Sensible Mathematics: Second Edition by Steven Leinward

Recently I read this book for my mathematics capstone course.  My summary and review of the book is below.  

Sensible mathematics is a book focused on empowering leaders to push for better mathematics school programs.  The book is written towards school leaders, but gives an interesting perspective for a future teacher like me.  Leinward explains that the common core state standards are the first step in creating a better math program.  It takes leadership and teacher support to implement the common core effectively.  He gives many reasons why change is important.  One example is the way society is changing.  This change demands a different mathematics classroom.  Students must be prepared for the workforce where calculators and excel spreadsheets are readily available.

    According to the author, one person can make a lot of change in a school’s mathematics program.  Schools must provide support for their teachers, but teachers must also provide support to each other.  Just one of these teachers has the power to influence a mathematics program.  As a teacher, helping my future colleges and challenging them to try new thing in the classroom is very important.  There are obstacles according to the author, like the fear of failing.  It is important though to encourage new methods and ideas in the classroom.  As a teacher, if I lead other teachers to try new strategies and share new strategies with my colleges, I am being a helpful leader, according to Leinward.    

    I also learned a lot about the shift in mathematics education from this book.  I would recommend it to leaders and administrators more than I would teachers, but it does provide great arguments for change.  The most interesting part of the book, for me, was looking at examples of lessons that promote sensible mathematics.  He shared one teacher’s story of a classroom exploring the speed at which toy cars go. The students discovered that under the conditions they were testing, the car speed was much slower than the advertised speed.  They used proportions and experiments to come up with data and sent it to the company that made the cars.  The company suggested they look at different situations to test in.  I can only imagine the excitement the students had when they heard back from the company, and to do more math testing.  This is the type of mathematics that I want to teach, mathematics that is real world, fun, and as the title says, sensible.   

Timeline of Mathematics

Below is a link to my prezi I created on the history of mathematics.  It provides a timeline and brief explanation of the topics we have covered so far in my MTH 495 class.

What fascinated me most about creating this timeline is there is a huge gap in time were mathematics wasn't making any strides.  I'm not a historian, but there has to be some reason for the 600 year gap.   Also what is interesting to me is how fast mathematics has moved since 600 AD.  It makes me excited to see the new things coming in the mathematics world!


History of Mathematics

This is the tessellation I created.  It was my first try and took a long time to create, but creating and analyzing tessellations are a great way to look at patterns.  I used Geogebra to create this one. 

Fun video for the mathematics classroom of any age! There's nothing like classic cartoons: 

Donald Duck in MathMagicLand. 

What is mathematics?

Mathematics is a fantastically broad, beautifully intricate, complexly connected concept of numbers and symbols.  Most days I think mathematics is problem solving, some days I have no idea what mathematics is because it tries to define the infinite.  As mathematicians we find relationships between these numbers and laws that already exist and make a language to help define them.  One of these concepts is infinity.

Infinity is a something that doesn’t exist.  No one can reach infinity and no one knows where it is.  It’s something humans created to try to grasp the concept of forever, the end of the number line.  It is a hypothetical construct that frankly, hurts to think about.  Although, the concept of infinity may be impossible to totally grasp, it is still captivating.
 
Mathematics is one of the few disciplines that even attempts to explain such a lofty concept.  In turn, there are many mathematicians who looked at infinity through logical thinking in subjects such as astronomy, geometry, and engineering.  They discovered key concepts that define the way we look at mathematics. 

There are a plethora of moments that could be argued are the greatest discoveries in mathematics, but here are the moments I think are the greatest.  First I think Al-Khwarismi and his book The Compendious Book on Calculation by Completion and Balancing was the most influential moment for mathematics.  The book summed up all of algebra at the time and opened the door for algebra in Europe.

Second, Euclid’s parallel postulate defines the way we look at geometry.  It challenged mathematicians to define geometry into subcategories and create proofs from these subcategories.

Third, the Pythagorean Theorem is among the most important discoveries in mathematics.  The Pythagorean Theorem gives us what we know about right triangles.  This is one of the first theorems we learn a children and for  good reasons.

The next greatest moment in mathematical history is the discovery of the First Fundamental Theorem of Calculus.  As the other discoveries define a category of mathematics, so does the First Fundamental Theorem of Calculus, which obviously created the way mathematicians look at calculus.

Finally, the discovery of Quadratic Equation hits the last spot of the top five.  It gives mathematicians a neat and concise way of looking at parabolas, but coming in at number five, it doesn’t define a huge category of mathematics.   Throughout history, the mathematicians that discovered these concepts helped us define what we call today, mathematics. 

*This post is thanks to all of my mathematics professors at GVSU for teaching me so much over my years here.  Special thanks to John Golden because of all he taught me I had to rework my top 5 greatest moments.  His worksheet also helped me write the section about Al-Khwarismi.