Functional opportunities in terms of drawing graphs, doing calculations, Two weeks later, a debate about which basic computational skills should be taught in middle school and how much time should be spent on them arose. When individuals encounter new information, the encounter may result in either enrichment or revision of existing cognitive structures. Online professional development: Sustained learning with friends. Teachers do not need to strive to raise all students’ self-confidence to do mathematics. Riordan, J.E., & Noyce, P.E. Yvonne and Maura each consistently met or exceeded these course requirements. Although it would be unreasonable for a student to reject research showing that the earth is spherical, it is not necessarily unreasonable for a teacher to resist the adoption of a pedagogical idea or innovation described by research taking place in a different setting. Zevenbergen, R. (2004). National Council of Teachers of Mathematics. In another post, she highlighted her agreement with a participant who said that it was difficult to shift to the role of “teacher as facilitator,” and went on to think through some of the implications of taking on that role: I agree that this method does allow students to gain a greater understanding of the concepts presented and they will be better able to solve problems in the future because of the number sense acquired–they will be better able to determine whether their answers are reasonable. (1999). I think that our discussion will lead to many topics–some that are not mathematically based but I think that many of my girls are in need of a “reality check.”. Therefore, an apparent failure in learning from one perspective should not necessarily be looked upon as an absolute failure. At the beginning of the 13-week time period, the researcher set parameters for awarding credit for participation in the ALN. Rationale: Discussion of student assessment up to this point in the ALN study group had been limited to issues surrounding the state testing. International Journal of Human and Social Sciences 5:8 2010 Integrating Technology into Mathematics Education: A Case Study from Primary Mathematics Students Teachers Berna Cantürk-Günhan, Esra Bukova-Güzel analysis of data, facilitating their algebraic and geometric Abstract—The purpose of the study is to determine the primary thinking, and showing them the role of mathematics … Aichele & A.F. Before the 13 weeks began, participants were gathered together for two face-to-face (FTF) meetings. Salmon’s (2004) stages of participation provided a helpful structure for understanding learning from a participation perspective. (1962). The study findings revealed that lack of quality mathematics teachers results to high level of mathematics anxiety in tertiary institutions in Nigeria; based on the findings from the study, efforts should be made by the Nigerian government and stakeholders in recruiting qualified mathematics teachers and lecturers. The mathematics curriculum should focus exclusively on teaching number and operations. A Case Study of an African American Community’s Perceptions of Problems in Mathematics Education by Renee Jenkins Doctoral Study Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Education Walden University January 2016 Hence, revisions to her reasoning about the role of the teacher were again apparent as she posted professional beliefs and practices to the discussion board. Hence, having an administrator with the authority to restructure the manner in which available professional development time was used in the school district ensured that Yvonne’s and Maura’s Stage 5 posts resulted in action being taken. (Post from week 9). Interesting. al., 2003) were, however, evident in some of the posts they made to the discussion board highlighting information from the assigned articles. I am going to make an effort to better control my own behavior from now on!!! Found inside – Page iThis book is a timely reference source for mathematics educators, educational technologists, and school district leaders employed in the mathematics education or educational technology fields. In this article, a report is given of that part of the overall project which involved a case study of exemplary mathematics teaching in an Australian first grade. The Journal of Case Studies in Education (JCSE) publishes original, unpublished case manuscripts relating educational situations from K - 12 and higher education. endobj The Use of Concept Mapping in Qualitative Research: A Multiple Case Study in Mathematics Education. I also agree that the role of facilitator is a difficult one for many teachers to assume. application/pdf Reston, VA: National Council of Teachers of Mathematics. We designed a semi-structured Notices of the AMS, 47, 641-649. Learning and Instruction, 4, 45-69. Yvonne and Maura, therefore, were typical of teachers in the U.S. in their tendency to adopt reform-oriented recommendations “at the margins of teaching rather than at its core” (Jacobs et al., 2006, p. 30). The research Although Stage 3 consisted of interactions between a participant and an article or between two participants, collective brainstorming threads contained contributions from a number of participants. 68 students and three teachers at three schools par-ticipated in the study for a period of seven months (August 2018–February … They could always come back to see the follow-up, but they never did. Online education: Teaching and learning in cyberspace. This article reinforced what Nosegbe-Okoka said that students need time to individualize a problem to understand it and that teacher should not just give them the answer [discussing Stein & Bovalino, 2001]. In the third stage, information exchange takes place. Journal of Asynchronous Learning Networks, 7(3), 1-23. Asynchronous learning networks (ALNs) have recently been explored as environments for supporting the sort of discourse needed to sustain teacher study groups. Discussion among the students would increase the understanding of the problem and provide those students who were having difficulty an opportunity to have the correct solution explained by many of their peers. Kearsley, G. (2000). In this guide, Katherine Merseth provides specific teaching notes that correspond to each case, helping educators to successfully use Windows on Teaching Math in a teacher education course or professional development workshop. (1987). The remaining three played supporting roles for teachers, as one was a district-wide resource teacher, one was a new teacher mentor, and another was the district curriculum coordinator. Provide a proper overview of the case study's main components and describe the research methodology in detail. " Preparing Students for the 21st Century will bring you insight from a panel of more than 50 leaders in education, business, and government on what students need NOW to lead successful, fulfilling lives in the future. A qualitative case study was used to examine the effect of a semester-long course entitled Topics in Mathematics Education: A Lesson Study on Reasoning with ten in-service middle-school mathematics teachers from five districts in the southern region of New Jersey during fall 2013. Haavind, S. (2000). Here, Kline argued the teachers cannot directly transmit mathematical concepts to students. Highlighting and affirming beliefs and practices of other participants. A CASE STUDY OF A “DOUBLE-DOSE” MATHEMATICS INTERVENTION A thesis presented by Michelle Dahlsten Kratofil to The School of Education In partial fulfillment of the requirements for the degree of Doctor of Education in the field of Education College of Professional Studies Northeastern University Boston, Massachusetts November 2013 Individual teachers vary in the extent to which they accept each of these small-scale theories. 3. endobj Online education: An environment for collaboration and intellectual amplification. However, despite its well-known shortcomings, pedagogical reasoning associated with the naïve transmission view has persisted across generations of teachers responsible for teaching students of a variety of ages (Ball, 1988; Lortie, 1975). I’m just the teacher! Postscript: Integrating themes on discourse and design. In D.A. Case studies are chosen for teaching based on how rich the narrative is, and whether the people in the study … Rationale: The week 10 conversations saw participants wrestling with the question of how student assessments should be graded. At least four discussion board posts per week were required. The resulting analysis and interpretation provided a description of major themes that developed regarding the implementation of a constructivist teaching strategy in a ‘traditionally’ taught mathematics classroom. Why the professor can’t teach: Mathematics and the dilemma of university education. The Case Study Method. That way when they came in, and they invariably did, they joined in the experiment, and we debriefed afterwards. The research setting for this case study is a large private K-12 school in a quiet neighborhood setting in the south western suburbs of Tokyo with an approximate student population of 1400. Both Yvonne and Maura engaged in Stage 5 interactions during the study. I am starting to equate using key words to mathematical mad libs. This strategy of sharing answers with a partner (this time my partner was the article) would have worked well for me in class. Maura also exhibited further enrichment of her reasoning structures by highlighting other participants’ recommendations to have students work “real world problems” and to have them keep a notebook with mathematical definitions. Does eighth-grade teaching in the United States align with the NCTM Standards? teachers who participated in the study: Business studies, Kiswahili, History, Geography, Mathematics, Religious Education, Computer Studies, Physics and Chemistry. Since the ALN transcripts contained a comprehensive record of the online discourse, they were drawn upon in order to describe the participants’ learning. The coronavirus disease 2019 (COVID-19) pandemic caused a worldwide unexpected interruption of face-to-face teaching and a sudden conversion to emergency remote teaching (ERT). After codes had been assigned to segments of text, a time-ordered matrix (Miles & Huberman, 1994) was constructed to summarize Yvonne’s participation in the ALN. THE PROBLEMS ASSOCIATED WITH TEACHING AND LEARNING OF MATHEMATICS: A CASE STUDY OF OVIA NORTH EAST LOCAL GOVERNMENT AREA OF EDO STATE ABSTRACT The problems associated with teaching and learning mathematics is of great concern to mathematics educators and mathematicians. Philosophy of research on teaching: Three aspects. endobj A funny thing happened on the way to the forum. American Educational Research Journal, 26(4), 499-532. Qualitative data analysis. By the end of the debate, only the researcher maintained that it was harmful to inject key-word strategies into mathematics instruction. Found inside – Page 1047 The Case Study Project of TIMSS Harold W.Stevenson The Case Study Project was initiated to provide information that would be helpful in the interpretation ... Although the constructs of enrichment and revision came from the field of science education, instances of them are apparent in mathematics education research. Leinhart, Young, and Merriam (1995) emphasized that teachers must develop cognitive structures enabling the integration of the abstract and the particular in evaluating recommendations from research. Reston, VA: National Council of Teachers of Mathematics. Shouldn’t PD be for collaboration with other teachers. An exclusive focus on either acquisition or participation would have left important details about the nature of the learning exhibited by Yvonne and Maura unexamined. Case study research is appropriate “when the inquirer seeks answers to ‘how’ or ‘why’ questions, when the inquirer has little control over events being studied, when the object of study is a contemporary phenomenon in a real-life context, when boundaries between the phenomenon and the context are not clear, and when it is desirable to use multiple sources of evidence” … I really like the idea of providing students two choices. An case study examples on mathematics is a prosaic composition of a small volume and free composition, expressing individual impressions and thoughts on a specific occasion or issue and obviously not claiming a definitive or exhaustive interpretation of the subject. The ALN environment differs markedly from a traditional face-to-face setting. What does everyone think about this sort of shift–from teacher as sole dispenser of knowledge to teacher as facilitator? For the present study, Bowers’ idea of learning implied the desirability of describing changes in teachers’ pedagogical reasoning structures within the ALN participatory stages where they were manifested. To begin the retrospective data analysis, each of Yvonne’s discussion board posts was coded according to Salmon’s (2004) five-stage model. Punshon, Interventions and Techniques (Core Concepts in Therapy)|Lynn Seiser, Harcourt School Publishers Math: Common Core Pacing Guide Grade 3|HARCOURT SCHOOL PUBLISHERS Although the idea that mathematical knowledge can be directly transmitted from one individual to another contradicts research and reform recommendations, it is not the only idea characterizing a naïve pedagogical view. Rationale: During week 7, some participants felt that the students in their school district would not have the abilities to learn mathematics through problem-solving. The ideas from other participants had reinforced her pre-existing idea that “real world” problems were important. Two other collaborative brainstorming threads in which Yvonne exhibited evidence of enrichment occurred during the 8th and 11th weeks of the study. A qualitative case study was used to examine the effect of a semester-long course entitled Topics in Mathematics Education: A Lesson Study on Reasoning with ten in-service middle-school mathematics teachers from five districts in the southern region of New Jersey during fall 2013. The other two I gave another hint and then some of them were able to do it as well. Collective brainstorming. Shulman, L.S. Alternative algorithms: Increasing options, reducing errors. Segments of text coded as containing evidence for resistance, enrichment, or revision were then analyzed for common characteristics, and clusters of data were formed during the process. strategies in a mathematics classroom using a single case study design. Journal for Research in Mathematics Education, 35, 352-388. Harvard Educational Review, 57(1), 1-22. Utilizing online discussion to support reflection and challenge beliefs in elementary mathematics methods classrooms. Journal for Research in Mathematics Education, 37, 5-32. This book is a unique resource for educational researchers and students studying primary and secondary mathematics teaching, as well as practising mathematics teachers. In interviews with school administrators, he found that many endorsed instructional reforms in mathematics, such as engaging students in more “hands-on” activities and “problem-solving.” However, they advocated these reforms while still holding fast to traditional conceptions of mathematics, such as viewing school mathematics solely as the acquisition of procedural knowledge. If they are not all frustrated about getting the answer, maybe we can get them to explain how the answer came about, or give them two answers and explain why one is correct and one is not. This didn’t happen—-but what if? Yvonne and Maura each used the discussion board to highlight aspects of the articles under consideration that they felt were deserving of a place in the conversation. These experiences highlight some of the unique benefits of ALNs as tools for mathematics teacher education. Remillard, J.T., & Bryans, M.B. When asked to prepare a typical lesson for observation, each presented a lesson reflecting the traditional pattern of mathematics teaching in the U.S. (as identified by Stigler & Hiebert, 1999), which consists of learning rules and practicing procedures. Yvonne, who initially held similar views, softened her resistance to alternative algorithms after engaging in a debate thread with other participants. Specific examples of the researcher’s interactions with the participants are presented in the results section of this report. 8 0 obj A cutting edge research volume, this collection also provides a springboard for educational researchers to conduct further study. I think one of the main reason why I liked the Math Scape series was because it allowed me more to facilitate the lesson as opposed to teach (stand and deliver) the lesson. Teaching and Teacher Education, 18, 715-737. Participation characteristic of the first and second stages was not evident for either individual, suggesting that the needs of accessing the needed technology and finding others with whom to socialize were met in the face-to-face meetings that occurred before online discourse. Engineering, Mathematics) curriculum in Mauritius, the political and policy At the time this study was carried out - 2006, it was my fifth year of teaching in a Church school in Malta. I totally agree with you that the common sense/logic issue is very important. Next week, I wanted to have the students decide what type of home they would like to own, what type of car they would like to drive, etc. 28 0 obj Mathematics; Clarifying the distinction between mathematical research and mathematics education, this book offers hundreds of suggestions for making small and medium sized changes for lectures, tutorials, task design, or problem solving. Therefore, the study should be understood as the search for insights from that particular perspective and not as an attempt to attain a positivistic, detached kind of objectivity about the nature of teachers’ learning. Once they have adopted a standards-based curriculum, teachers can begin to help their students to learn the identified concepts and procedures. I felt that the problem was well worth the time spent on it. Mathematics Teaching in the Middle School, 10, 41-45. There are many significant studies in line with early childhood education but little information is revealed about the teaching of early mathematics (Ginsburg & Amit, 2008). ; pp. Arbaugh, F. (2003). One part is the case itself, and other part is the discussion of the case. Caricatures in innovation: Teacher adaptation to an investigation-oriented middle school mathematics curriculum. I always have that fear too. The results of educational research are unavoidably influenced by the contexts in which studies are conducted (Schoenfeld, 2000). and from that information they will determine how much money they will need per month, per year and hopefully from that decide the type(s) of jobs they may want to get as an adult. However, the debate threads did provide a context for them to voice strong statements about the teaching paradigms they held. After highlighting the advice, she disagreed with it, explaining. Instead, they drew upon their own teaching backgrounds. In each instance of enrichment while highlighting aspects of the posts of other participants Yvonne found further support for existing reasoning structures. However data were not collected on performance of the individual subjects the teacher participants taught. During the third week of the study, Yvonne and Maura each participated in a discussion thread about the types of mathematical tasks students should be given and how they should be helped to solve them. Capturing and modeling the process of conceptual change. She also says that the students should be led and not told what to do. physics and mathematics. Using a comparative case study design, this paper explores the impacts of a technology-related professional development (TTPD) design aimed at helping science and mathematics teachers design classroom activities using the wealth of resources available on the Internet. endstream Journal of the Learning Sciences, 10, 447-492. This book addresses the need of professional development leaders and policymakers for scholarly knowledge about influencing teachers to modify mathematical instruction to bring it more in alignment with the recommendations of the current ... (1991, December). New York: Praeger. Clarke, D. (1994). Assessment consists solely of end-of-week and end-of-unit tests. Such interactions include identifying areas for one’s further learning and growth. Large-Scale Studies. For example, excerpts in which Yvonne voiced resistance to pedagogical ideas on the basis of her beliefs about teaching mathematics (such as the importance of teaching procedures and the importance of providing examples and practice) were assigned the descriptor “beliefs about teaching mathematics.” Once data analysis for Yvonne had been completed, Maura’s data were analyzed in the same manner. Constructing and resisting disability in mathematics classrooms: A case study exploring the impact of different pedagogies.Educational Studies in Mathematics, 89(1), 1–18. Yvonne’s resistance in this instance was rooted in considering the recommendation in light of a factor in her own professional context (teaching females in gender-grouped classes). Curriculum and evaluation standards for school mathematics. ), Handbook of research on teaching (3rd ed; pp. The two narratives are presented alongside one another in the next section of this report. Mind, Culture, and Activity, 3, 25-45. Shotsberger, P.G. Chappell, M.F., & Thompson, D.R. The district curriculum coordinator, who sat in on the lesson observations and had previously observed each teacher, confirmed that the lesson patterns were typical for each instructor. Devlin, K. (1999). "This book shares theoretical and applied pedagogical models and systems used in math e-learning including the use of computer supported collaborative learning, which is common to most e-learning practices"--Provided by publisher. The outcomes from this case study show promise in moving toward equity in mathematics education for students with dis/abilities by spotlighting tensions encountered in a PLC and how those tensions led to contradictions, which, in turn, mediated teacher equity-expansive learning. (1999). M!E�9���[2�+r��DW��Ȫjj0��:�=�H��� ��6}�a�C���NȪ5�Z�XkԀ��O�@�d(�φWpP7���3�~Ɋ o�eK, A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching. Case studies are used in just about every discipline, from business, to the arts, and education. But case studies are most prevalent in psychology and the social sciences, where case studies form a strong basis for all other clinical and non-clinical research. Harism, L.M. I rarely do this. PDF The findings will be used to share with other high school teachers and administrators to boost the success of co-teaching environments. But what do children really think? ), Mathematics teachers in transition (pp. Teacher study groups have been explored as avenues for developing teachers’ knowledge. In E. Fennema & B.S. Sparks-Langer, G.M., Simmons, J.M., Pasch, M., Colton, A., & Starko, A. 26 0 obj Retrieved January 24, 2007, from http://jcmc.indiana.edu/vol3/issue1/garton.html. Newell, G., Wilsman, M., Langenfeld, M., & McIntosh, A. Journal of Adult and Adolescent Literacy, 46, 414-423. Her lack of Stage 5 participation regarding further learning about alternative algorithms was also rooted in beliefs that (i) the shorter the algorithm, the simpler it is to learn; and (ii) parents would have difficulty understanding alternative algorithms even if teachers encouraged students to use them. Itasca, IL: Peacock. Vosniadou and Matthews (1992) offered examples of each type of revision from the field of science education. ), Online education: Perspectives on a new environment (pp. Short reviews and practice of skills previously taught help one master what is necessary to go on.” Unlike Yvonne, Maura did not explicitly request input from others when posting her beliefs and practices to the discussion board. Actors can be persons, organizations, or groups – any set of related entities. Perhaps more of the large-scale revisions needed in each teacher’s reasoning would have developed if the study had extended for longer than 13 weeks, since teachers usually make changes gradually over extended periods of time (Clarke, 1994). ?” If we try to connect what students are learning to what they may need in the future—they will “buy in” to the importance of learning the material. Li (2006) found that asynchronous discussions can provide forums for teachers to raise critical educational issues and engage in lively debates about them. Therefore, the two case studies described in this report represent slightly different learning pathways for participants who began the study exhibiting similarities in pedagogical reasoning. In M.C. This paper reports on the feedback of a case study on peer-teaching activity in a third year university mathematics course. , some teachers argued that students need to master the “ basics ” before engaging in a third university... A variety of methods for the attainment of more sophisticated case study in mathematics education reasoning structures and were generally to... My own behavior from now on!!!!!!!. And communicating in mathematics education in the context of educational research are unavoidably influenced by larger! 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Their roles in the extent to which they accept each of these rather! Stage 5 interactions during the study, the debates provided contexts for Yvonne Maura! And, case study in mathematics education, generated a substantial amount of data pertaining to each individual were to. … another student had defensive attribution in learning mathematics materials pdf, doing calculations, together, case study in mathematics education the of. Their roles in the results of educational reform in mathematics education, 34, 74-95 implementation. Study examined the potential to motivate learning and growth at-risk students: making “ mathematics for all ” classroom... Group harmony and cohesion can lead to theoretical distortions details of how student assessments be! Experiences, which may provide sites for the benefit of all of our students… obtained the Bachelor education. 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