Rich Tasks & Contexts

The article by Jennifer Piggott was about “Rich Tasks and Contexts”.  Her question which lead her to write the article was “what are ‘rich tasks’ and why are they important?”.  Piggott partially modeled a rich task in developing her own open-ended question, which is her “problem”.  She started with the information that she knew and then synthesized her own ideas with those of others.  She also connected her knowledge to the NRICH website which, she says, contains many examples of rich tasks and also discussed the Geoboard environment which provides a “rich context”, which is a series of related tasks.   

My understanding of a rich task is that it includes:

PROBLEM DEVELOPMENT:

-rich task environment is key: students drive learning; pose own problems

-accessible to wide range of learners; many entry points

-intriguing, enjoyable problem with real life application

-initial success with different levels of challenges (low threshold; high ceiling)

PROBLEM SOLVING:

-differentiated instruction: different start, middle, end with surprises

-broaden/deepen math content & understanding

-skills: confidence, independence, creative & critical thinking, collaboration & communication

SOLUTION TO PROBLEM:

-elegant, efficient, logical, creative solution & application

-emergence of patterns, generalizations, principles, connections, extensions

-evaluate findings

Teaching using rich tasks reminds me of inquiry based learning in science in which students are given a question based on a big idea (eg. What affects homeostasis in humans?) and then they have to develop their own intriguing problem to solve (eg. What is the effect of the tempo of music on short term memory?). The students then need to develop their own model, test it by collecting data and revisit their hypothesis.  This same task could be used with a math focus in mind and would bring out data collection, relationships between variables, graphic representation and all of the mathematical processes in the curriculum.  In science, we are always connecting ideas to real life applications.  Dr. Marion Small believes that teachers should present non-contextual math problems along with those based in real life.  She also believes in creativity and divergence in mathematical problem solving and to not just link math to the arts (or science, in my case!).  I found the idea of solving a problem just for the sheer challenge and enjoyment of the process quite freeing.   

Dan Meyer stated that many teachers don’t like the ambiguity of open-ended rich tasks.  Generally, our vast experience as students of mathematics has taught us that the product is what is valued and thus it is more comfortable to retreat to that same method of teaching math (ie. formula, plug in #’s, spit out answer).  Dr. Jo Boaler stated that our past and current model of education mostly prepares students to do calculations but with the advent of computers, jobs needing only these skills no longer exist.  Thus, we need people who are problem solvers.  In order to change our mindset, Jennifer Piggott suggests that doing rich tasks means that the teacher has to “let go” because this type of teaching is student driven instead of teacher directed.  Dr. Jo Boaler cited a study which found that after students struggle with a problem, they are more ready to learn the mathematical method because their brains are primed.  In class, we discussed that if each teacher increases their emphasis on process over product, that eventually the educational system will change and students will become better problem solvers which is what our society needs.

During our conversation, I showed the group the NRICH website.  Jennifer Piggott’s article was actually found on the website of which she is a proponent.  I didn’t find it easy to “search” for a particular topic (I was looking for a pendulum activity for our “rich task”) but found it easier to just “browse” through the website.  There are lots of great tasks presented on the website, but I wondered if they were all met the criteria of being “rich”.  Since I used one of these activities in my 3 part lesson plan, I brought it in and we tried it as a group and then discussed if it fit the criteria of a “rich task”.   The group liked the “Simplifying Doughnut” Go Fish game, and although it was intriguing and fun, it did not allow for enough diversity to make it a rich task.  I asked the group how we could make this activity into a richer task.  One idea was that given the dominoes, the students could devise their own set of “rules” to play the game.  This would allow for more student direction and diversity and they would own the task. 

I also asked our group if they thought that rich tasks support adolescent learners during this time of brain development.  We talked about how rich tasks would allow adolescents more creativity, choice, risk taking, independence (from the teacher) and sociability which they find rewarding.  As long as the task provided enough entry points and the students met with success, the challenge of the process of problem solving should reinforce the levels of dopamine to make it a pleasurable experience.

Rich tasks are done in group settings.  I asked how we should structure the groupings of students.  We concluded that mixed ability groupings would be the best choice theoretically because a rich task should provide lots of entry points and challenge all students, but practically, there may be times in which homogeneous grouping would allow for a more equal sharing.  I also posed the question to the group regarding how we assess students individually regarding their process when they are working in a group setting.  We are all hoping to gain more insight into the practicalities of assessment of rich tasks during tomorrow’s class!

I think that it is easier for me to let the students drive their own learning in science which I have taught for many years because I am already comfortable with the content.  I myself am capable of seeing the connections and big ideas in the science curriculum and thus am able to make the connections when consolidating their learning.  It is definitely a scarier thing to think of presenting a rich task in a math class which I have never taught nor have a good grasp of breadth of the curriculum.  As is backed up by the research, I believe that teaching using rich tasks supports more learning, for both the students and myself….I will just need to “let go”!!