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

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

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

Lecturing: There Are Better Ways ToTeach

Many widely used math textbooks seem written for a traditional “lecture-style” teacher. They can be challenging to teach from if you are trying to reduce time spent “talking at” the class.

Some of the NSF-funded mathematics texts published over the past decade make it much easier for a teacher to avoid lecture mode, but:

– from a parent’s perspective, some texts don’t seem to have much of a role for the teacher, so how can/should a teacher add obvious value (in student and parent eyes) to what is in the text?

– the lack of prominently highlighted boxes around all information needed for the test is a source of student gripes. Students need to re-learn “how to learn” when a text or teacher takes a different approach, so time and effort needs to be devoted to this at the start of the year.

– the format of each unit can begin to Continue reading Lecturing: There Are Better Ways ToTeach

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

Uncover the Hidden Game

The title of this posting is the title of a chapter in “Making Learning Whole”, by David Perkins (2009), which I mentioned in my previous posting.  I recommend it highly.

What is the “hidden game” in High School mathematics? What mindsets, approaches, techniques, etc. do those comfortable with the work asked of them rely upon, yet perhaps neglect to Continue reading Uncover the Hidden Game

Learn the Game of Learning

The title of this posting is the title of a chapter in “Making Learning Whole”, by David Perkins (2009). Of the books on education I have read to date, this is the first that resonated completely with me.  He describes the way I try to teach, and more – thus giving me much to reflect upon.  I recommend it highly.

The list of skills related to “the game of learning” I see as being most important for math and science students to acquire, and therefore worth devoting some time to teaching explicitly over the course of the school year (since they are also more generally applicable) are:

  • What is it you need to learn: a concept, a skill, or a fact? Concepts can often require thought, and time spent discussing them with others while being watchful for subtleties. Skills often require repetition and varying levels of difficulty. Facts can sometimes be obvious if they are based on an underlying concept; if the facts are not obvious, search for a way to link them to one or more concepts or themes, then practice retrieving them along with related information.
  • Frustration is a normal part of the learning process, one which can often lead to greater understanding and retention once you have worked your way through it. Expect to become Continue reading Learn the Game of Learning