MS_ED 457/TEACH_ED 357 Methods and Techniques: Mathematics Fall 2015 Wednesday 6-9 p.m. Annenberg G22

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1 MS_ED 457/TEACH_ED 357 Methods and Techniques: Mathematics Fall 2015 Wednesday 6-9 p.m. Annenberg G22 James Lynn Miriam Sherin Course Overview: The goal of this course is to help you develop the knowledge, skills, and dispositions to teach middle school and secondary mathematics in a way that supports meaningful student learning. We view mathematics teaching as a complex task that involves close attention to the mathematical entailments of the tasks used in class, to the ideas and methods that students use as they work on these tasks, and to the role of the teacher in supporting students explorations and in facilitating class discussions of these ideas. Furthermore, teachers need to know how to effectively reflect on lessons and learn from their ongoing experiences. As part of this class, you will have the opportunity to engage in mathematics, to study video and student work from mathematics classes, and to observe and interact with students from a local high school. Through a variety of class activities, you will rehearse several key aspects of classroom interactions including launching a task, supporting students explorations, and debriefing an activity through a whole class discussion. We believe that the most effective teachers are those that continue to learn long after they receive their initial teaching credentials. We hope that through this class, you will develop key tools that you can use as you begin your career as teachers, as well as resources that will support you in becoming a life-long teacher-learner. Week 1 Wed Sept 30 Ann G22 Introduction to Thinking Through a Lesson Protocol (TTLP) Week 2 Wed Oct 7 Ann G22 Selecting & Setting Up a Mathematical Activity Week 3 Wed Oct 14 Ann G22 Selecting & Setting Up a Mathematical Activity NCP Visit 1 Thurs Oct 15 NCP 323 Visit Northside College Preparatory 1:00 3:15 pm Week 4 Wed Oct 21 Ann G22 Exploring and Supporting Student Thinking Week 5 Wed Oct 28 Ann G22 Exploring and Supporting Student Thinking Week 6 Wed Nov 4 Ann G22 Orchestrating Discussion NCP Visit 2 Thurs Nov 5 NCP 323 Visit Northside College Preparatory 1:0 3:15 pm Week 7 Wed Nov 11 Ann G22 Orchestrating Discussion Week 8 Wed Nov 18 Ann G22 Rehearsing the TTLP Cycle Wed Nov 25 Ann G22 NO CLASS Thanksgiving Holiday Week 9 Wed Dec 2 Ann G22 Rehearsing the TTLP Cycle NCP Visit 3 Thurs Dec 3 NCP 323 Visit Northside College Preparatory 1:00 3:15 pm Week 10 Wed. Dec 9 Ann G22 Rehearsing the TTLP Cycle *Northside College Preparatory High School is located at 5501 North Kedzie Ave, Chicago.

2 Required texts: Smith, M.S. & Stein, M.K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. National Council of Teachers of Mathematics, Reston, VA. Horn, I. S. (2012). Strength in Numbers: Collaborative learning in secondary mathematics. National Council of Teachers of Mathematics, Reston, VA. Additional weekly readings posted on Canvas. 2 Response Papers You are expected to complete the assigned readings each week. In addition, for at least 6 weeks of the course, you should comment on the readings in a brief response paper of no longer than one page. The purpose of the response paper is not for you to summarize the readings. Instead, you should attempt to synthesize one or two of the ideas raised in the readings or draw connections among different readings. You may also want to raise a question or two that the readings prompted for you. Response papers should be posted on Canvas by 8am on Wednesdays. Weekly Assignments In addition to weekly readings, there will be an assignment each week related to the teaching and learning of mathematics. For example, this might involve analyzing a piece of student work or planning for a classroom discussion. Assignments will be discussed in class each week and will also be posted on Canvas. The due date/time of each assignment will be posted on Canvas. Student Interviews For this activity, you will explore student conceptions about a mathematics topic. Rather than explicitly teach students, your purpose will be to use the interview as a context for probing students thinking about a math concept. You will first select an interview topic and develop an interview protocol (we will provide several tasks that you can use for this purpose). Next you will conduct two independent interviews with students, each approximately minutes long. You will need to videotape at least one of the interviews. Following the interviews you will a) Post a five-minute excerpt from the interview on edthena and analyze the mathematical thinking of the student in the video. b) Write a 3-4 page report describing a) the selected topic, b) the students thinking about the topic, and c) the implications for instruction. This assignment will be discussed in more detail in class on Oct. 7. Oct. 14 Draft Interview Protocol due. Please post on Canvas prior to class. Oct. 28 Interviews should be completed. Nov. 4 edthna analysis due prior to class. Final report due. Please post on Canvas prior to class. Launching a Task An important focus of our class this quarter is the Thinking through a Lesson Protocol (adapted from Smith, Bill & Hughes, 2008). The protocol highlights three key aspects of mathematics instruction: a) selecting and launching a math activity, b) supporting students exploration and c)

3 debriefing an activity through whole-class discussion. We will explore all three of these activities in depth across the quarter. As part of this work, you will be asked to launch a task in class on two occasions. Prior to your launch you will submit a launch plan to the instructors for review and comment. All students will present a launch in the final class session on Dec. 9. In addition, each student will present a launch on one of the following dates: Oct. 21, Oct 28, Nov. 4, Nov 11, Nov. 18. This assignment will be discussed in more detail in class on Oct 14. Visits to Northside College Preparatory High School During the quarter, we will be visiting a classroom at Northside College Preparatory (NCP) on three occasions. These visits will provide an opportunity for you to see the TTLP come to life in a mathematics classroom. NCP uses the Interactive Mathematics Program (IMP), an interdisciplinary mathematics curriculum. We will be visiting an IMP Year I classroom taught by Jill Sullivan. We will have an opportunity to talk with Jill during each of our visits. During the first visit, we will act mainly as observers in the classroom. During our second visit we will have the opportunity to work with small groups of students. During our final visit, we will lead much of the class at NCP. Oct. 15 Visit 1 NCP Nov. 5 Visit 2 NCP Dec. 3 Visit 3 NCP For each visit, please plan to arrive at NCP at 1pm. You will sign in at the office and then we will meet together in the office before proceeding upstairs to Ms. Sullivan s classroom. The class we will be observing runs from 1:24 3:05. We will have a short debrief following class. Final Project As a final project for our class, you will prepare to teach a mathematics lesson. The instructors will provide a series of tasks from which you may choose, or you may choose a task from another source, pending instructor approval. The project will involve designing a launch for the selected task and launching the task in class on Dec. 9, anticipating how students will work through the task and planning a whole-class debriefing of the task. This activity will be discussed in more detail in class on Nov. 4. Nov. 11 Task selection due. Please post on Canvas prior to class. Nov. 25 Launch design due. Please post on Canvas prior to class. Dec. 9 Present launch in class. Please post final launch plan on Canvas prior to class. Dec. 11 Final project due. Please post on Canvas prior to class. Grades: It is expected that you will complete all course assignments, and attend all class sessions both in Annenberg and at NCP. You are also expected to participate in class discussions and activities each week. Assignments will be rated along the following dimensions: Highly Proficient (3 points), Proficient (2 points), In Progress (1 point), Minimum Standards Not Met (0 points). Final grade will be determined based on the following: Assignments (weekly, interview, response papers) 33% TTLP Rehearsals (Launch rehearsals & Final project) 33% Class Participation (including Northside visits) 33% 3

4 Academic Integrity Students in this course are required to comply with the policies found in the booklet, "Academic Integrity at Northwestern University: A Basic guide". All papers submitted for credit in this course must be submitted electronically unless otherwise instructed by the professor. Your written work may be tested for plagiarized content. For details regarding academic integrity at Northwestern or to download the guide, visit: Accommodations for Students with Disabilities Any student with a disability requesting accommodations must register with Services for Students with Disabilities (ssd@northwestern.edu; ) and request an SSD accommodation notification for his/her professor, preferably within the first two weeks of class. All information will remain confidential. Course Objectives: Course objectives are consistent with the Conceptual Framework of the Teacher Education unit at Northwestern University ( The course also explicitly addresses several of the Illinois Professional Teaching Standards (IPTS). 1) To view mathematics teaching as a dynamic activity that requires close attention to students thinking (CF 1.1; IPTS #3, #7) 2) To view learning as a process resulting from active engagement with the learning environment (CF 1.4; IPTS #4, #5) 3) To view mathematics proficiency as requiring both procedural fluency and conceptual understanding (CF 1.4, IPTS #5) 4) To enhance one s subject matter knowledge and pedagogical content knowledge in order to design and implement effective instruction (CF 1.2; IPTS #2) 5) To be able to use the classroom a context for reflection and learning (CF 1.2; IPTS #7); 6) To conduct oneself in a professional and ethical manner in working with students at a school site (CF 3.2; IPTS #9) Northwestern Teacher Education Conceptual Framework As active participants in the field of education, our candidates will strive for improvement and innovation, based on inquiry that is grounded in reflection and research. The candidates will have A Vision of Learning that focuses on: 1.1 understanding student thinking about the subject matter; 1.2 reflection and research as a means of learning; 1.3 Learning as social practice, which encourages collaborative learning in which people clarify doubts, examine beliefs and work together to address questions and concerns; 1.4 authentic experience, where class sessions and assignments are designed to engage students interests and to have implication for the student beyond the classroom; and 1.5 the use of technology to extend learning opportunities and thinking. 4

5 A Vision of Learners that focuses on: 2.1 lifelong learning and development shaped by social contexts; and 2.2 student diversity as a resource for the educational community. 5 A Vision of Teaching that focuses on: 3.1 Connecting theory to practice, where the candidates understand that theories suggest questions and ideas about practice, and practice suggests modification of theory; and 3.2 professional conduct that is responsible and ethical. Dispositions (as implied by the NUCF): 1. Willingness to systematically reflect on one s own practice. (NUCF 1.2, 3.1) 2. Commitment to understanding students thinking about the subject matter. (NUCF 1.1) 3. Belief in the value of seeing students as individuals. (NUCF 2.2) 4. Enthusiasm for learning and teaching through collaboration. (NUCF 1.3) 5. Willingness to take the risks associated with engaging students interests through real world experiences. (NUCF 1.4) 6. Energy for incorporating innovations in teaching, including the use of new technologies. (NUCF 1.5) 7. Commitment to conducting one s self professionally and responsibly. (NUCF 3.2) Illinois Professional Teaching Standards 1. Teaching Diverse Students The competent teacher understands the diverse characteristics and abilities of each student and how individuals develop and learn within the context of their social, economic, cultural, linguistic, and academic experiences. The teacher uses these experiences to create instructional opportunities that maximize student learning. 2. Content Area and Pedagogical Knowledge The competent teacher has in-depth understanding of content area knowledge that includes central concepts, methods of inquiry, structures of the disciplines, and content area literacy. The teacher creates meaningful learning experiences for each student based upon interactions among content area and pedagogical knowledge, and evidence-based practice. 3. Planning for Differentiated Instruction The competent teacher plans and designs instruction based on content area knowledge, diverse student characteristics, student performance data, curriculum goals, and the community context. The teacher plans for ongoing student growth and achievement. 4. Learning Environment The competent teacher structures a safe and healthy learning environment that facilitates cultural and linguistic responsiveness, emotional well-being, self-efficacy, positive social interaction, mutual respect, active engagement, academic risk-taking, self-motivation, and personal goal-setting.

6 5. Instructional Delivery The competent teacher differentiates instruction by using a variety of strategies that support critical and creative thinking, problem-solving, and continuous growth and learning. This teacher understands that the classroom is a dynamic environment requiring ongoing modification of instruction to enhance learning for each student. 6. Reading, Writing, and Oral Communication The competent teacher has foundational knowledge of reading, writing, and oral communication within the content area and recognizes and addresses student reading, writing, and oral communication needs to facilitate the acquisition of content knowledge. 7. Assessment The competent teacher understands and uses appropriate formative and summative assessments for determining student needs, monitoring student progress, measuring student growth, and evaluating student outcomes. The teacher makes decisions driven by data and curricular and instructional effectiveness and adjusts practices to meet the needs of each student. 8. Collaborative Relationships The competent teacher builds and maintains collaborative relationships to foster cognitive, linguistic, physical, social and emotional development. This teacher works as a team member with professional colleagues, students, parents or guardians, and community members. 9. Professionalism, Leadership, and Advocacy The competent teacher is an ethical and reflective practitioner who exhibits professionalism, provides leadership in the learning community, and advocates for students, parents, or guardians, and the profession. 6

7 Readings 7 Note: Readings are due on the date listed Sept. 38 Introduction to Thinking Through a Lesson Protocol IPTS 1B, 1C, 1F 1K, 3H, 4I, 9A, 9H Oct. 7 Selecting & Setting Up a Mathematical Activity Weiss, I. R., & Pasley, J. D. (2004). What Is High-Quality Instruction? Educational Leadership, 61(5), Introduction and Chapter 1 of Five Practices for Orchestrating Productive Mathematics Discussions National Council of Teachers of Mathematics. (2009). Focus in High School Mathematics: Reasoning and Sense Making. Reston, VA: National Council of Teachers of Mathematics. pp Chapter 1 of Strength in Numbers What is the role of algorithms in mathematics instruction? Excerpted from EDThoughts: What We Know About Mathematics Teaching and Learning. IPTS 1B, 1C, 2B, 2C, 2F, 2G, 3H, 3K, 3Q, 4A, 5A, 5B, 6E, 6G, 6J, 6L, 6N Oct. 14 Selecting & Setting Up a Mathematical Activity Chapters 2 3 of Five Practices for Orchestrating Productive Mathematics Discussions Smith, M. S., & Stein, M. K. (1998). Selecting and Creating Mathematical Tasks: From Research To Practice. Mathematics Teaching in the Middle School, 3(5), Friel, S. N. & Markworth, K. A. (2009). A framework for analyzing geometric pattern tasks. Mathematics Teaching in the Middle School, 15, (1) English, L. D. & Warren, E.A. (1998). Introducing the variable through pattern exploration. The Mathematics Teacher 91, Ruchti, W. P. & Bennett, C. A. (2013). Develop reasoning through pictorial representations. Mathematics Teaching in the Middle School, 19, (1) Russ, R.S., & Sherin, M.G. (2013). Using interviews to uncover student ideas in science. Science Scope 36(5), IPTS 2A, 2B, 2C, 2G, 2I, 2J, 3H, 3K, 3Q, 5A, 5E, 5F, 5H, 6L, 6N, 8A

8 8 Oct. 15 Oct. 21 Visit to Northside College Prep 1:00 Check-in at NCP (IDs required) 1:24 3:04 Observe Class (We will stay for Task Launch and Student Independent Work) Exploring and Supporting Student Thinking Jackson, K., Shahan, E., Gibbons, L., & Cobb, P. (2011). Launching Complex Tasks. Mathematics Teaching in the Middle School, 18(1). Steele, M. D., Smith, M. G., & Taylor, C. E. (under review). Modifying textbook tasks: A strategy for enhancing opportunities for students to reason and prove. Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Organizing a Curriculum around Mathematical Habits of Mind. Mathematics Teacher, 103(9), Cirillo, M., Drake, C., Herbel-Eisenmann, B. (2009). Curriculum vision and coherence: Adapting curricula to focus on authentic mathematics. Mathematics Teacher, 103(1), IPTS 1A, 1B, 1C, 1E, 1I, 1K, 2A, 3E, 4E, 5G, 5J, 6E, 7I, 7J, 7K, 7N Oct. 28 Exploring and Supporting Student Thinking Chapters 4 of Five Practices for Orchestrating Productive Mathematics Discussions Knuth, E. (2000). Understanding connections between equations and graphs. Mathematics Teacher, 93(1), Kalder, R. S. (2012). Are we contributing to our students mistakes? Mathematics Teacher, 106(2), Stephens, A. C. (2005). Developing Students Understandings of Variable. Mathematics Teaching in the Middle School, 11(2), IPTS 1A, 1B, 1C, 1E, 1H, 1I, 1K, 2A, 2E, 2L, 4C, 4E, 4N, 5S, 7A, 7B, 7E, 7I, 7J, 7N Nov. 4 Orchestrating Discussion Wiliam, D. (2007). Five Key Strategies for Effective Formative Assessment. National Council of Teachers of Mathematics Research Brief. Reston: VA. Choppin, J. (2012). Developing formal procedures through sense-making. Mathematics Teaching in the Middle School, 17(9),

9 Usiskin, Z. (1999). Conceptions of school algebra and uses of variables. In B. Moses (Ed.), Algebraic Thinking, Grades K-12: Readings from NCTM s School-Based Journals and Other Publications (Vol. 8, pp. 7-13). Reston, VA: National Council of Teachers of Mathematics. Gonzalez, G. & DeJarnette, A. F. (2013). Leading classroom discussions. Mathematics Teaching in the Middle School, 18, (9) IPTS 1B, 1C, 1H, 2M, 2P, 3D, 3E, 3I, 3M, 3N, 5K, 5L, 5P, 6E, 6S, 7K, 8G 9 Nov. 5 Nov. 11 Visit to Northside College Prep 1:00 Check-in at NCP (IDs required) 1:24 3:05 Observe Class (We will stay for Student Independent Work and Classroom Debrief) Orchestrating Discussion Chapters 5 6 of Five Practices for Orchestrating Productive Mathematics Discussions Vacc, N. N. (1993). Questioning in the Mathematics Classroom. Arithmetic Teacher, Herbal-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning Our Patterns of Questioning. Mathematics teaching in the middle school, 10(9), Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D.E. McDougall, & J A. Ross (Eds.), Proceedings of the twenty-sixth annual meeting of the North American Chapter of the International Group for Psychology of Mathematics Education - Volume 2 (pp ). Toronto, Ontario. Stein, C. C (2007). Let s talk: Promoting mathematical discourse in the classroom. Mathematics Teacher, 101(4), IPTS 1B, 1C, 1H, 2M, 2P, 3M, 4L, 4M, 5L, 6S Nov. 18 Rehearsing the TTLP Cycle Chapter 2 4 of Strength in Numbers Manouchehri, A. & Lapp, D. A. (2003). Unveiling student understanding with questioning. Mathematics Teacher, 96(8), Knuth, E. & Peressini, D. (2001). Unpacking the nature of discourse in mathematics classrooms. Mathematics Teaching in the Middle School, 6(5), Staples, M. & Colonis, M. M. (2007). Making the most of mathematical discussions, Mathematics Teacher, 101(4),

10 IPTS 1B, 1C, 1H, 1J, 1L, 2K, 2P, 3C, 3F, 3G, 4K, 5I, 5O, 5R, 8F, 8G, 8L, 8M, 9K 10 Nov. 25 No Class Thanksgiving Holiday Dec. 2 Rehearsing the TTLP Cycle Chapter 5 & 6 of Strength in Numbers Knuth, E. J. (2002). Proof as a tool for learning mathematics. Mathematics Teacher, 95(7), Reinhart, S. C. (2000). Never Say Anything a Kid Can Say! Mathematics Teaching in the Middle School 5 (8), Sherin, M. G., Louis, D. A., & Mendez, E. P. (2000). Students' building on each other's mathematical ideas. Mathematics Teaching in the Middle School, 6(3), IPTS 1B, 1C, 1H, 1J, 1L, 2K, 2Q, 3C, 3D, 3F, 4K, 7K, 8F, 8L, 8M, 8N Dec. 3 Visit to Northside College Prep 1:00 Check-in at NCP (IDs required) 1:24 3:05 Observe Class (We will stay for Task Launch Student Independent Work & Whole-class debrief) Dec. 9 Rehearsing the TTLP Cycle IPTS 1B, 1C, 1F, 1H, 1J, 1L, 2J, 2K, 3C, 3D, 4I, 4K, 9I, 9K, 9O