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The Mathematical Education of K-8 Teachers at t he University of Nebraska-Lincoln, a Mathematics Mathematics Education Partnership Jim Lewis and Cheryl Olsen University of Nebraska-Lincoln. The Mathematics Semester for future elementary school teachers and - PowerPoint PPT Presentation

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<ul><li><p>The Mathematical Education of K-8 Teachers at the University of Nebraska-Lincoln, a Mathematics Mathematics Education Partnership</p><p>Jim Lewis and Cheryl OlsenUniversity of Nebraska-Lincoln</p></li><li><p>The Mathematics Semesterfor future elementary school teachers</p><p>and</p><p>Math in the Middle Institute Partnership a professional development program for middle level teachers </p></li><li><p>The Mathematics SemesterMath Matters, an NSF-funded CCLI grant began in 2000, and became The Mathematics Semester in Fall 2003</p><p>VisionCreate a mathematician mathematics educator partnership with the goal of improving the mathematics education of future elementary school teachersLink field experiences, pedagogy and mathematics instruction Create math classes that are both accessible and useful for future elementary school teachers</p></li><li><p>The Mathematics Semester(For all Elementary Education majors starting Fall 2003)MATHMath 300 Number and Number Sense (3 cr)PEDAGOGYTEAC 308 Math Methods (3 cr)TEAC 351 The Learner Centered Classroom (2 cr) FIELD EXPERIENCETEAC 297b Professional Practicum Exper. (2 cr)(a field experience in a local elementary school)Students are in an elementary school on Mondays and Wednesdays (four hours/day)Math 300 & TEAC 308 are taught as a 3-hour block on Tuesday and ThursdayTEAC 351 is taught on site at a participating elementary school</p></li><li><p>A look inside The Mathematics SemesterCurriculum materials Homework to develop mathematical habits of mindProfessional writingsThe curriculum projectLearning and Teaching ProjectActivities at the elementary schoolTeaching a Math LessonChild Study</p></li><li><p>Curriculum Materials</p><p>Sowder, J. et al. (2007). Reasoning about Numbers and Quantities. W. H. Freeman. (prepublication copy)Schifter, D., Bastable, V., & Russell, S.J. (1999). Number and operations, part I: Building a system of tens. Parsippany, NJ: Dale Seymour.Reys, Lindquist, Lambdin, Smith, & Suydam (2007). Helping Children Learn Mathematics. John Wiley & Sons.Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University.</p></li><li><p>A problem to get started Making change What is the fewest number of coins that it will take to make 43 cents if you have available pennies, nickels, dimes, and quarters? After you have solved this problem, provide an explanation that proves that your answer is correct? </p><p>How does the answer (and the justification) change if you only have pennies, dimes, and quarters available?</p><p>Note: We first encountered this problem in a conversation with Deborah Ball.</p></li><li><p>A Typical Weekly HomeworkAll Shook UpFive couples met one evening at a local restaurant for dinner. Alicia and her husband Samuel arrived first. As the others came in some shook hands and some did not. No one shook hands with his or her own spouse. At the end Alicia noted that each of the other 9 people had shaken the hands of a different number of people. That is, one shook no one's hand, one shook one, one shook two, etc., all the way to one who shook hands with 8 of the people. How many people did Samuel shake hands with?Note: This problem is a slightly modified version of Exercise #14, page 32, in The Heart of Mathematics, by Burger and Starbird, Key Curriculum Publishing, 2005. </p></li><li><p>Professional Writings Dear Math Professors,</p><p>We are 1st and 2nd graders in Wheeler Central Public School in Erickson, Nebraska. We love to work with big numbers and have been doing it all year! Every time we read something with a big number in it we try to write it. Then our teacher explains how to write it. We are getting pretty good at writing millions and billions!</p><p>We have a problem that we need your help with. We were reading amazing Super Mom facts in a Kid City magazine. It told how many eggs some animals could lay. We came across a number that we dont know. It had a 2 and then a 1 followed by 105 zeros!! We wrote the number out and it stretches clear across our classroom! We know about a googol. We looked it up in the dictionary. A googol has 100 zeros. Then what do you call a number if it has more than 100 zeros? Is there a name for it? </p></li><li><p>Another problem is that we learned about using commas in large numbers. In the magazine article they used no commas when writing this large number. That confused us. Also, if you write a googol with 100 zeros, how do you put the commas in? It doesnt divide evenly into groups of 3 zeros. There will be one left over.</p><p>We appreciate any help you can give us solving this big problem. Thank you for your time.</p><p>Sincerely,Mrs. Thompsons 1st & 2nd gradersMegan Kansier, Mark Rogers Marcus Witt,Ashley Johnson </p></li><li><p>clipping from Kid City magazineApple Of My EyeThe tiny female apple aphid is a champ as an egg-layer. This insect can lay as many as 21000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 eggs in 10 months.</p></li><li><p>What do Math Teachers Need to Be?Read What do Math Teachers Need to Be?* by Herb Clemens, a mathematics professor at The Ohio State University. Where does your own practice of teaching mathematics stand in relationship to what Clemens says mathematics teachers need to be: unafraid, reverent, humble, opportunistic, versatile, and in control of their math. If Clemens came to your classroom and watched you teach math, how would he answer his question: Can this teacher teach it [math] with conviction, and with some feeling for its essence? Explain. </p><p>* Published in 1991 in Teaching academic subjects to diverse learners (pp. 84-96).M2 InnovationsProfessional Writings</p></li><li><p>Curriculum ProjectThe goal is to investigate a new mathematical area of the elementary curriculum and consider what teachers need to know as well as what children need to learn the topic in the deep and meaningful ways suggested by the NCTM Standards (2000).</p><p>1)Pick a topic: data analysis and probability, geometry, reasoning and proof, or algebra.2)Read, analyze, and synthesize the mathematical topic in the NCTM Standards.3)Analyze and synthesize the topic in a set of reform curriculum materials (Everyday Math, Trail Blazers, Investigations, local curriculum).4)What do teachers need to know to teach this?5)Create 5 math problems that would help teachers learn. Create 5 math problems that would help children learn.</p></li><li><p>Learning and Teaching Project Area and PerimeterThe task began with a homework problem. It is taken from Reconceptualizing Mathematics: Courseware for Elementary and Middle School Teachers, Center for Research in Mathematics and Science Education, 1998.Is there a relationship between the area and the perimeter of a polygonal shape made with congruent square regions? (For fixed area, find the minimum and maximum perimeter. For fixed perimeter, find the minimum and maximum area.) Squares must be joined complete-side to complete-side. The outside boundary should be a polygon. In particular, this would not permit a shape with a hole in the middle. </p></li><li><p>A couple of weeks later we told our students:We want to revisit the Area and Perimeter problem. This is to be the basis for a mathematics lesson that you will videotape yourself teaching to one elementary school student. </p><p>How can you present this task to the student you will teach? How can you set the stage for the student to understand the problem? How far can the student go in exploring this problem? Remember that you want your student to discover as much as possible for himself (or herself). But there may be some critical points where you need to guide the student over an intellectual bump so that he (she) can move on to the next part of the problem.</p><p>Finally, produce a report analyzing the mathematics and your teaching experience.</p></li><li><p>Activities at the elementary school Math Lesson. You will teach a math lesson that connects to the curriculum in the classroom in which you are working. You should make use of the textbook and other resources from your cooperating teacher and what you are learning and reading in the Mathematics Semester.</p><p>Child Study. This assignment will give you some experience watching, listening to, probing, and assessing one childs understanding of several math problems focused on a particular area of mathematics. You will write a report of your interview and suggest instruction for the child based on the information you gathered in the interview session. </p></li><li><p>Math in the Middle Institute PartnershipPrincipal InvestigatorsJim Lewis, Department of MathematicsRuth Heaton, Department of Teaching, Learning & Teacher EducationBarb Jacobson, Lincoln Public SchoolsTom McGowan, Chair, Department of Teaching, Learning & Teacher Education</p><p>(Funding began August 1, 2004)</p></li><li><p>Invest in high-quality teachers* To improve K-12 student achievement in mathematics and to significantly reduce achievement gaps in the mathematical performance of diverse student populations. M2 Goal</p></li><li><p>M2 Partnership VisionCreate and sustain a University, Educational Service Unit (ESU), Local School District partnershipEducate and support teams of outstanding middle level (Grades 5 8) mathematics teachers who will become intellectual leaders in their schools, districts, and ESUs.Provide evidence-based contributions to research on learning, teaching, and professional development. Place a special focus on rural teachers, schools, and districts. </p></li><li><p>M2 Partnerships People and OrganizationsAll 14 rural Educational Service Units plus LPS65 Local School Districts91 Schools130 Teachers (4th cohort will begin summer 2007)29 teachers earned their Masters Degree 2006 </p></li><li><p>M2 Major ComponentsThe M2 Institute, a multi-year (25-month) institute that offers participants a coherent program of study to deepen their mathematical and pedagogical knowledge for teaching and to develop their leadership skills;</p><p>Mathematics learning teams, led by M2 teachers and supported by school administrators and university faculty, which develop collegiality, help teachers align their teaching with state standards, and assist teachers in examining their instructional and assessment practices; and</p><p>A research initiative that will transform the M2 Institute and the M2 mathematics learning teams into laboratories for educational improvement and innovation. </p></li><li><p>Math in the Middle Institute PartnershipM2 courses focus on these objectives:enhancing mathematical knowledge enabling teachers to transfer mathematics they have learned into their classrooms leadership development and action research </p></li><li><p>Math in the Middle Institute Design Summer Fall SpringWk1 Wk2&3Yr 1M800T Teac800 & M802T M804T M805T</p><p>Yr 2M806T Teac801 & Stat892 Teac888 M807T</p><p>Yr 3M808T Teac889/M809T and the Masters Exam</p><p>- A 25-month, 36-hour graduate program.</p></li><li><p>M2 Summer InstituteCombination of 1 week and 2 week classes.Teachers are in class from 8:00 a.m. - 5:00 p.m.32-35 teachers 5 instructors in class at one time.Substantial homework each night.Substantial End-of-Course problem setPurpose long term retention of knowledge gained.Presentation of solutions/celebration of success at start of next class.</p></li><li><p>M2 Academic Year CoursesTwo-day (8:00 5:00) on-campus class session.</p><p>Course completed as an on-line, distance education course using Blackboard and Breeze.Major problem setsProfessional WritingsLearning and Teaching ProjectsEnd-of-Course problem setSubstantial support available for teachers</p></li><li><p>M2 Institute CoursesEight new mathematics and statistics courses designed for middle level teachers (Grades 5 8) including:Mathematics as a Second LanguageExperimentation, Conjecture and ReasoningNumber Theory and Cryptology for Middle Level TeachersUsing Mathematics to Understand our World</p><p>Special sections of three pedagogical courses:Inquiry into Teaching and LearningCurriculum InquiryTeacher as Scholarly Practitioner</p><p>An integrated capstone course:Masters Seminar/Integrating the Learning and Teaching of Mathematics</p></li><li><p>Math 800T - Mathematics as a Second LanguageThe text was written by Kenneth and Herbert Gross of the Vermont Mathematics Initiative.Ken helped us kick off our first weekend.Innovations (i.e. additions)Habits of Mind problemsLearning and Teaching Project</p></li><li><p>M2 InnovationsHabits of Mind ProblemsA person with the habits of mind of a mathematical thinker can use their knowledge to make conjectures, to reason, and to solve problems. Their use of mathematics is marked by great flexibility of thinking together with the strong belief that precise definitions are important. They use both direct and indirect arguments and make connections between the problem being considered and their mathematical knowledge. When presented with a problem to solve, they will assess the problem, collect appropriate information, find pathways to the answer, and be able to explain that answer clearly to others. </p><p>While an effective mathematical toolbox certainly includes algorithms, a person with well developed habits of mind knows both why algorithms work and under what circumstances an algorithm will be most effective. </p></li><li><p>M2 InnovationsHabits of Mind ProblemsMathematical habits of mind are also marked by ease of calculation and estimation as well as persistence in pursuing solutions to problems. A person with well developed habits of mind has a disposition to analyze situations as well as the self-efficacy to believe that he or she can make progress toward a solution. </p><p>This definition was built with help from Mark Driscolls book, Fostering Algebraic Thinking: A guide for teachers grades 6-10.</p></li><li><p>The Triangle GameA Habits of Mind Problem(Paul Sally, U. Chicago) Consider an equilateral triangle with points located at each vertex and at each midpoint of a side. The problem uses the set of numbers {1, 2, 3, 4, 5, 6}. Find a way to put one of the numbers on each point so that the sum of the numbers along any side is equal to the sum of the numbers along each of the two other sides. (Call this a Side Sum.) Is it possible to have two different Side Sums? What Side Sums are possible?How can you generalize this game?</p></li><li><p>Select a challenging problem or topic that you have studied in MSL and use it as the basis for a mathematics lesson that you will videotape yourself teaching to your students. </p><p>How can you present this task to the students you teach? How can you set the stage for your students to understand the problem? How far can your students go in exploring this problem? You want your students to discover as much as possible on their own, but there may be a critical point where you need to guide them over an intellectual bump.</p><p>Produce a report analyzing the mathematics and your teaching experience.M2 InnovationsLearning & Teaching Projects</p></li><li><p>Action ResearchEach teacher takes TEAC 888, Teacher as Scholarly Practitioner, an action research course. Each teacher then conducts their own research project and writes a report about their findings.Action research is research done by teachers for themselves; it is not imposed on them by someone else (Mills, 2003, p. 5, italics in original).In conducting action research, drawing conclusions isnt about making generalizations for others...</p></li></ul>