Fifth Annual TEAM-Math Partnership Conference
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| Title: P3: Property-Opoly and other Powerful Preservice Field Experiences
Presenters: 1) Jane Ries Cushman, Mathematics Department, Buffalo State College, Buffalo, New York 2)Jodelle S.W. Magner, Mathematics Department, Buffalo State College, Buffalo, New York
Outline of Presentation: Field experience is an integral part of the secondary mathematics education program at Buffalo State College. There are primarily three different types of experiences for our students, for a minimum of 100 hours of field experience prior to student teaching. All of the experiences are mediated by course instructors and are connected to and discussed in our college classroom. The proposed presentation shares the various field experiences of our students. Each speaker will highlight one specific field experience and its connections to its corresponding college course. For their initial field experience, sophomore level students have placements in both urban and suburban middle and high schools. Students are matched with a middle school mathematics teacher and assist in their classroom approximately 2 hours each week for the semester. They spend half of the semester in an urban placement and the other half in a suburban placement. As part of this initial experience, BSC students provide after school tutoring for urban children. The field experiences with high school are not as structured. For the high school level, students are required to observe/assist in a specific urban high school, which is a Professional Development School (PDS) for Buffalo State. The entire mathematics department of this high school participates in the PDS partnership and welcomes the preservice teachers to assist in their classes. This allows our students to see a variety of high school teachers and courses over the semester. The junior/senior level middle school methods course has both 7 – 12 preservice math teachers and elementary preservice teachers who are completing a 5 – 9 math extension and will be certified to teach mathematics in those grades. The students in this course develop and teach a full day of manipulative-based math lessons to all 250 6th grade students at a local suburban middle school. The 6th grade students attend different math lessons all day, with no classes in the other academic areas. For several years, the theme was Property-Opoly and the lessons focused on the various math properties in the 6th grade New York State curriculum. Last year, the focus was on fractions, decimals, percents and the connections between them. Reflections of the preservice teachers from this experience will be shared. The secondary methods students co-register for a field experience course in which they are responsible for developing and teaching daily lessons in an urban high school. The preservice teachers taught in either a Geometry course or an Algebra course. Working in teams of 3 or 4, they developed lessons plans and assessments for 12 weeks of instruction in the high school classes. Students were responsible for implementing the lesson of the day – even if their team did not write the lesson. Each college student attended the field experience on Monday and Wednesday or on Tuesday and Thursday. So, one team consisted of two Monday/Wednesday students and two Tuesday/Thursday students. Each day, the team members were responsible for communicating with other team members what was successfully covered and who was absent. Every Friday the individual students were able to conduct whole group instruction and assessment. This collection of field experiences prepares our students for student teaching in both urban and suburban schools. 5th Annual Pre-Session Information|General Conference Information |
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Title: Exploring Beliefs and Practices of Teachers of Secondary Mathematics who Participated in a Standards-Based Pre-Service Education Presenter: Mary Alice Smeal, Mathematics Department, Alabama State University, Montgomery, Alabama Outline of Presentation: The National Council of Teachers of Mathematics (NCTM: 1989, 1991, 1995, 2000) has challenged all mathematics teachers to use their principal documents as guidelines for Standards-based approaches. The Standards-based approach purports strategies that include student-led inquiry, discovery learning, and the teacher as a facilitator (NCTM, 1991, 2000). Pre-service programs are now presenting curricula that are Standards-based (Cooney et al., 1998; Hart, 2002b; Van Zoest & Bohl, 2002; Wilkins & Brand, 2004). Since most mathematics teachers experienced a teacher-led direct approach in their own primary and secondary education, they encounter a conflict between their own education and their pre-service education as they enter their own classroom. The change from traditional to Standards-based teaching in the field of mathematics requires repeated efforts by teachers and time for them to modify their teaching style (NCTM, 2000). The purpose of the study was to contribute to an understanding of the relationship between the beliefs of secondary mathematics teachers who have participated in a Standards-based pre-service education and their teaching practices using a Standards-based perspective. This study was guided by the following research questions:
The research questions stemmed directly from the conceptual framework, literature review, and purpose of the study. The research questions were all exploratory. This study contributed to the scarcity of research concerning the current beliefs and practices of secondary education teachers who participated in a Standards-based pre-service education (Frykholm, 2004; LaBerge & Sons, 1999; Phillip, 2007). Qualitative, descriptive, case study research as defined by Merriam (1998) was chosen as the methodology for this particular study because the goal was to obtain a “rich, ‘thick’ description of the phenomenon under study” (p. 29) and to “study the experience of real cases operating in real situations” (Stake, 2006, p. 3). Graduates from a large, public research university provided an excellent opportunity to research secondary mathematics teachers who have participated in a Standards-based pre-service education. In order to gather a diverse sample for the qualitative portion of the study, a purposeful, maximal sample was selected from secondary mathematics education graduates who returned a survey exploring mathematics teachers’ beliefs and practices. In this study, five teachers were selected were for individual case studies. All of the mathematics teachers experienced a traditional pre-college education while they all participated in a pre-service education that stressed a Standards-based philosophy. However, the teachers' beliefs were very diverse at the completion of their pre-service education. The total atmosphere in which each teacher was currently teaching also differed widely by curriculum, administration, resources, etc. The observation of the case-study participants occurred during one school semester. Data sources included in this study consisted of multiple sources: a survey about teachers’ beliefs and practices; classroom observations; Reformed Teaching Observation Protocol (RTOP) instrument; two observation periods of five consecutive days; observation notes taken during each observation period; and post-observation interviews. The data were triangulated to analyze the results in light of the research questions. Results and Conclusions References: Cooney, T., Shealy, B., & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. Journal for Research in Mathematics Education, 29(3), 306-333. 5th Annual Pre-Session Information|General Conference Information |
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| Title: How Alignment/Misalignment of Beliefs and Teaching Practices Effect the Internship Experience
Presenters: April C. Parker, Regional Coordinator of General Studies, Southeast Region and Outline of Presentation: One of the biggest challenges to NCTM’s proposed change(s) has been changing teachers’ views of mathematics. Up to this point, math has always been associated with following the teacher’s rules and finally getting the “one right answer” (Taylor, 2002). Now, teacher educators and mathematics supervisors must “move teachers away from mathematics as they have most likely experienced it as students for over a decade and guide them toward a view of mathematics that is more consistent with the standards” (Taylor, 2002, p. 138). Ultimately, teachers must build a new image of teaching and learning (Taylor, 2002). Taylor (2002) reported that teachers can be categorized into one of two states of being. The first is the teacher in motion. These are the teachers that see themselves as learners. Because they view themselves as learners, they are more likely to evolve and grow in their teaching (Taylor, 2002). The second is the teacher that is at rest. These are the teachers who see themselves as having completed their fundamental learning upon receiving their certification. These teachers tend to make only superficial changes to their teaching if they make any changes at all (Taylor, 2002). According to Taylor (2002), in order for any kind of significant change to occur, teachers must continually reflect on their teaching, reflect on how their teaching affects their students, seek professional development, and be willing to make changes based on the new understanding(s) they gain from the whole process. Taylor (2002) recommended a strategy of immersion to help overcome the above mentioned challenges. The immersion strategy is designed to encourage pre-service mathematics teachers to implement standards-based teaching upon entering the field as a certified teacher. According to Taylor (2002), there are three key factors to immersion. First, the teacher educator must have standards-based materials readily available for the pre-service teachers and use them on a regular basis with the pre-service teachers (Taylor, 2002). The second key to immersion is to immerse the pre-service teacher in both theory and practice by engaging them as mathematical learners with an inquiry approach (Taylor, 2002). Bristor et. al. (2002), stated that many times, “teacher preparation programs fail to link theory with practice, leave content area knowledge disconnected from methods, and do a poor job of relating instructional practices to learning and development” (p. 689). The third key of immersion is to transition the pre-service mathematics teacher into the real classroom. This can sometimes be an issue if there is inconsistency between the kind of teaching the pre-service teacher has been prepared for and the experience they have through their field experiences and student teaching. Taylor (2002) stated that if this type of inconsistency occurs, the teacher educator would then have to find a way to bring the two worlds closer together. According to Taylor (2002), the best way to avoid inconsistencies is to make sure the pre-service teacher gets placed with a teacher whose teaching is in line with the standards. If no such teachers exist, professional development should be done to train the needed cooperating teachers (Taylor, 2002). Peterson and Williams (1998) warn that if this does not occur, the pre-service teachers will be less inclined to utilize the standards-based strategies they have been taught throughout their teacher preparation program. As stated by Pourdavood, 1999), existing classroom norms and the cooperating teachers’ methods of instructions have profound impact on pre-service teachers’ beliefs and practices. According to the research, it seems that if pre-service teachers are to internalize coherent applications to teaching and learning mathematics, the environment in which they complete their internship and the support they receive need to be consistent with the principles being advocated in their professional preparation program (Vacc & Bright, 1999). As quoted by Vacc and Bright: It seems that extensive field experiences and linkages between theory and practice are essential elements for changing pre-service teachers’ beliefs (Vacc & Bright, 1999). The problem is finding field placements that support the philosophy of reform-based teacher preparation programs. According to the research, recent evidence suggests that incongruent field placements may be counterproductive and damaging in developing open-minded attitudes toward reform among pre-service teachers (Curcio & Artzt, 2005). Curcio and Artzt (2005) further stated that in order for fieldwork to be most effective, it needs to take place in an environment in which the philosophy is aligned with that of the teacher preparation program. The bottom line is that the framework underlying the content presented in mathematics methods courses needs to be consistent with the framework of the mathematics education program that pre-service teachers observe and implement during field experiences. If the two frameworks are not in sync, the theories and concepts presented during the mathematics methods course may not seem plausible and may ultimately be rejected by the pre-service teacher (Vacc & Bright, 1999). Research Design and Methodology: The researcher utilized case studies of four different cooperating teacher/pre-service teacher pairs located in three different school systems. The cooperating teachers were all teachers currently involved in the systemic change project. The pre-service teachers were all students that were completing requirements in a mathematics education program that focused on mathematics reform. Various types of data were collected in an attempt to better understand the pairs, including: a beliefs survey that was completed by the cooperating teachers and pre-service teachers at the beginning and the end of the study; observations of the pre-service teachers in their methods course; four classroom observations of the cooperating teachers; three classroom observations of the pre-service teachers; interviews with the cooperating teachers at the beginning and end of the study; and interviews with the pre-service teachers at the beginning and end of the study. This data was then analyzed and used to draw conclusions about each pair. Results: With the exception of one pre-service teacher, all others eventually aligned with their respective cooperating teacher. The pre-service teachers complied with their cooperating teachers instead of implementing the newer methods they had been taught in their methods courses, which may be due to the comfort level of the cooperating teachers. The cooperating teachers were comfortable with allowing the pre-service teachers to try new strategies but could not help them refine less-effective strategies. As a result, the pre-service teachers generally reverted to the teaching methods of their cooperating teachers, a comfortable solution for both parties. 5th Annual Pre-Session Information|General Conference Information |
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Title: Using a High School Reform Curriculum in a Methods Course for Preservice Secondary Mathematics Teachers Presenters: W. Gary Martin, Department of Curriculum and Teaching, Auburn University, Auburn, Alabama Outline of Presentation: Preservice teachers face a number of obstacles in being able to implement the vision of the NCTM Standards (2000, 1991, 1989) in their future mathematics classrooms. First, most preservice teachers have themselves experienced mathematics in ways that are fundamentally different from the Standards (Ball, 1996), which may limit their understanding of the new vision. Second, they may not possess the necessary depth of mathematical knowledge (Stump, 1997; Llinares, 2000) or even understand that they only possess a surface knowledge of mathematics. Third, they may have limited opportunities to “practice” the new instructional strategies implied by the Standards. To address these obstacles, I have implemented intensive attention to a unit taken from the Interactive Mathematics Program (Fendel et al., 2000) in my senior-level methods class for preservice secondary mathematics teachers. In this talk, I will describe how I use these experiences to help my students better understand the NCTM Standards and how they can be enacted in the high school mathematics classroom. 5th Annual Pre-Session Information|General Conference Information |
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Title: Assessing the Effects of Mathematics Content Courses Designed Specifically for Middle Childhood Mathematics Education Majors at Xavier University Presenters: 1) Joy Moore, Mathematics Department, Xavier University, Cincinnati, Ohio 2) Sheila Doran, Mathematics and Computer Science Department, Xavier University, Cincinnati, Ohio Outline of Presentation: MATH 211: Foundations of Arithmetic for Middle Childhood Teachers: Concepts necessary for understanding the structure of arithmetic its algorithms and properties (with whole numbers, integers, rational and irrational numbers), basic set theory and introductory number theory. Implemented Fall 2006. MATH 212: Geometry and Measurement for Middle Childhood Education Majors: Concepts necessary for an understanding of basic geometry: shapes in one, two, and three dimensions, scientific measurement and dimensional analysis, congruence and similarity of figures, compass and straightedge constructions, transformations, coordinate geometry, conjecture and proof, perspective drawing and introductory trigonometry. Use of computer software to explore geometric concepts. Implemented Spring 2007. MATH 213: Algebra Concepts for Middle Childhood Education Majors: Development of algebraic problem solving, polynomials, linear, quadratic and exponential equations, functions, pattern representation, sequences and series. Use of technology and manipulative materials in the teaching of Algebra. Implemented Fall 2007. MATH 214: Math Problem Solving for Middle Childhood Education Majors: Problem solving, drawing from a wide range of school mathematics topics, logic, combinatorics, and basic probability theory. Implemented Spring 2008. The research team investigated the following question: What effect has the newly developed middle childhood mathematics courses had on the content knowledge and self efficacy of the pre-service middle childhood mathematics candidates? The subjects of the study included all middle childhood mathematics majors at Xavier University, Cincinnati Ohio, who have taken or will take the Middle Childhood Mathematics Praxis II Test from September 8, 2007 through September 30, 2008. The Middle Childhood Mathematics Praxis II Assessment measures both the general and subject specific teaching skills and content knowledge of middle childhood mathematics educators. The test consists of forty multiple choice and three open response questions. Content categories included in these questions include arithmetic and basic algebra; geometry and measurement; functions and their graphs; data, probability, statistical concepts, discrete mathematics and problem-solving exercises. Process categories include problem solving, reasoning, proof, connections, representation and use of technology. Two thirds of the candidates score is based on their performance on the multiple choice and one third on the open response questions. The Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) was adapted from the Science Teaching Efficacy Belief Instrument for the purpose of this evaluation. The instrument measures two aspects of teacher efficacy, the personal teaching efficacy, (PTE), and the teaching outcome expectancy, (TOE). The PTE subscale consisted of 13 items and the TOE subscale was comprised of 10 items. The MTEBI was structured using a 5-point Likert scale, where 5 is “Strongly Agree,” 4 is “Agree,” 3 is “Uncertain,” 2 is “Disagree” and 1 is “Strongly Disagree.” Questionnaires accompany the MTEBI instruments that ask the student to compare the General Mathematics courses taken to those designed specifically for the middle childhood educator in regards to enhancing self efficacy towards teaching mathematics, along with providing content knowledge needed to take the Middle Childhood Mathematics Praxis II test. Participants also took Diagnostic Mathematics Assessments for Middle School Teachers developed by The University of Louisville Center for Research in Mathematics and Science Teacher Development (CRMSTD). The assessments serve two purposes: (1) to describe the breadth and depth of mathematics content knowledge so that researchers and evaluators can determine teacher knowledge growth over time, the effects of particular experiences (courses, professional development) on teachers’ knowledge, or relationships among teacher content knowledge, teaching practice, and student performance and (2) to describe middle school teachers’ strengths and weaknesses in mathematics knowledge so that teachers can make appropriate decisions with regard to courses or further professional development. The assessments measure mathematics knowledge in four content domains (Number/Computation, Geometry/Measurement, Probability/Statistics, Algebraic Ideas). Each assessment is composed of 20 items—10 multiple-choice and 10 open-response. Middle Childhood Mathematics Praxis II test scores will be examined and grouped according to the number of new middle childhood mathematics courses the student completed prior to taking the Praxis II test. The groups are: Group One: Completed the math requirements without any new courses, Group Two: Completed at least one, but not more than two new courses; and Group Three: Completed at least three new courses. Comparisons will be made between the mean differences of the participants. A two-tailed t-test for dependent samples will be calculated to determine if the degree of change in Praxis II scores among the groups is significant with a .05 alpha level. Scoring of the Diagnostic Mathematics Assessments for Middle School Teachers is performed by the CRMSTD. At the writing of this proposal, data collection and analysis is ongoing. An interim report is due August 15, 2008, with the final report due December 12, 2008, thus this presentation will include preliminary results of our analysis. 5th Annual Pre-Session Information|General Conference Information |
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Title: Lifelong Learning: Mathematics Faculty Work to Improve Their Practice Presenter: Julie Cwikla, Department of Mathematics, University of Southern Mississippi Gulf Coast, Outline of Presentation: The National Council of Teachers of Mathematics and the National Science Teachers Association advocate professional teaching standards that support learning environments that are contextual and meaningful for the learner, are student-centered, and involve the learner as an active participant in their education. The empirical data that support these recommendations are not only applicable to the K-12 environment but also to higher education and undergraduate studies. However, little empirical data have accumulated to guide the professional development for faculty members in higher education and how they might learn to teach to these Standards. This session will (1) report findings from a five year project that involves five institutions in Mississippi to provide support for the professional development of mathematics faculty in higher education and (2) allow for the exchange of ideas about professional development in higher education. Long-term retention and understanding for undergraduate students are most likely to develop from student-centered, question-generating exercises (King, 1992) and inquiry based learning in the collegiate classroom. An interview study of university students further supports student-faculty interactions as critical for student learning, concluding that for students’ learning, meaningful classroom interactions with the professor ranked as one of the six most important classroom features (Clarke, 1995). However, in a study of university faculty and the stresses in their profession, “interactions with students” were found to be one of the facets of their profession that brought about the most angst (Gmelch, Wilke, & Lovrich, 1996). Sherman, Armistead, Fowler, Barksdale, & Reif (1987) describe a four-step developmental process faculty members undergo as they improve their teaching. Faculty members begin by simply presenting information to their classes in the first stage. It is not until the fourth stage that the faculty member can facilitate a classroom that involves meaningful interactions between the students, the content, and themselves. Based on these findings it is likely that there are many undergraduate students who are dissatisfied with their university courses because (1) faculty might have limited interactions with students and (2) it is not until the fourth stage of faculty development that their teaching reaches a level to incorporate meaningful classroom interactions with the student and content. Universities and teachers’ colleges nationally are concerned about elementary mathematics teacher preparation. These students in general are not exceptionally strong mathematically (Ball, 1990; Post, Cramer, Harel, Kieren, & Lesh, 1998; Silver, & Stein, 1996) and in most cases did not learn K-12 mathematics in a standards-based environment. But these future teachers will be expected to facilitate a reform-minded mathematics classroom. Therefore, it is the task of the preservice program and this project’s Professional Mathematics Educators’ Forum (PME) to help future teachers shift their views about mathematics learning as well as extend and/or correct their understanding of the content. The faculty members (N=18) who were part of this forum called the Professional Mathematics Educators Forum (PME) will be the focus of this presentation. The eighteen faculty members’ educational backgrounds vary from masters level mathematicians and computer scientists to doctorates in mathematics education. These faculty members’ classroom practice is not uniform in the group, varying from traditional lecture format to student-centered group investigation. Similarly their beliefs about teaching and learning vary widely. Their beliefs and current practice are being monitored and used as a lens to examine their reactions and reflections on Standards based practice, the ways they analyze and then use K-8 video excerpts in their mathematics education courses, and how they learn from watching classroom videos of other PME members. Despite their differences, they are all serving the same student population, future K-8 teachers, and share a common language. This year’s presentation will provide a full 5-year project timeline of the professional development events and activities the PME have completed. I am attempting to partially answer the global questions: How can faculty in higher education develop a better rapport with their students and better serve them as learners in a Standards based learning environment? This National Science Foundation Early CAREER funded project is exploring this question by fostering a professional learning community that has helped faculty members: (1) be more attentive to their students’ understanding of the content, (2) provide a more inquiry based learning environment for undergraduate students, and (3) better address the learning needs of their undergraduate students. The professional experiences and growth of the mathematics faculty members in the PME will be shared during this presentation. It is hoped this session will provide a presentation and spawn discussion of this study and others in the audience to elaborate issues and constraints unique to professional development in higher education. Session Timetable
5th Annual Pre-Session Information|General Conference Information |
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Title: Statewide cooperation to improve the mathematical education of elementary teachers. Presenter: Jim Gleason, Department of Mathematics, The University of Alabama, Tuscaloosa, Alabama Outline of Presentation: In the state of Alabama, 30% of 4th graders and 45% of 8th graders scored below the basic proficiency level in mathematics on the 2007 NAEP . This poor performance in mathematics hinders racial equity and limits the economic opportunities for individuals and the state . This deficit in the mathematical education of our children is a demonstration of a vicious cycle within our mathematics education system. Many of our elementary students are weak in mathematics because their teachers are generally weak in mathematics and teach the way they were taught . In an effort to break the cycle of poor mathematics education, we followed the recommendation of the conference held at The University of Chicago in 1991 on the Mathematical Preparation of Elementary School Teachers to create an institute for the college faculty in Alabama who teach the mathematics courses for pre-service elementary teachers. This two-day professional development workshop had three primary objectives:
The primary focus of this talk is on the second objective regarding the articulation of the objectives for the mathematics courses for elementary teachers. In particular, we will describe the objectives stated by the participants before attending the workshop and after completion. Additionally, we will give a summary of the current state of the mathematics courses in Alabama including the influences of the statewide articulation agreement and the Alabama Mathematics, Science, and Technology Initiative. Kenschaft, P.C. (2005). Racial equity requires teaching elementary school teachers more mathematics. Notices of the AMS, 52(2): 208-212. Committee on Prospering in the Global Economy of the 21st Century: An Agenda for American Science and Technology, National Academy of Sciences, National Academy of Engineering, Institute of Medicine (2007). Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future. The National Academies Press: Washington, D.C. 5th Annual Pre-Session Information|General Conference Information |
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Title: Getting Education and STEM Faculty on the Same Page Presenter: Marilyn E. Strutchens, Department of Curriculum and Teaching, Auburn University, Auburn, Outline of Presentation: This session focuses on a series of seminars that have been conducted at Auburn University to help develop a common vision for preservice and inservice mathematics education among mathematics education and STEM faculty members, and their graduate students involved with the MSP (TEAM-Math). The seminars have focused on research and activities related to teachers’ pedagogical content knowledge, reform curriculums across the grades, and content courses for both elementary and secondary teachers. 5th Annual Pre-Session Information|General Conference Information |
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Title: Teaching Mathematical Concepts through Problem Solving Presenter: Deirdre C. Greer, Early Childhood Education, Columbus State University, Columbus, Georgia Outline of Presentation: I. What is problem solving? Often, pre-service and in-service teachers misunderstand problem solving. Based on their own school experiences, they assume that problem solving refers to word problems. This misconception can lead to a superficial implementation of problem solving at the elementary level. Research shows that learning mathematical concepts through problem solving can develop understanding. An understanding of problem solving and the framework for problem solving instruction is an essential element of pre-service teachers’ education and in-service teachers’ professional development. II. Selection of appropriate problems The implementation of a problem-solving curriculum begins with the selection of appropriate problems. Textbook word problems often lack the depth necessary for true problem solving. If pre-service and in-service teachers are not able to select appropriate problems, their attempts at implementing a problem-solving curriculum will not be successful. III. Assessment & planning based on students’ needs If teaching mathematical concepts through problem solving is to be successful, pre-service and in-service teachers must be able to examine student work, assess their developing understanding of the underlying concepts, and plan for subsequent lessons that will promote further development. The ability to perform this critical component of teaching through problem solving requires the pre-service and in-service teachers to identify the mathematical concepts that are inherent in a particular problem. IV. Facilitating the development of mathematical thinking A critical component of teaching mathematical concepts through problem solving is the facilitation process. While students must be allowed to develop their own understandings, pre-service and in-service teachers must understand when and how to intervene and how to make the mathematical concepts and connections clear to the students. Additionally, the ability to facilitate students’ sharing of their solution methods requires pre-service and in-service teachers’ to be able to understand students’ correct and incorrect thinking. V. The role of content knowledge in teaching problem solving Pre-service and in-service teachers must have sufficient mathematical content knowledge to identify the mathematics involved in a given problem, to follow and understand students’ mathematical thinking, and to plan effective follow up lessons. Pre-service and in-service teachers who lack the necessary content knowledge tend to rely more on algorithms in their teaching and are less likely to allow students to build their own understanding. The presentation will focus on each of these components and will include examples from my experiences working with children, pre-service, and in-service teachers. I will also share some research data from my experiences teaching mathematics through problem solving with a class of third graders that shows the effectiveness of this method. 5th Annual Pre-Session Information|General Conference Information |
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Title: Who are we teaching and how do we teach them? Presenters: 1) William O. Bond, Graduate Student, University of Alabama at Birmingham, Birmingham, 2) John C. Mayer, Department of Mathematics, University of Alabama at Birmingham, Outline of Presentation: “The Wu Li master does not teach but the student learns,” or so says Gary Zukav in his book The Dancing Wu Li Masters, a book on quantum physics for a general audience. We use this maxim as our point of departure to challenge the traditional paradigm of the sagacious mathematician delivering carefully packaged knowledge to the eager (or not so eager) student.
We will discuss an approach taken in response to these questions by the Greater Birmingham Mathematics Partnership. 5th Annual Pre-Session Information|General Conference Information |
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Title: Changes in Content Knowledge and Pedagogical Content Knowledge of Algebra Teachers Resulting From Participation in Professional Development Presenter: Joy Black, Mathematics Department, University of West Georgia, Carrollton, Georgia Outline of Presentation: Algebra I serves as a gateway course in dividing students into classes with significantly different opportunities to learn and in turn differences in future success in more advanced mathematics courses (RAND, 2003), to college preparation (Pascopella, 2000, Lawton, 1997, Chevigny, 1996, Silver, 1997, Olson, 1994),and for the preparation of the world of work (Silver, 1997). Teachers play a key role in ensuring that all students have the opportunities and experiences needed to learn mathematics (Mewborn, 2003). What knowledge do Algebra I teachers need to posses in order to ensure all students have equitable opportunities to learn Algebra I? While limited research has been conducted in the areas of teacher content knowledge and pedagogical content knowledge of elementary teachers, far fewer studies have focused on these same types of knowledge of secondary teachers. These studies have shown that teacher’s content knowledge is often thin and inadequate to provide the instructional opportunities needed for students to successfully learn mathematics (Ball, 1998a, 2003b, Ball & Bass, 2000; Fuller, 1996, Ma, 1999, Mewborn, 2001, Stacy, et al., 2001). This study suggests results similar to studies done with elementary teachers, algebra teachers have inadequate content knowledge and pedagogical content knowledge for successful mathematics instruction. Four areas of this study will be addressed. First, it might be noted that a mathematics degree does not always ensure the content knowledge and pedagogical content knowledge to teach mathematics (Ball et al., 2001). Results from a written instrument given to sixty-five teachers indicated strong procedural knowledge, weak conceptual knowledge and limited use of mathematical processes as well as weak pedagogical content knowledge. Second, four case study teachers, from this pool of sixty-five teachers, were further studied with attention given to their content knowledge and pedagogical content knowledge and its reflection in their instructional practices. Third, case study teachers exhibited increases in both types of knowledge after attending professional development provided through an NSF grant that gave attention to increasing both of these types of knowledge by providing opportunities for teachers to revisit the big ideas of mathematics as well as using the types of pedagogical content knowledge they would be expected to use. These results suggest that coursework and professional development should be designed to provide these same types of opportunities for pre-service and in-service teachers. Last how these changes in content knowledge and pedagogical content knowledge were manifested in instructional practices by these case study teachers will be noted. 5th Annual Pre-Session Information|General Conference Information |
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Title: Achieving Proficiency on State Mathematics Standards for all Pre-service Teachers Presenter: S. Kathy Westbrook, Mathematics & Statistics Department, University of South Alabama, Mobile, Alabama Outline of Presentation: As a result of the recently mandated mathematics standards for all teachers being certified in Alabama, an online computer module was developed to “remediate” and assess pre-service teachers. In 2008, more that 300 students were assessed, and these students included all secondary and elementary majors in the college of education at the University of South Alabama. Consequently, students’ mathematical training varied in content, scope, and institution. An analysis of the assessment compared types of questions missed and conceptual misconceptions to students major and mathematics course taking history. The results of the analysis will be shared with participants in this session as well as the structure and format of the modules and the assessment. Other institutions might consider these modules or a similar format to address state standards for teacher certification. Questions examined by the analysis:
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Title: A Model Teacher-Scholar Program in Mathematics Presenter: Saad I. El-Zanati, Department of Mathematics, Illinois State University, Normal, Illinois Outline of Presentation: We report on the development, implementation and evaluation of a model teacher-scholar program in secondary mathematics. The yearlong program consists of two junior/ senior level research capstone courses. In the first course, Introduction to Research in Mathematics (offered in the spring), students explore several research topics (from the instructor's main research interest/expertise areas) with emphasis on experimentation, conjecture, careful justification, and clear, precise reporting. The second course, Research in Mathematics II (offered in the fall), places emphasis on further examination of specific research topics and on writing and disseminating results. The main objective of the program is to graduate teacher-scholars. Teacher-Scholars are highly qualified teachers who have experienced scholarship in mathematics in a setting that emphasizes the interconnections among theory, procedures and applications and who "develop habits of mind of a mathematical thinker" (CBMS, 2001). A two-year run of the program is being supported by a grant from the Division of Undergraduate Education at the National Science Foundation. 5th Annual Pre-Session Information|General Conference Information |
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Title: A Reflective Project for Pre-service Teachers in University Mathematics Courses Presenter: Angela Hodge, Departments of Mathematics and Teacher Education, North Dakota State Outline of Presentation: As part of the requirements to complete their undergraduate degrees pre-service secondary mathematics teachers (PSMTs) complete many mathematics courses, including a geometry course (Committee on Undergraduate Program in Mathematics [CUMP], 2004). The role of this coursework in their classroom teaching; however, is not always apparent to PSMTs (Author). This presentation describes a study in which the mathematics instructor was able to get the PSMTs thinking about the connections between classroom teaching and axiomatic geometry throughout a semester long geometry course. As a final project, all members of the class reported on how the course would help them in their future careers. This presentation serves three purposes: (a) to describe a project that can easily be integrated into university geometry courses, (b) to report on the responses from PSMTs, and (c) to discuss consequent implications for other mathematics courses populated in part by PSMTs. Participants: Fourteen students were enrolled in the geometry course and 14 students participated in the class. Of these 14 students, nine of them were PSMTs. The students were placed into groups near the four groups at the beginning of the semester. Each group contained at least one PSMT. The following paragraphs will describe the portion of the project aimed at the PSMTs. Project: Each group was expected to make a 45-minute presentation to the class on how learning axiomatic geometry can help secondary teachers in their classrooms. The presentations could be given in any form (e.g., Powerpoint, activity based, lecture). The only stipulation was that each group had to have handouts for each member of the class. Specific topics taught in the course were to be used to illustrate points made by each group. The relevance of the class as a whole was also expected to be apparent in each group’s presentation. Other applications of geometry and/or the history of geometry were also allowed to supplement each group’s claims. Here were some possible supplemental topics: (a) plane tilings, (b) fractals, (c) development of Lobachevskian geometry, or (d) development of Riemennian geometry. The groups were also encouraged to examine high school or middle school textbooks to support their assertions. In addition to their presentations, the groups were required to include a summary of their projects. This summary was required to include, but was not limited to, answers to the following questions:
These questions were targeted at obtaining the students’ perceptions of why PSMTs should take a university geometry course to help them prepare for classroom teaching. Results: The group presentations contained two categories of responses to the questions relating the axiomatic geometry course to secondary mathematics classroom teaching. The first category of responses was related to the structure of the class. The second category compared specific topics covered in the axiomatic geometry course to specific topics the PSMTs may teach in a secondary classroom. In this presentation, I will discuss both types of connections made by the PSMTs. The geometry students claimed that the axiomatic geometry class was structured in a manner such that it would benefit future secondary mathematics teachers. This structure included working in groups, teaching other students, and learning in a non-lecture based fashion. Most of the class period was used for students to work on problems learning from each other while the instructor moved around the room acting as a facilitator of learning rather than the bearer of knowledge. The students reported that seeing a non-traditional type of learning and teaching in one of their own mathematics classes would help future teachers be prepared for reform-oriented classrooms. In addition to the structure of the course, the students stated in their presentations and papers that the topics in the axiomatic geometry course related to secondary mathematics. Some of these topics related directly to the secondary classroom such as Euclidean geometry. Other topics such as projective geometry helped the students to understand how an axiomatic system develops and how to help secondary mathematics students learn how to construct mathematical proof. Further details, including specific examples, will be discussed in the presentation. Discussion: The axiomatic geometry project provided the students in the course, in particular the PSMTs, a way to think about and discuss how the course related to their future careers. The project and the work put into the project addresses a need called for by research groups such as the LIST THESE for PSMTs to make connections between their content courses and their further teaching. The project could be linked to a number of upper-division mathematics courses. Integrating such projects into mathematics curriculum serves several purposes: (a) to help mathematics professors understand the future work of their students, including PSMTs, (b) to engage students in thinking about how their coursework relates to their future careers, and (c) to provide discussion related to the relevance of abstract mathematics coursework in the classroom. During this presentation, time will be allotted for further discussion on the implications of such projects in university mathematics courses. Reference Barker, W., Bressoud, D., Epp, S., Ganter, S., Haver, B., & Pollatsek, H. (2004). Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide. Washington, DC: Mathematical Association of America. 5th Annual Pre-Session Information|General Conference Information |
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Title: Using Algebra Video Case Studies for Professional Development with Middle School Math Teachers Presenter: Lisa Kasmer, Department of Curriculum and Teaching, Auburn University, Auburn, Alabama Outline of Presentation: As number and computation are the focus of elementary school mathematics, the primary concentration in middle school mathematics classrooms is on algebra. Beyond middle school, understanding algebraic concepts is fundamental not only for the ongoing study of mathematics in high school and college but also for citizenry. Because students’ proficiency in algebra unlocks both career and educational opportunities, algebra has long been considered the gatekeeper of educational and vocational success (Christmas & Fey, 1990; Phillips, 1995; RAND Mathematics Study Panel, 2003). The significance of algebra as a core subject of emphasis in K-12 mathematics education is substantiated in documents such as Principles and Standards for School Mathematics (NCTM, 2000), Benchmarks for Science Literacy, (AAAS, 1993) and National Science Education Standards (NRC, 1996). The Principles and Standards for School Mathematics specifically advocates with respect to algebra that students should (a) understand patterns, relations, and functions; (b) represent and analyze mathematical situations and structures using algebraic symbols; (c) use mathematical models to represent and understand quantitative relationships; and (d) analyze change in various contexts (NCTM, 2000). In their analysis of grade-level expectations pertaining to algebra, Newton, Larnell, and Lappan (2006) found that 39 of the 42 states they analyzed expected students to study algebraic expressions in grade 7, and 32 states expected students to study algebraic expressions in grade 8. By grade 8, nearly 200 grade-level expectations nationally were recorded pertaining to algebra. The College Board Standards for College Success (2006) further delineated the algebraic focus for middle school students. The College Board maintained that emphasis should be centered on the development and of the meaning of rates of change in a variety of contexts. The College Board asserted that students should be provided opportunities to interpret contextualized situations using various types of representations and “reason with expressions, equations, and functions to model and solve problems in linear settings and to investigate nonlinear settings (exponential and quadratic) in order to further their understanding of linear and nonlinear settings” (College Board, 2006, p. 21). The teaching of algebra or for that matter mathematics in general requires teachers develop the necessary skills and content knowledge. While middle school mathematics teachers A Case of Middle School Professional Development Often teachers rely on professional development to hone their knowledge and practice. However, professional development opportunities to specifically address the needs of middle school mathematics teachers in a suburban school district located in southwestern Michigan were virtually non-existent. Many of these teachers understood the importance of teaching algebra and felt somewhat “comfortable” with the content, but also expressed frustration with their inability to bridge between this content and practice. Learning and Teaching Linear Functions: Video Cases for Mathematical Professional Development, 6-10 (Seago, Mumme, & Branca, 1999) provided 10 middle school mathematics teachers an opportunity to further explore some of the “problems of teaching” (Lampert, 2001) characteristic of the challenges specific to teaching linear functions. Eight sessions offered over the course of 2 months were facilitated to focus on linear functions with an additional goal of teachers reflecting on their own teaching practices throughout the professional development segments with respect to the ideas brought forth during participant discussions during the sessions. The importance of linking the sessions to teaching practice and reflecting on those practices was considered paramount to teachers applying their new knowledge in their own classrooms. Special attention was given to both the socio-mathematical norms developed during the professional development sessions as well as the mathematical knowledge for teaching which Ball and Bass (2000) describe as the mathematics teachers do to teach. The mathematical work of teaching (Ball, Bass, & Hill, 2004, p. 59), which situated this professional development, is described below:
Figure 1 Mathematical work of teaching (Ball, Bass, & Hill, 2004, p. 59) Throughout these sessions it was noted that teachers were able to begin to anticipate and consider alternative solutions to the tasks, pose questions to colleagues that “pushed” their thinking, and improve their propensity to reflect on their own teaching practices. Teachers also reported they were becoming more cognizant of students’ approaches to tasks and the corresponding reasoning to their solutions. Of equal importance, the 10 teachers in this professional development series began to think about the nature of the tasks they presented to students in terms of what ideas could potentially be problematic for their students, and consequently consider the strategies they would enact to address these struggles. Furthermore, this reflective process engaged teachers in thought provoking opportunities to begin to get at their own instructional practices. 5th Annual Pre-Session Information|General Conference Information |
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Title: The Mathematical Education of Teachers: One University’s Approach Presenters: 1) Cecelia Laurie, Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 2) Julie Herron, Department of Curriculum and Instruction, University of Alabama, Tuscaloosa, Alabama Outline of Presentation: The Connection between the Two Departments In 2003, professors from the mathematics and education departments collaborated to create a series of three mathematics courses for the elementary education majors to take to meet the mathematics requirements for the university as well as the teacher education program. The teacher education program at UA requires the students take 4 math courses that are above Math 100 (Intermediate Algebra). The collaborative efforts resulted in the development of following courses: 1) numbers and operations, 2) geometry and measurement, and 3) algebra, data analysis, statistics, and probability. The purpose of these courses is to provide the content knowledge needed for teaching elementary mathematics. The courses were developed based on results from educational research and recommendations of national organizations (in particular, the CBMS Mathematical Education of Teachers report). The framework for these courses is based on two big ideas – profound understanding of fundamental mathematics as described by Liping Ma and mathematical knowledge for teaching as described by Ball & Bass. The Data 5th Annual Pre-Session Information|General Conference Information |
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Title: A Triad Approach to Elementary Mathematics Teacher Preparation Presenter: 1) Megan Burton, Instruction and Teacher Education, University of South Carolina, Columbia, South Carolina 2) Debra Geddings, Mathematics Department, University of South Carolina, Columbia, South Carolina Outline of Presentation: This pre-session proposal relates to the theme of improving mathematics education offered by institutions of higher learning by addressing a program that connects content exploration, examination of pedagogy, and real school experiences. Pre-service elementary teachers need to be equipped with conceptual knowledge of both the discipline of mathematics and the school curriculum of mathematics as well as an understanding ofhow these two areas relate (NCTM, 1991). In addition to knowing the mathematics, teachers need the ability to hear and guide individual students through mathematical situations flexibly and with understanding of diverse needs (Ball & Bass, 2000). Field experiences allow one to explore student thinking and develop understanding with assistance from experienced educators (Mewborn & Stinson, 2007). Feiman-Nemser (2001) suggests that by analyzing student work, interviewing students, and studying other teachers, teachers can develop the tools to study teaching. When these activities are carried out in the company of other teachers, they advance norms for professional discourse as teachers gain confidence in critically examining teaching. This belief guided the collaborative efforts by faculty in the mathematics department and college of education to create meaningful mathematical content and methods courses for pre-service teachers at the University of South Carolina. This session will describe the positive affective and cognitive benefits of connecting pre-service teachers to students in the elementary schools during content and methods courses. One innovation in the content courses that has been a particular success is the “Pen Pal/Math Buddies” journal program. This program pairs the pre-service teachers with elementary students at a local elementary school. Pen pal journals provide opportunities for students to develop mathematical problems, explore student responses, and connect these with the content they have learned and the NCTM standards. The culminating activity for this project is a celebration where the elementary students take a field trip to the USC campus to meet their math penpals. The methods course is taught at a local elementary school. Moyer and Husman (2006) found that pre-service teachers whose methods courses were held at an elementary school seemed more focused on developing the skills necessary to become a teacher. The pre-service teachers in the methods course spend time weekly working with elementary students. They are involved in observing how elementary students approach problem solving and how they communicate their mathematical thinking. Class discussions and connections to readings follow their sessions with the elementary students. The collaboration between the departments to connect experiences to each other and to the local schools through pen pals in the content courses and working directly with students during the methods course creates a unique situation. The triad of collaboration and experiences between the mathematics department, college of education, and local schools has been seen to enhance preservice preparation through observations, student reflections, and case study interviews. The session will begin by describing the courses, displaying student work, and sharing insights gained from the two years of coordinated coursework. If time permits, there will be a question/ answer session and participants will be asked to share strategies they have used to connect elementary mathematics methods and content courses to real world situations. This format was chosen as it appears to be the most effective way to share the information and foster reflection by participants. References: Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and 5th Annual Pre-Session Information|General Conference Information |
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Title: Using a MKT Developmental Framework to Guide Instruction in Our K-8 Mathematics Specialization Program Presenters: 1) Sherry L. Meier, Mathematics Department, Illinois State University, Normal, Illinois 2) Beverly S. Rich, Mathematics Department, Illinois State University, Normal, Illinois Outline of Presentation: Illinois State University is uniquely positioned within mathematics education. They have the largest secondary mathematics teacher education program in the State of Illinois, as well as one of the three largest in the country. The Mathematics Department also houses an undergraduate mathematics specialist program for elementary and middle level teachers, as well as Masters and PhD programs in math education. Our elementary and middle-level programs Overview of our MKT Framework The framework of indicators includes four components of deep and connected mathematical knowledge for teaching, and provides a five-level progression of indicators that demonstrate growth for each component. The four components we have identified as central to growth in MKT were the students’ ability to: explain and justify their work, use multiple representations, recognize and generalize relationships among conceptually similar problems, and pose problems. Each component begins with an entry level of knowledge that is characterized by common content knowledge and procedures expected of any mathematically literate person, and builds to Level 4 which represents deep and connected mathematical knowledge for teaching. The framework is not linear, and the levels do not represent discrete jumps in ability. Students do not move strictly in one direction along a component row of indicators. Students will often loop back, as content areas change or the content progresses to more sophisticated or abstract concepts. Students will also frequently oscillate between levels before moving more consistently to the higher level. Students are rarely at the same level in all components simultaneously, unless they have already achieved deep and connected MKT. A student can be at level 2 in his/her ability to explain and justify and remain at the entry level in his/her ability to pose problems. However, one of the most striking findings in our development of the framework was the presence of an “anchoring” effect. That is, if one component area had not progressed, it hindered the advancement of other components as well. For example, students may have progressed in their ability to explain and justify, reaching level 2, but if they were unable to pose problems above an entry level, they stagnated in their ability to explain or justify as well and did not easily advance to level 3. So while we see the four components as separate, they are interconnected. This interconnectedness is clearly seen in students who possess deep and connected MKT. The framework Dr. Rich and Dr. Meier have developed has given the department a new lens through which to examine our courses and instruction. We are now able to look at individual classroom activities and assess how they are helping to improve a student’s MKT. In the past we have known the mathematical concepts being developed with various activities, but we sometimes struggled to see how these activities were helping students develop their MKT as well as their content knowledge. The manner in which the courses were structured was based on a constructivist approach to learning, but each course was focused specifically on the development of appropriate mathematical ideas, and often seemed to miss the mark in developing deeper connections needed for teaching related content. The framework provides a clearer picture of the development of various components of deeper connected understanding that teachers need, and helps instructors ensure they address all these components in the courses. 5th Annual Pre-Session Information|General Conference Information |
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Title: From Parker to Haley: Pre-Service Teachers Developing Geometry and Pedagogical Knowledge Presenters: 1) Kimberly Nunes-Bufford, Graduate Teaching Assistant, Curriculum and Teaching and 2) Mary Johnson, Instructor, Department of Mathematics & Statistics and Assistant Manager of TEAM-Math, Auburn University, Auburn, Alabama 3) Elizabeth Senger, Department of Curriculum and Teaching, Auburn University, Auburn, Alabama Outline of Presentation: For the past five years, Auburn University, along with other K-20 partners, has been involved in TEAM-Math (Transforming East Alabama Mathematics), a Math-Science Partnership (MSP) program funded by the National Science Foundation (NSF). As part of this systemic effort to improve the teaching of mathematics, the departments of Mathematics & Statistics and Curriculum & Teaching have been collaborating to improve the mathematical training of pre-service elementary teachers. Prompted by No Child Left Behind (NCLB), the professors in the Department of Mathematics & Statistics in Parker Hall revamped the Mathematics for Elementary Education courses. The primary change was to create three courses and select curricular materials that reflected recommendations of the Conference Board of the Mathematical Sciences (CBMS) and the National Council of Teachers of Mathematics (NCTM). Due to these changes, professors in the Department of Curriculum & Teaching in Haley Center have perceived differences in the students in their methods courses. In this presentation we will focus on the geometry and pedagogical knowledge of preservice teachers. First, we will review what is known about the geometric content knowledge of elementary teachers and consider how we can assess that knowledge. Next, we will look at a comparison of the new and old approaches in the teaching of the geometry and measurement course for elementary education (and other related) majors. Finally, we will discuss informal observations in subsequent methods courses as related to the Van Hiele levels. 5th Annual Pre-Session Information|General Conference Information |
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Title: The Preparation of Elementary Teachers at Austin Peay State University Presenter: Dorothy Ann Assad, Department of Mathematics, Austin Peay State University, Clarksville, Tennessee Outline of Presentation: The mathematics education faculty at Austin Peay State University (APSU) is part of the general mathematics faculty, and there is a unique collegial relationship within that department. Led by Dr. Mary Lou Witherspoon, the mathematics education faculty works within the mathematics department and the greater university as well as with local school districts to improve the mathematics education of all students. In addition, the mathematics education faculty has worked extensively with statewide efforts to improve teacher education. This presentation highlights some of those efforts. Statewide conference on the preparation of teachers. Several years ago, the mathematics education faculty at APSU hosted a statewide meeting, the MATH 1410 – 1420 Conference, to address the challenges of teaching Structure of Mathematical Systems, a six-hour mathematics course that is taken by pre-service elementary and middle school teachers. Since then, the conference has been hosted annually at various universities and colleges in Tennessee and, in order to broaden the discussion to the overall mathematics education of pre-service teachers, has recently been re-named the Math for Elementary School Teachers Conference. APSU mathematics education faculty continues to provide leadership in this statewide effort. Implementation of new state K-12 mathematics curriculum. Members of the APSU faculty have taken a leadership role in developing and implementing a new curriculum aimed at a more focused approach to mathematics education. In the fall, APSU will host the statewide Tennessee Mathematics Teachers Association meeting which will highlight this new curriculum. University elimination of developmental classes. Although developmental classes have not been completely eliminated at APSU, there is a statewide effort to move away from these classes in the universities.
Curriculum.
Strategies.
5th Annual Pre-Session Information|General Conference Information |
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