Teaching with Complexity

Cognitive Demand

• The kind and level of thinking required of students to successfully engage with and solve a task • Ways in which students interact with content

Cognitive Complexity in MathLow 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 MathModerate 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 MathHigh 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 byCognitive Complexity Level

for FCAT Math

Grades Low LevelModerate

LevelHigh Level

6-8 10-20 60-80 10-20

Algebra I EOC

10-20 60-80 10-20

Geometry EOC

10-20 60-80 10-20

Algebra I and Race to the Top(1) What knowledge, skills and experiences in

math do students most often lack that they should have acquired in earlier grades?

(2) What skills, knowledge and experiences in math separate students who enter and succeed in more advanced math classes from those who do not?

(3) What skills and knowledge in math that students acquired in elementary school take the most time to re-teach?

(4) What deficiencies in knowledge and understanding are most difficult to remedy and which ones continue to plague students in later courses?

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.

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%

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.

Race to the Top STEM Timeline2nd Quarter 2010-2011

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.

Race to the Top STEM Timeline3rd Quarter 2010-2011

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)

Race to the Top STEM Timeline4th Quarter 2010-2011

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)

Race to the Top STEM Timeline2011-2013

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

Race to the Top STEM Timeline2013-2014

Complexity and Instruction

The 5 E Model

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?

Revise your text to make the questions more complex.