Reflections

After completion of the final project for this class I can say without doubt that I learned a lot about technology integration. I found it rather difficult to integrate technology for math because a lot of math is usually completed with a pencil and paper. At least, I find that to be the most effective way to learn mathematics. It is good to incorporate the technologies since this is still a world where computers are taking over our lives...for the better of course. Even looking past math, technology is useful in all subjects areas, it just need to be used in the right places and for the right reasons. It is one thing to use technology in the class to merely use technology in the class, but it is another thing to use the technologies effectively.

Although an effective and exciting tool, it will never replace good old pencil and paper

Final Project

            A lesson plan for a high school geometry class that I felt would be an excellent example for technology integration is called “Hands-On Geometry: Using Manipulatives in Math 10: Lines and Line Segments Angles and Polygons,” written up by Kathleen Bracken. The idea of the lesson is to increase student understanding in the area of lines, line segments, angles, and polygons. For this particular assignment, I chose to stick with sections one and two, “Mira Constructions: Lines and Line Segments” and “Pythagorean Puzzles.” The total completion time of this unit plan is four hours or approximately one week of lecture, modeling, and practice, given the length of a class is approximately forty-five minutes.

Sessions 1 and 2: Access/Analysis

            The first mathematics standard I found based on this lesson plan is one about rotation, reflection, and translation of lines and line segments using physical technologies and virtual geometry software. Students will be using a tool called a Mira, a transparent device that creates a reflection of a written line or shape which acts as a mirror, for constructing reflections of given lines or line segments. Students would be actively participating in discussion based on their findings and constructions using this tool. There is also a basic mirror tool online which acts similarly to the Mira which can be used for simple simulation and modeling. As an alternative, students can use Geometer’s Sketchpad, computer geometry software, to construct lines and shapes in order to perform reflections, rotations, and transformations. This is a tool I am very familiar with and would be used for any and all geometry plans. It is useful for giving students a more accurate representation of geometric ideas and can help with understanding.

            The second standard which corresponds to the lesson is about explaining the criterion for two triangles being congruent. As a teacher I would lecture about the criterion for triangles to be considered congruent. Then, in order to better students understanding of triangle congruency, students will be asked to work in groups using rulers and protractors to collaboratively construct congruent triangles based on the criterion for triangle congruency. They can also use Geometer’s Sketchpad to construct congruent triangles as well as add the correct markings which could be used to show congruency when triangles are not drawn to scale. After students complete their work they will be asked to use the Smartboard to interactively display their findings to the rest of the class. The Smartboard will allow for manipulations of their work in case there needs to be correction.

            The third standard is about students knowing how to make constructions using a variety of tools. They will use tools such as a straightedge and a protractor to construct shapes such as triangles, squares, and other shapes with larger numbers of sides and angles. They will also use a compass and string to construct circles. For more complicated constructions such as using circles to construct an equilateral triangle, students can use the geometry software which can create more perfect circles which would lead to more accurate constructions of more complicated figures. As a teacher I would model for the students, using these technologies, how to perform these constructions and from there, students will work either at their desks or at computers to individually complete the work. After completion there would be a group discussion about how the constructions were completes as well as sharing the difficulties some students may have experienced.

Sessions 3 and 4: Communication/Evaluation

            The final standards covered in this lesson plan are proving theorems about triangles and using the Pythagorean theorem to solve right triangles. Essentially this is leading into the basic understanding of the Pythagorean theorem. What students will do is use Geometer’s Sketchpad to use the congruency of triangles to show relationships between them, more importantly, those for right triangles. There is an online tool known as NOVA which gives a clear demonstration of a proof of the Pythagorean theorem by breaking down squares which have side lengths of that of the triangles and fit the leg’s squares  into the hypotenuse square. As a teacher I would lecture about the proofs of triangles and about the basic of the Pythagorean theorem. Students would then individually use NOVA or Geometer’s Sketchpad to practice basic proofs of triangles and solve problems using the Pythagorean theorem. After they practice I would check for understanding by administering a brief examination about their understanding of triangle congruence and the Pythagorean theorem.

            It is clear that technology can be easily and effectively integrated into this lesson plan and using them, along with specific teaching strategies, would make mathematics more interesting and enjoyable.

Link to Speadsheet

Link to Lesson Plan

Math Using Technology

I have tried to write mathematics on a computer and all i can say is that it was a failure. If we want to bring math into the computer world, we need to find more effective ways of doing it. In this short clip, you will understand what I mean.

Less Ink, More Power