Each year, I try to work on one thing to improve my teaching. In 2007, I worked on lecturing for only 10 minutes at a time (research has shown that this is as long as an adult’s attention span). In 2008, I mainly concentrated on learning about the students at my new school. In 2009, I focused in decreasing extrinsic rewards.

In 2010, I have two problems that I would like to solve:

- Not enough of my students really understand the material. In a good semester, maybe 50% of the students have a reasonable understanding of the material.
- My grading system has not been accurate enough. I have too many students who get different grades than they deserve; furthermore, my grading system does not tell students what they need to work on—a 70% on an exam does not give much information about what the student should study.

The first problem will be addressed by a serious implementation of Cooperative Learning (CL). This is different from “group work.” CL is a specific type of group work that has 114 years of history and an overwhelming amount of evidence in the psychology literature that it improves student learning.

To be CL (and not just vanilla group work), these five principles must be in place:

- Positive interdependence—the group members must sink or swim together. This creates an incentive for the students to work together.
- Individual accountability—students will work in groups, but will be graded and assessed as individuals. This makes it impossible to be a “freeloader.”
- Face to face interaction—it is difficult to work together if you cannot see each other.
- Explicit instruction of group skills—one should not assume that students (or anyone, for that matter) already knows how to work in a group.
- Group processing—groups need to reflect on how they performed and create plans for improvement.

If all five of these principles are in place, the average student will perform somewhere between 0.61 and 0.88 standard deviations higher than the average student who is not taught with these five principles (see *Cooperation and Competition: Theory and Ressearch* by Johnson and Johnson). According to Wolfram Alpha, this is like the average student being 5’6″ and an average CL student being between 5’11” and 6’1.5.”

The problem is that it takes valuable class time to do this. My solution: do away with the lecture as much as possible to create time for the students to work. My solution: “invert” my classroom (thanks to Robert Talbert for the idea and name). I am planning to use online videos to introduce the topic to them outside of class. I am definitely using Khan Academy for linear algebra, although these videos are not quite appropriate for my “essential calculus” students. I may have to give 10-15 minute lectures in this calculus class instead of employing the videos.

The class time will largely be spent on fielding questions about the video, small group projects, formal and informal assessment, and group processing.

In many ways, it sounds like Patrick Bahls and I are having a similar semester. We both have a calculus and a linear algebra, both are working on minimizing lecture time (although he is further along than I am), and we are both working on changing our grading systems (although mine is a more radical change—see the forthcoming post).

August 21, 2010 at 7:03 pm |

All of the Kahn stuff that I’ve seen seems to be focused just on procedures and solving problems (instead of problem-solving). Have you thought about using something like this:

http://www.eric.ed.gov:80/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ752633&ERICExtSearch_SearchType_0=no&accno=EJ752633

September 7, 2010 at 11:45 am |

You are correct that The Kahn Academy is mostly solving problems. This is an important component of the course, but it does not address the more conceptual issues in the course.

The in-class exercises are designed to get more at the conceptual questions. The reading questions are a good idea, although I am not doing them. Rather, I am having the students do a self-assessment with their cooperative learning team. This is not directly as good as the reading questions (it asked students “how they did” rather than “what they did”), but I am hoping that it builds community.

Maybe I will incorporate the reading questions in a later semester; I appreciate the suggestion.

Bret

August 27, 2010 at 5:46 pm |

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September 29, 2010 at 4:37 pm |

[…] Recall that I am teaching Essential Calculus and Linear Algebra this semester. I have been using Cooperative Learning (CL) this semester with mostly positive, but still mixed, […]

December 17, 2010 at 10:00 pm |

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January 20, 2011 at 3:12 am |

Well,

This is certainly interesting. As the Numeracy Coach at our high school, i am charged with helping teachers teach. After many years of taking workshops, many of which were interesting, i felt that maybe I had something I could return. Our school is a Title school meaning most students are on free or reduced lunches, i.e., most students are from disadvantaged homes and certainly lower income homes. Having just become a Title school recently, our demographics are changing and we are not meeting Average Yearly Progress (AYP). In particular, students just aren’t getting it when teachers teach by traditional techniques (lecture), so teachers must change their delivery.

This inverted classroom concept seems interesting, although it assumes that students have an interest in learning the material. To spent that time outside of class reading and listening to podcasts, etc., would be great if they did it. I have a website with which I have had limited success. I have tried doing videos of my lessons or parts of them recently. i hope to continue that because I believe that only through providing these opportunities to students will they increase their use of them.

My first comment, “it assumes that students have an interest in learning the material,” is related to he idea the book you’re reading is talking about. Students come to math with the misunderstanding that you can only be good at math if you’re born with it. And if you’re not “born with it,” then it’s futile. “Just do what it takes to get through it,” seems to be the mode of thinking. Depressing, but we, as teachers and as a society, must overcome this way of thinking. Students can turn their thinking around. “Good” students must understand that if they don’t get it , then it’s Ok to ask questions, and “bad” students need to understand that through perseverance and hard work, they can become good students. Check out “Best Practices” to see more of what you were talking about with good cooperative learning.

January 20, 2011 at 7:12 pm |

Chuck,

I am happy that you are trying these ideas at the high school level. Right now, I am trying to figure out if I can make these ideas work at my particular college with my particular students and my particular teaching style. I have no hopes of generalizing the inverted classroom beyond a 20 foot radius around me right now. So I would be interested to hear how it goes with you at the high school level.

Also, I am blessed because my students are—with few exceptions—interested in learning the material. That makes my job easier. I understand that K-12 schools and other colleges may not be like this. On the other hand, I agree that lectures are failing these semi-uninterested students, and a different approach might help make them interested.

Stay in touch, Chuck.

Bret