Search Results for: linear algebra

Connected Educator Month

As part of Connected Educator Month, I contributed to the New York Times Learning Network’s “What Connected Education Looks Like”, a collection of viewpoints on what being connected means to teachers in this day and age.

Here’s my piece, which was inspired by two mathematicians on Google+ who inspired me to create a Linear Algebra course at my school this year.

I’m teaching Linear Algebra at my high school this year, and social media is to blame.

Two mathematicians I’m connected to on Google+, Theron Hitchman andVincent Knight, regularly post engaging pieces about mathematics, teaching and technology. Theron’s enthusiasm and insight and Vince’s cool applications to operations research rekindled my interest in Linear Algebra. So when discussing what electives to offer our mathematics majors at Brooklyn Tech, I volunteered to create a Linear Algebra course.

As usual, I’m in over my head, but Theron and Vince are there to help, sharing their views on the big ideas in Linear Algebra, using technology to docool things with matrices and pointing me to resources like free e-books and open-source mathematical software. I probably wouldn’t have taken on this challenge without my connections to these mathematicians, but being connected to them and others will help make it work for me and my students.

You can read the NYT LN piece here, and find out more about Connected Educator Month here.

By MrHonner, ago

Applications of Mathematics

This is an amazing resource from the British Columbia Institute of Technology:  a cross-referenced list of how various mathematical ideas are used in various technology fields.

http://commons.bcit.ca/math/examples/

Interested in how Linear Algebra can be applied to Nuclear Medicine?  Or how Logs and Exponentials can be applied to Forestry and Wildlife?  Or how Differential Equations can be applied to Mechanical Engineering?

Well, look no further!

By patrick honner, ago

Real World Problems

I’ve been shopping for a new cell phone (doesn’t yours have an antenna?) and it reminded me about cell phone plans and linear algebra.

Cell phone plans used to be the prototypical real world problem for high school math classes.

Plan A costs $10 a month plus 25 cents a minute, while Plan B costs $30 a month plus 12 cents a minute.  Which plan should Sue Consumer choose?

Figure out the equations of some lines, find the intersection, make some conclusions.  Math in action!

Fast forward to the present, and it’s embarrassing how confused I am by all the options:  a serious multivariable analysis is necessary to figure out which plan is the right one for me.  This was once an exemplar of simple, relevant application, but now it has become ugly with the real real world details.

By patrick honner, ago

Regents Recap — August 2015: Modeling Data

Here is another installment in my series reviewing the NY State Regents exams in mathematics.

Data and statistics play a much bigger role in algebra courses now, due in part to their increased emphasis in the Common Core standards.  I am generally supportive of this, but I do worry about how statistical concepts are presented and assessed in these courses and on their exams.

For example, here is question 27 from the August, 2015 Common Core Algebra exam.

2015 August CC Alg 27

Evaluating mathematical models is an extremely important skill in many aspects of life.  But properly evaluating mathematical models is subtle and complex.

The following sample response, provided by New York state as an example of an answer deserving of full credit, does not respect that complexity.  And it makes me worry about what we are teaching our students about this important topic.

2015 August CC Alg 27 MR 1

It’s true that the given data does not grow at a constant rate.  But that isn’t a good reason to reject a linear model for this set of data.  Models are used to approximate data, not represent them perfectly.  It would be unusual if a linear model fit a real set of data perfectly.

The weakness of this argument becomes even more apparent when we notice that the data isn’t perfectly fit by an exponential model, either.  Therefore, how could it be wrong for a student to say “We should use a linear model, because the data doesn’t grow at a linear rate and thus isn’t exponential”?

This is another example of the problems we are seeing with how statistics concepts are being handled on these high stakes exams, which is a consequence of both the rushed implementation of new standards and an ever-increasing emphasis on high-stakes testing in education.  It is also an example of how high-stakes tests often encourage terrible mathematical habits in students, something I address in my talk “g = 4, and Other Lies the Test Told Me“.

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By MrHonner, ago
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