What is the difference between a Problem and a Project? While it is difficult to draw a definitive line that separates one from the other, the attributes of each and their differences as I see them are:
Problems
- Require less student time to complete (usually less than an hour)
- Focus on a single task, with fewer than 10 questions relating to it
- Can involve open-ended questions, but more often does not
- Are often one of a series of problems relating to a topic
- Look similar to many exam questions
- Can be used to introduce new concepts (Exeter Math)
- Can be used as practice on previously introduced concepts (most math texts)
Projects
- Require more student time to complete (hours to weeks)
- Focus on a theme, but with many tasks and questions to complete
- Provide an opportunity to acquire and demonstrate mastery
- Ask students to demonstrate a greater depth of understanding
- Ask students to reach and defend a conclusion, to connect ideas or procedures
- Can introduce new ideas or situations in a more scaffolded manner
Why Use Problems?
- Convenience
– Short time to completion makes it easier to fit into a class plan
– Multiple problems allow a concept to be illustrated in a variety of settings - Student time constraints
– Less risk of excessive student frustration if they get stuck
– Less focus time required, if that is an issue for a student - Teacher time constraints
– Less complex setting requires less time to introduce
– Less student work on a solution means less time is needed to assess it - Risk
– If the theme of one problem does not engage a student, perhaps the theme of the next problem will
– Elapsed time differences between fast and slow workers will not be too great, so less risk of faster students having “too much” unproductive time
– If timing estimates are off, a final problem can easily be added or skipped towards the end of class
Why Use Projects?
- Less total time is spent “setting the stage”, more time spent accomplishing goals
- Greater student pride in their work, particularly when it will be exhibited publicly
- Students can learn “just in time” as they encounter new or more complex situations as they progress through project requirements.
- The richer context of the project can make the relevance of a skill or concept more apparent to students
- Greater student time spent producing the requirements of the project can work well with a “flipped classroom” approach.
- Mathematics can be credibly connected to skills, facts, and concepts from other disciplines (research, graphic design, writing, computer skills, etc.).
- The early stages of a project can rely heavily on the positive aspects of group work:
– build and test initial understanding
– develop ideas and creative approaches to the situation
– consider alternative approaches
– solicit peer feedback - Middle-of-project tasks can include deliverables intended for peer-assessment to help students:
– learn that first drafts can almost always be significantly improved
– master skills and procedures by re-using them a number of times over multiple drafts and days as they implement changes
– see the approaches their peers took to the same problem, and decide for themselves which approach seems most effective, efficient, elegant, etc. - The later stages of a project can require solo work, and have each student begin to work with unique data to ensure that the final product(s) accurately reflect each student’s understanding and ability.
A well designed project, with enough time devoted to it, should be able to produce better outcomes for students with a range of ability levels than a series of problems focusing on the same topic(s). Developing projects which have sufficient depth and breadth to justify the student time devoted to them, and which are engaging for students, can be the challenge.
MathMaine 