The National Research Council
"Current U.S. teaching practices for mathematics often are at odds with approaches that would support deeper learning."
Research on why we must stop lecturing and implement more active learning strategies in our classroom that encourage deeper learning and mathematical discourse.
DEEPER LEARNING IN MATHEMATICS
-The National Research Council
"Current U.S. teaching practices for mathematics often are at odds with approaches that would support deeper learning and transfer. Studies of upper elementary school and middle-grade classrooms have revealed that students generally work alone on low-level tasks that require memorizing and recalling facts and procedures—the hallmarks of rote learning. They do not engage in the high-level cognitive processes that are the hallmarks of deeper learning, such as reasoning about ideas and solving complex problems...Hallmarks of teaching mathematics for understanding include using: (1) Cognitively demanding mathematical tasks drawn from a broad array of content areas. Although research has shown that it is not easy for teachers to use cognitively demanding tasks well in classrooms, those tasks can lead to increased student understanding, the development of problem solving and reasoning, and greater overall student achievement. (2) Teaching practices that support collaboration and mathematical discourse among students and that engage them in mathematical reasoning and explanation, consideration of real-world applications, and use of technology or physical models. "
http://sites.nationalacademies.org/cs/groups/dbassesite/documents/webpage/dbasse_084153.pdf?_ga=2.52795360.937796049.1530646271-251245262.1530646271COMMITTEE ON DEFINING DEEPER LEARNING AND 21ST CENTURY SKILLS JAMES W. PELLEGRINO (Chair), Learning Sciences Research Institute, University of Illinois–Chicago; GREG J. DUNCAN,University of California, Irvine; JOAN L. HERMAN, National Center for Research on Evaluation, Standards, and Student Testing, University of California, Los Angeles; MARGARET A. HONEY, New York Hall of Science, Queens; PATRICK C. KYLLONEN, Center for New Constructs, Educational Testing Service; HENRY M. LEVIN, Teachers College, Columbia University; CHRISTINE MASSEY, Institute for Research in Cognitive Science, University of Pennsylvania; RICHARD E. MAYER, University of California, Santa Barbara; KENT McGUIRE, Southern Education Foundation, Atlanta, Georgia P. DAVID PEARSON, Graduate School of Education, University of California, Berkeley; EDWARD A. SILVER, University of Michigan; MARGARET L. HILTON, Study Director
WHAT DOES ACTIVE LEARNING MEAN FOR MATHEMATICIANS?
-Benjamin Braun, Priscilla Bremser, Art M. Duval, Elise Lockwood, and Diana White
"Active learning often has a particularly positive impact on student persistence and sense of belonging."
"For many faculty using active learning, these techniques inspire richer discussions with students and provide a window into the reality of students’ mathematical experiences. This allows faculty to be more responsive to students’ misunderstandings, which in turn causes students to feel more supported in the course, frequently leading to increased engagement."
"Active learning provides opportunities for faculty-student interaction not present in courses focused on direct instruction. Active learning methods can reach and excite some students who might not typically be vocal or engaged in class—students who are quiet and reserved by nature frequently demonstrate their full potential when provided with the right opportunity. On the other hand, active learning methods can uncover deep misconceptions about mathematics, even from straight-A students, that homework and exams do not reveal. Further, students often respond to active learning tasks with interesting observations and thought-provoking questions, infusing standard courses like calculus with fresh energy."
"Expect resistance from some students. For many reasons, it is common for some students to resist active learning methods, especially at the beginning of a course. Some students are not particularly interested in mathematics and do not want to engage at a deeper level. Other students have experienced significant success in traditional mathematics courses and feel threatened by an unfamiliar environment. With all students, instructors need to clearly articulate the value of the active learning methods they use and maintain high expectations for student participation and engagement. Often, students who are initially resistant find themselves surprised at the end of a course by how much they appreciate active learning."