Polynomials and VEX Drive Motor Control

VEX Robots can be more competitive when they have addressed several drive motor control challenges:

  1. Stopping a motor completely when the joystick is released. Joysticks often do not output a value of  “zero” when released, which can cause motors to continue turning slowly instead of stopping.
  2. Starting to move gradually, not suddenly, after being stopped. When a robot is carrying game objects more than 12 inches or so above the playing field, a sudden start can cause the robot to tip over.
  3. Having motor speeds be less sensitive to small joystick movements at slow speeds. Divers seeking to position the robot precisely during competition need “finer” control over slow motor speeds than fast motor speeds.

These challenges can be solved using one or more “if” statements in the code controlling the robot, however using a single polynomial function can often solve all of these challenges in one step. A graph can help illustrate the challenges and their solution:

Continue reading Polynomials and VEX Drive Motor Control

What A Parent Wants From A School

As a parent, I look for two categories of attributes when choosing a school for my child:
– Ones which benefit my child directly
– Ones which benefit my child indirectly, by helping others (teachers, parents) do their jobs more effectively

Schools that satisfy more of the attributes in both categories are likely to have happier parents and more successful students.

The Administration and Teachers Should Help My Child

Directly By:

  • Being aware of history. Before the start of each school year, my child’s current teacher(s) should have reviewed all of
    – last years’ teacher comments for my child
    – my child’s transcript (all courses, all years at the school)
  • Helping my child to both pursue existing  Continue reading What A Parent Wants From A School

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:


  • 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)


  • 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?

Linear Equation Activity Ideas

Once a set of learning objectives have been settled on for an activity, problem, or project, what should the problem’s context be? Since linear equations model situations where there is a constant rate of change, common contexts for linear equation projects often include the following:

  • Steepness, height, angle
    Examples: road grade, hillside, roof, skateboard park element, tide height over the two weeks before (or after) a full moon, sun angle at noon over a six month period
  • Estimating time to complete a task (setup plus completion)
    Examples: mowing a lawn, painting a wall, writing a research paper
  • Purchase and delivery costs of bulk materials
    Examples: mulch, gravel, lumber
  • Purchasing a service that charges by consumption
    Examples: cell phone, electricity, water, movie rental, etc.
  • Total earnings over time from differing wage and bonus plan structures
    Examples: hiring bonuses, longevity bonuses
  • Energy use over time
    Examples: calories burned, electricity, heating oil, gasoline
  • Game points accumulated over time
    Examples: by a professional athlete, a team, a video game player
  • Pollutant levels over time Continue reading Linear Equation Activity Ideas

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?


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 research project, art or engineering project, dramatic or musical performance could each count as a challenge, as could a varsity sport, as could 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

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

Standards Based Grading Trial

After reading a number of blog postings about Standards Based Grading (SBG), I tried a hybrid version of it during the Fall semester of 2010 in an Algebra I class and three Algebra II classes. What follows is a description of how I approached things, what worked, and what didn’t.

Grading Policy

Approximately 40% of each student’s semester grade was based on SBG quiz scores, 30% on traditional chapter test scores, and 30% on the semester exam.

I was not obligated to test to specific standards, so I picked quiz “topics” which were timely and allowed for challenging questions. My goal was to have most questions be challenging enough to make perfect scores unlikely on the first try.

Each student’s best two scores for each topic counted towards their overall Quiz grade. All lower scores for the topic were dropped, regardless of the sequence in which the scores were obtained.

Each answer received a maximum of five points:
– One point for attempting the problem
– One point for using a valid approach to the problem
– Three points for working the problem to a solution
– One point taken away (up to three) for each algebra or arithmetic error

Quiz Opportunities

My grade book consisted of a three-ring binder with one page for each student. Each page had a Continue reading Standards Based Grading Trial