Sunday, October 6, 2013

Students constructing their own understanding

How could we use questions or problems to assist in helping students construct their own understanding?
"Education research has shown that an effective technique for developing problem-solving and critical-thinking skills is to expose students early and often to “ill-defined” problems in their field. An ill-defined problem is one that addresses complex issues and thus cannot easily be described in a concise, complete manner. However educators are also required to have specific objectives and outcomes for students to reach. Often students stray from or miss the path you would like like them to take to reach your objectives and outcomes. How would you facilitate and guide students, during a project, who are “lost or off track” to help them reach the stated course objectives and outcomes?"

My homework for Week 4 is to consider the above.  It goes perfectly with what I found from last spring, when organizing photos from a recent trip: a video of students working in groups to answer a complicated math problem.  

I interviewed the students as they were busily using and creating representation of items in the problem. The question involved how many given items would be divided equally into 3 baskets. There were many different ways to solve the problem, especially since 2nd graders had limited exposure to formal lessons on division.  I interviewed a boy who had flat checked out, and was designing a basket with blocks.  It was interesting listening to myself try to get him back on track.  His partner had solved the problem without him, and he didn't care.  I think if he had seen himself in the video, he would have paid more attention in the next opportunity to shine mathematically.

Others had divided the problem evenly into tasks, having no idea how to mentally solve it without concrete objects.  So they were all super busy, but they took so long creating the visuals that they ran out of time.

Another table had self-divided into two groups who were attacking the challenge differently.  One GT student quickly mentally calculated and colored in a graphic, then back tracked to show a more hands on explanation.  The others used blocks instead of laborious other means of creating manipulatives.  They also discussed and paid strict attention to the tally marks.  This table was entirely successful.

All of the students in the class were successful in some way.  Was the teacher successful?  I think the follow through was missing.  I wished I had highlighted the successful and unsucessful efforts through showing the video, and asking the students to evaluate and propose suggestions for each group.

What is needed for my future problem-solving and critical-thinking opportunities is time.  I need time for the set-up, the exploration of a solution, the solving and explaining, and then the sharing and evaluating with a relevant audience.  


  1. Melanie,
    Thank you for sharing your post. It's wonderful you are doing problem-based activities with young students. I enjoyed reading about your student activity, especially how the different groups took different approaches to the problem. I also enjoyed reading your "what you would do differently next time" thoughts.

    Excellent idea on videotaping the group's efforts. I recently facilitated a problem-based learning activity for faculty development and was fascinated by hearing the dialogue that occurred in the teams. I witnessed the thinking processes each was taking and learned how they were learning. I wished I had videotaped it.

    I agree, problem-solving and critical-thinking activities take time for all the things you mentioned, but so rewarding for the students! Thanks for sharing.

  2. Hi Melanie,
    Why didn't the boy whose partner solved the problem without him, care? How would you have had the students reflect on theri learning?

  3. Greg, the boy was intrigued by a more open ended, personally chosen challenge of creating a basket with math manipulatives (shape blocks). That is a good question, and suggests I should reword the problem to have more than one right answer.

    Reflections could (and should) have been in journals, on KidBlog or Edmodo.