case study in mathematics education

37-49). Rationale: By the end of week 8, participants began to discuss how it might be possible to teach mathematics using problem-solving. Unlearning to teach mathematics. Even Piaget says that higher order thinking skills do not arrive at this age. Paper presented at the annual meeting of the American Educational Research Association, San Francisco. (2001). These posts illustrate Yvonne’s ability to make revisions to her reasoning along the dimensions of standards-based pedagogy by mining information from other participants’ discussion board posts and reflecting upon their content. (1995). She also says that the students should be led and not told what to do. Study groups: Conduit for reform. Yvonne had 12 years of teaching experience, and Maura had 16. I really like the idea of providing students two choices. Student Teacher Knowledge and Its Impact on Task Design, Tenille Cannon. (1992). In the mainstream section of the school, there are no individualized or special education plans Before the 13 weeks began, participants were gathered together for two face-to-face (FTF) meetings. These comments from Yvonne and Maura came while discussing an article that emphasized the importance of careful lesson planning when one uses manipulatives in a lesson (Stein & Bovalino, 2001). https://citejournal.org/volume-7/issue-1-07/mathematics/case-studies-of-mathematics-teachers-learning-in-an-online-study-group. 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 Schoenfeld, A.H. (2000). Both Maura and Yvonne held to the position that the manner in which computational skills and procedures were taught should not be altered and did not show evidence of being open to revising their pedagogical reasoning structures in this area. 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. Group harmony and cohesion can lead teachers to identify and pursue further professional development opportunities with one another, as in the present study. Student-to-student interaction is a distraction from learning. On at least one occasion, it seemed that Yvonne swayed another participant toward her point of view, as shown in the following exchange: Maura, along with most other discussion board participants, adopted a similar position and did not deviate from it. (1989). In this editorial, we argue that how mathematics … I am going to try to have paraphrase what other students say in class. At least four discussion board posts per week were required. The impact of two Standards-based mathematics curricula on student achievement in Massachusetts. I will try to pose more questions in my own class that spark debate and discussion and that may have varying solutions. American Educational Research Journal, 26(4), 499-532. <>/Rotate 0/Type/Page>> Teacher Learning as Acquisition of Pedagogical Reasoning Structures. The case-study on mathematics, as a tool, can allow students to apply the theoretical knowledge to solve practical problems, to promote their independent thinking, the ability to listen and take into account an alternative point of view, and to give their own reasons. Hmmm. Chicago: University of Chicago Press. Valued relations between actors are depicted as links between corresponding nodes. On one other occasion, a debate provided a context for both Maura and Yvonne to exhibit resistance to a reform-oriented pedagogical idea. Sparks-Langer, G.M., Simmons, J.M., Pasch, M., Colton, A., & Starko, A. application/pdf I felt that the problem was well worth the time spent on it. Spillane, J.P., & Zeulli, J.S. Kieran, C. (2001). Standards & curriculum: A view from the nation. 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. Boaler, J. 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.”. From the questionnaires conducted, students welcomed the peer- teaching activity and their learning motivation was also improved. Teachers at times exhibit similar reasoning patterns, as it is not uncommon for them to endorse changes in their forms of instruction while leaving the functions of their instruction largely unexamined (Saxe, Gearhart, Franke, Howard, & Crockett, 1999). 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. From this perspective, “hands-on” activities and “problem-solving” were seen as useful insofar as they facilitated the mastery of mathematical procedures. In another discussion of ALN-based professional development for mathematics teachers, Newell, Wilsman, Langenfeld, and McIntosh (2002) noted that “holding a discussion over a period of days or weeks allows time to reflect, experiment with new ideas, share successes and failures, and receive feedback from others who are undergoing the same experiences” (p. 506). The four year course dealt with various units in general and Mathematical pedagogy. To conclude this report, some of the most striking similarities and differences will be discussed along with the researcher’s reflections on their meaning for the field of mathematics teacher education. New York: Macmillan. The text-based nature of the ALN also affords unique learning opportunities that both case study participants capitalized upon. Li, Q. <>stream Stigler, J.W. Cases from a broad range of topics are appropriate for consideration in the JCSE providing the focus of … These brief offerings of teaching ideas were considered examples of Stage 3 participation, because they served the function of information sharing but did not result in the types of extended Stage 4 conversations that will be described later in this report. 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. Each cluster was assigned a qualitative descriptor. <> 27 0 obj " 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. Constructing and resisting disability in mathematics classrooms: A case study exploring the impact of different pedagogies.Educational Studies in Mathematics, 89(1), 1–18. 3 0 obj (pp. Two other collaborative brainstorming threads in which Yvonne exhibited evidence of enrichment occurred during the 8th and 11th weeks of the study. I, personally, am going to attempt to provide more wait time for my students in the coming school year.” Maura’s posts highlighting article aspects neutral to shifts in reasoning about the dimensions of standards-based pedagogy extended beyond wait time to encompass having students keep a notebook of mathematical terms and problems, using take-home letters to communicate with parents, and writing her thoughts on lessons in a journal rather than leaving them unrecorded. However, at least three of the four were to be replies to posts made by others, so that the group would not become a collective monologue. Oxford Online Maths Club (OOMC) The OOMC is run by Dr James Munro (Admissions Coordinator for Maths at Oxford) and began in HT21. The issue my case study sets out to address is the identification and analysis of the positioning of the teacher within a framework of psychology of mathematics education. Enrichment occurs when new information is perceived to be consistent with existing ideas. Online professional development: Sustained learning with friends. endobj 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. 3. Lott, J.W., & Nishimura, K. Haavind, S. (2000). PDF The researcher also conducted a classroom observation of each teacher before interaction in the ALN took place. Aviv, R., Erlich, Z., Ravid, G., & Geva, A. Edwards, D. (1993). The researcher moderated the group. (2001). teachers who participated in the study: Business studies, Kiswahili, History, Geography, Mathematics, Religious Education, Computer Studies, Physics and Chemistry. Student Teacher Knowledge and Its Impact on Task Design, Tenille Cannon. 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. For example, both teachers professed a preexisting belief in the importance of real world problems. Subject Acceleration Case Study: Mathematics Submitted by: Mother of an Accelerated Student The student in this case study is my son "George", who was radically accelerated in math beginning in first grade. They did not consider making real world problem-solving an organizing focus for classroom discourse and a vehicle for learning skills, as envisioned by NCTM (2000) and realized by teachers participating in programs such as CGI (Franke, Fennema, & Carpenter, 1998; Lubinski & Jaberg, 1998). (1986). I think we all fear being observed on the one day when even the class that you can usually count on as being with it comes in but you soon find that they have left their brains at home, or don’t seem to be quite awake. Learning and Instruction, 5, 401-408. Rationale: Since the idea of dividing fractions without using the “invert and multiply” algorithms was a novel idea to participants during week 6, this article was intended to provoke thought about how one might teach a lesson without invoking the algorithm and how students might respond. A funny thing happened on the way to the forum. Three large-scale studies were retrieved, two in primary education [7, 18] and one in secondary education [].All three studies used a mixed method research design including surveys, interviews with both teachers and students, in-depth case analyses, and statistical analyses of students’ attainment in national tests. Like Yvonne, Maura showed evidence of revisions in her pedagogical reasoning while highlighting aspects from articles. Core Education: Advanced Mathematics vs. Business ... At the end of the day, abstract mathematics is what the majority of students struggle with, and are often considered to be the least applicable in every day life. The students were given the opportunity to discuss their reasoning and justify their solutions. physics and mathematics. As Yvonne highlighted aspects of posts of the other participants, she found support for a number of her pre-existing beliefs, such as the importance of requiring students work things out on their own, monitoring students as they work, teaching to a variety of different “learning styles,” and having students work “real world” problems. Vosniadou and Matthews (1992) provided an example of enrichment in a science classroom where most children found it easy to learn that the moon has craters because that idea was easily appended to their existing beliefs. Preview the ‘table of content, abstract and chapter one to Five with references and questionnaires. <. The ongoing analysis helped situate this retrospective analysis in a larger context. Relational understanding and instrumental understanding. In the present study, the constructs of enrichment and revision of pedagogical reasoning structures were used to describe teachers’ acquisition of knowledge within an ALN study group environment. One of the choices could provide an erroneous answer that students would get by misreading the problem or choosing the incorrect operation. If you feel as though you want to provide students with a grade for putting forth effort on any given assignment—do just that—provide them with a “grade” for completion. Great idea—that also removes the element of surprise. strategies in a mathematics classroom using a single case study design. On the cognitive conflict as an instructional strategy for conceptual change: A critical appraisal. This strategy of sharing answers with a partner (this time my partner was the article) would have worked well for me in class. The mathematics curriculum should focus exclusively on teaching number and operations. Highlights and implications. Found insideHow can we deal with the diversity of theories in mathematics education? This was the main question that led the authors of this book to found the Networking Theories Group. Clement, L., & Bernhard, J.Z. I found Principle 4 of the article particularly interesting. It was assumed that much could be learned from case studies of exemplary practice that would stimulate and guide improvements in science and mathematics education. Mahwah, NJ: Erlbaum. Carpenter, Fennema, Peterson, Chiang, and Loef’s (1989) study of Cognitively Guided Instruction (CGI) illustrated that teachers sometimes exhibit large-scale revisions of pedagogical reasoning structures. 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). Both Yvonne and Maura pushed for more collaborative planning of mathematics lessons among teachers in the middle schools in the district. Teaching and Teacher Education, 18, 715-737. Found insideThis volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. Paper presented at the Meeting of the National Staff Development Council, St. Louis, MO. endobj Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program, Rachelle Myler Orsak. 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. Assessment consists solely of end-of-week and end-of-unit tests. ), Professional development for teachers of mathematics: 1994 yearbook (pp. The researcher’s ongoing analysis of each teacher’s ALN participation resonated with these observations. For example, Yvonne wrote, “I do have one question to which some of you may have suggestions—What do you do with that reluctant learner(s) in the class?” This question prompted the new teacher mentor, the curriculum supervisor, the district resource teacher, and Maura all to post suggestions and in some cases respond to the ideas set forth by others. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content ... Developing teacher knowledge through peer discourse. (1997). Mathematics Teaching in the Middle School, 4, 224-227. Thought and language. The two narratives are presented alongside one another in the next section of this report. Illustrates how concept mapping can benefit qualitative research to clarify relationships between and among various elements through nonstructured interviews. In D.A. Intersubjectivity without agreement. As Maura highlighted aspects of other participants’ posts, she showed further evidence of resistance and enrichment about issues in her reasoning discussed earlier. +1-515-393-6211. However in all the states in Nigeria including Edo State, teaching … endobj The assessment of knowledge and skills acquired by the student at each academic stage is crucial for every educational process. These experiences highlight some of the unique benefits of ALNs as tools for mathematics teacher education. In the case study narratives, the constructs of resistance, enrichment, and revision were useful for tracking teachers’ attainment of pedagogical reasoning structures. AppendPDF Pro 5.5 Linux Kernel 2.6 64bit Oct 2 2014 Library 10.1.0 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]. 42 0 obj Since the participants were dispersed among various buildings in the school district, the ALN study group played the practical role of breaking down geographic and scheduling boundaries that otherwise would have impaired conversations among them. Alternative algorithms: Increasing options, reducing errors. They believe that if they state a series of concepts, theorems, and proofs correctly and clearly, with plenty of symbols, they must necessarily be understood” (p. 117). I wonder too if the administrator would enjoy an excuse to get away from the hallways and discipline issues in the office!??! Though I think it is good to have the students find patterns or relationships, combine and compare quantities, and draw diagrams, I don’t think it is rational to throw out the key word approach. Rationale: The week 10 conversations saw participants wrestling with the question of how student assessments should be graded. A debate during the seventh week of the study helped reveal more of the sources of Yvonne’s resistance to revising pedagogical reasoning structures while also providing insight into why teachers in the district had actively opposed the adoption of a reform-oriented approach to mathematics instruction: In the excerpt above, Yvonne’s belief in the importance of “real world” examples was not enough to convince her to wholeheartedly adopt a reform-oriented curriculum, since in her estimation, “examples and practice” needed to occur before students approached problems. Yvonne, on the other hand, showed enrichments and revisions to her reasoning that did not appear in the context of either of the two other types of Stage 3 interaction. Therefore, an apparent failure in learning from one perspective should not necessarily be looked upon as an absolute failure. The researcher gathered background data about Yvonne and Maura to build a frame of reference for analyzing their ALN interactions. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics (STEM) as a result, closing doors to scientific, engineering, and technological careers.
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