A continuum of activity types are used in classrooms around the world. They range in duration from long (weeks or months) to short (seconds or minutes), from “projects” to “problems”. There are differing styles of activities, ranging from context-rich to almost context-free. There are also differing roles for activities in a curriculum: they can serve as warm-ups, practice, assessment, and/or a primary means of instruction (as at Phillips Exeter Academy and elsewhere).
The activities that seem most effective to me tend to require at least 15 minutes, if not more, to complete unless the context for the activity has been previously introduced. Longer (or recycled from the recent past) activities require fewer mental transitions for students, and hopefully lead to greater focus on the core concepts and skills. Obviously short duration activities cannot include as many of the attributes below as longer ones might. The “laundry list” of attributes I consider when creating or modifying an activity now includes:
1) A warm-up section which:
– engages the student in the context of the activity (Very important! But how… does it include: an interest of theirs? a topic they find relevant or important? a puzzle they wish to solve? etc.)
– provides background information for the activity
– provides some practice with key skills that will be needed
– (re)familiarizes students with the units of quantities involved
The warm-up could involve watching a short video, asking students to describe what they already know about the subject, and/or answering short questions based on information provided. It should also, if necessary, prime students to convert quantities to a consistent and appropriate unit of measurement.
2) A description of the activity, which includes visual information (pictures, drawings, videos, graphs), text (numbers, explanations), and one or two relatively simple initial questions. The intent of the questions is to help students “get their arms around” the nature of the activity and increase their engagement. The questions should:
– prompt restatement of the activity description by every student to build comprehension and identify potential ambiguities
– encourage students to form hypotheses about likely results, as they are likely to be more engaged if they are curious about the accuracy of their own prediction
– help students understand that the tasks to come are within their abilities – confidence is important when embarking on a multi-step task
Typical first questions might ask the student to describe the activity in their own words, look up some information from one or more primary data sources, make a “common-sense” prediction based on what know so far, then answer some specific questions based on the data (perhaps doing some unit conversions in the process).
3) An opportunity for the student to make one or more choices or decisions. This can increase engagement, and also customizes the activity. By customizing, a student’s ability to copy computational results or conclusions from the work of others is reduced, allowing group work to be more beneficial. Examples of possible student choices could include which…
– primary question(s) to answer, if multiple options are provided
– data set to use (which subset of available data is most relevant, which image will I use, which product size will I analyze, what numbers should I “randomly” pick to use?)
– function type(s) to use when modeling (depending on the level: linear, quadratic, exponential, logistic, sinusoidal, etc.)
4) A primary question or set of questions that ask students to make extensive use of skills and approaches mastered previously, while also giving them opportunities to use ones they are in the process of mastering:
– find and describe a relationship within the data
– make a prediction based on data
– reach a data-based conclusion
– describe the data or result in a more personally meaningful way. This will often involve converting to different units, or describing quantities as multiples of quantities from their experience (our school generates x pounds of trash per week, our town generates y times what our school does, and our state/province generates z times as much as our town).
5) One or more follow-on questions that extend or add depth to the analysis. These questions should also ask students to use a combination of skills and approaches they have mastered previously as well as ones they have yet to master. The first such question might be one that all students in the class should be able to answer, and subsequent questions might become increasingly challenging. The later questions could reach a level that is intended to challenge the most advanced students in the class, but might might only count as a small proportion of any grade on the activity. Examples could be:
– is there a different approach you could take to answering the question? How does its answer compare to your first method? Which method do you prefer, and why?
– re-examine the model/conclusion if one or two data points were different (for example, if outliers were excluded)
– further refine the initial model by making it more complex. This might entail introducing either the next scaffolding step in the activity, or an expanded data set.
– analyze a second, related, data set in addition to the first one
– make a prediction or conclusion using all information from this activity
6) A requirement that students interpret their answer(s) for “the general public”. This could entail describing the answer using a sentence or two, or using their quantitative results to defend an opinion or prediction about the topic. If the analysis is statistical in nature, or if the data lends itself to this, we can also ask students to defend a contradictory conclusion based on the same data (to build critical thinking skills).
7) A requirement that students reflect on their work for this activity:
– What parts did they handle efficiently, appropriately, thoughtfully, thoroughly?
– What parts did they handle inefficiently, cursorily, etc.
– What, if anything, might they do differently next time to achieve a better result?
The intent of this is to help build meta-cognition skills, which could also be modeled by the teacher at the end of the activity to consider how the activity itself could be improved for future use.
8) A rubric that clearly describes how student work is to be assessed. One interesting point is that, even on long-duration activities, not all work on the activity need be assessed by the rubric. If an activity is intended to be used toward the end of a unit where core skills/concepts have been assessed earlier, its rubric could focus exclusively on a shorter list of higher-order elements. If an activity will be self-assessed or peer-assessed, then a longer rubric could be practical; however if an activity will be assessed by the teacher, a rubric focused on selected higher order items can greatly reduce the time required to assess student work for an entire class.
Update 7/18/11: I just came across Gary Stager’s “Eight elements to guide great project design”, which provides a different and complementary perspective on the topic.
MathMaine 