Using+the+computer+to+make+concepts+alive+and+visible+to+students.

Created by F-4 Group: Sediqa Nazari, Sedda Antekelian, Kerri Du, and Rhonda Maranan

toc =Introduction =

Today, in our growing world of technology use, we as a society have come to a point where the computer has not only been a great tool for communication, information and word processing but it has also been a providing source of educational learning. This device has helped and continues to help students of all ages and grade levels.

An area in which computer technology has greatly contributed would be to the field of Mathematics. [|Mathematics] is a complex field of study that involves numbers, graphs, shapes, statistics and more. It is a subject that students grow up learning from their early childhood and even still, as an adult are continuing to learn.

Computer technology has provided teachers in math classrooms excellent tools for communicating mathematical concepts to students, appealing to all student learning types. Of those technological tools that assist teachers to develop student understanding and methods of problem solving are four notable forms of approaches for mathematical learning in the classroom: Virtual Manipulatives, Microsoft Excel, PowerPoints and Blogs.

Lets begin with an outline of each form of Computer Technology that make Math concepts come alive!

=Virtual Manipulatives =

**What is it?**
To understand what a visual manipulative is, let's first focus on the word manipulative. A manipulative, in an academic setting is any concrete object that will allow a student (s) to discover, explore and further develop an idea with an active and hands-on approach, in this case, mathematical. To connect the terms together, a virtual manipulative is a similar tool as it is a concrete representation of an abstract mathematical concept that is demonstrated online by the use of modern day technology. Research has shown that students feel more of a connected understanding to mathematical ideas when the teacher uses [|virtual manipulative] tools.

**Uses, Users and Grade Levels**
Visual Manipulators can be used across all Mathematics subject areas. Students, no matter what grade level or age will enjoy the engagement that a visual manipulative brings into the classroom. When appealing to EL students in a main stream course, a virtual manipulator does not have to be an alternative resource, rather virtual manipulatives are just the right amount of interaction, engagement and positive student thinking and understanding for all learning levels.

**Examples**
Manipulatives can be anything from basic blocks, Legos, kitchen bowls or even folded paper. These materials altogether help students to visually see complex ideas come to life. They even give students something to relate to whether they are in the classroom participating, taking a test or even paying the cashier at a register. Visual Manipulators can be anything from an online quiz game, animated shape figures, video clips, or even hands-on work with computer technology.



There are many great websites and programs that offer the opportunities for teachers to use virtual manipulatives in their classroom. Though there are so many out there, below is a list of related links that may help in a teacher's search toward success in the classroom (See Suggested Websites).

**Suggested Websites**
[|Illuminations] [|Math Playground] [|National Library of Virtual Manipulators] [|MathATube]

=**Microsoft Excel** =

What is it?
Another way to bring math concepts alive and visible to students is by using the software called [|Microsoft Excel]. Excel software (also known as [|Microsoft] Excel) is a spreadsheet program for Windows and Macintosh computers which allows one to enter numerical values or data into the rows or columns of a spreadsheet, and to use these numerical entries for such things as calculations, graphs, and statistical analysis.It is part of the Microsoft Office suite, which includes other productivity programs, such as Word and PowerPoint. Microsoft Excel software is the most common spreadsheet software used by [|businesses].

What areas of math we can use it?
There are different areas of math that using excel could be useful in teaching students math conceptually. First, students who are in K-6 can use Excel as a calculator once they understand the concept of adding and subtracting. A student can create a formula to solve simple problems that could be time consuming. On a worksheet, a student can enter simple formulas to add, divide, multiply, and subtract two or more numeric values. They can also enter a formula that uses the SUM function (also known as AutoSum) to quickly total a series of values without having to enter any of them manually in a formula. Once you have created a formula, you can fill it into adjacent cells — no need to create the same formula over and over again. Second, in 7th grade the students can use Excel to graph linear, quadratic, cubic, and many different functions. Third, the students can use Excel to represent data in many different forms. In statistic the use of Excel could be very useful in analyzing the data. There are many different tools that could be very helpful in statistic such as creating [|bar graphs], [|pie chart], [|scatter plots], and many more. Last month I assigned [|Statistic Project] that required students to use Excel software to make bar graphs and pie charts to represent their data. The students were expected to do a survey and represent that data using different tools of Excel. Below are some of the examples the students came up with using Excel software.

Examples
==

=Powerpoints =

Definition
Another tool available to make math more visible to students is using Powerpoint. This software program can be used to create a slide presentation for the Jeopardy game. The program enables teachers to create different slides with answers and questions for the students. Each slide contains a different answer or question. With a click of a mouse, the teacher can ask a new question that is provided on a separate slide. This interactive program creates a game format that engages students and provides an exciting forum for learning. All students can participate individually or in teams. It can be used with any size classroom equipped with a computer, projector, and projector screen.

Examples
The benefit of this Jeopardy game is the flexibility to use it for any math class. Any teacher can adapt the questions and answers for the content they are teaching. Jeopardy can be used as a formative assessment and/or review for a quiz/test. The difficulty of questions can be adjusted to the grade level and ability of yours students. For example, elementary students can have a jeopardy questions regarding the four different operations; while, calculus students can have questions varying from derivatives, maximums and minimums, and integrals. Examples of the home page, questions, and answers for the Jeopardy game are shown below.







This game format is very useful in keeping the students engaged in the learning process. The range of point values make this a differentiated activity because the lower point-valued questions are accessible to the lower end students; while the more difficult/ higher point-valued problems make this challenging for the higher achieving students. One strategy to make this a collaborative task among students is to make students get into strategically planned teams, which the teacher selects based on student skill level. The members of each team are instructed to work together to arrive at the answer of the slide. This requires the teacher to strictly enforce the practice of teamwork for all the members. When this is not being practiced, the teacher should point this out to the class a bad example of teamwork. On the other hand, when the teacher notices a team productively working together, the teacher should highlight this.

=**Blog Use**=

A more innovative technology that can be applied in math learning is blog. Most mathematics teachers believe that math is not about numbers or formulas, but about problem solving. A key factor for problem solving is critical thinking. Blog, especially the one created for a math class or group, provides a good way for the whole class to participates together and brain storming. As the article [|The Courage to Blog with Students]”states, blogging engages students and helps them do more work than they could if they had only to use pencil and paper.

A typical mathematics instructional blog could start with the teachers provide the writing prompt, and students reply in the comments section. (Ratzel, 2011) The following is a geometry project that I design for class blogging:

 You are the vice president of Marketing for “Good Guys Golf”(GGG), which produces all sports equipment related to the game of golf. It has come to your attention that a competitor is selling more of their packaged golf balls than your company, and you have decided that a new advertising marketing ploy is in order. The president of GGG has asked that you and your colleagues design a few prototypes of new ways to package the golf balls that might cause in increase in sales. It is necessary to sell the balls in packages of 12. Because you and your colleagues have a commanding knowledge of surface area and volume, you begin the task with vigor.
 * The Situation**
 * ﻿ **

**Teachers Prompt:**

 * 1) Draw sketches of the possible ways to package the 12 golf balls. As the vice-president, you will want to make your prototypes cost-effective… therefore, the sides of your container should be tangent to the balls with no extra space.
 * 2) Find the surface area and volume of your prototype.
 * 3) If the material to make the package cost $0.025 per square centimeter, how much will your package cost to produce per unit?
 * 4) Show the design, as well as the production cost of your container. Prepare a presentation to the president of GGG and explain why you believe your design is the best.

**Students will reply in the comments section by: [[image:ball_golf_pw_6_lg.jpg width="150" height="219"]]**
1) Sharing their designs; 2) Finding the cost of their design; 3) Finding errors or problems in the other people’s ideas (such as waste of space, not cost-efficient); 4) Justifying their ideas by supporting data (such as surface areas, volumes, cost per container, etc).

There are multiple benefits by using blogging in the project. First of all, students think more independently. Second, during the process of brain storming, students might be inspired by each others’ ideas and be more creative. Third, it’s good for the students to comment and criticize on the others’ work. It is a process of learning for both parties. Last, and the most important, the blogging may result more than one solution to the project. The whole purpose of the project is not to find out what the right answer is, but to find out solutions for the problem.

Blogging is an excellent way for class review as well. The traditional way of class review is always teachers summarize and students take notes. How much have students learned or understood is unknown. Blogging provide a new way for teachers checking on students’ learning. For example, the teacher can assign students to summarize the big ideas/major concepts in each learning section, post them in the blog, then review the ideas/ concepts with the whole class.

=Summary = = = Computer programs such as Microsoft Excel and visual manipulative are great ways to bring math concepts alive and visible to students. Microsoft Excel could be a great tool in making math fun and educational. I learned this through my experience because my students put a lot of effort and did really well on this project. In addition, the students did really well on the quiz that was given after the completion of the project. Another program to help students learn mathematics is PowerPoint. The flexibility of topics, questions, and answers allows it to be adapted to any math curriculum and educational ability of students. The combination of competition and learning are two factors that make this an positive, enjoyable, educational activity for the students.

In addition, technologies such as blog make students' thinking/learning more accessible to teachers. By checking on students’ comments in blog, teachers can analyze whether the students have good understanding on the contents, or they still have misconceptions. By sharing their ideas with the whole class, students would be more responsible for their posting and more involved in the learning process. Technologies, alone with all the other instructional strategies, serve the ultimate goal of education: to encourage students' learning.

=Citations=

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 * //MathATube.com//. YouTube. <www.mathatube.com>
 * "Illuminations Standards." //Illuminations//. National Council of Teachers of Mathematics,
 * Using Excel to graph math function []
 * Creating a Chart in Excel []
 * Statistic Project Rubric/Survey Sheet []
 * Creating Slides in Powerpoint []
 * Jeopardy Images [],[|http://www.teacherspayteachers.com/data/thumbnails/math%20jeopardy1.ppt.03.jpg,]
 * The Courage to Blog with Students: []