Vol 4 Issue 1, 9-28-07
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AL PHA Bits Volume 4, Issue 1 September 28, 2007 Introduction: Project ALPHA’s At the beginning of yet another school year, the learning gap between your class(es) at the end of the last school year and that of your new Monthly Newsletter class(es) can seem overwhelming. With all the new challenges that come with new students, it’s often difficult to remember how you managed to fill Algebra Preparedness that gap instructionally, much less think about ways to improve on it. for Higher Achievement That’s where we come in. We hope that ALPHA Bits, in conjunction with Project ALPHA’s website, will serve not only as a collection of resources but as your constant reminder of all our math professional development Inside this issue: past, present and future. With that said, in this issue you’ll find articles on the Math Curriculum Council’s Leadership Retreat and the ERUSD math CGI Workshop 2 focus for this year, the ALPHA Summer Institute, the CGI Workshop, moti- vating puzzle activities and common misconceptions to avoid as you con- Events Calendar 3 tinue your CLS this year. We hope you enjoy them! -Dawn, Lorena, Steve and Tor Professional Develop- 3 ment Opportunities Motivating MCC’s 2007/2008 Focus 4 Math Puzzles Since 2004, El Rancho teachers and collaborative lesson study. have had the benefit of a repre- Their conclusion: We need to Sudoku & Puzzle 5 sentative council which has coor- focus on “standards-based, bal- dinated and facilitated the math anced” math instruction. CLS: Key Elements & program district-wide. Represen- 5 Misconceptions tatives from each school meet • Standards-Based Instruc- monthly to analyze the progress tion: As we become more Standards-Based, of our students in math, discuss adept at designing lessons 6 Balanced Instruction directives and initiatives from the and interacting with students state and county, and find ways around problem-solving and 07’ Summer Institute 7 to address the issues most af- conceptual understanding, we fecting us as teachers of mathe- need to rely less and less on matics. our textbooks. Instead, we can guide our math programs Last spring, our representatives by the state standards – or discussed a professional devel- even by clumps of standards opment focus for 2007-2008 related to various mathemati- which would unify our many pro- cal big ideas. In this way, we fessional development initiatives are able to create learning ex- and program activities, including periences that are more co- the summer institute, CGI training (Continued on page 6) Volume 4, Issue 1 ALPHA Bits, Page 2 Cognitively Guided Instruction Workshop During the coaches: Dawn Esqueda and Steve Me- summer, the doza. Educational Services De- In the workshop, the participating teachers partment of El learned a framework for how children learn Rancho Uni- mathematics by focusing on the students' fied School intuitive understanding of number. They District held a studied various problem types and learned four-day Cog- methods for teaching them to students. n i t i v e l y Children's intuitive and learned understand- Guided Instruction (CGI) Workshop. CGI is a ing of the purpose of the equal sign were teacher professional development program also explored. based on over twenty years of research by Tho- mas Carpenter, Megan Franke, Linda Levi, Thanks to all participating teachers. We Susan Empson and Victoria Jacobs. While the look forward to working with you this year as workshop was open to all district math teach- you implement CGI in your classrooms. ers, the content focused on lower elementary mathematics. The purpose was to help teach- ers design instruction to develop stronger un- derstanding of numbers and greater fluency with mathematics for problem solving. The participating teachers were Guillermina Al- varez (Selby Grove), David French (Meller), Don Gaitan (Rivera Elementary), Irma Garcia (Birney), Jacquelyn Jauregui (Magee), Bonnie Kahler (Rio Vista), Leticia Lopez (North Ran- chito), and Kathleen Navarro (Rio Vista). Facili- tators were two district math instructional Mathtoon Volume 4, Issue 1 ALPHA Bits, Page 3 Events Calendar October 2007 ♦ Math Curriculum Council Sun Mon Tue Wed Thu Fri Sat October 8, 2007 1 2 3 4 5 6 3:30 - 4:45pm 7 8 9 10 11 12 13 Rivera Middle School Library 14 15 16 17 18 19 20 ♦ 4th - 7th Intervention In-Service October 11, 2007 21 22 23 24 25 26 27 8am - 3:30pm 28 29 30 31 Location TBD ♦ Principals’ In-Service November 2007 October 23, 2007 DO1 Tech Center Sun Mon Tue Wed Thu Fri Sat ♦ Math Study Meeting October 24 or 25, 2007 1 2 3 3:30 - 4:30pm 4 5 6 7 8 9 10 Rivera Middle School Library 11 12 13 14 15 16 17 ♦ CMC-South Conference 18 19 20 21 22 23 24 November 2 - 3, 2007 Palm Springs, CA 25 26 27 28 29 30 Professional Development Opportunities CMC-South Conference UCLA Math Content Program for Teachers (Formerly LUCIMATH) “Learning Mathematics Together: Representing, For the Fall 2007 schedule, visit: Reasoning, Reflecting” http://www.math.ucla.edu/mcpt/enrollment_fall_2007.htm November 2-3, 2007 For more information, visit: http://www.math.ucla.edu/mcpt/ Palm Springs, CA Call: Theresa Lee For more info, visit: (310) 794-6588 http://www.cmc-math.org/PS Volume 4, Issue 1 Page 4 Motivating Students with Puzzles Motivating students is always a challenge. Students who follow the five steps correctly Quite often students have other things on are often amazed that any combination of the their mind besides math. One way to engage four numbers has a sum of 45. students is with math puzzles. The Constant- Sum Grid (see Fig. 1), for example, is an in- How does this work? teresting puzzle taken from the August 2004, • Encourage students to look for patterns. MATHEMATICS TEACHER article, Motivating • Show how original numbers are generated Activities That Lead to Algebra by Ramakrish- (see Fig. 3). nan Menon. + 1 8 6 9 Directions 5 6 13 11 14 11 12 19 17 20 Step 1: Circle any one of the sixteen numbers in the grid, say, 17. Keep the circled number, 3 4 11 9 12 but cross out all the other numbers that are in 2 3 10 8 11 the same row and column as the circled num- ber (see Fig. 1). Figure 3 6 13 11 14 • Use variables to replace values (see Fig. 12 19 17 20 4). 4 11 9 12 + E F G H 3 10 8 11 A+E A+F A+G A+H A B B+E B+F B+G B+H Figure 1 C C+E C+F C+G C+H Step 2: Circle another number, say, 6, that D D+E D+F D+G D+H has not already been circled or crossed out. Keep the circled number, but cross out all the Figure 4 other numbers that are in the same row and column as the circled number. • A+B+C+D+E+F+G+H = 45. A circled value is the sum of two addends, say, A + Step 3: Circle a third number, say, 12, that G = 17, since A = 11 and G = 6. When has not already been circled or crossed out. the rest of the values are crossed out in Again, keep the circled number, but cross out the appropriate row and column this elimi- all the other numbers that are in the same row nates the possibility of repeated addends. and column as the circled number. Thus, essentially this puzzle is simply add- ing up all the addends A through G. Step 4: Circle a fourth number, say, 10, which is the last available number. Visit our website, www.erusd.k12.ca.us/alpha, for the complete article and more information Step 5: Only the four circled numbers remain. on the Constant-Sum Grid. The article also Add the four circled numbers. Is your answer includes other motivating puzzles and activi- 45? ties. Volume 4, Issue 1 ALPHA Bits, Page 5 Sudoku Difficulty Level: Medium Puzzle The figure below is composed of congruent 9 7 1 8 4 6 squares. How many rectangles are in the 6 4 2 1 figure? 4 3 8 4 2 5 6 4 6 6 5 1 8 5 7 1 1 2 9 8 5 7 CLS: Key Components & Common Misconceptions At the onset of any new professional development endeavor we must be open to the likelihood that immediate and/or great success isn’t always possible within our first attempt. There will always be a learning curve and only time and practice will lead to efficient modifications. We must keep this in mind as we begin a second year of Collaborative Lesson Study implementation. We could now re- flect on our efforts from last year and, not only summarize the key components of Collaborative Les- son Study, but highlight important misconceptions to avoid in our continued attempts. Key Elements of Collaborative Lesson Study • Collaboratively develop learning goals for the lesson as well as the overall math concept. • Collaboratively plan a lesson that will address these goals. • Select one teacher to implement the lesson while the rest make focused observations. • Collaboratively reflect and discuss on the effectiveness of the lesson and make revisions ac- cordingly. • If possible, implement the revised lesson with your own class. Reflect and revise, if necessary. Important Misconceptions to Avoid1 • Lesson study is about creating a unique, original, or never-before-seen lesson. • There will be no benefit from just a few lesson study lessons; it’s important to conduct lesson study for as many lessons as possible. • Lesson study is about perfecting a single lesson. • Lesson study is about producing a library of tried-and-tested lessons for others to use. Collaborative Lesson Study is about improving on the best available lessons in order to meet your goals for your students. You will never attain the perfect, “tried-and-tested” lesson because the needs of your students will always be different. 1Excerpted from “Challenges to Importing Lesson Study: Concerns, Misconceptions, and Nuances” by Sonal Chokshi and Clea Fernandez. Volume 4, Issue 1 Page 6 Standards-Based, Balanced Instruction (Continued from page 1) herent, connected and comprehensible and that align closely with state assess- ments without slavishly teaching to the test. • Balanced Instruction: Good mathemat- ics programs help students understand mathematics at a conceptual level and be- come more adept at solving problems in addition to developing their skills in com- putation. The state framework calls this conceptual understanding, problem- solving and procedural fluency. Good vention outlines and lists of resources and classroom instruction must also balance teaching strategies that will guide district opportunities for students to explore intervention programs in grades 4 through mathematics independently with guidance 7. Intervention teachers can attend a full- and direct instruction from the teacher. day in-service on October 11 at the re- The Math Council’s professional develop- quest of their principals. ment focus encompasses both types of balance. • Algebra Readiness: Representatives from the middle and high schools created In June, the Math Council attended a three- a pacing guide and assembled instruc- day leadership retreat at the scenic Pico Park tional materials for 8th-graders who are not Community Center. Representatives devel- yet taking Algebra I. Nine teachers at- oped action plans for a Math Field Day, tended an in-service day on September cross-grade articulation, intervention, parent 10 and will follow up on November 5 and workshops and district workshops – all de- February 9. Both the intervention and signed to further the focus on standards and algebra readiness outlines follow the balanced instruction. At the September coun- guidelines set out in the 2006 Mathemat- cil meeting, work continued on the action ics Framework. plans with the following results: In addition to these specific initiatives, math • Field Day: Building on the success of last council representatives will continue to work year’s county field day teams, El Rancho closely with math coaches to implement vari- mathletes will have the chance to com- ous types of collaboration: Course-specific pete in a district field day before moving to meetings at the high schools focusing on Al- the county competition. Council represen- gebra I and Math A; grade-level and depart- tatives will present information as it be- ment meetings at the elementary and middle comes available; the competition has schools for the implementation of detailed been tentatively scheduled for April. curriculum planning and lesson study; and data analysis workshops at all levels to re- • Intervention: Elementary and middle view benchmark exam results from the new school representatives have created inter- Edusoft assessment system. Project ALPHA’s Monthly Newsletter Contact Information Dawn Esqueda El Rancho Unified School District firstname.lastname@example.org Lorena Ponciano email@example.com Categorical Programs Burke Middle, 801-5059 North Park Middle, 801-5137 9333 Loch Lomond Dr. Steve Mendoza Pico Rivera, CA 90660 firstname.lastname@example.org Tor Ormseth email@example.com Rivera Middle, 801-5088 Phone: 562-801-5224 El Rancho High, 801-5355 Fax: 562-949-0519 Categorical Programs, 801-52 26 El Rancho Unified Sch firstname.lastname@example.org El Rancho Unified School District ool District Board of Education Dr. Joseph Board of Education Rivera Vincent Vincent Chavez Rita Jo Ramir Chavez Del Rita Jo Ramirez ez Delia Alvidrezia Alvidrez las Lup Joseph Rivera, Ed. D. e Sa Lupe Salas Superintendent Look for us on the web! Superintendent Norbert D. Genis Norbert D. Genis www.erusd.k12.ca.us/alpha Assistant Superintend Susanna Assistant Superintendent Susanna S.S. Smith Dr. Kaent n thry Smith Kathryn EnloeEnloeD. , Ed. 2007 ALPHA Summer Institute The 2007 ALPHA Summer Institute was held Thank you, teachers, for taking time in the June 28 through July 12. Thirty-six El Rancho summer to attend the institute. Your interest Unified teachers participated in the eighty in increasing your math content and pedagogi- hours of intensive training focused on rational cal knowledge and willingness to participate in numbers. Topics included: the many activities is greatly appreciated. Mathematics for Teaching Math: Teach- For more information on the 2007 Summer ers must be attuned to mathematics dif- Institute, please visit our website: ferent from that of engineers and scien- http://www.erusd.k12.ca.us/ProjectALPHAweb/ tists in order to meet the needs of their index_files/Page1791.htm students. The teachers therefore ex- plored questions like: What does it mean to divide 1¾ by ½? Student Misconceptions: Teachers inter- viewed students to determine their mis- conceptions of rational number concepts and discussed typical misconceptions as they solved problems. Balanced Instruction: Through lesson study and collaborative planning, teach- ers developed and taught lessons that balance conceptual understanding, problem solving and computational pro- cedures.