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Teacher Quality Workshops for 2010/2011. Group Norms. Be an active learner Be an attentive listener Be a reflective participant Be conscious of your needs and needs of others. Year-long Objectives.

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Group norms
Group Norms

  • Be an active learner

  • Be an attentive listener

  • Be a reflective participant

  • Be conscious of your needs and needs of others


Year long objectives
Year-long Objectives

  • Strengthen our mathematical knowledge for teaching to foster in our students conceptual understanding and mathematical thinking

  • Develop activities with high cognitive demand for students to engage

  • Orchestrate productive math discussion in our classrooms

  • Build a professional learning community


Mathematical Knowledge for Teaching

Subject Matter Knowledge

Pedagogical Content Knowledge

Knowledge of

Content and Students (KCS)

Common Content

Knowledge (CCK)

Specialized Content Knowledge (SCK)

Knowledge of curriculum

Knowledge at

the mathematical horizon

Knowledge of Content and

Teaching (KCT)



“There is no decision that teachers make that has a greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying mathematics.”

Lappanand Briars, 1995

… because …

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in which students engage determines what they will learn.”

Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver & Human, 1997


Four levels of cognitive demand greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the

Memorization

Procedures without connections to concepts or meaning

e.g., remember a ratio is written as A : B or A/B.

e.g., use a scale-factor to find equivalent ratios

Procedures with connections to concepts or meaning

Doing mathematics

e.g., use diagrams to explain why the scale-factor method works

e.g., the watermelon problem

Stein, Smith, Henningsen, & Silver, 2000


Two Lower-Level Cognitive Demands greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the

  • Involve either reproducing previously learned information (facts, rules, formulae, or definitions) OR committing them to memory

  • Involve exact reproduction of previously-seen material

  • Have no connection to the concepts or meaning that underlie the information being learned or reproduced

  • Memorization

  • 2. Procedures Without Connections

  • Are algorithmic (specifically called for OR based on prior work)

  • Has obvious indicator of what needs to be done or how to do it

  • Have no connection to the concepts or meaning that underlie the procedure being used

  • Are focused on producing correct answers rather than developing mathematical understanding

  • Requireonly “how” explanations, no “why” explanations


Two Higher-Level Cognitive Demands greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the

  • To deepen student understanding of concepts and ideas

  • Suggest pathways that are broad general procedures that have close connections to underlying conceptual ideas

  • Can be represented in multiple ways

  • Cannot be followed mindlessly (require cognitive effort)

3. Procedures with connections to concepts or meaning

  • 4. Doing Mathematics

  • Require complex and non-algorithmic thinking (ie. non-routine)

  • Require students to access relevant knowledge/experiences

  • Require students to analyze tasks and examine task constraints

  • Require students to explore and understand relationships

  • Demand self-monitoring

  • Require considerable cognitive effort (may lead to frustration)


Let’s Compare These Two Tasks greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the


Let’s Compare These Two Tasks greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the

What key understandings can be fostered in each task?


Comparing the Two Tasks greater impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the

  • Which task involves a higher-level cognitive demand? Why?

  • Which task is more appropriate for your students?

  • Which task better prepares students for STAAR?


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