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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 Math Low Complexity.

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Teaching with Complexity

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Teaching with Complexity


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


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.

  • Analyze current offerings in STEM accelerated course offerings to use as baseline data.


Race to the Top STEM Timeline3rd 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 Timeline4th 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 Timeline2011-2013

  • 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 Timeline2013-2014

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


Complexity and InstructionThe 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?

Low

DOK


Revise your text to make the questions more complex.

Low

DOK


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