# Unit 1: The Student Centered Approach

## Contents

**Student Centered Learning**

**What is Student Centered Learning?**

Student centered learning is best described in its name. It is a style of teaching that focuses the attention on the learner. This is diametrically opposed to a teacher centered approach in which the teacher lectures. In this approach we expect the student to listen, relying heavily on auditory learning, understand and retain the information relayed to them. We even expect them to perform at higher levels of Bloom's Taxonomy such as; analyzing, evaluating and creating. The problem is that the student is not given a chance to experience and interact with the information.

Learning is a **combination** of learning modalities. I can tell you, verbally, how to fish. I can explain how the worm gets put on a hook, how to lower it in the water and lightly pull when you feel a tug. However, if you have ever experienced fishing you will know... how does one accurately articulate the slimy and spherical nature of a worm? How do you fully understand HOW to effectively bait a hook until you have actually experienced it for yourself? Once you actually DO something, you don't forget as easily! It becomes a part of your experience and even a part of you!

Watch this video on a more formal explanation of active learning, a form of student centered teaching. Active Learning {*Please click "back" in your browser to return to this course*.}

As you go through this course think about how you can use desmos.com, not only as an individual learning tool, but also as a tool in which students can share and discuss their knowledge with the each other and the world.

**What Does Desmos.com Have To Do With Student Centered Learning?**

A function is just a function..until you begin to make them your own. Once a student is able to see a graph "respond" to changes in variables, terms, exponents and signs, they realize graphs are something they can control and create through functions. Desmos.com gives each student an opporunity to manipulate a cartesian graph.

Desoms allows students to:

- Plot points on a cartesian graph.
- Graph lines by typing in a function.
- Graph more complex functions such as conics, parabolas, sine and cosine.
- Set up "sliders" which will move points on a graphed function or change the value of any part of a function which will show how the graph changes when a value changes.
- Change the color of each graphed function.
- Shade areas of a graph.

The website is set up so that a graph is displayed with a series of boxes on the left side. Anyone can easily enter a function and create its graph. Participants can graph more than one function or point by "adding an expression". Each function will graph in a different color. Not only does this make it more fun and interesting but it allows students to quickly discern, not only the difference between various written functions, but differences in the functions' graphed appearance.

Go to this link, https://www.desmos.com/calculator/xnugitwjre , where you can manipulate the value of "a", "b" or "c" in the graph below with a "slider". Simply move the slider in the boxes with the "wrench" and watch the graph change.

**The Advantages of Student Centered Learning**

The advantages to this kind of learning is that the students are given the opportunity to construct their own knowledge. It is information that can be discovered and * interacted* with, thus making it a part of their own experience. It is THEIR knowledge. They construct their own graphs and visuals, take ownership and are encouraged to discover new information that can be shared with the world and their peers.

This is in line with James Henderson, Dewey, Piaget and Vygostky. Maria Montessori was way ahead of her time when she said, **"Scientific observation has established that education is not what the teacher gives; education is a natural process spontaneously carried out by the human individual, and is acquired not by listening to words but by experiences upon the environment. The task of the teacher becomes that of preparing a series of motives of cultural activity, spread over a specially prepared environment, and then refraining from obtrusive interference."**

Desmos provides a way for students to be directed, taught and left to explore the "world of cartesian planes and graphs". Our physical world has not changed much since Maria's time, however, we now have a technical world that students are actively immersed in. Let's let them "explore" that world using a student centered approach.

**Example of Teacher Centered VS. Student Centered Teaching**

Watch this video from a well-known virtual academy, Khan Academy,as they teach the slope formula. This would be a bit more "visual" than a typical classroom setting but it carries the same idea as your typical teacher centered approach. http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/slope-of-a-line {*Please click "back" in your browser to return to this course*.}

Now, go to www.desmos.com and follow this series of instructions.

- Go to the graph and enter y=x in the f(x) equations box.
- Click on "add and expression" and type in the point [0,0]
- Click on "add and expression" and type in the point [1,1].
- Now click on "add and expression" and type in [a,b].
- You will see something that says "add a slider". Click on "all".
- You can now move the "dot" by moving the slider. Note what number b is currently at and move the slider so that it is on the same line as the next "marked" dot. Note the new number for b. Record the difference of the two numbers as the numerator for excercise A on your worksheet.
- Now do this with the "a" slider. Note the current number and move the slider so that the point lays on top of another point on the line. Record the difference of these numbers as the denominator for excercise A on your worksheet.

Here is a link to view and manipulate the graph... Lesson 1 {*Please click "back" in your browser to return to this course*.}

The black dot represents the point that you can "slide". You will see it "moved" in the picture above.

Although this is not the complete excercise,and we have not discussed how to manipulate the program yet, it is important to note the level of active participation of the learner.

Please write down what the learner did in the Khan Academy video and what the learner did in the graphing excercise? What were the differences, with respect to the learner's participation, in the two teaching styles?

In which lesson is the leaner more engaged?

In what way is the learner more responsible for thier own learning in the graphing excercise?

### References

"MONTESSORI." , International Montessori Index of Schools, Teachers, Materials, Method, Teacher Training, Preschools,. 7 May 2012. Web. 07 May 2012. <http://www.montessori.edu/>.

Overbaugh, Richard C. "Bloom's Taxonomy." Bloom's Taxonomy. Web. 11 May 2012. <http://www.odu.edu/educ/roverbau/Bloom/blooms_taxonomy.htm>.

"Slope of a Line : U04_L1_T1_we1 : Slope of a Line." Khanacademy.org. Web. 07 May 2012. <http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/v/slope-of-a-line>.

Trego, Mark. "What Is Active Learning?" YouTube. YouTube, 08 Feb. 2011. Web. 07 May 2012. <http://www.youtube.com/watch?v=UsDI6hDx5uI>.

Go to Unit 2: Student Centered Lessons Using Desmos.com

Go back to homepage Mathematics Inquiry Based Learning Via Desmos.com