Critique
How well does it work?
This applet works well. Students are able to change the measure of the angle in increments of 10 to change the lengths of two of the sides of the triangle, while the hypotenuse remains at 10. Students are also given the values of the sine, cosine, and tangent functions for the specific angle and must use a calculator to figure out how those values were determined. Finally, students are able to change the size of the triangle, having the angle measure remain fixed while the measure of all three sides change, allowing them to make the conjecture that these three trigonometric functions are not dependent on the size of the triangle.
The only downside to how well this applet works is the students only being able to change the angle measure by 10 degrees, so they are unable to make conjectures about angle measures in between increments of 10.
The only downside to how well this applet works is the students only being able to change the angle measure by 10 degrees, so they are unable to make conjectures about angle measures in between increments of 10.
Are the written materials well organized and useful?
There aren't any written materials provided with this applet. However, there are three prompts on the applet that instruct students on how to use the applet to aid them in their exploration of trigonometric functions. For example, the instructions at the top of this applet prompt students to "Use the slider and point D to figure out how sin(A), cos(A), and tan(A) are related to a, b, and c and to the size of the triangle. Record your observations in an organized table." This prompt is instructing students on how to use the applet and to also make a conjecture about their observation.
Furthermore, if students are confused on how to figure out the relationship between the ratios and the side and angle of the triangle underneath the initial instructions students are prompted to "Explore this applet to try to figure out how the trigonometric functions are defined. You may want to have a calculator handy." These instructions prompt students to try to figure out how the trigonometric functions are defined given the side lengths of the triangle and the vales for the three functions. Also, it is suggested that students may want to use a calculator, hinting at the fact that they will be making some type of calculation.
Lastly, the prompt at the bottom of the applet asks students to make up their own rules to find the sine, cosine, and tangent of any right angle in a right triangle and to include a diagram of their rules. This allows students to generalize their findings so that they are able to apply them to any right triangle.
These instructions provide students with a good idea of what the applet is trying to have them do. However, the order which the prompts are presented could be confusing for the students. I think that if the prompt at the top of the applet was moved to the bottom with the final prompt that students would clearly understand what they are supposed to do first and then make a conjecture about the relationship of the sides and size of the triangle to the three ratios. Also, while this applet does lack written materials I do think that it could provide a good introduction to trigonometric functions.
Furthermore, if students are confused on how to figure out the relationship between the ratios and the side and angle of the triangle underneath the initial instructions students are prompted to "Explore this applet to try to figure out how the trigonometric functions are defined. You may want to have a calculator handy." These instructions prompt students to try to figure out how the trigonometric functions are defined given the side lengths of the triangle and the vales for the three functions. Also, it is suggested that students may want to use a calculator, hinting at the fact that they will be making some type of calculation.
Lastly, the prompt at the bottom of the applet asks students to make up their own rules to find the sine, cosine, and tangent of any right angle in a right triangle and to include a diagram of their rules. This allows students to generalize their findings so that they are able to apply them to any right triangle.
These instructions provide students with a good idea of what the applet is trying to have them do. However, the order which the prompts are presented could be confusing for the students. I think that if the prompt at the top of the applet was moved to the bottom with the final prompt that students would clearly understand what they are supposed to do first and then make a conjecture about the relationship of the sides and size of the triangle to the three ratios. Also, while this applet does lack written materials I do think that it could provide a good introduction to trigonometric functions.
What are the purposes and goals for using this technology? Does this technology reach this goal?
The purpose and goal of this technology is to help students explore and discover the definitions for sine, cosine, and tangent of a right triangle without having any previous knowledge of their definitions, such as the commonly use mnemonic device SOHCAHTOA. This technology aims to help students understand the three trigonometric functions before becoming reliant on the use of SOCAHTOA.
I think that this technology does reach the goal of having students explore the definitions of the three trigonometric functions. Since this applet is intended for students who have no previous knowledge of the definitions of sine, cosine, and tangent, it would lead students to develop their own definitions of the functions based on their own calculations and exploration of the applet. Furthermore, this applet also leads students to make conjectures about the relationship of the size of the triangle to the three ratios, furthering their exploration into the subject.
I think that this technology does reach the goal of having students explore the definitions of the three trigonometric functions. Since this applet is intended for students who have no previous knowledge of the definitions of sine, cosine, and tangent, it would lead students to develop their own definitions of the functions based on their own calculations and exploration of the applet. Furthermore, this applet also leads students to make conjectures about the relationship of the size of the triangle to the three ratios, furthering their exploration into the subject.
Is this technology relatively easy to learn how to use?
This applet is very simple and easy to use. There are only two sliders and instructions are provided as to what each slider controls.
Does this technology enhance or extend the teaching and learning process for the intended mathematics concepts? How and why?
I think that this technology does enhance the teaching and learning process for the intended concept. This applet aids students in developing a better understanding of the three trigonometric functions. By having the students figure out for themselves how the three functions are related to the sides of a right triangle, they are developing for themselves a better understanding of those functions and not just relying on SOHCAHTOA.
I also think that this applet extends the teaching and learning process for the intended mathematics concept in that it provides a good transition into the introduction of trigonometry, specifically right triangle trigonometry. The teacher could use this applet in the beginning of a unit and use it to transition into special right triangles.
I also think that this applet extends the teaching and learning process for the intended mathematics concept in that it provides a good transition into the introduction of trigonometry, specifically right triangle trigonometry. The teacher could use this applet in the beginning of a unit and use it to transition into special right triangles.
Would you recommend this product for purchase to a school? Why or why not?
This applet can be found on geogebratube which is a free website, so all a school needs is internet access. I would recommend the use of this applet in school because I think that it would help students develop their own understanding of sine, cosine, and tangent, rather than simply being told what they are. Furthermore, while this applet is very specific to one topic I think that it could be a great tool to be used as either an introduction to the topic or a review for the topic later on in the year.