the ideal of research-driven curriculum and instruction for K-12 mathematics.

Mathematically literate students should view mathematics as a way of looking at their environment that aids understanding and adds insight This attitude toward mathe matics can be fostered in the daily routines of the classroom. Mathematical experiences need not be restricted to the “math period” but can be incorporated throughout the school day. The importance of making mathematical connections, both within mathematics and between mathematics and other curriculum areas, is emphasized by the inclusion of “mathematical connection” as one of the curriculum standards for school mathematics (NCTM 1989). This article how how a simple manipulative device useful for taking attendance can be used to exercise mathematical thinking processes in a variety of contexts at different grade levels throughout elementary school.

This September 1995 article approaches creating a modern mathematics curriculum using a metaphoric tree of Mathematics. Author describes problem of optimal selection and sequencing of subjects. He supports the ladder of technology for reaching higher branches of the tree and argues for clearing the dead leaves of centuries of curricular material, clearing the view of beautiful tree of Mathematics.

This September 1995 article approaches creating a modern mathematics curriculum using a metaphoric tree of Mathematics. Author describes problem of optimal selection and sequencing of subjects. He supports the ladder of technology for reaching higher branches of the tree and argues for clearing the dead leaves of centuries of curricular material, clearing the view of beautiful tree of Mathematics.

An underlying view of mathematics education expressed in the Curriculum and Evaluation Standards (NCTM 1989) is that a student should be actively involved both mentally and physically in constructing his or her own mathematical knowledge: “The K-4 curriculum should actively involve children in doing mathematics. … [They should] explore, justify, represent, solve, construct, discuss, use, investigate, describe, develop, and predict” (NCTM 1989, 17).

During this past year, NCTM has produced a working draft of a set of curriculum and evaluation Standard for school mathematics (Commission on Standards for School Mathematics of the National Council of Teachers of Mathematic 1987). As chair of the Commission, I have been asked to respond to four questiona.

Every contemporary K–12 mathematics curriculum must contain a substantial amount of geometry. Geometry organizes and clarifies our visual experiences and provides visual models of mathematical concepts. Applications of geometry are ubiquitous—we encounter them daily. Thus, every student needs to study geometry. This idea is noncontroversial.

In 1989, NCTM published the Curriculum and Evaluation Standards for School Mathematics, which presented the mathematics profession with a broad view of the important mathematics that should be taught in schools. Two years later, the Professional Standards for Teaching Mathematics gave teachers the opportunity to address the pedagogical issues inherent in teaching a broad-based, thinking curriculum as described in the curriculum standards. The next link, assessment, though part of the first document, required specific attention. Assessment Standards for School Mathematics, currently in progress, will present the criteria for judging the appropriateness and quality of assessment tools and systems.

The Six Through Eight Mathematics (STEM) project is one of the National Science Foundation's (NSF) funded middle school mathematics curriculum projects. The project received initial funding in 1992; the finished product is expected to be available in 1998. The STEM curriculum is organized in teaching units called modules. Each module is organized around a conceptual theme, such as “flight” or “wonders of the world.” The use of thematic modules promotes students' developing and applying mathematical concepts in broad contextual situations so that they do not view mathematics as a collection of separate and unrelated topics.