Report

“There was one time during class that I put a problem up at the board and got the entire thing correct. I was actually, in a way, disappointed because I feel like I learn “Whenever I have a question about a problem I ask the question, why?” better from my mistakes.” “I like how it is focused on yourself figuring out the problem – though “I think that presenting my solution is that was hard for me to adjust to – most however it’sbecause made meI am much moreto useful forced independent math-wise.” participate and learn from other people.” “You can see that everyone here wants to figure out how they got a certain problem. There’s more of an interest than just getting something right, instead of just getting an A. It’s something you know that they want to understand how. “ “My best description is that of a light bulb. I could see where the rest of “I was presenting a problem that I wasn’t quite sure I had the problem might lead and the concept that it covered.” answered right, and with a little push from the class, the concept suddenly clicked in my mind. I was able to finish the rest of the problem quickly and felt good about my success.” Sunshine Greene and Carmel Schettino Mathematics Department, Emma Willard School CREATING A GEOMETRY CLASSROOM BASED ON THE RELATIONAL LEARNING OF GIRLS Sunshine Greene and Carmel Schettino Mathematics Department, Emma Willard School Comparison of Traditional and Relational Classroom Traditional Relational Lecture, direct-instruction Student-centered instruction Separate Knowing* Connected Knowing* Dualistic view of truth Appreciation of multiple views of truth Authority in meaning-making lies in teacher Perception that meaning-making is constructed by learning community Majority of classroom practice is individual work+ Majority of classroom practice is group problem solving and presentation+ Group/Pair Work Process-Oriented Group/Pair Work Construction of Knowledge Oriented *Belenky,et al, 1986, +Boaler, 2008 The Theory of Girls’ Learning Preference for Collaboration Active Learning Connected Prior Knowledge People Current Knowledge Need to feel valued, listened to Questioning, Curious for real understanding The Pedagogy Feminist Mathematics Pedagogy Dissolution of Hierarchy Empowerment and Agency Inclusion of all Voices Ownership in Learning A Pedagogy of Relation Relational Equity Relational Authority Solar, 1995, Anderson, 2005, Bingham, 2004, Boaler, 2008 Teacher Behaviors Schettino, 2009 The Curriculum Problem-Based Discourse-Driven Spiraled and Parallel Topics Built on Prior Knowledge Student Construction of New Knowledge Teacher Facilitation and Scaffolding - Key Multiple Representations Assessment Variations Ownership of New Knowledge via Metacognitive Journaling Problem Purposes reviewing material from past courses triggering prior knowledge for an upcoming problem inspiring construction of new knowledge introducing new terminology practicing a new skill challenging the more able students (differentiated instruction) seeing the same new idea from a different representation Slope – Multiple Perspectives The vertices A, B and C are collinear. Find the dimension n. Slope – Multiple Perspectives An airplane is flying at 36000 feet directly above Lincoln, Nebraska. A little later the plane is flying at 28000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln. Assuming a constant rate of descent, predict how far from Des Moines the airplane will be when it lands. Slope – Multiple Perspectives The diagram at right shows the graph of 3x + 4y = 12. The shaded figure is a square, three of whose vertices are on the coordinate axes. The fourth vertex is on the line. Find the lengths of the sides of the square. Right Angles – Multiple Perspectives Let A = (3, 2), B = (1, 5), and P = (x, y). Find xand y-values that make ABP a right angle. Describe the configuration of all such points P. Right Angles – Multiple Perspectives Find coordinates for the vertices of a lattice rectangle that is three times as long as it is wide with none of the sides horizontal. References Anderson, D. L. (2005). A portrait of a feminist mathematics classroom: What adolescent girls say about mathematics, themselves, and their experiences in a "unique" learning environment. Feminist Teacher, 15(3), 175-193. Belenky, M., Clinchy, B., Goldberger, N. and Tarule, J. (1986). Women’s Ways of Knowing: The Development of Self, Voice and Mind. Basic Books:. Biesta, G. (2004). Mind the gap. In C. Bingham & A. M. Sidorkin (Eds.), No education without relation (pp. 11-22). New York: Peter Lang. Bingham, C. (2004). Let's treat authority relationally. In C. Bingham & A. M. Sidorkin (Eds.), No education without relation (pp. 23-38). New York: Peter Lang. Boaler, J. (2008). Promoting 'relational equity' and high mathematics achievement through an innovative mixed-ability approach. British Educational Research Journal, 34(2), 167-194. Fisher, B., M. (2001). No Angel in the Classroom: Teaching Through Feminist Discourse. Lanham, MD: Rowman & Littlefield Pulishers, Inc. Hmelo-Silver, C., & Barrows, H. (2006). Goals and strategies of a Problem-Based Learning facilitator. The Interdisciplinary Journal of Problem-Based Learning, 1(1), 21-39. Hmelo-Silver, C., & Barrows, H. (2008). Facilitating collaborative knowledge building. Cognition and Instruction, 26, 48-94. References Solar, C. (1995). An inclusive pedagogy in mathematics education. Educational Studies in Mathematics, 28(4), 311-333. Taylor, C., & Robinson, C. (2009). Student voice: Theorising power and participation. Pedagogy, Culture and Society, 17(2), 161-175. Thayer-Bacon, B., J. (2004). Personal and social relations in education. In C. Bingham & A. M. Sidorkin (Eds.), No education without relation. New York: Peter Lang. Our Curriculum can be accessed at my website at a geometry course link http://community.emmawillard.org/Math/Schettino/index.htm or directly by using this url http://tinyurl.com/2djncvb