Last year, I had a great discussion with a colleague about how many times a student needs to demonstrate "learning'.

Learning is a broad concept and so is "understanding". I like to refer to Blooms taxonomy on what entry level understanding looks like and how it leads up to higher order thinking skills. See a rough chart below:

As a teacher, we want students to have a deep understanding of a concept rather than a surface level grasp that we see in the chart above under "knowledge" or "comprehension". For example a surface level understanding of the Vietnam war might be:
  • Being able to recall where Vietnam is on the map
  • Remembering the dates of the war.
Supericial. However, if we try to structure learning around deeper understandings of "evaluation" and "synthesis" students can begin to explain:
  • Lasting legacies of the war
  • Major policy changes following the conflict
  •  How the Vietnam war was similar or different to other conflicts in the past.
As learning is often scaffolded with surface level understanding which eventually builds to such deeper understandings of "knowledge" or "comprehension" there are many opportunities for formative checking to ensure that students are in fact learning towards this higher order thinking skills. However, if students show a deep level of understanding early in a unit of study, why should they be required to show it again and again?

I'm not the first person to coin this term, although it goes by many other names. Basically, it exempts students from subsequent demonstration if there are opportunities for higher level thinking that the students have meet early on. With our "challenge by choice" system (Green-Standard and Blue-Advanced) students are given some entry level application with "Green" level work but higher order evaluation and synthesis opportunities through some "Blue" level questions. It's meant to give the students that are challenged to meet the curriculum the chance to feel successful and diagnose their strengths and weaknesses. However, for students that quickly learn, they have the chance to "compact" out of future demonstration. See the example below:

The problem above is very entry level. It's assessing whether or not they can manipulate operations with negative numbers. This is a problem from our "Green Level" quiz. See the same problem on the advanced "Blue" quiz below:

Obviously the problem above is a word problem but implicit in it are a number of learning standards regarding operations, algebra and problem solving skills. Problems like this are more prominent in our summative and performance based assessments. It's obviously more difficult too. If a student gets the above COMPACT question correct, I exempt them from doing it again on a final test.

Conditions for COMPACTING
Taking a more challenging quiz is a gamble for students. The Blue level has three opportunities for compacting out and the green has only 1. (For this quiz only, but the number can be adjusted.) My policy regarding homework is that it is self-assessed by students but I do check their flipped notes at the beginning of class to ensure that they're done. To keep up with assignments is a necessary student skill, so if students have shown good work ethic, they may have this opportunity to "compact out'

Condition #1-Homework in that unit up to that point must be complete and on time
Students that have good homework skills will find that they will have opportunities to compact out of some our learning standards. If students struggle to get homework in on time, if they get a compact question correct, they still have to do it later. If all assignments have been completed, students can compact out. This is a powerful motivator but does not penalize students in any way which is consistent in the assessment philosophies of Tom Shimmer and Ken O Conner.

Compacting is a new pedagogy that I hope to try this year. I've read a little about it, but the theory is sound in mixed ability classrooms. Teachers must continue to provide opportunities for remediation, but must also consider the problem of "double taxation" of talented and gifted learners. I hope to collect data on compacting and share it by the end of the school year.

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Understanding: If it's shown once, is that enough?
Challenge by Choice 

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