Unrealistic Expectations and Compromised Observations in School Mathematics Research

This report is the fourth of four that stem from a study of the Impact of Approved Induction

This chapter looks at an in-depth application of meaning equivalence reusable learning objects (MERLO) to mathematics education and teacher professional development. The study has been conducted during professional development courses for in-service teachers and is focused on mathematics teachers' praxeologies, namely their didactical techniques and theoretical aspects embraced to accomplish a task. Specifically, the task given to the teachers consists in designing MERLO items to be used in their classrooms, working in groups or individually, after having been trained by researchers in mathematical education. The chapter presents two case studies with data, one dealing with secondary school teachers in Italy and one concerning primary teachers in Australia. One of the main aims of the study is the analysis of the praxeologies of these teachers when they are engaged in designing MERLO items during professional development programs. The chapter demonstrates, with these examples, the generalizability potential of MERLO items and that they can be used in different cultural and institutional ecosystems.

Children's Mathematics Learning: The Struggle to Link Form and Understanding

School Reform: The District Policy Implications of the Effective Schools Literature

Teachers' experience and knowledge with the construction and use of teaching materials influences the teacher's classroom activities. This study intended to explore mathematics teacher's experience on the construction and use of teaching materials in the classrooms. This study used a narrative inquiry approach to explore the use and construction of teaching materials in mathematics teaching, focusing on the experiences of mathematics teachers from secondary schools in Dang district of Nepal. The findings suggest that the experienced mathematics teachers used only text-books and whiteboards as teaching materials. They did not use additional teaching materials in their mathematics classrooms at the beginning of their careers. Further, with the help of in-service teacher training, the research participants got the knowledge and skills to construct and use teaching materials, like the prism models, pyramids, cones, and cylinders. Furthermore, the findings also suggested that the teachers do not use these teaching materials regularly due to poor classroom management and overwork load. The findings of this study can be helpful for mathematics teachers, teacher trainers, school administrations, and policymakers for meaningful mathematics teaching and learning.

The study investigated Senior High School (SHS) mathematics teachers’ preparedness to implement inclusive mathematics education principles and practices in their mathematics classrooms. A sequential explanatory mixed methods design was employed with a sample of 195 SHSs mathematics teachers selected conveniently and purposefully, from the then 10 political regions of Ghana, to participate in the study. Data was collected using a cross-sectional survey that used a structured questionnaire, administerd online, to elicit information on SHS mathematics teachers’ preparedness to implement pedagogical practices assoiated with inclusive mathematics education in the classroom. This was followed by interviews with 4 mathematics teachers from the 4 of the five Ghana Education Service school placement categories. The study revealed that mathematics teachers in senior high schools are inadequately prepared to implement an inclusive mathematics education curriculum principles and practices in their classrooms. Most of the teachers’ knowledge of inclusive education principles and practices is low. It was observed that approximately 59% of the mathematics teachers sparingly use inclusive education practices or strategies in their mathematics classrooms. It is therefore recommended that various stakeholders, particularly, the Ghana Education Service, should put measures in place to organize training on inclusive mathematics education to upgrade in-service mathematics teachers’ knowledge on inclusivity. Also, mathematics teacher education programmes in teacher education colleges and universities should be reviewed to include inclusive mathematics education principles and practices so that mathematics teachers from various institutions would be equipped to practice inclusivity in their mathematics classrooms.

Teaching Secondary and Middle School Mathematics combines the latest developments in research, standards, and technology with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics today. In the fully revised fifth edition, scholar and mathematics educator Daniel Brahier invites teachers to investigate the nature of the mathematics curriculum and reflect on research-based "best practices" as they define and sharpen their own personal teaching styles. The fifth edition has been updated and expanded with a particular emphasis on the continued impact of the Common Core State Standards for Mathematics and NCTM’s just-released Principles to Actions, as well as increased attention to teaching with technology, classroom management, and differentiated instruction. Features include: A full new Chapter 7 on selection and use of specific tools and technology combined with "Spotlight on Technology" features throughout clearly illustrate the practical aspects of how technology can be used for teaching or professional development. Foundational Chapters 1 and 2 on the practices and principles of mathematics education have been revised to build directly on Common Core State Standards for Mathematics and Principles to Actions, with additional references to both documents throughout all chapters. A new Chapter 4 focuses on the use of standards in writing objectives and organizing lesson plan resources while an updated Chapter 5 details each step of the lesson planning process. A fully revised Chapter 12 provides new information on teaching diverse populations and outlines specific details and suggestions for classroom management for mathematics teachers. Classroom Dialogues" features draws on the author’s 35-year experience as an educator to present real-world teacher-student conversations about specific mathematical problems or ideas "How Would You React?" features prepares future teachers for real-life scenarios by engaging them in common classroom situations and offering tried-and-true solutions. With more than 60 practical, classroom-tested teaching ideas, sample lesson and activities, Teaching Secondary and Middle School Mathematics combines the best of theory and practice to provide clear descriptions of what it takes to be an effective teacher of mathematics.

The 13th International Congress on Mathematical Education in Hamburg was not only a scientific experience for researchers in mathematics education from all over the world. As Convenor and Local Chair of ICME-13, we are particularly pleased that also more than 250 teachers from all over Germany and five other countries have benefited from this congress. Despite the school holidays taking place in many federal states of Germany in July, mathematics teachers could take part in a special conference for teachers taking place parallel to ICME-13 on the 27th–29th of July 2017. On three days, the teachers were able to participate in a comprehensive lecture and workshop program, which included not only professional development courses in the area from primary to secondary mathematics education, but also thematically relevant excursions.

Previous articleNext article No AccessA New Use of Randomization in Experimental Curriculum EvaluationHerbert J. Walberg and Wayne W. WelchHerbert J. Walberg Search for more articles by this author and Wayne W. Welch Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 75, Number 4Winter, 1967 Article DOIhttps://doi.org/10.1086/442821 Views: 3Total views on this site Citations: 26Citations are reported from Crossref Journal History This article was published in The School Review (1893-1979), which is continued by the American Journal of Education (1979-present). Copyright 1967 University of ChicagoPDF download Crossref reports the following articles citing this article:Joy Cumming, Adrian Coulston, John Elkins Planning for incomplete data collection in educational research, Research Papers in Education 2, no.11 (Jul 2006): 31–46.https://doi.org/10.1080/0267152870020103Barry J. Fraser Learning environment in curriculum evaluation: A review, Evaluation in Education 5, no.11 (Jan 1981): 1–93.https://doi.org/10.1016/0191-765X(81)90014-8VICTOR L. WILLSON Research Techniques in AERJ Articles: 1969 to 1978, Educational Researcher 9, no.66 (Jul 2016): 5–10.https://doi.org/10.3102/0013189X009006005Frances Lawrenz The stability of student perception of the classroom learning environment, Journal of Research in Science Teaching 14, no.11 (Jan 1977): 77–81.https://doi.org/10.1002/tea.3660140113Frances Lawrenz Student perception of the classroom learning environment in biology, chemistry, and physics courses, Journal of Research in Science Teaching 13, no.44 (Jul 1976): 315–323.https://doi.org/10.1002/tea.3660130405William H. Ward A test of the association of class size to students' attitudes toward science, Journal of Research in Science Teaching 13, no.22 (Mar 1976): 137–143.https://doi.org/10.1002/tea.3660130206Frances Lawrenz The relationship between science teacher characteristics and student achievement and attitude, Journal of Research in Science Teaching 12, no.44 (Oct 1975): 433–437.https://doi.org/10.1002/tea.3660120415Wayne W. Welch The process of evaluation, Journal of Research in Science Teaching 11, no.33 (Sep 1974): 175–184.https://doi.org/10.1002/tea.3660110303Wayne W. Welch Review of the research and evaluation program of harvard project physics, Journal of Research in Science Teaching 10, no.44 (Dec 1973): 365–378.https://doi.org/10.1002/tea.3660100411Wayne W. Welch, Arlen R. Gullickson A Strategy for Evaluating the NSF Comprehensive Program for Teacher Education, School Science and Mathematics 73, no.99 (Dec 1973): 759–767.https://doi.org/10.1111/j.1949-8594.1973.tb09166.xBikkar S. Randhawa, Lewis L. W. Fu Assessment and Effect of Some Classroom Environment Variables, Review of Educational Research 43, no.33 (Jun 2016): 303–321.https://doi.org/10.3102/00346543043003303Wayne W. Welch, Herbert J. Walberg A National Experiment in Curriculum Evaluation, American Educational Research Journal 9, no.33 (Jun 2016): 373–383.https://doi.org/10.3102/00028312009003373Gary J. Anderson Effects of Course Content and Teacher Sex on the Social Climate of Learning, American Educational Research Journal 8, no.44 (Jun 2016): 649–663.https://doi.org/10.3102/00028312008004649Wayne W. Welch, Herbert J Walberg Pretest and Sensitization Effects in Curriculum Evaluation, American Educational Research Journal 7, no.44 (Jun 2016): 605–614.https://doi.org/10.3102/00028312007004605Gary J. Anderson Effects of Classroom Social Climate on Individual Learning, American Educational Research Journal 7, no.22 (Jun 2016): 135–152.https://doi.org/10.3102/00028312007002135Herbert J. Walberg, Andrew Ahlgren Predictors of the Social Environment of Learning, American Educational Research Journal 7, no.22 (Jun 2016): 153–167.https://doi.org/10.3102/00028312007002153Herbert J. Walberg Predicting Class Learning An Approach to the Class as a Social System, American Educational Research Journal 6, no.44 (Jun 2016): 529–542.https://doi.org/10.3102/00028312006004529Herbert J. Walberg Class Size and the Social Environment of Learning, Human Relations 22, no.55 (Oct 1969): 465–475.https://doi.org/10.1177/001872676902200507Wayne W. Welch 4: Curriculum Evaluation, Review of Educational Research 39, no.44 (Jun 2016): 429–443.https://doi.org/10.3102/00346543039004429Herbert J. Walberg, Wayne W. Welch, Arthur I. Rothman Teacher heterosexuality and student learning, Psychology in the Schools 6, no.33 (Jul 1969): 258–266.https://doi.org/10.1002/1520-6807(196907)6:3<258::AID-PITS2310060307>3.0.CO;2-KRobert L. Baker 4: Curriculum Evaluation, Review of Educational Research 39, no.33 (Jun 2016): 339–358.https://doi.org/10.3102/00346543039003339Gary J. Anderson, Herbert J. Walberg, Wayne W. Welch Curriculum Effects on the Social Climate of Learning: A New Representation of Discriminant Functions, American Educational Research Journal 6, no.33 (Jun 2016): 315–328.https://doi.org/10.3102/00028312006003315Wayne W. Welch Correlates of courses satisfaction in high school physics, Journal of Research in Science Teaching 6, no.11 (Mar 1969): 54–58.https://doi.org/10.1002/tea.3660060112Wayne W. Welch, Herbert J. Walberg, Andrew Ahlgren The Selection of a National Random Sample of Teachers for Experimental Curriculum Evaluation, School Science and Mathematics 69, no.33 (Mar 2010): 210–216.https://doi.org/10.1111/j.1949-8594.1969.tb08443.xHERBERT J. WALBERG, GARY J. ANDERSON The Achievement-Creativity Dimension and Classroom Climate*, The Journal of Creative Behavior 2, no.44 (Dec 2011): 281–291.https://doi.org/10.1002/j.2162-6057.1968.tb00118.xWayne W. Welch, Robert G. Bridgham Physics Achievement Gains as a Function of Teaching Duration*, School Science and Mathematics 68, no.55 (Mar 2010): 449–454.https://doi.org/10.1111/j.1949-8594.1968.tb15413.x

The European Union promotes STEM education to train citizens for the needs of a growing technological society. The engineering design process (EDP) has been greatly suggested for school implementation. Researchers in mathematics education have, however, criticized this approach for its difficulty to exploit mathematical content. This chapter analyses how technology and mathematics teachers (out-of-field and in-field, respectively) address high-school mathematics content in STEM projects elaborated through the EDP. The results reveal that teachers’ specialization plays an important role in project execution. Out-of-field teachers unconsciously focus on technology curricular content with a lack of mathematics exploration, whereas in-field teachers rely on their mathematical experiences to develop the projects. Our findings show that teachers’ specialization affects content integration. This suggests that future secondary education teachers should pursue a subject-specific degree followed by a continuous training where collaboration with other STEM-related teachers must be promoted.KeywordsSTEM educationEngineering design processDesign-based learningMathematics teacherTechnology teacher

This paper introduces a schema for classifying research in mathematics education that deepens and extends the Romberg/Bourne model. It employs dual hierarchical systems, one relating to the research task and the other to the research technique. The six task categories—descriptive, interpretive, prescriptive, analytic, synthetic, and theoretic—are defined with respect to breadth, depth, and scope of a study. The six technique categories—reflective, referential, evidential, clinical, empirical, and experimental—are defined in terms of utilization of resources and design intentions of the investigator. The pairing of task categories with technique categories permits the creation of a classification matrix for research in mathematics education. By examining the location of studies within this task‐technique matrix, both producers and consumers of research in mathematics education can discern historical trends influencing current and future investigations.

This paper aims to discuss the Technological Pedagogical Content Knowledge (TPACK) development by mathematics teachers (preservice and inservice) that participated in an online course for developing educational apps and puzzles with GeoGebra. Theoretical foundations are based on the authors Punya Mishra, Matthew J. Koehler et al, regarding TPACK framework and Margaret Niess et al regarding the development of TPACK by mathematics teachers. The research method is qualitative, and to analyze the thoughts and ideas discussed by the participants, we used the Discursive Textual Analysis. In this regard, three representative categories were used to build the following metatexts: instructional approaches, classroom environment management and teacher’s professional development. Through the Discursive Textual Analysis, it was possible to understand the participants concerns in creating different instructional approaches using Information and Communication Technologies, once they realized that dealing with digital natives requires pedagogical innovations, supported by new technologies, and new ways to configure and manage classroom environments permeated by digital resources.

This chapter explores the ways in which the discipline of mathematics underpins, illuminates or can be integrated with other disciplines in the context of mathematics pre-service teacher education. Drawing on my experience as a mathematics teacher educator and mathematics education researcher, I compare different models of integration I have used or observed in pre-service teacher education courses. These include mathematical modelling, curriculum integration and numeracy across the curriculum approaches. My analysis investigates the theoretical and philosophical rationales for these different approaches, the positioning of mathematics and assumptions about the relationship of mathematics to other disciplines, barriers to and enablers of integration and implications for both teacher education and classroom practice more generally.

This article describes two teacher educators' efforts to understand ownership, a core concept in a learner-centered program. The context for this self-study is a collaborative master's program guided by constructivist theory. Participants included 20 kindergarten through fifth grade teachers and two faculty guides. One faculty worked with the teachers in mathematics and the other worked with the teachers in literacy. To understand what ownership is in a graduate teacher education program, the two teacher educators gathered information from several sources. From their analysis of the information, they (a) identified strategies they used to encourage ownership, (b) gained insights into classroom Teachers' perceptions of ownership, and (c) identified ways classroom teachers encourage ownership in their classrooms. From this information, they developed a framework to represent how to encourage ownership in teacher education.

Mathematics has maintained an enduring image as a field of knowledge lending its resources to many intellectual pursuits and utilitarian enterprises. School mathematics, however, has increasingly learned to respond to a commonly conceived purpose of supplying the world’s workforce with the resources needed to support economic wellbeing. The emergent regulation in support of this response has in some instances tempered more humanistic or idealistic conceptions of why we want to study mathematics. What had been introduced to measure school mathematics now defines and polices its boundaries. It has also privileged Western concerns in setting internationalized agenda. Mathematics, mathematics education and mathematics education research, this chapter suggests, are each conceptualized according to their location, reflecting and shaping each other, yet with each being governed by slightly different priorities. It is argued that schooling is increasingly shaped and judged by its perceived capacity to deliver success in terms of international competitiveness linked to economic agenda. This results in school mathematics being shaped to meet assessment requirements. The chapter shows how research increasingly finds its terms of reference set according to measuring delivery in these terms. It also shows how researchers become complicit in promoting particular conceptions of teaching and in constructing the field as an ideological battleground. Such complicity, it is suggested, combined with the relative insularity of the field, prevents us from occupying other worlds that might define us and serve us in different ways. The chapter concludes with a consideration of the prospects of research in mathematics education and the extent to which this activity is enabled or restricted by existing institutional contexts in re-shaping its ambitions to engage with the diversity of future needs.