Flipped Classroom: It’s About Timely Formative Feedback

The phrase “Flipped Classroom” is appearing with increasing frequency in publications and blog postings. Yet, it seems to mean different things to different people. Many of the references I see to flipped classrooms are made by people or organizations who have a vested interest in selling goods or services, which probably affects their view of the issues.

As proposed by Salman Khan in his TED Lecture, flipping the classroom involves using internet-based video to move “lecture” out of the classroom to some other place and time of a student’s choosing. Class time can then be used for student problem solving and group work. Dan Meyer and others have critiqued aspects of Salman Khan’s approach, with some such as Michael Pershan offering constructive ideas for improvements.

Eric Mazur, a physics professor at Harvard, has also been advocating a “flipped” approach  – and for considerably longer than Salman Khan. His conception of “flipping” focuses on getting students to Continue reading Flipped Classroom: It’s About Timely Formative Feedback

Projects vs Problems in Math Class

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?

“Hidden” Learning Objectives for a Linear Equations Problem or Project

The lesson plans I find most interesting, both to read and to teach from, have both “public” and “hidden” learning objectives.  The public objectives focus student attention and help interest students in the problem: they need to be short, to the point, and tightly related to the problem or project at hand.

The “hidden” objectives are the focus of teacher attention. They reflect the skills and concepts that the teacher hopes to see students grappling with, discussing with peers, and mastering over time while working on successive problems. If students are informed about a teacher’s list of objectives in assigning a task, students are likely to use only that list in their work. By not publicizing the teacher’s objective list, students are more likely to try a wider variety of approaches to solving a problem. I think the problem solving process starts with determining which concepts and skills seem relevant to the problem, therefore keeping the teacher’s objective list hidden helps students become better problem solvers.

The list below covers topics typically taught over a large percentage of the school year, so not all objectives are appropriate at any given point in the year. However, by the end of the year hopefully most of the following objectives will have been mastered by most students in a class:

Continue reading “Hidden” Learning Objectives for a Linear Equations Problem or Project

Peer Instruction Network

I recently came across a start-up organization called the Peer Instruction Network. It sounds like it is seeking to expand on Eric Mazur‘s teaching approach, something which would be very interesting to me on the Mathematics side of things.  Check out their web site, and sign up to be included in their network if it sounds interesting.

Ten Skills Every Student Should Learn

A recent eSchool News article by Meris Stansbury lists ten skills cited by its readers as being most important for today’s students to acquire:

  1. Read
  2. Type
  3. Write
  4. Communicate effectively, and with respect
  5. Question
  6. Be resourceful
  7. Be accountable
  8. Know how to learn
  9. Think critically
  10. Be happy

The list is interesting to ponder. I would not argue that any skills on the list should be dropped, however I suspect we could have endless debates about what order to list them in or how to best group them. I am happy to note that all of the skills are beneficial in studying just about any subject or discipline.

There are a few additional skills that I would advocate adding to, or being more explicit about in the above list:

Scheduling for Curricular Depth and Challenge

What was “the best” course you ever took? Probably one for which you had to work quite hard, one that you perceived as challenging from the outset, one for which you rose to the challenge. The course probably had a reputation as a tough course, so you probably added it to your schedule with care and made sure you did not take another really challenging course at the same time.

Major time commitments are regularly called for in schools: for musical or dramatic performances, athletic seasons, and some classes too. Could we improve the way such opportunities are scheduled so that  students can experience as many as possible each year without creating a killer workload for themselves at critical times during the year?

Challenges

What if schools offered “challenges” that lasted for either half or a full semester? Each student could be required to be enrolled in two challenges at all times. A dramatic or musical performance would count as a challenge, as would a varsity sport, as would any number of academic and extra-curricular offerings. To qualify as a “challenge”, an offering would have to:

  1. Culminate in a public performance, presentation, or display of student work.
  2. Involve extensive Continue reading Scheduling for Curricular Depth and Challenge

Integrating Mathematics With Other Subjects

What if most activities in school asked students to “reach and defend a conclusion”?

  •  in Math, about quantitative or geometric relationships, about measurements of worldly phenomena, etc.
  • in Music, about the effect of a melody line, about a particular mix of instruments, etc.
  • in English, about effective use of language or metaphor, about storytelling techniques, etc.
  • in Visual Arts, about the effective use of color or negative space, about how a work can be interpreted, etc.
  • in History, about a set of events, about relationships between societies, etc.
  • in Physical Education, about the effects of various activities on the human body, about the effectiveness of various strategies in a sport, etc.
  • in Science about whether two measurements are related in some way, why they might be related, the consistency with which they seem related, about cause and effect, etc.

What might our schools look like under such an approach?

Game-like Engagement

A New York Times Magazine article titled “Games Theory” (September 19, 2010) mentioned some interesting points:

– “going to school can and should be more like playing a game, which is to say it could be made more participatory, more immersive and also, well, fun.”

– One way to “make school more relevant and engaging” to those who find it boring and are therefore at risk of dropping out is “to stop looking so critically at the way children use media and to start exploring how that energy might best be harnessed to help drive them academically”

– Games provide “‘failure-based learning,’ in which failure is brief, surmountable, often exciting and therefore not scary.” Students will “Fail until they win.”

– “Failure in an academic environment is depressing. Failure in a video game is pleasant. It’s completely aspirational.”

– “When it comes to capturing and keeping Continue reading Game-like Engagement

The Purpose of High School Mathematics

The 2011 Anja S. Greer Conference on Secondary School Mathematics at Phillips Exeter Academy provided many opportunities to hears others’ ideas about the purpose of our High School Mathematics Curriculum.  Some of the statements I noted were (with apologies that none are exact quotes, and my lack of attribution on some):

In life, not to mention just about any academic subject, students should question information they come across, then work to support or refute it using numbers as needed.

Quantitative situations can be found in poems, literature, environmental claims, social justice issues, and social service needs.  We teach mathematics so that students can decide for themselves whether the quantities involved make sense or not.  Ray Williams (St. Mark’s School, Perth, AU) presentation.

Let the students ask Continue reading The Purpose of High School Mathematics

Re-thinking Our High School Math Curriculum

Nils Ahbel of Deerfield Academy gave a thought provoking presentation at the 2011 Anja S. Greer Conference on Secondary School Mathematics (held at Phillips Exeter Academy in Exeter, NH) on the history and potential future of the American High School mathematics curriculum.  The Prezi that he used to illustrate his talk can be found here.

As I recall, his core points about the state of things today were that:

– our curriculum has remained largely unchanged for 119 years (witness the content of the textbook whose pages fill the number 8 in his prezi).

– the current goal of most high school curricula is to Continue reading Re-thinking Our High School Math Curriculum