Presentation on theme: "Silicon Valley Math Initiative Professional Development Series"— Presentation transcript:
1Silicon Valley Math Initiative Professional Development Series NUMBERSanta Cruz County, September 2012
2Agenda Lunch Math Talk MARS Performance Assessment tasks Welcome and IntroductionsGoals and NormsProblem of the Month (POM)Common Core - Math PracticesPerformance Assessment introductionFormative Assessment Lesson (FAL)Math TalkMARS Performance Assessment tasksEvaluation8:30-8:35 Welcome/Introductions8:35-8:45 Goals and Norms8:45-10:00 POM – do the math, posters (justification & status)10:00-10:15 break10:15-10:40 CCSS MP – read/discuss, connect POM posters to MP10:40-11:00 MP questioning sort; article – questioning11:00-11:15 gallery walk with post-its (think about questioning)11:15-11:30 debrief POM11:30-11:45 Performance assess intro; do FAL pre-assess11:45-12:30 lunch12:30-1:45 FAL1:45-2:00 Math talk 21x19 (difference of two squares)2:00-2:15 debrief math talk and read/discuss articles2:15-2:45 MARS2:45-3:00 wrap-up and evaluationLunch
3Goals To advance teachers’ own understanding of mathematics To enhance teachers’ pedagogical knowledge in teaching mathematics
4NormsReflection:Think of a time when you worked well with others (in collaboration). How would you describe that experience and what made it successful for you?Think of a time when you had a negative experience working in a group. How would you describe that experience and what made it negative for you?
5NormsIdentify norms:From your reflection, identify norms you feel need to be in place to foster a community of learners.Share ideas at your table. Be prepared to share whole-group.
7Doing Mathematics Making Sense by Hiebert et al Ideas, expressed by any participant, have the potential to contribute to everyone’s learning and consequently warrant respect and response…. Examining an idea thoughtfully is the surest sign of respect, both for the idea and the author.”Making Sense by Hiebert et al
8Why a Problem of the Month (POM)? George Polya, said, “A problem is not a problem if you can solve it in 24 hours.”Doing math is solving non-routine problems.Perseverance and learning from mistakes are important attributes of good mathematicians.
9How are the POMs used?The POMs are used school-wide to promote problem solvingEach problem is divided into five levels, A-E, to meet the learning development needs of all students.A great tool for Differentiated Instruction.Students, teachers and parents learn to ask questions and persevere in solving non-routine problems.The whole school celebrates doing mathematics at school.
10POM: “Measuring Up” Individually, read through all the levels. Then, go back to Level A and start working on the tasks in order.When everyone has had an opportunity to think through the mathematics, then you can begin to collaborate.
11Creating Posters You will create 2 group posters… Your concluding thoughts on an explanation poster for a level you feel you have completed.ANDYour current thoughts on a status poster for a level you are still exploring.
12Explanation Poster: The focus of your poster should be on how your findings can be justified mathematically and how your findings make sense. Include words and visuals (such as drawings) as a part of your justification.Status Poster: The focus of your poster should be on your processes so far and where you think you want to go next and/or questions/wonderings you have about this level. Include words and visuals as a part of your justification.*Remember to justify or explain your processes you have used so far and why they make mathematical sense as clearly as you can.
13NORMS for Gallery WalkDiscussion is focused on what each of us can learn from each otherBe respectful of ALL workThe FOCUS of a gallery walk is on the MATHEMATICS of the problem.
14Gallery Walk ProtocolStart by looking at EXPLANATION posters for the level you worked on.Are the explanations clear? Have the groups made a viable argument?If they aren’t, what question might your group ask that will push for more precise explanation? (Write your question on a post-it. Notice others’ questions.)Next look at STATUS posters of the level you worked on.Compare and contrast people’s way of thinking on those posters to your own way of thinking.Finally, visit posters of a different level than yours. Compare and contrast.
15Quick Write What would you like to remember about this POM…. As a learner, what are you interested in further exploring for your own learning?As a teacher what should you consider when using this POM with students?
18Math TalksA daily ritual with the entire class for the purpose of developing conceptual understanding of and efficiency with numbers, operations and mathematics. (approximately 10 minutes per day)Math Talks are used to:Review and practice procedures and conceptsIntroduce concepts and properties about numbersReinforce procedures and number concepts.Explore mathematical connections and relationships.
19Math Talk Norms We share ideas and listen to others We ask “why does this work” until we understand.We respect one another's opinionsWe know that we learn from mistakes as well as from correct answersOur goal is for the students, the teacher and the mathematics to agree in the end!
20Performance Assessments and Formative Assessment Lesson (FAL)
21Overview of Performance Assessments Purposes:To make sense of student thinkingTo flush out misconceptionsTo design instructionDesired responses: students’ explanations of their solution strategiesPromotes multiple solutions strategies
22Formative Assessment Lesson “Proportion and Non-proportion Situations”Outline:Give pre-assessment.Use pre-assessment results to inform instruction – do not “correct” student work.Implement lesson.Students return to their original assessment task and try to improve their own responses.
39Performance Assessments To Inform Instruction And Measure Higher Level Thinking The Mathematics Assessment Resource Service (MARS) is an NSF funded collaboration between U.C. Berkeley and the Shell Centre in Nottingham England.The Assessments target grades 2- Geometry and are aligned with the State and NCTM National Math Standards.
40Performance Assessments To Inform Instruction And Measure Higher Level Thinking RampTopEntry level - (access into task)Core Mathematics - (meeting standards)Top of the Ramp - (conceptually deeper, beyond)CoreAccess
41A Look at a Progression of MARS Tasks Familiarize yourself with the tasksQuiet Think TimeWhat is the mathematics in each of the tasks?What are the mathematical connections between and among these tasks?What misconceptions might students have when completing the task?Each table group will have an opportunity to talk about these questions.Share out to the whole group.
42Common Core State Standards Standards of Mathematical Practice
43Mathematical Practice Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.