Blog Post #6

The.Secret.Life.of.Chaos. by costello74

This week's learning module had two main focuses, they are, connecting mathematics with the world and using technology to teach mathematics.  I will address each focus in this respective order.

Connecting mathematics with the world is important for establishing a practical relationship between the sometimes arduous work of mathematics and its inherent relationship with our common experiences. Developing an understanding of this relationship is important because it helps to foster in students an appreciation for the value of mathematics and its far reaching applicability.  Above is a BBC documentary called "The Secret life of Chaos."  This video explore the multifaceted ways in which mathematics is deeply rooted in the world we inhabit.  The kinds of examples it explores in this documentary provide valuable insights into how the world functions and how mathematics can be used to help us understand the nature of those functions.  I think that bringing to light some these more profound ideas to student awareness is a positive step in reinforcing an understanding of the awesome nature and broad applicability of mathematical concepts.  I believe that creating an educational environment that would allow students to study these kinds of concepts in more detail would not only increase student engagement with mathematics but would also enlighten their understanding of the world by engrossing them in some of the underlying concepts that define it.

The other focus in this week's learning module was the use of gaming applications to help teach students mathematical concepts.  Gaming application are a fun and engaging way to get students interested in mathematics.  By approaching mathematics as a form of 'play,' students are more likely to enjoy mathematics as something desirable to interact with.  Good gaming apps also have the added benefit of offering students various levels of engagement.  They are able to challenge students who are more advanced or provide scaffolding opportunities by lowering the difficulty for students that are struggling.  Offering students a variety of gaming apps that focus on a big idea also allows for a level of choice that should increase student engagement with mathematics.  Finally, gaming apps often provide students will useful visual aids when demonstrating various mathematical problems.  These visual aids create a diverse learning environment where the differentiation of instruction can optimize student learning preferences.

Blog Post #5

Youcubed - Stanford University - Visual Math Image

       This week's online learning module included a focus on using visual images.  In this post I will discuss the benefits of using visual images when teaching or learning mathematics.  In particular, I will discuss the importance of using visual images and their significance for differentiating instruction.

       It is important for both teaching practice and student learning that differentiated instruction be undertaken in the classroom.  Incorporating the use of visual images can help achieve this latter end in various ways for mathematics.  Perhaps the most obvious way visual images help students learn a variety of mathematical concepts is that they offer an alternative representation of a math problem or question.  In most cases, mathematical problems are posed to students using numbers.  Numbers have an abstract quality that can be alienating for some students.  For instance, sometimes students have trouble understanding the value that numbers represent or have difficulty connecting numbers to their 'real world' applications.  Using visual images to represent math problems or their subsequent solutions offers students a means to understanding mathematics that is simultaneously less abstract than numbers and often a closer reflection of the 'real world' around us.  Furthermore, visual images are naturally a tremendous benefit for visual learners.  Providing a means for visual learners preferred method of acquiring knowledge creates a bridge to understanding that is not always available in the traditional format of teaching mathematics.

       While visual images are beneficial to student learning they should also be incorporated into teaching assessment.  Differentiated instruction usually focuses on how to offer a variety of learning opportunities for students.  But it is sometimes overlooked in terms of its applications for assessment.  Allowing students to use visual images in mathematics to demonstrate their solutions to problems should be adopted as a valid form of submitting work for assessment.  What is important is that students are able to demonstrate their understanding of a subject, as oppose to demanding students demonstrate their understanding in only one particular chosen format.  That is, good pedagogy strives for student comprehension in all of its potential forms.  Bad pedagogy demands that students limit their potential for understanding by narrowing their opportunities for learning and stifling their potential for creativity.  Since the use of visual images in mathematics diversifies student learning and assessment potential it should be incorporated as valid mathematical format and tool for twenty-first century teaching.