Friday, May 4, 2012

Calculus Speed trap

Catching speeders from our math class

Instead of using a worksheet, or pseudo-context question from a textbook you can show how related rates can be used to estimate the speed of a car from our classroom window.

1)      I used the Distmeasure app to determine the distance my classroom window is from the road.

2)      A student extended his arm and followed a car with arm until it hit a 45 degree angle.  Different students timed how long it took and we averaged the times.  [This will allow us to calculate the average rate of change of his arm in radians/second] in our class this took 4.6 seconds, as the following:

3)      Perform the calculations below
Since we know that student stopped at 45 degrees we can use the special triangle of 45/45/90 to substitute into the above formula.

We can then deduce that car is speeding through the school zone.

4)      Talk about the limitations of this activity, and how accurate this is.

Wednesday, May 2, 2012

Changing Assessment Presentation

I am putting on a session called "Globablization of Assessment" Below is my presentation and talking points:

My Talking points:

Math teachers indicated that they rely on a textbook for more than 80% of their teaching and most math teachers (at least 60%) reported that their instruction is quite similar to textbook tests. – Center for the study of testing, evaluation, and education policy.

Mayor of New Jersey strongly backed the pedagogical approach of using “constant drill and repetition” and even said “It is not that hard to give answers if someone just told you what to say.  They memorize back and know and get used to a lot of A’s on quizzes”  But when asked if he would send his own children to this type of school, he answered “no, those schools are best only for certain children”.

Imagine the difference between your child running home and saying “I had a great day because I got an A, got the highest mark in the class, won the math challenge” or saying “I know understand how to reduce fractions, multiply two digit numbers, or argue critically”.  One is saying learning is a means while the other is regarding learning as an end.

Research has shown that an overemphasis on achievement:

1)      Undermines students interest in learning

2)      Makes failure overwhelming

3)      Leads students to avoid challenging themselves

4)      Reduces the quality of learning

5)      Invites students to think about how smart they are instead of how hard they tried.

When we get carried away with results, we wind up, paradoxically, with results that are less than ideal.  Evidence has shown that our ideal long term goals for our children and students are less likely to become reality when the education system and its stakeholders become preoccupied with standards and achievement.

If the point of school is to achieve and demonstrate success instead of stretch your thinking and be challenged, then it is completely logical that a child will always take the easiest route; sometimes the unethical easier route.

501 mothers were questioned and more preferred their children to complete projects that would involve less struggling but result in success than those where their children would learn a lot more, struggle through it, and could potentially make a lot of mistakes.  Is this right?

Candle project – rewards slowed down the thinking.

The probability of getting a reward has the same brain action as someone who is addicted to drugs.  Rewards promote just as much bad behaviour as good ones.

People of different abilities tend to learn more effectively on a range of tasks when they’re able to cooperate with one another than when they are trying to defeat one another.

Grades divert attention from education itself and otherwise prove counterproductive.  They also do not provide accurate and reliable information.

Interesting studies:

When teachers use hands-on interactive learning activities, students who were not graded at all did just as well on a proficiency exam as those who were.  Students who attended elementary schools where no grades were used matched a sample of students who had received traditional report cards for 6 years.  5th graders who were told they would be graded on how well they remembered the social studies curriculum had more trouble understanding the main point of the text than did those who were told no grades will be used.  Even on strict recall the graded group remembered less.

Studies have shown over and over the more creative the task the worse of the performance of students when grades are used.  Only when comments are given, instead of numerical scores, will the learning increase.  Ruth Butler’s experiment
Tests and grades may make students learn today but will they may not want to tomorrow