Thursday, February 28, 2013

Ratio, Rate and Proportion Series - Post 1



Many of us successfully solve ratio problems partly because we know how to represent them algebraically and can solve for the unknown, and some of us because we have innate or developed number sense and can “see” the relationships between and among quantities that are being compared. We are lucky again partly because as adults we have been working on these types of relationships for a long time and have been successful implementing the algorithms we were taught. 

BUT, think back to when you were learning about ratios and did not understand what it meant to be related to some other value. I recall being told that the ratio of two things were in a 5 : 7 ratio and there were a total of 763 items. I sat mesmerized when my math teacher proceeded to write 5x + 7x = 763. It was like magic. At no time was I shown a visual representation of what was going on nor was I encouraged to think about the fact that there was a multiplicative relationship happening. 

When I finally realized that teaching as telling is totally ineffective I became a deeper thinker, sought out ways in which to help students visualize, touch and manipulate the mathematics and relate it to things they are interested in I discovered my students, no matter how old, started to progress in their own learning.

I hope that after today’s class the inclusion of the bar model makes sense to you and it is something that you can bring into your own battery of teaching strategies. Modeling how the original problem looks and comparing it to the results after an activity has occurred allows students to make sense of a given situation and adds sense making to doing the mathematics.

Anne

Tuesday, February 26, 2013

Upcoming Workshop: Rational Numbers

Dr. Anne M. Collins will be leading a workshop on Saturday, March 9th on Rational Numbers: Hard to Teach, Harder to Learn.

The workshop begins at 9am at University Hall, 1815 Massachusetts Ave located in Porter Square.

In this workshop participants will explore visual representations of rational numbers that seamlessly develops an understanding of the slope of a line. We will examine bar diagrams and graphing ratios. Graphing ratios on the Cartesian coordinate plans allows participants to connect slope to linear equations. Problems involving proportions can also be solved using the Cartesian plane. This novel approach is required in the CCSS and the 2011 Massachusetts Curriculum Frameworks.

Cost is $50 per participant and there is still room available!

To register or to get more information, follow this link http://www.lesley.edu/EventDetail.aspx?id=7995.

We hope to see lots of you there!

Monday, February 4, 2013

Recognizing Effective Implementation of the Standards

We hope you all enjoyed the first weekend in February.  This past weekend was full of mathematics to bring into the classroom in discussions about Groundhog Day or the Superbowl!  In addition, we received the February issues of our NCTM journals and are excited for what's included in those as well.

Last Thursday, I participated in a class on Ratio, Rate and Proportion being held in one of our partner districts.  During this class we had a really lively discussion about the relationship between fractions and ratios.  Are ratios fractions?  Are fractions ratios?  What is the difference?  How can we denote them differently? 

This morning, I was speaking with Anne about the class, and it reminded her of a presentation she did at the MassMATE conference in 2012.  Please find a link to it below.  It will link to a Scribd site and open in a new window.

Effective Implementation of the Standards Power Point


There are some really good problems within the presentation, so I hope you enjoy it!

Katie