The University of Massachusetts Amherst

Course Descriptions

SANDRA MADDEN
UMass Amherst
COURSE SUMMARIES
(From most recent syllabi)

 EDUC 463 – Principles and Methods of Teaching Elementary School Mathematics

This course is designed to help education minors develop personal understandings and confidences in mathematics so that they will be able to design experiences and guide interactions to teach early childhood and elementary school mathematics to   diverse populations of children.  Students in this course will have the opportunity to identify “worthwhile mathematics tasks” and “tools for enhancing discourse” (including concrete manipulatives and educational technology) while examining the teacher’s role and learners’ responsibilities in classroom discourse.  The course emphasizes a concrete-to-abstract developmental approach to learning.  The course attempts to integrate technology as a means of exploring mathematics topics and as a means of staying abreast of the changes in mathematics education reform efforts. Students in the course will be expected to be active problem solvers in constructivist-fashioned lessons, where the “best practices” in mathematics teaching are modeled.  Students will build on their strengths in mathematics and technology in order to analyze the elements needed for successful work in elementary school settings. Students will be expected to reflect on their experiences and communicate these reflections in oral and written formats.

EDUC 497TM – Teaching Mathematics in Grades 4-12

The course is designed to introduce students to mathematics education with a focus on engaging all students in worthwhile mathematical learning experiences. The course is activity-based and problem-oriented and will introduce students to the contemporary work of teaching mathematics. The course may appeal to undergraduates planning to become middle or high school mathematics teachers as well as other mathematics students who plan to teach at other levels.

 EDUC 511 – The Principles and Methods of Teaching Middle and High School Mathematics

 This course is designed to prepare pre-service middle and high school mathematics teachers for student-teaching in a secondary mathematics classroom. The work of contemporary mathematics teaching will be the focus of the course. Students will be expected to participate fully in written and video case study analyses of mathematical teaching episodes and to critically examine the characteristics of classroom environments with a goal of explicating characteristics of classrooms in which productive mathematical dispositions are systematically supported for all students. Students will analyze mathematical tasks with an eye on the mathematical potential of the task and investigate characteristics of teaching which support maintaining the cognitive demand of worthwhile mathematical tasks. The course and related instructional materials reflect the Vygotskian-perspective that learning occurs on two planes, first on the social plane and later on the psychological plane.

The course is structured into three general categories, each roughly one-third of the course: 1) building capacity to design and implement mathematical lessons; 2) supporting the development and improvement of mathematical lessons; and 3) critically examining the work of teaching and preparing to work in the context of schools. Students will be expected to create at least three distinct lesson plans, implement lessons with students while attending to multiple forms of assessment, and reflect critically upon each lesson during this course utilizing the course readings, activities, and discussions to guide their thinking. Self-evaluation, peer-evaluation, and instructor-evaluation will be utilized in this course.

EDUC 524 – The Work of the Middle and High School (Mathematics) Teacher

Education?524?is?the?introductory?course?in?the?Secondary?Teacher?Education?Program?(STEP).?This?section?is?specifically?designed?for?secondary?mathematics?teacher?candidates.?The?course?uses?field?observations,?texts,?practice?teaching?and?response?papers?to?develop?habits?of?mind?that?attend?to?evidenced?based?practice,?the?taking?of?multiple?perspectives,?and?reflection?upon?the?practice?of teaching?and?ourselves?within?this?practice.?Further,?through?class?discussions?and?readings,?students?are?encouraged?to?listen?to?and?respect?multiple?ways?of?knowing?and?making?meaning.?A?focus?on?issues?of?access,?equity?and?fairness?is?infused?throughout?the?course,?but?in?particular?within?topics,?readings?and?assignments?such?as?the?social?identity?paper,?inclusion?and?social?justice?education.

Education?524 ?is ?designed ?to ?introduce? prospective?mathematics?teachers?to?the complexities?of?the?work?of?teachers?through:

  1. Exploring?some?of?the?historical,?philosophical?and?theoretical?issues?and ideas?that?impact?mathematics?teaching?and?the?experience?of?schooling?in America.
  2. Relating?prospective?teachers’?understanding?of?the?work?of mathematics teachers?to?the?social?and?organizational?context?in?which?that?work occurs.
  3. Relating?the?motives?and?goals?for?becoming?mathematics?teachers?to?the?reality?of?the?work?that?middle?and?high?school?teachers

EDUC 592S – Microteaching Lab

The seminar in mathematics is designed to support students in their pre-practicum experiences in middle or high school classrooms.  Students will be invited to reflect upon their classroom experiences and examine particular issues and concerns that arise for teachers and students in mathematics. Discussions and writings for the seminar will focus on students’ practices, reflections and assigned readings with a goal of providing opportunities for students to make meaning of the realities of secondary classrooms, and the teaching and learning of mathematics. Through observation and participation as student teachers under the supervision of experienced public school teachers, students are expected to begin to integrate pedagogical theory into practice, and develop specific goals for the student teaching experience.  The seminar will support students with their development of effective lessons that incorporate the National Council for Accreditation of Teacher Education (NCATE) and Massachusetts learning standards. 

EDUC 615TT – Education in Context

 This course is designed to support Noyce secondary mathematics Master Teaching Fellows (MTFs) and Teaching Fellows (TFs). MTFs are experienced teachers teaching in high needs partner schools and TFs are prospective teachers who will be mentored by MTFs during a one-year intensive internship experience. During this course, MTFs and TFs will collaboratively engage, through a one-week intensive experience, to explore ways in which coming to know the community in which you work and to build on strengths and resources availed through the community, are practices to be leveraged in order to invite and engage all students in productive school experiences. By creatively attending to curriculum connections within the contexts of partner district communities, students will be encouraged to develop counter narratives. Furthermore, this course is designed to foster community at several levels: Between MTF and TF; within partner schools; within partner districts; across participants in the S2TLC project; among STEM researchers, teachers, and others stakeholders; and more broadly among geographical community stakeholders.

EDUC 693Y – MSLT Research

The purpose of this course is to support graduate students as they move forward in their research and scholarly work in science and mathematics education and learning technology. One intent of the course is to encourage the development of a community of learners and scholars who will continue to support each other throughout the doctoral program and into professional lives. The seminar meets formally meet a total of eight times, each for two-and-a-half hours.  During non-meeting weeks, students may meet informally in full or small groups as needed to support ongoing work with professor support. Students in the course outline a plan for the semester during the first class meeting and individuals construct a contract for what they intend to accomplish during the semester. Students collectively engineer the course to address scaffolds identified with potential to further students’ scholarly writing and research needs.  Possible course activities include:

  • engaging in group discussions about particular journal articles, books, or book chapters that participants consider important to their work;
  • sharing research designs, data, analyses, and/or writing to receive suggestions or feedback from the group;
  • working on comprehensive writing tasks;
  • developing a “critical friend” stance toward critiquing other’s work;
  • practicing presentations for conferences and job interviews.

During each class meeting, we discuss the planned readings and/or engage in the activities outlined by the group.  We are guided by the above stated purposes and issues that students believe are pertinent to their ongoing research.  In order to accomplish the goals of the course, all participants attend scheduled meetings, prepare adequately for each class, and participate in discussions.  Each student will take responsibility for at least one class discussion (may be done in pairs) and present his/her research at least once during the semester.

EDUC 695 – Statistics and Probability for Middle School Teachers

This is a statistics and probability content course offered in conjunction with a weeklong workshop in which area teachers are introduced to TinkerPlotsDynamic Statistics Software and instructional investigations to support middle school student inquiry in statistics. Participants explore methods of collecting, organizing, analyzing, and presenting data; fundamental principles of probability; and methods of statistical inference. The course meets MTEL objectives 47-0016 and 47-0017 and Massachusetts Curriculum Frameworks learning standards 4.D.1 – 4.D.6, 6.D.1 – 6.D.4, and 8.D.1 – 8.D.4. We will, however, consider pedagogy as part of our study, and make every effort to model appropriate teaching pedagogy that is consistent with the NCTM Standards and the Massachusetts Curriculum Frameworks.

The emphasis of the course is on understanding statistical concepts and interpreting and communicating the results of statistical analyses. The vast majority of class time is spent being actively engaged with the material. We adopt the workshop model where participants work through activities designed to discover fundamental statistical ideas.

EDUC 697CC – Secondary Mathematics Curriculum Topics & Innovations

This course is designed to explore secondary mathematics curriculum topics and innovations (Secondary is taken to mean grades 7-12). You will investigate current trends in national, state and local professional curriculum recommendations as well as contemporary and innovative instructional materials designed to support current curricular recommendations. The course will expand your understanding of mathematics teaching and learning, while at the same time, support your mathematical and statistical content knowledge, content knowledge for teaching, and facility with technological tools appropriate for use in the secondary mathematics or science classroom. Mathematics and statistics education research will be explored as we consider similarities and differences among intended, enacted (implemented), and achieved (attained) curricula as well as student opportunity to learn.

During Spring 2018, the course will focus on exploring the influence of exploratory data analysis and statistics on middle and high school curricula. Students will be engaged as learners of statistical content as well as teachers of statistical content or researchers in the realm of statistics education. Students will learn to use innovative statistical software tools for analyzing data and making decisions as well as to support student learning of data analysis and statistics. The course will emphasize statistical reasoning, thinking, and literacy and will have implications for secondary classroom implementation. Contemporary secondary curricula will be examined for potential to support professional curricular recommendations. Though this course is largely designed for teachers of mathematics and/or science, it will be broadly applicable to all students with interest in using data and dynamic technology in secondary classrooms to engage and foster student interest in myriad content areas.

EDUC 697ME – Professional Seminar in Mathematics Education

 This course is designed to support NSF Noyce secondary mathematics Mentor Teaching Fellows (MTFs) and Teaching Fellows (TFs) in the Supporting STEM Teaching and Learning through Communities (S2TLC) project. MTFs are experienced teachers teaching in high needs schools and TFs are prospective teachers who will be mentored by MTFs during a one-year intensive internship experience, is in its second semester. The course examines the influence of local, state and national standards and current research perspectives on mathematics instruction, in particular, inquiry and problem-based practices. Course participants will focus on the importance of reflective practice, enhanced content knowledge, student learning and socio-cultural awareness of the students and school community. Participants will develop mentoring and leadership skills to work with school colleagues as well as beginning teachers. A community of practice will be co-constructed among the instructor and participating fellows with the goal of supporting and interrogating the teaching and learning of mathematics at the secondary level.

EDUC 697SM – Statistics and Modeling in the Secondary Curriculum

This course is designed to explore secondary mathematics curriculum topics and innovations (Secondary is taken to mean grades 7-12). You will investigate current trends in national, state and local professional curriculum recommendations as well as contemporary and innovative instructional materials designed to support current curricular recommendations. The course will expand your understanding of mathematics teaching and learning, while at the same time, support your mathematical and statistical content knowledge, content knowledge for teaching, and facility with technological tools appropriate for use in the secondary mathematics or science or other content area classroom. Mathematics and statistics education research will be explored as we consider similarities and differences among intended, enacted (implemented), and achieved (attained) curricula as well as student opportunity to learn.

During Summer 2018, the course will focus on exploring the influence of exploratory data analysis and statistics on middle and high school curricula. Students will be engaged as learners of statistical content as well as teachers of statistical content or researchers in the realm of statistics education. Students will learn to use innovative statistical software tools for analyzing data and making decisions as well as to support student learning of data analysis and statistics. The course will emphasize statistical reasoning, thinking, and literacy and will have implications for secondary classroom implementation. Contemporary secondary curricula will be examined for potential to support professional curricular recommendations. Though this course is largely designed for teachers of mathematics and/or science, it will be broadly applicable to all students with interest in using data and dynamic technology in secondary classrooms to engage and foster student interest in myriad content areas.

EDUC 697SN – Rate of Change and Modeling in the Secondary Curriculum

This course will focus on exploring rate of change, as a watershed concept, across middle and high school curricula. Rate of change is a conceptually rich area, most commonly associated with the study of Calculus that can be developed from a very early age and with connections across scientific disciplines. Students in this course will be engaged as learners of mathematical content as well as teachers of mathematical content or researchers in the realm of mathematics education. Students will learn to use innovative software tools for mathematical modeling as well as to support student learning of big ideas associated with rate of change. Contemporary secondary instructional materials will be examined for potential to support professional curricular recommendations.  Mathematics education research will be explored as we consider similarities and differences among intended, enacted (implemented), and achieved (attained) curricula as well as student opportunity to learn.

The course will incorporate ideas about functions, graphs, and patterns and how to investigate change and rate of change in a variety of ways– algebraically, graphically, numerically, etc., and using a variety of tools – paper an pencil, calculators, with manipulatives, and using a variety of technological tools.   Teachers will have the opportunity to reflect on their own teaching of these ideas, and trace the development of ideas of change and of rate of change from middle school to high school.  They will answer questions such as, How does rate of change appear in the curriculum? How is the concept enhanced or developed through the grades? How are different representations of this idea incorporated?  How can we tell?

This blended-format course is largely designed for teachers of mathematics and/or science and will combine mathematical investigations, readings, discussions,
collaboration, and a capstone project to include the design, implementation, and analysis of student learning of rate of change. PDPs available.

 EDUC 711 – Recent Developments in Secondary Mathematics

 Students will explore the use of dynamic technological tools for teaching and learning mathematics. In addition to developing facility with some of these tools, students will explore issues of visualization, simulation, and animation and their impacts on learning. Mathematical investigations will form the basis for utilizing technology and innovative curriculum materials will be utilized. The course will incorporate critical evaluation of current literature, research, and studies in curriculum and teaching of secondary school mathematics and is relevant to practitioners and researchers. This course serves as the Advanced Methods course for STEP Mathematics students and incorporates an assessment of student learning as required for licensure.

The class will likely explore Geogebra, Desmos, Cabri Plus II, Cabri 3D, Fathom2, Tinkerplots, CPMP-Tools, and CODAPas tools for supporting students’ mathematical problem solving, reasoning, and connections. It is possible that explorations will include the use of TI-84 or TI-Nspire calculators, but familiarity with handheld function graphers is assumed. As technologies emerge, they may be incorporated into class or independent investigations (e.g., TuvaLabs, Plottly, Pixar in a Box, etc.).\

EDUC 715 – Secondary School [Mathematics] Curriculum

This course is designed as an introductory study of the work of the middle and high school mathematics teacher with an emphasis on the sociopolitical and organizational contexts in which the work is embedded. This semester, with a cohort of Mentor Teaching Fellows and Teaching Fellows, the development of a shared vision for teaching and learning in high needs schools is foregrounded.

For Teaching Fellows (TF), the course is designed to encourage the process of reflection on observations, practice, and theory in order to consider teachers’ instructional choices in the classroom. TFs will conduct field observations in their own school and other schools, with the goal of noting and reflecting upon patterns, assumptions, questions and surprises. TFs will reflect upon themselves, their social identity and their school experiences in order to understand who they are as beginning teachers of mathematics.

Mentor Teaching Fellows (MTF) will share expertise from their teaching practice while at the same time expanding their own understanding of mentoring and teaching in high need schools. They will use their own practice as a site of reflecting in preparation for their mentoring role and join TFs in further exploring their social identities and impact on their practices in schools.

Approaching Teaching as a Researcher

Students will examine the realities and challenges of a teacher’s life, including working hours, organizational support and constraints, and relationships to family and community. They will  examine how teachers approach their work and how the setting impacts what happens in the classroom as well as develop and implement lessons and consider factors such as differentiated instruction, cooperative learning, classroom management, and assessment.

Work and the Self

This course will ask you to examine yourself – your attitudes, behaviors, beliefs, expectations, identities, and world views – as situated knowledge that may or may not encompass the realities of the student, the classroom, the school and the larger society.

EDUC 790A – Mathematics Curriculum Issues and Trends

This doctoral-level course is designed to help students develop a solid understanding of school mathematics curriculum from an historical perspective. Assigned readings, class discussion, projects, and individual research will enable students to become familiar with the key issues and forces that have influenced mathematics curriculum change from about 1890 to 2010 and to become knowledgeable of the major reports, conferences, and curriculum development efforts that have provided direction for and trends in school mathematics.

EDUC 792Q – Introduction to Research in Mathematics, Science, and Learning Technologies

 This course examines current research issues, challenges, and opportunities in Mathematics Education, Science Education, and Learning Technology (MSLT) in formal and informal settings. The course is designed to provide first or second year MSLT doctoral students and other graduate students with a broad understanding of a range of topics central to our field, from research methods to theories of learning and teaching in the disciplines, to structural/institutional issues (e.g., equity and social justice) bearing on MSLT practices and education. Toward these ends, the course also covers some foundational material on learning and instruction, especially theories of knowledge and learning, and how these are reflected in teaching and learning of mathematics, science, and technology.

A second goal of the course is to begin preparing MSTL doctoral students to write in the academic genre, including formulating and supporting an argument, using appropriate style, and referencing the literature correctly. In this regard, both classroom discussions and assignments will be geared towards unpacking such things as theory and evidence, and making explicit how authors articulate these into coherent scientific arguments.

As a result of participating in this course and completing course assignments, students will have the potential to achieve the following general learning outcomes:

  • Develop a broad understanding of current research issues, challenges, and opportunities in the fields of mathematics education, science education, and learning technology.
  • Construct a basic understanding of theories of learning and teaching currently held in the field, in particular how methods of instruction are reflexively related to theories of knowledge and learning.
  • Develop initial facility in writing in the academic genre, particularly as it relates to constructing and supporting scientific arguments.