InteGreat
Critiques
![Picture](/uploads/3/1/6/0/31605851/3047074.png)
How well does it work?
The applet is user-friendly for both students and teachers. The purpose of the applet to teach students about integrals through limits and Riemann sums, which will ultimately lead them to definite integrals. The applet works as foundation towards that concept. It helps students to understand how to break down a curve into segments, why more segments are better, how to get a better estimate etc. The applet uses step-by-step approach to lead students towards limit to infinity.
Some of the graphics, however, could use some improvement. Specially, I found the graphing window too small and it makes graphs hard to move. Another feature to highlight, on a particular exploration of sine function with the applet, it treats y=sinx and y=sin(x) as two different equations. The applet treats y=sinx as y=sin*x, hence a linear function. On the other hand, it treats y=sin(x) as regular trigonometric function. This is an significant feature of the applet to preserve the mathematical fidelity. We often see students consider, for example, y=sin2x and y=sin(2x) as same functions; this kind of misconception compromises the mathematical fidelity.
Are the written materials well organized and useful?
The written materials are very well organized and helpful for both students and teachers. For example, student have easy access to the help menu which guides them how to navigate the applet. The help tab have easy to understand instructions on how to enter information, what does each option do, and how to customize the screen according to viewers' preference. On the other hand, the applet has detailed instructions for teachers as well. The instructor tab has description of the activities, the type of preparation teachers need to use the applet, and plenty of resources related to the applet, as well as for future explorations based on the applet.
What are the purposes and goals for using this technology? Does the technology reach the goal?
The goal for students is to graph functions, specify boundary/limits of the functions to evaluate, and specify the number of partitions to be used to find the area under the function. Students can also select different integration method to investigate which option gives a better approximation of the area. The technology works as an excellent tool to meet these objectives. Through various partitions and integration methods, using limits and Riemann sums, students will develop an understanding of finding area under curve and estimation.
On the teachers' side, the applet will give them options to deliver the materials with plenty of resources and less distractions for students. With a well guided activity sheet, teachers can deliver the topic, clear any misconceptions (specially about left/right end-point method and what is upper/lower sum), and pose cognitively challenging questions that could be explored further with the applet.
Is the technology relatively easy to use?
I found the applet very easy to use with the guidelines. At the beginning, the applet may seem overwhelming. However, few minutes of demonstration using the sample guidelines, teachers can make this an effective and efficient tool to deliver the materials. Few recommendations for improvement would be to get a bigger graphing window and make the use of zoom/pan feature more interactive. I would also like to see actual values of integration on the screen so that students can compare their answer and perform some error analysis.
Does the technology enhance or extend the teaching and learning process for the intended mathematics concepts? How and why?
The applet definitely enhances and extends the concept of limits and Riemann sum. Using the applet students will understand the use of rectangle and trapezoid sums to approximate the area under curve. This objective will use students' current knowledge of area of rectangle and trapezoid and extend it to find the area under a function which does not have straight edge. By using the boundary of functions and partitioning techniques students will understand the logic of taking limits of sums. Finally, the overall activity will lead them to understand various approaches of finding area under curve and justify which option gives better approximation, as well as, why taking more partitions (i.e. limits to infinity) give better accuracy. If we can add the actual value of integration, we can extend the use of this applet to find the best approximation technique and error approximation.
Would you recommend this product for purchase to a school? Why or why not?
The applet is available free to use for teachers and students from shodor.org. I would definitely recommend the applet to use in classroom. The tool is easy to use and comes with plenty of resources for teachers. Using the sample worksheet, teachers can stimulate students' thinking and engage them into productive classroom discussions. With some improvement in graphics, this can serve as an effective medium to deliver the lessons on limits and Riemann sums.
The applet is user-friendly for both students and teachers. The purpose of the applet to teach students about integrals through limits and Riemann sums, which will ultimately lead them to definite integrals. The applet works as foundation towards that concept. It helps students to understand how to break down a curve into segments, why more segments are better, how to get a better estimate etc. The applet uses step-by-step approach to lead students towards limit to infinity.
Some of the graphics, however, could use some improvement. Specially, I found the graphing window too small and it makes graphs hard to move. Another feature to highlight, on a particular exploration of sine function with the applet, it treats y=sinx and y=sin(x) as two different equations. The applet treats y=sinx as y=sin*x, hence a linear function. On the other hand, it treats y=sin(x) as regular trigonometric function. This is an significant feature of the applet to preserve the mathematical fidelity. We often see students consider, for example, y=sin2x and y=sin(2x) as same functions; this kind of misconception compromises the mathematical fidelity.
Are the written materials well organized and useful?
The written materials are very well organized and helpful for both students and teachers. For example, student have easy access to the help menu which guides them how to navigate the applet. The help tab have easy to understand instructions on how to enter information, what does each option do, and how to customize the screen according to viewers' preference. On the other hand, the applet has detailed instructions for teachers as well. The instructor tab has description of the activities, the type of preparation teachers need to use the applet, and plenty of resources related to the applet, as well as for future explorations based on the applet.
What are the purposes and goals for using this technology? Does the technology reach the goal?
The goal for students is to graph functions, specify boundary/limits of the functions to evaluate, and specify the number of partitions to be used to find the area under the function. Students can also select different integration method to investigate which option gives a better approximation of the area. The technology works as an excellent tool to meet these objectives. Through various partitions and integration methods, using limits and Riemann sums, students will develop an understanding of finding area under curve and estimation.
On the teachers' side, the applet will give them options to deliver the materials with plenty of resources and less distractions for students. With a well guided activity sheet, teachers can deliver the topic, clear any misconceptions (specially about left/right end-point method and what is upper/lower sum), and pose cognitively challenging questions that could be explored further with the applet.
Is the technology relatively easy to use?
I found the applet very easy to use with the guidelines. At the beginning, the applet may seem overwhelming. However, few minutes of demonstration using the sample guidelines, teachers can make this an effective and efficient tool to deliver the materials. Few recommendations for improvement would be to get a bigger graphing window and make the use of zoom/pan feature more interactive. I would also like to see actual values of integration on the screen so that students can compare their answer and perform some error analysis.
Does the technology enhance or extend the teaching and learning process for the intended mathematics concepts? How and why?
The applet definitely enhances and extends the concept of limits and Riemann sum. Using the applet students will understand the use of rectangle and trapezoid sums to approximate the area under curve. This objective will use students' current knowledge of area of rectangle and trapezoid and extend it to find the area under a function which does not have straight edge. By using the boundary of functions and partitioning techniques students will understand the logic of taking limits of sums. Finally, the overall activity will lead them to understand various approaches of finding area under curve and justify which option gives better approximation, as well as, why taking more partitions (i.e. limits to infinity) give better accuracy. If we can add the actual value of integration, we can extend the use of this applet to find the best approximation technique and error approximation.
Would you recommend this product for purchase to a school? Why or why not?
The applet is available free to use for teachers and students from shodor.org. I would definitely recommend the applet to use in classroom. The tool is easy to use and comes with plenty of resources for teachers. Using the sample worksheet, teachers can stimulate students' thinking and engage them into productive classroom discussions. With some improvement in graphics, this can serve as an effective medium to deliver the lessons on limits and Riemann sums.