2.9+What+is+pedgogical,+mathematical+and+cognitive+fidelity?

Read the following research paper. [] In your wiki reflection, I want you to define pedagogical, mathematical, and cognitive fidelity. Include one specific example that highlights each idea. This reflection is due Tuesday April 17 by 5am.

Just for fun, let's make this a whole class reflection. However, you ALL must make significant contributions. One person should not develop the bulk of the wiki response while others add only 2 lines. Work together to ensure that all contribute equally and that all contributions are done well. Use the discussion section of this page or emails to encourage or assist your peers to write their portion; use the style option above to show your edits or make suggestions. Do whatever it takes. I won't read this until class starts so see what you can do collaboratively. Think of this as a new strategy "Wacky Wiki Work ". : )

Group- I put this on the discussion post yesterday and didn't know if it was sent to all. I can't check back in until after 8:00pm tonight. I've read the article and wondered if anyone else has. How should we set this up?

One idea:

Maybe 2 people can write about pedagogical fidelity, 2 people write about mathematical fidelity, 2 people write about cognitive fidelity, and 1 person write an intro and conclusion to the Wiki.

(Susan C)  With the turn of the 21st century technology has been thrust to the forefront of the learning environment in today’s classroom, with this push to use technology there is an inherent problem. That problem is that teachers feel conflicted on how to approach the use of technology in the classroom in a way to promote the idea of instructing with technology, pedagogy, and content knowledge. In order to avoid the misuse of this new technology, teachers can examine/analyze three different areas in fidelity to determine its effectiveness; __Pedagogical Fidelity__, __Mathematical Fidelity__, and __Cognitive Fidelity__.

__"Pedagogical fidelity__ refers to the art and science of teaching" (P5 under Treatment Fidelity).This means that it is referring to the study of how to teach students. This can relate to technology, mathematics, or any other facet of teaching that revolves around strategies and understanding teaching. An example of this would be when a teacher makes classroom decisions based off of what the students already know about the topic, and know what students need to learn. This teacher would then form a task using both of this criteria (16-2).KP  Another example of this, is strongly related to technology. Pedagogical fidelity of technology means that the teacher understands how the technology is used in his/her classroom, and whether it is helpful or not. Pedagogical fidelity just means how well you are following your own pedagogical beliefs, so are you teaching according to your beliefs. Or how well are you following the pedagogy suggested by the curriculum materials you are using? For instance, the reform materials were written mostly with a constructivist pedagogy in mind. When teachers use say CMP, are they teaching with a constructivist pedagogy? How well does their pedagogy match a constructivist pedagogy? Dr B

 __Mathematical fidelity__ maximizes the use and interpretation of patterns to develop conceptual understanding at a deep and lasting level. __Mathematical fidelity__ implies that the activity is believable, is concrete, and related to how mathematics is a functional part of life (5-5). When utilizing technology in the learning environment and judging its effectiveness, the __mathematical fidelity__ of the website/software must be evaluated. The technology-generated representations must be faithful to the underlying mathematical properties of the object. The actions taken and the resulting behavior should accurately reflect the expected mathematical characteristics and behavior. The degree to which this takes place reflects its __mathematical fidelity__ (5-4). Using a task that people actually perform, for instance the article suggests using the Web to find these (5-5), is a good example of this.

While mathematical fidelity is the use and interpretation of patterns, __cognitive fidelity__ uses mathematical objects to get a better understanding of the patterns. Mathematical objects are used with __cognitive fidelity__ to construct and deconstruct, test, and revise to understand the patterns and structure of concepts. So, in a sense, mathematical fidelity is kind of like a researcher; they study and interpret certain things, but cognitive fidelity is a scientist, that experiments with those things to better understand them. One example of this could be using manipulatives (5-6)-- the article suggests those online.

Pedagogical, mathematical, and cognitive fidelity can be used in real life interpretations. Pedagogical is how to teach the students, Mathematical is what to teach the students, and cognitive is how to further understanding for the students.