# Lesson 2 of Media in Math

Shauna Caroselli's Mini Course

Graphics

*"Graphics are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone to inform, illustrate, or entertain." [1]*

**Overview:**

Using graphics may not originally be considered for teaching mathematics. Usually graphics are used more in history or science courses, where the content being discussed is portrayed within the graphic. Yet this is just one way to use graphics. What about discussing the balance, color, or depth within the image? In regards to mathematics, the lines, shapes, and proportions can become the main form of discussion. This lesson will go over some examples that can be applied to mathematics and the corresponding benefits.

**Examples:**

Graphics can especially be great in mathematics for:

- Geometry

- Trigonometry

- Calculus

...The list goes on! Being creative is the most important key in incorporating media into mathematics. Because so many teachers are not used to teaching this way, it may be hard at first, but at the same time you may just find out how engaging it can be!

The following are some examples of certain graphics that could be used in various lessons pertaining to the topics listed above:

Geometry:

Students can use this visual to see how the lines and shapes create new shapes. This can easily turn into a topic of discussion for the class, and is differentiated since students can choose basic shapes such as circles or triangles, or more complex such as trapezoids. This can be a great visual activity and could be used in multiple ways.

Even a simple graphic like this, students can easily visualize three dimensional shapes. Viewing the shapes through a graphic like this is probably easier than drawing it on the board. It is also nice to have all the shapes in one graphic, rather than searching for examples of each. Maybe students can find their own graphic of real life objects that are the same shape. This will allow students to be creative in their mathematical thinking. http://tccl.rit.albany.edu/knilt/index.php?title=Lesson_2_of_Media_in_Math&action=edit

Trigonometry:

One aspect that trigonometry covers is angles within triangles. There are many different examples that can be used such as the above shadow picture, in which students can measure the angle on the graphic, use their own height and figure how tall their own shadow would be as if they were in this picture. This could be a nice change from the usual word problems students have to read for these kinds of problems.

Many angles come into play during billiards. Examples using pool would be great for both geometry or trigonometry, and could easily be altered to fit the topic being learned. Students could maybe create some sort of pool table model and try to figure out the degree measure they need to hit the ball using various mathematical concepts.

Calculus:

Even though this is something that wouldn't be introduced until an AP Calculus course (or more specifically calc III), this is one of many three dimensional shapes that is hard to draw and/or describe to students without having some graphic representation (although this example is called a Klein Bottle and is known to exist in the 4th dimension).

This is also another example that is hard to depict without a graphical representation. This image would be perfect to show students what happens when shapes are rotated around an axis (in this particular example it is rotated around the y-axis and the washer method would be used).

**More About Using Graphics:**

*Using Images to Reinforce Learning* Has some great suggestions and ideas when choosing a graphic for a lesson:

- The image should be as simple as possible, but no simpler. [1]It should be enough to get the point across, yet not so much to confuse or overwhelm the student.

- Graphics are good for those students who have less advanced verbal skills, yet at the same time the image may have little to no meaning because everyone learns differently. [2]

- The left side of the brain is verbal, and the right side of the brain is visual. Thus, if the right side of the brain is not stimulated, it will be harder for students to connect ideas. [3]

- Graphics are good for illustrating concepts and giving visual cues [2]. They are a good way to supplement instruction and help introduce ideas to students. This way, they have an image to relate to and can often be used to model a math problem. Many times, students need to draw a picture relating to a problem, yet sometimes this is the most difficult part of students. By providing an image, you set a good building block for them for them to better understand the concept.

**Benefits:**

Now that we talked about some examples, let's go over some of the added benefits of using such graphics in a math class (and most of these can apply to any classroom!)

- **Helps visual students learn.** If a picture can accompany a mathematics problem (and in most cases in can), then some sort of graphic will most likely be useful. Not only will this give all students a clearer picture and/or allow them to be creative, but will allow students who learn visually flourish as well.

- **Allows to show representations** that would otherwise be difficult to show on the board. Teachers can spend a lot of wasted class time and effort to perfect a drawing for a class for them to get a good idea of the mathematical concept. Choosing a graphic before class will save on time and will be more accurate.

-**Offers a change of pace**. Students are not used to seeing pictures being used in certain ways as the examples previously listed. Switching it up from time to time will help students stay engaged.

-**Can be used for a broad range** of mathematical concepts. As long as you are creative, graphics can be applied to any math topic. This allows flexibility and with time it will become easier.

*Here is an example math lesson using a graphic* File:Graphics Lesson.pdf

**Take a peek at some of these suggested articles**

For additional information on using graphics in education, click here

For some ideas of where to find graphics, click here (Although this is geared towards an ESL class, the same concepts apply)

For more on imagery, click here (Focus on strategies for enhancing memory and comprehension)

**YOUR TURN!**

Under the discussion tab, please do the following:

- Find a graphic that is related to a math concept

- Provide a brief explanation as to why you chose this particular graphic and how it enhances the lesson (about 100 words)

- In about 100-200 words, discuss graphics in math. You may include, but are not limited to:

- What you learned about using graphics in a math class
- How graphics can enhance learning
- How you plan on using graphics in your own lessons
- Your thoughts on teaching math through the use of graphics

⇨ You will be assessed using the following rubric: Media in Math Rubrics

Images Retrieved from:

http://www.dreamstime.com/stock-image-geometry-figures-image8739821

http://mathforum.org/mathimages/index.php/Solving_Triangles

http://plus.maths.org/content/imaging-maths-inside-klein-bottle

http://www.mathdemos.org/mathdemos/washermethod/gallery/gallery.html

References:

[1] Graphics. Retrieved from: http://en.wikipedia.org/wiki/Graphic

[2] Using Images in Learning, Teaching, and Research Materials. Retrieved from: http://www.jiscdigitalmedia.ac.uk/guide/using-images-in-learning-teaching-and-research-materials