The EML is part of the Teacher Education Initiative (TEI), a project housed in the School of Education to redesign how teachers are prepared for practice at the University of Michigan and to build knowledge and tools that will inform the field of teacher education more broadly.
ElEmEntary mathEmatics laboratory
ElEmEntary mathEmatics laboratoryWhat is involved in holding high expectations for every student and in enabling complex mathematical work? How can professional educators make the skilled and often invisible work of teaching available to and learnable by novices? How can teachers work to reverse patterns of inequity related to race, family income, language, and gender in their teaching of mathematics? What does it take to build a respectful and mathematicallyfocused learning environment?
These are just several of the questions on which researchers and teacher educators are working through the Elementary Mathematics Laboratory (EML) at the University of Michigan School of Education. Teaching is notoriously difficult to study and to improve, and numerous educational interventions in the United States have failed to influence teachers work at the level of individual classrooms. This is especially true in mathematics. The United States has worried about the quality of math instruction in its public schools for decades. And despite efforts to increase funding for special curricula and raise standards for teachers and students alike, American children continue to lag behind their peers in other countries on international exams. In the EML, we put teachingparticularly elementary mathematics teachingunder a magnifying glass. Our goal is to slow down and make visible every aspect of this complex workinstructional planning, the design and preparation of materials, improvisational decision-making, the arrangement of board space, analysis of students mathematical ideas, and consideration of the crucial relational aspects of classroom instruction, to name just a few examples. The EML offers a rare opportunity for researchers, teachers, and other observers to unpack and study the often invisible elements of teachers work and to collaborate in tackling the challenge of improving mathematics instruction. The EML is part of the Teacher Education Initiative (TEI), a project housed in the School of Education to redesign how teachers are prepared for practice at the University of Michigan and to build knowledge and tools that will inform the field of teacher education more broadly. Through work on the Initiative, researchers and educators at Ann Arbor are developing instructional materials and activities that will prepare teachers to carry out the core tasks of their work effectively with all American schoolchildren.
The Inner CIrCle: The FIFTh-Grade MaTheMaTICs ClassThe fifth-grade mathematics class offers a chance for students from public schools in southeast Michigan to work with University of Michigan faculty members on important and challenging topics in mathematics. The class is designed for all incoming fifth grade students, and no special interest or skill in mathematics is required. Most of our students come from the neighboring city of Ypsilanti, Michigan. This year just as last year, the class will focus on several topics important for doing well in fifth grade, including fractions, permutations, number lines, equivalence, and place value. We will also help students develop core mathematical practices, including explaining, representing, proving, and defining, as well as practices of learning math, including recording, summarizing, attending to language, and studying. Students will participate in highly interactive activities each day, and will have opportunities to use a variety of mathematical manipulatives and tools such as overhead calculators and Cuisenaire rods. For the first time this year, students will have the benefit of a full-day program which will include daily opportunities to participate in hands-on art activities with professional art instructors and to improve their mathematics skills in afternoon workshops. At the conclusion of the two-week program, students invite their family and friends to a celebration at which they demonstrate the mathematical activities that they have been working on during the two weeks.
The OuTer CIrCles: TeaCher eduCaTIOn and researChProfessionals travel to Ann Arbor from all over the country and from several foreign nations to observe the EML and
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contribute to the research and activities that surround the fifth-grade math class. On any given day the observers include research mathematicians, often of international renown; education researchers studying different aspects of mathematics instruction as well as investigating questions about achievement among children from
various racial, ethnic, and socioeconomic backgrounds; veteran teachers aiming to improve their own instruction; and student teachers studying expert practice together as part of their professional training. The discussions range across many topics but focus on mathematics teaching and childrens mathematical thinking.
Research Group Meetings
The EML math teacher Dr. Deborah Ball purposefully strives to make her work and that of the entire instructional team visible and available to the wide variety of professionals who come to observe the class every day and actively solicits ideas, suggestions, and feedback from everyone.
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dOCuMenTaTIOn and reCOrds COlleCTIOn To enable close study of the course from multiple perspectives (and with the permission of the students and their families), the laboratory class is videotaped every day and careful records are made of the childrens work and of the lesson plan and other elements of the instructors work. All of the records that we collect are labeled, catalogued, and made available (again with the permission of the students and their families) for review, commentary from multiple perspectives, and deeper study by different kinds of professionals.
course on mathematics content and teaching methods. Through a concentrated course structure organized around the EML, the interns will develop mathematical knowledge, skills, and ways of reasoning needed for teaching while learning to enact high-leverage practices of teaching mathematics. A live video feed allows classroom events to be paused and replayed, creating an environment in which the complex practice of teaching can be slowed down and discussed to make it more available for learning. These daily observations create a rich site for collectively investigating problems of practice, anticipating and listening closely to student thinking, studying teaching moves and their consequences, tracking student learning over time, and experimenting with the design of instruction and assignments. MaTh ClInIC In the afternoon the interns play a central role in a new component of the EML: the Math Clinic. During
Math Clinic interns teach the children who participated in the morning math class, implementing instructional activities that deepen and broaden students engagement with mathematics. Interns lead large-group problem solving activities, direct small-group learning stations, and develop targeted instruction for individual students based on their homework from the math class. Interns also have daily opportunities to learn from records of their own teaching, from a variety of teaching materials and resources, and from peers and instructors who are part of the professional community engaged in the clinic. PrOFessIOnal develOPMenT OPPOrTunITIes FOr TeaChers and TeaCher eduCaTOrs We offer several formal learning experiences for educators who participate in the EML. This year three courses and workshops are available. One is a mathematics course taught by Dr. Hyman Bass, University of Michigan mathematician, mathematics educator,
ObservaTIOn and dIsCussIOn Each morning interns from the Elementary Master of Arts with Certification (ELMAC) program observe the fifth-grade mathematics laboratory class and use it as a common text for studying teaching and mathematics. The interns participate directly in the Laboratory as part of their summer
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Before ClassEach morning Dr. ball meets with observers in a pre-class briefing, during which she presents the days lesson plan, explains the goals and activities for the class, and raises any concerns she and other lesson-planners have about the lesson or particular students in the class. observers are invited to share ideas, make suggestions, and ask questions.
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and recent winner of the National Medal of Science. Another is a workshop for practicing teachers taught by Dr. Alison Castro-Superfine, mathematics educator and education researcher at the University of Illinois Chicago. A third is a workshop for University of Michigan graduate students who are preparing to be field instructors in teacher education programsi.e. to support student teachers as they observe and practice teaching in actual elementary, middle, and secondary schools. Participants in these courses observe the mathematics class every day, take part in the pre- and post-class briefings, and then attend their own cour