Geometer’s Sketchpad

Geometer’s Sketchpad is an educational software for students of most grade levels ranging from 3^rd grade to college. This software allows students to visualize math in a new way that engages students and allows students to have a deeper understanding of mathematical concepts. This program not only helps students solve problems, but also allows them to prove why things work such as theorems, by using pre-built construction in the software and dragging around shapes, graphs and more.

Geometer’s Sketchpad allows students to prove geometric definitions. Each shape has properties whether they are regular or irregular. Using this software, students can visualize why certain shapes have these properties. An example would be, to prove the angle sum of any type of triangle is 180 degrees students can create a triangle. With the triangle, created students could measure each of the angles and side lengths using the program and have it displayed. While the angles are displayed, students can also use the program to add up the angles. After the angles are added, the student can drag the corners of the triangles changing the angle measurements and side lengths. While doing so the students can observe that although the angles and side lengths of the triangles change, the triangle angle sum remains at 180 degrees. This will allow students to visually see and understand that the angle sum of any triangle is 180 degrees.

With the use of Geometer’s Sketchpad, students can manipulate models, number lines, geometric patterns, explore ratio, proportion, explore numerical functions, and relationships using graphical representation.  The measure option in this software also allows students to measure any model, shape, side length, perimeter, area, and ratio accurately. With all these tools, students have the ultimate “interactive whiteboard” in their hands where they can explore, interact, and learn. With these tools present, teachers as well as students do not have the hassle of wasting time trying to create these shapes, graphs, models and more on paper. In addition, the measuring tool also saves time and allows both students and teachers to be accurate, because there is always an uncertainty measuring on paper. Overall, Geometer’s Sketchpad provides a quick efficient way for teachers to prove, supplement, or just simply make their lesson more engaging. Similarly for students Geometer’s Sketchpad provides students with the tool to better understand mathematical concepts, proofs, and use manipulatives to support their thinking. 

Technology & Pedagogy

I chose this lesson plan because probability is a difficult topic in math, so I wanted to explore lesson plans that teachers have made that would help students and me in the future.

 For the most part the curriculum goals, teaching strategies, and technologies used were aligned, with a few exceptions. One of the curriculum goals was missing, which is an important factor in learning probability. Students not only need to learn how to find the probability of a given event, but also should be able to visually represent it. The missing curriculum goal covered the visual representation of probability events of one or more event occurring. The strategies were also mostly aligned, except for two, the one that was missing and the last one. A strategy that would be good is working with hands on manipulatives and discussing in groups. The technology was not aligned very well, the teacher provided a couple of opportunities for the use of technology, but did not go through with them and just made it an option for the students.

The technology listed is essential to support the instructional strategies because it proves what the teacher tells the students. The video Probability and odds provides another viewpoint for students understanding, which allows the students to see in more than one way. The students were also provided to access on the computer, which did not really support the lesson, but allowed them to look up any additional information they needed to know. Other technologies that would better support the strategies for the goals would be the smart board/power point for visual representation, calculators, online manipulatives, and Microsoft excel. Each of these technologies would allow students to see what they are trying to find and support their answers.

URL: https://docs.google.com/spreadsheet/ccc?key=0Al-Ug3kw0QuYdHQ3TzdEbDZBZ1ZPYjRJVUloR18wR2c&usp=drive_web#gid=0

Math Can be Fun too

            Students who sit in a lecture listening to a teacher talk have a harder time concentrating and learning. There are so many fun, engaging learning math games for every subject. Sheppard Software is a website that has games for most content areas that goes up until some high school level. These games are interactive activities for students to play to be supplementary to lesson plans. In addition, these games are completely free and students can access it from their homes as well.

There are many fun interactive materials for almost any lesson plan, and this website is one of the many out there. There are also available questions that students could try that will tell the student within a second whether they are right and why. The website also encourages students to beat high scores of previous players that have played that game and has a scoreboard with names of students. These high scores not only serve as a positive reinforcement, but also encourage the students to learn the material even more by making them play more to get a higher spot. When students get a high score, they will most likely have a more positive attitude about the material and want to keep learning.

These games include math skills and math literacy. This website includes games ranging from solving problems to becoming familiar with math vocabulary. Some math skill games include counting, decimals, divisions, fractions, factors, measuring, and much more. Some math literacy games include identifying math operations, naming geometric shapes ranging from polygons, non-polygons, distinguishing the difference between similar and congruent, different types of triangles, different types of quadrilaterals, identifying basic and 3-D shapes. Both math skills and math literacy are equally important, so it is even better that there are games to help students with both.

Overall, not all students learn the same; some need more help than others need. Often times students who struggle find a harder time catching up, but this website holds a range of games from k-10^th grade and there are many other websites like this. Even if a student is falling behind, having a hard time understanding, or even just wants to refresh their memories these games allow students to learn and practice to make sure that they will succeed. These games provide a fun interactivity for student whether or not they need the help, it could also just be for fun.

Boards Can be Smart too

            The smart board has revolutionized how students learn curriculum. From blackboards to whiteboards, education takes a giant leap with smart boards. A smart board is able to do anything a whiteboard can do and more. It allows the material taught to be displayed and interactive through many of its functions. A great tool to use for math teachers while using a smart board would be the SMART Notebook Math Tools software, which combines math tools and interactive practices at a teacher and students’ hands.

            A smart board alone has many features for a teacher. With a smart board, teachers and students could display notes and are not limited to the space because the page can be expanded; the notes could later be saved to be shared or printed for notes. This is beneficial to students who missed the day. There are also many fun education games to play as a class, by touching the smart board. Along with the educational games, there are also interactive worksheets and interactive websites that can supplement to learning about a topic. There is also a click and drag feature, which can be used for moving around measuring tools if learning about angles or different types of measurements.

            Although any of these features could be used for math features, the SMART Notebook Math Tools software focuses mainly on math topics. The software includes a geometry tools where students can create any shapes even personalized shapes, measure from side lengths to arcs, select angles or personalize angles based on the degree. There is even a tool that allows shapes to be divided into equal parts for learning fractions. There is even a function for students to learn and create irregular polygons, curved lines, semi-circles, and even all the different types of triangles there are. There are also features that include displaying functions as graphs and charts. This allows any function to be visually displayed for a better understanding. Another feature is a resizable ruler, so students could have an easier time measuring small or big side lengths with just one ruler. The software also has built in problems that will take students through a systematic procedure to learn how to solve the problem, while interacting with the board. Overall, the smart board has many great features for any classroom. The SMART Notebook Math Tools software however focuses greatly on math and allows students participate in it.

History of Technology in Mathematics

Slateboard: imprinting math and erasing mistakes since the 19^th century.