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• 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

Pedagogical Content

Knowledge

Common Content

Knowledge (CCK)

Specialized Content Knowledge (SCK)

Knowledge of

Content and Students

(KCS)

Knowledge of Content

and Teaching

(KCT)

Subject Matter

Knowledge

Knowledge at the

mathematical horizon

Knowledge of

curriculum

Mathematical Knowledge for Teaching

Cognitive Demand Levels

“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.”

Lappan and Briars, 1995

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

Stein, Smith, Henningsen, & Silver, 2000

… because …

“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

Stein, Smith, Henningsen, & Silver, 2000

1. Memorization

2. Procedures without connections to concepts or meaning

3. Procedures with connections to concepts or meaning

4. Doing mathematics

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

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

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

e.g., the watermelon problem

1. Memorization• 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

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• Require only “how” explanations, no “why” explanations

Two Lower-Level Cognitive Demands

3. Procedures with connections to concepts or meaning• 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)

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)

Two Higher-Level Cognitive Demands

Let’s Compare These Two Tasks

What key understandings can be fostered in each task?

Let’s Compare These Two Tasks

Comparing the Two Tasks

i. Which task involves a higher-level cognitive demand? Why?

ii. Which task is more appropriate for your students?

iii. Which task better prepares students for STAAR?