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

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?

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 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

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?

Eight Attributes of Effective Activities, Problems, or Projects

A continuum of activity types are used in classrooms around the world.  They range in duration from long (weeks or months) to short (seconds or minutes), from “projects” to “problems”. There are differing styles of activities, ranging from context-rich to almost context-free. There are also differing roles for activities in a curriculum: they can serve as warm-ups, practice, assessment, and/or a primary means of instruction (as at Phillips Exeter Academy and elsewhere).

The activities that seem most effective to me tend to require at least 15 minutes, if not more, to complete unless the context for the activity has been previously introduced. Longer (or recycled from the recent past) activities require fewer mental transitions for students, and hopefully lead to greater focus on the core concepts and skills. Obviously short duration activities cannot include as many of the attributes below as longer ones might. The “laundry list” of attributes I consider when creating or modifying an activity now includes:

1) A warm-up section which:
– engages the Continue reading Eight Attributes of Effective Activities, Problems, or Projects