For teaching statements, there is plenty of excellent advice online, see e.g. the links below:

http://sciencecareers.sciencemag.org/career_magazine/previous_issues/articles/2006_04_14/nodoi.14633728089694563528

http://theprofessorisin.com/2011/09/16/thedreadedteachingstatement/

https://cft.vanderbilt.edu/guides-sub-pages/teaching-statements/

http://www.acs.org/content/acs/en/education/students/graduate/six-tips-for-writing-an-effective-teaching-statement.html

http://www.crlt.umich.edu/publinks/CRLT_no23.pdf

http://ctl.yale.edu/sites/default/files/basic-page-supplementary-materials-files/sampleteachingstatements.pdf

http://ucat.osu.edu/professional-development/teaching-portfolio/philosophy/

And here go some links on research statements:

http://cll.stanford.edu/~willb/research_statement.php

http://theprofessorisin.com/tag/how-to-write-a-research-statement/

http://www.academiccoachingandwriting.org/academic-writing/academic-writing-blog/vi-writing-the-research-statement-how-and-why-you-research-what-you-do/

https://career.ucsf.edu/sites/career.ucsf.edu/files/PDF/ResearcherResearchStatementTips.pdf

https://www.cmu.edu/gcc/handouts/ResearchStatement.pdf

https://postdocs.cornell.edu/research-statement

https://studentaffairs.duke.edu/career/graduate-students/academic-career-preparation/research-statement

I would say that a teaching statement should reflect the objectivity of learning and techniques adopted by a teacher  so as to cater to the needs of all types of students who are part of an egalitarian society .The purpose behind such methods adopted should be clearly mentioned . There are so many websites relating to the teaching statement preparation and the user may use his or her discretion to choose the right one for himself or herself in order to adopt that style of writing.

Regarding a teaching statement, I would explain the principles of my teaching and then give examples of ways those principles have been successfully applied in the classroom.

Dear colleague,

There’s no standard way to write a statement of the problem, but strive to make it relevant, definitive, and free of ambiguities. In many disciplines, especially those based in quantitative approaches to research, there is an expectation that the problem statement expresses the relationship between two or more measurable properties and thus can be empirically tested. The problem can then be written in the form of a hypothesis, or be stated as a single question such as ‘To what extent do …..’ This could be posed as a declarative sentence followed by a series of sub-problems or questions, over the course of your research, return to your problem statement on a regular basis and continue to refine it. With an eye on what you are discovering and the current research, ask yourself if your problem is still relevant, sufficiently narrow, and focused more on its underlying reasons than on approaches and techniques.

Problem Statement (or Motivation for the Study)

– Identify a key point of concern (for example, increasing use or prominence, lack of research to date, response to an agenda, a new discovery, or perhaps one not yet applied to this context).

– Refer to the literature only to the extent needed to demonstrate why your project is worth doing. Reserve your full review of existing theory or practice for later chapters.

– Be sure that the motivation, or problem, suggests a need for further investigation.

Regards

Here is a blog post that I wrote that you may find helpful. In it I include links to a variety of additional resources, too: How to prepare a teaching dossier https://wp.me/pNAh3-2hu