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Teaching with Complexity

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Cognitive Demand

- The kind and level of thinkingrequired of students to successfully engage with and solve a task
- Ways in which students interact with content

Cognitive Complexity in Math

Low Complexity

- Relies heavily on recall and recognition of previously learned concepts.
- Test items typically specify what the student is to do, which often is to carry out some procedure that can be performed mechanically.
- It is not left to the student to come up with an original method of solution.

Cognitive Complexity in Math

Moderate Complexity

- Involve more flexible htinking than low complexity test items do.
- Requires a response that goes beyond the habitual, is not specified, and ordinarily involves more than a single step or thought process.
- Requires students to decide what to do—using informal methods of reasoning and problem-solving strategies—and to bring together skill and knowledge from various domains.

Cognitive Complexity in Math

High Complexity

- Makes heavy demand on student thinking.
- Engages students in abstract reasoning, planning, analysis, judgment, and creative thought.
- Requires students to think in an abstract and sophisticated way, often involving multiple steps.

Percentage of Points by

Cognitive Complexity Level

for FCAT Math

Low

DOK

Algebra I and Race to the Top

- What knowledge, skills and experiences in math do students most often lack that they should have acquired in earlier grades?
- What skills, knowledge and experiences in math separate students who enter and succeed in more advanced math classes from those who do not?
- What skills and knowledge in math that students acquired in elementary school take the most time to re-teach?
- What deficiencies in knowledge and understanding are most difficult to remedy and which ones continue to plague students in later courses?

Low

DOK

Algebra I Readiness Skills

- High school graduation requirements are increasing with the inclusion of state algebra tests required for a high school diploma. (Race to the Top)
- Algebra I is the key—and the barrier—to students’ ability to complete a challenging mathematics curriculum in high school.
- In a 2001 ninth grade study, 62 percent of students in HSTW sties who took something called algebra in the middle grades took college preparatory math in grade nine.
- According to a 2002 HSTW study, 56 percent of career/technical students completed four or more mat courses during high school.

Low

DOK

Percent of graduates enrolled in Algebra I or equivalent in a FL public school prior to 9th grade

- State Average – 29.60%
- Leon County – 18.40%
- Hillsborough – 41.80%
- Palm Beach – 59.70%
- Alachua – 33.50%
- Bay - 32.90%
- Duval – 46.10%

Low

DOK

- Review current course offerings at middle and high school to determine what changes are needed in the progression plan to ensure students are prepared for more rigorous STEM course work.
- Analyze current offerings in STEM accelerated course offerings to use as baseline data.

- Review current course offerings at middle and high school to determine what changes are needed in the progression plan to ensure students are prepared for more rigorous STEM course work.
- Develop a plan for expansion of STEM Accelerated offerings at the high school level.

- Develop a plan for expansion of STEM Accelerated offerings at the high school level
- Explore the use of distance learning to increase STEM accelerated offerings at the high school level.
- Develop and refine courses that serve as prerequisites to Advanced Placement and/or dual enrollment classes in the STEM areas, including , but not limited to, Algebra I and Earth/Space Science in middle school. (ongoing)
- Provide professional development for teachers to effectively teach accelerated STEM courses. (ongoing)
- Analyze student performance data to determine support needed for students in rigorous STEM courses. (ongoing)

- Develop a list of potential STEM Accelerated courses, including Advanced Placement and Dual Enrollment to add to high school course offerings.
- Implement revised course progression plan to include, but not limited to: Algebra I and Earth/Space Science in middle school and additional STEM courses in Advanced Placement and/or dual enrollment.
- Document implementation of additional accelerated STEM courses and industry certifications offered at each school to check progress in expanding opportunities. (ongoing)

- Documentation of increased STEM accelerated course offerings, including a comparison of baseline data to end-of-grant period date.

Engage.

Explore.

Explain.

Elaborate.

Evaluate.

Depth of Knowledge/Level of Cognitive

Complexity on the FCAT

Depth of Knowledge/Level of Cognitive

Complexity on the FCAT

Depth of Knowledge/Level of Cognitive Complexity on the FCAT

How complex are the items on your tests?

Low

DOK

Revise your text to make the questions more complex.

Low

DOK