Arithmetic for Middle Grades Teachers
University of Georgia
Mondays, Wednesdays, and Fridays, 10:10 – 11 am, room 111 Aderhold Hall
Dr. Sybilla Beckmann, Josiah Meigs Distinguished Teaching Professor of Mathematics
501 Boyd Graduate Studies Building
Please contact me as soon as possible (by email or phone) if an illness or emergency prevents you from attending class.
Office hours: Regular times to be determined. Please don’t hesitate to e-mail me or call me with questions or to make an appointment to meet.
Writing Intensive Program (WIP) Teaching Assistant:
427J Boyd Graduate Studies Building
Office hours: Regular times to be determined.
This course is part of your preparation to teach math in grades 4 through 8. When you teach, you will select mathematically worthwhile tasks and problems, ask questions, listen to your students’ mathematical ideas, orchestrate discussions, and expect students to reason about and make sense of math. To do so, you must develop a strong and flexible understanding of the concepts you will teach. Therefore we will go deeply into the ideas about numbers and arithmetic that students learn in grades 4 – 8.
The course content is closely linked to the Common Core State Standards for Mathematics, which include Standards for Mathematical Content and Standards for Mathematical Practice. When you teach, you will help your students develop habits of mind of mathematical thinkers by engaging in the mathematical practices. In doing so, you will help your students develop 21st century competencies, which include critical thinking, reasoning and argumentation, flexibility, appreciation for diversity, communication, collaboration, and responsibility (see the National Research Council report, Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century). Therefore, in this course we aim to foster the following dispositions and practices:
Adopt a “growth mindset” – Ability is not fixed but is something that can be improved by working at it. “[A] proven intervention is to tell junior-high-school students that I.Q. is expandable, and that their intelligence is something they can help shape. Students exposed to that idea work harder and get better grades. That’s particularly true of girls and math, apparently because some girls assume that they are genetically disadvantaged at numbers; deprived of an excuse for failure, they excel.” (From the NY Times 4/16/2009 article How to Raise our I.Q. by Nicholas Kristof. See also the Institute of Education Sciences (of the US Dept. of Education) Practice Guide, Encouraging Girls in Math and Science, Recommendation 1). And: “People who believe in the power of talent tend not to fulfill their potential because they’re so concerned with looking smart and not making mistakes. But people who believe that talent can be developed are the ones who really push, stretch, confront their own mistakes and learn from them.” (Dr. Carol Dweck, as quoted in the NY Times 7/6/2008, If You’re Open to Growth You Tend to Grow).
Engage actively with mathematical ideas and stretch your thinking about math – People learn through active engagement with ideas and by building the ideas in their own minds. In class, you will often be asked to solve and discuss problems and to think about mathematical ideas in new or different ways. Make productive and active use of that time. This includes allowing yourself time to think and grapple, even when you are stuck or struggling. Throughout the course, try to think critically about ideas and work towards expressing ideas with greater precision. Look for interesting connections to other ideas and look for things that are surprising or neat. Try to ask and answer deep explanatory questions. There is strong evidence that the practice of asking and answering deep explanatory questions is important for learning according to the Institute of Education Sciences (of the US Department of Education) Practice Guide on Organizing Instruction and Study to Improve Student Learning. Understand that lines of reasoning, explanations, and making sense of concepts and ideas are just as important in math as skills and procedures. At its core, math is about ideas.
Persevere – Keep trying to understand an idea or solve a problem even when you don’t “get it” right away. Persistence and commitment to continued learning are vital to success in the long run, much more so than being talented or “quick.” See mistakes as opportunities to learn. Note that the very first practice standard in the Common Core State Standards for Mathematics (page 6) is “Make sense of problems and persevere in solving them.”
Monitor your understanding and reflect on the ideas you are learning – Think about your thinking and look for ways to extend and improve your learning and understanding. According to the Institute of Education Sciences (of the US Department of Education) Practice Guide, Improving Mathematical Problem Solving in Grades 4 Through 8, there is strong evidence that monitoring and reflecting are important for learning. Take responsibility for your learning and seek help when you need it.
Be an active part of a learning community – Learn with and from your classmates. Listen carefully to their ideas, explanations, and problem-solving approaches. Think critically about what you hear. Listening to others can be difficult and confusing at times, but it’s an especially important skill for teachers. As a teacher you will need to listen closely to your students to determine how they are thinking about mathematical ideas so that you can build on what your students know. Recognize that in class we are working together to make sense of ideas, which will involve some false starts and errors. Incorrect answers are valuable opportunities to determine where the flaws lie. Be comfortable agreeing or disagreeing (you may feel more comfortable saying you “respectfully disagree”). Support each other’s learning. Nudge each other towards greater participation and engagement.