Text Set 2: Trigonometry

Text Set 2: Trigonometry

·      S.O.S. Mathematics: Trigonometry

http://www.sosmath.com/trig/trig.html

Grade level: 12.0

While the reading level of this collection of pages may be a bit high, it has excellent diagrams that present trigonometry in a variety of ways.  Here, the links between the geometric and the algebraic conceptions of trigonometry are made clear.  This is a good extension for a high performing student, or a student who has been accelerated and is studying independently.

·      Math is Fun: Introduction to Trigonometry

http://www.mathsisfun.com/algebra/trigonometry.html

Grade level:  6.8

This page from Math is Fun is written in a simple, conversational style and is accessible to both those reading below grade level and those whose math vocabulary may be weaker.  However, I find that the greatest value is in the interactive flash elements halfway down the page – students can move a point around the unit circle to create a right triangle and examine its trigonometric ratios.

·      Khan Academy:  Basic Trigonometry

https://www.khanacademy.org/math/trigonometry/basic-trigonometry

Grade level:  12.0

Khan Academy is a great resource for those students that prefer auditory methods of taking in information (most of the information is conveyed graphically or verbally).  The videos show trigonometric concepts and how to use them, in the form of notes that the author puts on a slide.  The author talks the students through what he is doing, and is clear and direct; as well, his mouse/pointer is always visible and follows which element of the notes at which he happens to be looking at any given point.  And of course, this lesson includes the interactive quiz questions that Khan Academy is famous for. 

·      Trig Cheat Sheet

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Grade level: 2.4

This is a sheet of trig formulas and trig identities, conveniently condensed, with figures illustrating the general case.  There isn’t much reading (verbal) in this resource, but math-specific literacy is necessary for comprehension.

·      Cliff’s Quick Review Trigonometry

https://play.google.com/store/books/details?id=qo8GBrUfGIcC&source=productsearch&utm_source=HA_Desktop_US&utm_medium=SEM&utm_campaign=PLA&pcampaignid=MKTAD0930BO1

Grade level:  9.4

Cliff’s Quick Review is exactly what is says – a quick crash-course review of trigonometry concepts.  It is heavily verbal, though the reading level appears to be accessible for the majority of high school sophomores.  It is available as an e-book download from this link in the Google Play store (which is great for tech schools, though Apple users may run into some compatibility issues), as well as a hard copy from your local bookstore. 

·      Trigonometry (Corral, M.)

http://www.mecmath.net/trig/trigbook.pdf

Grade level:  11.0

Corral’s text on trigonometry is a good extension for students who would like to read trigonometry in the context of how mathematics looks when it is published within the field.  It connects trigonometry to history and other branches of mathematics.  

·      Wikibooks: Trigonometry

http://en.wikibooks.org/wiki/Trigonometry

Grade level:  7.8

Wikibooks has a good collection of information, free and available on the web to anyone, on trigonometry.  It gives us three books, organized by increasing difficulty and frequency of use of concepts present in other branches of mathematics (matrices, calculus, computing).  Topics are arranged by page, and include many diagrams.  This resource is also useful for students and teachers to think and talk about what makes a good figure – there are editors’ notes on how figures will be updated to be clearer and more useful.

·      Applications of Trigonometry (Clark University)

http://www.clarku.edu/~djoyce/trig/apps.html

Grade level: 10.9

This page gives a quick run-down of some trig applications, and the historical context in which they developed. 

·      Math Central: Applications of Trigonometry

http://mathcentral.uregina.ca/RR/database/RR.09.01/trigexamples1.html

Grade level: 8.2

This page gives a couple of unconventional examples of applying trig.  In addition, they’re examples that the average layperson can encounter, not just examples found in physics or engineering contexts. 

·      Fascinating Facts of Mathematics

http://malini-math.blogspot.com/2011/08/applications-of-trigonometry-in-real.html

Grade level: 8.6

A quick succinct list of traditional applications of trigonometry, complete with example pictures.  The pictures have figures overlaid that connect the trigonometric model with the real world context.  

·      Slideshare: Real World Uses of Trigonometry

http://www.slideshare.net/ihatetheses/real-world-application-of-trigonometry

Grade level: 12.0

The reading level on this is a bit high, but this slideshow is an excellent resource for connecting trigonometry to the real world.  It showcases how certain careers make frequent use of trigonometry, and then give details about those careers such as salary and areas of study needed. 

·      WISC-Online: Practical Trigonometry

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=MSR3603

Grade level: 4.6

This is an interactive slideshow that poses some really great application problems within the context of a machine/prototyping shop.

·      Clark University: History of Trigonometry Online

http://www.clarku.edu/~djoyce/ma105/trighist.html

Grade level:  12.0

This is a brief online outline of the beginnings of trigonometry, complete with figures and historical context.

·      Applications; Web-Based Calculus

http://ualr.edu/lasmoller/trig.html

Grade-level: 12.0

This page gives a brief history of trigonometry, with a focus on its journey through various cultures and its (mis-)translations.

·      TI-Nspire: Sinusoidal Modeling

http://education.ti.com/en/timathnspired/us/detail?id=469A5FBBB74F4031882FEC9806D32867&t=3270A55B10BB4BF29C7D8883E3990203

Grade level: 6.9

This exploratory activity extends knowledge of trigonometry from geometry to algebra and statistics, and models the use of trig functions to model oscillating phenomena. 

Text Set Topic Redux

Trigonometry

Reflection 10: Technology

I think the strategies in BBR Chapter 10 were useful as a macro-structure for web-based searches, but I feel like some of the other strategies that are nested in these structures bear some investigation as well. How do students decide that a website is credible?  The -AND (Analyze and Note Details) and -SD- (Slow Down) steps from the SAND and ISSDaT strategies require students to evaluate the credibility of web sources, but do't mention more than making sure to stay away from .com sites and sites clearly trying to sell you something.  I can think of plenty of examples of .org websites that may be of dubious credibility -- I'm sure the KKK and crazy Doomsday/Rapture Preppers have websites ending in things other than .com, but they're hardly credible sources (except as primary sources to examine how bleeding insane they are).  I'm at a one-to-one school and the students almost exclusively use the web for resources when doing projects, but few of them know how to differentiate an academically credible source (e.g. a scholarly one) from one that appeals to sensationalism, trends, and popular culture -- beyond "Don't use Wikipedia."  I think a more useful strategy to analyze would be how to determine credibility, and how credibility requirements change depending on the project.

Web Resource 2: Khan Academy's Geometry section

https://www.khanacademy.org/math/geometry

Khan Academy's geometry section has been a fantastic resource for me because of the interactivity of the 'quiz' sections.  I feel like the quiz sections are almost more valuable than the videos; the videos are nice because they offer a clear verbal walkthrough of problems, but the interactive quiz sections let students experiment with figures to see if constructing counterexamples (per say) is even physically possible with the given conditions.  I feel like nothing is quite as instructive as a hands-on session of trial and error.

As well, students can sign up for an account through the website and earn points through a cute little game system and earn rewards.  In addition to the points and badges that accounts keep track of for students, student accounts can also be linked to a teacher account.  The teacher/coach account that is associated with it can view statistics for each student, including frequency of use and success rates.

One drawback to Khan Academy is that it requires student access to one-to-one technology to use successfully (in my opinion).  Even if you don't have one-to-one access, you might be able to make a couple of computers with a Khan Academy activity set up one center in a set of stations that the whole class participates in.

Reflection 9: CCSSI... everyone's favorite!

I liked reading the article that showed us that there is some difference of opinion on the CCSSI, or, more accurately, that there is some difference of opinion on how much preparation the transition will take.  I thought it was interesting to note that the article says there is some push back against CCSS adoptions, but that usually this isn't coming from teachers and parents, i.e. the educational community.  Teachers and parents seem to be largely in support of Common Core, though many think they may need some more time to develop their new curriculums and resources.  Detractors seem to be from camps that are concerned about 'looking bad' -- since CCSS will (ideally) reduce ratings inflation among schools (not every school can be 'above average'!).

One of the most interesting things mentioned in the article is some speculation on how students will react to this transition and how they will initially perform.  There is some fear that students will have difficulty with the new, rigorous, in-depth approaches to material presented under CCSS after having been acclimated to the drill-and-kill approach to material under NCLB.  I  can understand this fear, as I see it in my students every day.  The transition has not been kind to these children; being constantly asked 'why?' and 'explain' is totally foreign to these kids.  They're used to being able to pop out a numerical answer and then move on with their lives.  It's a shame that a there will be whole grade levels of students who are thrown under the bus b y this transition, because I think that in the end, after we're fully ensconced in CC, it'll be work it.