our learning journey continues shelly r. rider. the overarching habits of mind of a productive...
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Our Learning Journey ContinuesShelly R. RiderThe Overarching Habits of Mindof a Productive Mathematical Thinker
Handouts Classroom Visits Tally for Students, and Practice Standards with Domain Progression
Table discussion:How are classroom visits connected to the process of sequencing instructional change?How do leader and teacher dialogue help with the process of instructional change?2Are you looking in the mirror or out the window?PausingParaphrasingProbing for specificityPutting ideas on the table
Paying attention to self and othersPresuming positive intentionsPromoting a Spirit of Inquiry
Seven Norms of Collaboration
DuFour,Richard,et.al.Learning by Doing.Bloomington:Solution Tree,2006. (p. 104)3Handout 7 Norms definitions
Handout 7 Norms Discussion Tool
PLT Goal StatementWhat can we do differently in our leadership skills in order to
have powerful conversations with our PLT members and
grow in our capacity to lead the implementation of the CCRS, through the application of best practices?After this slide Look at Tool 2.5 Again
4Professional Learning Team TrainingPLT Big Ideas
PLT Big Ideas overall
5Professional Learning Team TrainingQuality Instruction Scaffolding Professional Development Process
- Talk Moves Conceptual Learning Environment [physical & emotional] Productive Math Discussions Task Selection Quality QuestioningPLT 2012-2013PLT 2013-20146Classroom ImpactType ofTrainingKnowledgeMastery SkillAcquisitionClassroomApplicationTheory 85%15%5-10%PLUSPractice 85%80%10-15%PLUSPeerCoachingStudy TeamsClass Visits90%90%80-90%7The following table summarizes Showers and Joyce's research on increasing the positive impact of professional development.
The table shows the impact on classroom application when three methods of professional development are applied. When professional development focuses only on learning the theory of good instructional practice the result is a 5-10% rate of classroom application. The rate of classroom application increases slightly, to 10-15%, when the professional development experience includes opportunity to practice as well as learning about theory. Significant increase in classroom application occurs only when coaching, study teams, and/or peer visits are included with learning about theory and opportunity to practice.Levels of Cognitive DemandHigh LevelDoing MathematicsProcedures with Connections to Concepts, Meaning and Understanding Low LevelMemorizationProcedures without Connections to Concepts, Meaning and Understanding
8Tasks can be identified as either high or low-level. There are two kinds of high level tasks: Doing mathematics tasks and Procedure-with-Connections tasks. The differences between these two will be explained shortly.
The two kinds of low-level cognitive demand are procedures-withOUT-connections to underlying meaning or concepts and memorization. Memorization tasks are self-explanatory. Procedures-without-connections tasks are activities that ask students to perform a set of routinized procedures without knowing why they are doing them or anything about the underlying meaning associated with the operations that they are performing. Hallmarks of Procedures Without Connections TasksAre algorithmicRequire limited cognitive effort for completionHave no connection to the concepts or meaning that underlie the procedure being usedAre focused on producing correct answers rather than developing mathematical understandingRequire no explanations or explanations that focus solely on describing the procedure that was used9Procedures without Connection to Concepts, Meaning, or Understanding Convert the fraction to a decimal and percent383.008.375 = 37.5%2 460.37556404010Hallmarks of Procedures with Connections TasksSuggested pathways have close connections to underlying concepts (vs. algorithms that are opaque with respect to underlying concepts)Tasks often involve making connections among multiple representations as a way to develop meaningTasks require some degree of cognitive effort (cannot follow procedures mindlessly)Students must engage with the concepts that underlie the procedures in order to successfully complete the task11Procedures with Connections TasksUsing a 10 x 10 grid, identify the decimal and percent equivalent of 3/5.
EXPECTED RESPONSEFraction = 3/5Decimal 60/100 = .60Percent 60/100 = 60%12Hallmarks of Doing Math TasksThere is not a predictable, well-rehearsed pathway explicitly suggestedRequires students to explore, conjecture, and test Demands that students self monitor and regulated their cognitive processesRequires that students access relevant knowledge and make appropriate use of themRequires considerable cognitive effort and may invoke anxiety on the part of studentsRequires considerable skill on the part of the teacher to manage well.13Doing Mathematics TasksShade 6 squares in a 4 x 10 rectangle. Using the rectangle, explain how to determine each of the following: a) Percent of area that is shadedb) Decimal part of area that is shadedc) Fractional part of the area that is shadedSince there are 10 columns, each column is 10% . So 4 squares = 10%. Two squares would be 5%. So the 6 shaded squares equal 10% plus 5% = 15%.One column would be .10 since there are 10 columns. The second column has only 2 squares shaded so that would be one half of .10 which is .05. So the 6 shaded blocks equal .1 plus .05 which equals .15.Six shaded squares out of 40 squares is 6/40 which reduces to 3/20.
ONE POSSIBLE RESPONSE14The Importance of Student DiscussionProvides opportunities for students to:
Share ideas and clarify understandingsDevelop convincing arguments regarding why and how things workDevelop a language for expressing mathematical ideasLearn to see things for other peoples perspective
15Our Learning Journey ContinuesShelly R. Rider