Upside-down Problem Solving
•Download as PPT, PDF•
0 likes•59 views
Instructional strategies for solving mathematics problems
Recommended
More Related Content
What's hot
What's hot (20)
Similar to Upside-down Problem Solving
Similar to Upside-down Problem Solving (20)
More from Jeffrey Miller
More from Jeffrey Miller (9)
Recently uploaded
Recently uploaded (20)
Upside-down Problem Solving
- 1. Upside-Down ProblemUpside-Down Problem SolvingSolving Developed by Jeffrey Miller, M.A.T.Developed by Jeffrey Miller, M.A.T. K-12 Mathematics FacilitatorK-12 Mathematics Facilitator
- 2. Session NormsSession Norms The Overall Goal of all this session is to advance our own learning, not “fix” the practice of others! Time Management Personal Technology Management Positive Interaction
- 3. Intended Learning for TodayIntended Learning for Today Zone of Proximal Development What’s Next? Upside Down Problems Closed Ended vs. Open Ended Task Can Our Students Get Smarter?
- 4. ActivityActivity 11 Quick Write:Quick Write: Examining Our BeliefsExamining Our Beliefs About Effort and AbilityAbout Effort and Ability Can a student become smarter? If yes, how? If no, why not?
- 5. What Does Research Say?What Does Research Say? • Aptitude does not determine how much students learn. • Sustained and directed effort can yield high achievement for all students. • Everything is organized to evoke and support this effort, to send the message that effort is expected, and that tough problems yield to sustained work. • All students are taught a rigorous curriculum matched to the standards, along with as much time and expert instruction as they need to meet or exceed expectations.
- 6. …Intelligence is learnable. People can become more intelligent by living and working every day in a particular kind of environment: one that coaches them in using problem-solving skills and praises them for using the skills; one that holds them accountable for using them well because it assumes they are smart and capable. This kind of learning environment can create the beliefs and dispositions that constitute intelligence. Principles of Learning for Effort-Based Education Lauren Resnick and Megan Williams Hall
- 7. Zone of Proximal DevelopmentZone of Proximal Development
- 8. Zone of Proximal DevelopmentZone of Proximal Development
- 9. Closed Ended vs. Open EndedClosed Ended vs. Open Ended Task?Task?
- 10. How to go from Closed Ended toHow to go from Closed Ended to Open EndedOpen Ended M. Kabiri, and N. Smith (2003), Turning Traditional Textbook Problems into Open-Ended Problems • Multiple solutions or solution strategies (open approach) • Focus on the pathway, not the solution • Solution must not be immediately obvious • Minimal scaffoldling steps
- 11. ActivityActivity 22 Identify the TaskIdentify the Task As a group, search through the textbook resources for an example of a traditional closed- ended problem solving task. Identify two characteristics that make it closed ended.
- 13. ActivityActivity 33 Lesson Activity: TextbookLesson Activity: Textbook PracticePractice As a group analyze traditional textbook task. Modify the task to make it an upside-down problem.
- 14. Mathematical Task Analysis GuideMathematical Task Analysis Guide HighlightsHighlights Lower-Level Demands • Reproducing or committing to memory facts, rules, formulas, or definitions. • Are algorithmic. • There is little ambiguity about what needs to be done and how to do it. • Are focused on producing correct answers rather than developing mathematical understanding. • Require no explanations, or explanations that focus solely on describing the procedure that was used Higher-Level Demands • Suggest multiple broad pathways procedures. (not a predictable, well- rehearsed approach) • Usually are represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations). • Although general procedures may be followed, they cannot be followed mindlessly. • May involve some level of anxiety for the student due to the unpredictable nature of the solution process required. From: “Implementing Standards-Based Mathematics Instruction” by Stein, Smith, Henningsen and Silver
- 15. What is next…What is next… • You should visit at least one classroom, preferably in your content/grade level group, apply the mathematical task analysis guide, and look for rigor. Document your findings. • When I visit your classrooms and content lesson planning meetings I will be applying the mathematical task analysis guide & looking for evidence of rigor.
- 16. Impacting OurImpacting Our PracticePractice Red lightRed light 1 thing I will stop doing… Yellow LightYellow Light 1 thing I will continue doing… Green lightGreen light 1 thing I will start doing…
- 17. THANK YOU For Attending Upside-Down Problem SolvingUpside-Down Problem Solving
Editor's Notes
- Looking deeply at our practice helps us to understand how we enact our beliefs.
- 1. A clear, high, minimum set of standards that every student is expected to meet is established in each subject. 2. All students are taught a curriculum that prepares them to meet the standards. 3. Additional instruction and learning time is provided for students who need it in order to meet the standards. Tutoring or specialized small group instruction is available for children who are beginning to fall behind the average learning level of the class. Title I funds are used to provide after-school and weekend classes, not for "pullout" instruction during school time. Some special education funds are also used this way. Staff assignments are organized so that maximum time of all adults in the school is used for group or individual instruction. Arrangements are made with other agencies in the community (e.g., community centers, scouts, 4-H, after- school day-care operators) to provide tutoring and other learning support activities that are linked to the curriculum students are studying in school. Community funding sources for weekend and summer school programs are tapped. Volunteer tutors (including older students) are used, and are organized and trained for their tutoring work. Parents and families understand why extra study time is needed and support the program. Homework includes practical suggestions for family activities that will support student learning. 4. When there are special learning opportunities, a willingness to do the work is the primary admission criterion. 5. Students are responsible for completing academic work that has been specified and negotiated. 6. There are specified bodies of work (e.g., reading a certain number of books, writing a research paper, performing school service) that students must accomplish by the end of key stages of schooling.