PROBLEM SOLVING IN MATHEMATICS Spring 2020 EMAT 6600 Syllabus Robyn Ovrick Phone: 770-241-1302 Class times: See schedule below Email: [email protected] Office hours: After class; by appointment COURSE TEXT Mason, J., Burton, L., & Stacey, K. (2010). Thinking Mathematically. Harlow, England: Prentice Hall. Van De Walle, J.A., Karp, K.S., & Bay-William, J.M. (2016). Elementary and middle school mathematics: Teaching developmentally (Tenth Edition). Boston: Pearson. Chapter 3: Teaching through Problem Solving COURSE DESCRIPTION Mathematical problems with emphasis on exploring various mathematical contexts, on posing and extending problems, and on communication mathematical problems and solutions. COURSE GOALS & OBJECTIVES 1. Build new mathematical knowledge through problem solving 2. Solve problems that arise in mathematics and in other contexts 3. Apply and adapt a variety of appropriate strategies to solve problems 4. Monitor and reflect on the process of mathematical problem solving 5. Improve content knowledge 6. Experience the problem-based classroom as a learner 7. Communicate and collaborate about mathematics 8. Investigate, explore, and question mathematically 9. Become a problem poser and choose/create/adapt worthwhile tasks 10. Develop enjoyment of and self-confidence with mathematics 11. Understand mathematical practices and learn how to support students engaging in these practices ASSIGNMENTS – Refer to the class schedule below for due dates All work should be submitted electronically or in person. Be sure that the assignment title and your name are both on the document itself and in the title of the document. Ex: ROvrick.Reflection.1.doc Make sure handwritten homework is legible. In-Class Participation – (8 points per class) You will be assigned partners with whom to work. And you will be expected to intentionally cultivate within yourself (and your partners), as a student and a teacher, the listed goals and objectives stated above. Active participation is expected in all class discussions. See in class participation rubric below. Weekly Assignments – (4 points per problem, typically 2 problems per assignment) Your weekly assignments can be found under Content in ELC in the folder “Homework Assignments” and are listed below the schedule in this syllabus. They will include reading a chapter from Thinking Mathematically, working through the tasks each time the book says “Try It Now”, and choosing which task you want to write up to submit along with additional assigned tasks. Although only 3-4 tasks are options for homework, you are expected to try all tasks within a chapter. Some tasks in the chapters are fully discussed by the author. I am not looking for you to simply copy what is written in the book. You are to make sense of the problem for yourself. Try to solve completely each task before reading further. These assignments are going to go against some personality preferences who “do your best work at the last minute”. You simply cannot wait until the night before to start a chapter. Chapter 1 will likely take you two weeks to work your way through! When working on problems within the chapter, be sure to note in your work where you stopped or got stuck and when you started back up after reading further in the chapter. Use homework problem rubric below as a guide. Reflections – (2 points each) Two reading reflections are due at the beginning (VDW Ch. 3) and near the end of the semester (TM Ch. 9). Use the reflection rubric below as a guide. For the three class reflections choose one or two experience(s) or problems solved in class. Submit a 1-2pg written reflection on any of the assigned class dates for that reflection. Your paper should show true personal reflective thinking. I do NOT want a summary of what you did in class – I will have been in class with you. Cite any sources that you reference. Use the reflection rubric below as a guide. Suggested topics (but not limited to) for your reflections are these: What you learned What was difficult or surprising How this could be adapted to your classroom or how does an experience apply to your classroom Mathematical extensions of a problem An alternate way of solving a problem, different from what was done in class, etc. Final Exam- The exam will consist of a set of problems from which you can choose to solve. More information closer to exam time. Policy on Late Submission of Work: Work submitted by the due date is eligible for full credit. Work submitted after the due date will have 5% of the grade deducted for every day it is late up to 7 days. Regardless of grade, students are expected to complete all assignments and will not receive credit for the course until all assignments are completed. The instructor reserves the right to make exceptions in extenuating circumstances. Grade: In-Class Participation (8 pts each day = 56 points) Weekly Assignments (~8 pts each week = ~56 points, depends upon resubmits) Reflections (2 pts each = 10 points) Final Exam (24 points) Final grade calculated as percent from total possible points for each individual. Grading: See UGA grading system at http://bulletin.uga.edu/bulletin/acad/Grades.html. More specifically, A=93, A-=90 B+=87, B=83, B-=80 C+=77, C=73, C-=70 D+=67, D=63, D-=60 In Class Participation Rubric 8: The student does the following: (1) actively participates in all group and class discussions, including the assigned reading; (2) actively participates in all group tasks; monitors personal role within the group (3) being careful to withhold information if you are aware you know too much before the rest of the group, (4) employ good teaching practices to support the learning of your group, or (5) speak up for yourself if the group is going off without you and you need more support. 7: 5: 3: 1: 0: The student does 4 of the 5 above actions. The student does 3 of the 5 above actions. The student does 2 of the 5 above actions. The student does 1 of the 5 above actions. The student does not attend class or does none of the 5 above actions. Homework Problem Rubric 4: The problem is fully solved, and all conclusions are proved or justified mathematically. (After reading chapter 2, the problems begin with an Entry.) The problem write up includes a thorough description of your activity and steps, an analysis of what did or did not work as you worked through the problem, what you did to shift gears or become unstuck if you were stuck, and a reflection on your thought processes and how they evolved, if at all, through solving the problem. The write up and solutions are clear, thorough, and free of grammatical errors. 3.5: The problem is almost fully solved or is solved without a complete mathematical justification of all the relevant claims. (After reading chapter 2, the problems begin with an Entry.) And the problem write up includes a thorough description of your activity and steps, an analysis of what did or did not work as you worked through the problem, what you did to shift gears or become unstuck if you were stuck, and a reflection on your thought processes and how they evolved, if at all, through solving the problem. Or the problem is fully solved and proved but the write up is lacking a component described above. 2.75: Represents a strong attempt at a solution, (After reading chapter 2, the problems begin with an Entry.) and the problem write up includes a thorough description of your activity and steps, an analysis of what did or did not work as you worked through the problem, what you did to shift gears or become unstuck if you were stuck, and a reflection on your thought processes and how they evolved, if at all, through solving the problem. Or problem is almost fully solved or is solved without a complete mathematical justification, but the write up is lacking a component described above. Or the problem is fully solved and proved but the write up is lacking many components. 2: An attempt is made on the problem, with one or more lacking significant steps to a solution. Or student did not make sense of the problem or added an assumption to the problem but correctly solved the problem as they understood it. (After reading chapter 2, the problems begin with an Entry.) The problem write up includes a thorough description of your activity and steps, an analysis of what did or did not work as you worked through the problem, what you did to shift gears or become unstuck if you were stuck, and a reflection on your thought processes and how they evolved, if at all, through solving the problem. Write up and solutions are clear and thorough, with minor if any grammatical errors. Or a strong attempt is made on the problem but the write up is lacking a component. Or the problem is almost fully solved or is solved without a complete mathematical justification but the write up is lacking many components. 1.5: An attempt is made on the problem, with one or more lacking significant steps to a solution but the write up is strong. Or a strong attempt is made on the problem, but the write up is lacking many components. 1: An attempt is made on the problem, with minimal progress. Reflection write up may be missing or may be too brief to discern how you solved the problem. *Extra Credit will be given for working on extensions of the problem. It does not matter if the extension was recommended by the book or generated by your own questions. Reflection Rubric 2: 1: 0.5: Well-developed paper; shows evidence of reflection and/or metacognition; is not a summary Shows some evidence of reflection but not well-developed Shows little evidence of reflection and is primarily a summary University Policies: As a University of Georgia student, you have agreed to abide by the University’s academic honesty policy, “A Culture of Honesty,” and the Student Honor Code. All academic work must meet the standards described in “A Culture of Honesty” found at: https://ovpi.uga.edu/academic-honesty/academic-honesty-policy. Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor. Documented Disability If you are a student with a documented disability, you must inform the instructor of this fact at the close of the first class meeting. You will be referred to the Assistant Director of Academic Affairs in Flynt 105 for consultation regarding evaluation, documentation of your disability, and a recommendation as to the accommodation, if any, to be provided. The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary. Mandatory Reporting UGA Students and Faculty who have reasonable cause to believe that child abuse has occurred must notify the organization’s lead administrator (e.g., school principal, facility director) immediately, and subsequently notify their university supervisor or program director. Class Schedule on next page. Class Schedule and Assignment Due Dates Dates 1 Sat 9am-12 1.11.20 2 Sat 9am-12 1.25.20 Open visit 3 Sat 9am-12 2.8.20 Class Content Introduction Strategies, Tactics SMPs Worthwhile Tasks Thinking Mathematically Making sense of Growing Patterns Assignments Due VDW 10th ed, Chapter 3 Reflection Specializing and Generalizing Assignment 2 Read Chapter 2 Class Reflection 1 (on 1/11, 1/25) Assignment 3 Read Chapter 3 4 Sat 9am-12 2.22.20 Open visit 5 Sat 9am-12 3.7.20 Mathematical Phenomena Getting Stuck 6 Sat 9am-12 3.21.20 Convincing Others 7 Sat 9am-12 4.4.20 Task Analysis 8 Sat 9am-12 4.18.20 Conjecturing Final Assignment 1 Read Chapter 1 Assignment 4 Read Chapter 4 Class Reflection 2 (2/8, 2/22) Assignment 5 Read Chapter 5 Assignment 6 Read Chapter 9 Bring to class HW problems and/or assessments you have recently given to your students Assignment 7 Class Reflection 3 (3/7, 3/21, 4/4)