Teaching Guide

Hands-On Technology in Mathematics

I began my teaching career as an elementary school teacher. In college and district professional development classes I learned how to incorporate hands-on math activities to help students understand abstract concepts. When I moved to the middle school level, I noticed that many teachers taught mathematics using traditional methods. One reason for this is because class periods usually don’t have enough time to incorporate these types of activities or teachers haven’t had enough professional development to feel comfortable using various manipulatives in class.

I put this web curriculum together to give learners an opportunity to try various activites that involve technology. If used in the classroom, these activities will help create a hands-on learning environment. Not only will the learner enjoy the interactiveness of the activites, but they will better understand the concepts they enhance. After completing the activities, it is my hope that learners will understand the importance of technology in the classroom.

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Aim

The purpose of this curriculum web is to introduce different types of technology into the classroom that will expand students' understanding of abstract mathematical concepts in the classroom. Another reason for it is to allow learners (teachers) time to explore various types of technology so that they feel comfortable incorporating them in the classroom.

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Rationale

All students can and should understand mathematics. Through constructivism, children are active participants in the development of their own understanding. To construct and understand a new idea requires actively thinking about it. Mathematical ideas cannot be “poured into” a passive learner (Van de Walle, 2007). By having students partake in hands-on learning activities they are figuring out how a concept fits with what they already know. Instead of having students participate in activities that require them to listen, copy, memorize, and/or drill, students should be engaged in activities that allow them to explore, investigate, construct, predict, and explain. Technology is one avenue of exploring mathematics in this way.

According to the National Council of Teachers of Mathematics, NCTM, technology is an essential tool for both learning and teaching mathematics effectively; it extends the mathematics that can be taught and enhances students’ learning. It is important not to think of technology as an extra burden added on to the list of things you are trying to accomplish in your classroom. Rather, technologies should be another of the many real tools at your disposal for helping children learn mathematics. Technology can enlarge the scope of the content students can learn and broaden the range of problems that students are able to tackle (Ball & Stacey, 2005; NCTM Position Statement, 2003). I hope that after you complete this curriculum web you will feel comfortable integrating technology into your classroom because it will aid in helping students truly understand mathematics.

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General Goals

Emphasize the importance of developing a hands-on learning environment
Expose the learner to a variety of ways to incorporate technology in students’ learning of mathematics
Engage the learner in classroom activities that incorporate technology

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Learner Description

Middle school or high school mathematics teachers who want to learn how to use different types of technology and incorporate them into their classroom to create a hands-on learning environment
This curriculum web supports the adult learning theory for the following reasons:

It is relevant to what learners teach
It is convenient because learners can complete the curriculum web anywhere, as long as they have Internet access
There are useful resources for learners
There is a possibility to connect with other learners with similar interests

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Prerequisites

Familiarity with Excel and its basic functions – i.e. sorting, mean, median, mode, and graphs

If you are unfamiliar with Excel, click here for tutorials with its functions.

Facility with a web browser
Interest in creating a hands-on learning environment

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Subject-Matter

Understand the importance of a hands-on learning environment with technology by reviewing the teaching guide and completing all activites in the curriculum web
Explore Virtual Manipulatives to enhance various mathematical concepts
Geometry - Classify two-dimensional objects using their defining properties
Data Analysis - Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

The construction of a math lesson that incorporates technology to help students understand an abstract mathematcial concept

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Learning Objectives

On completing this curriculum web, learners will be able to:

Describe the importance of a hands-on mathematics classroom at the middle and high school level
Name two of their favorite Virtual Manipulatives activities
Classify shapes using Venn diagrams and Shape Sorter
Incorporate technology effectively in a mathematics lesson

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Instructional Plan

This curriculum web is designed to allow the learner to use it on his or her own, without the assistance of a teacher or facilitator. Learners will access the curriculum web and follow the directions they find there. The activities that learners will follow include:

Activity 1: Learning with Virtual Manipulatives

Explore the Virtual Manipulatives web site
Try at least 5 different activites
Choose 2 favorites and explain why the learner likes them at the Activity 1 Reflection Blog

Activity 2: Shape Sorting

Use the NCTM’s Illuminations web site to access the Shape Sorter activity
Complete 3 activities using Venn diagrams
Optional: Complete the Sorting Polygons lesson on the Illumination web site

Activity 3: Exploring Excel

Create spreadsheets using Microsoft Excel to manipulate rows and columns of numeric data
Organize and display data graphically using Microsoft Excel

Culminating Activity: Create a Lesson that Integrates Technology

Create, or update, a lesson that integrates technology in a mathematics classroom

Use one of the types of technology learned in this web curriculum or one you want to learn more about

Self-assess the lesson using the given rubic

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Materials

Web browser to access Virtual Manipulatives and Illuminations web sites
Microsoft Excel - download a free 60-day trial
Adobe Reader - download for free if you don't have it; works for PC or Mac computers
Possible piece of technology learner wants to explore

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Plan for Assessment and Evaluation

Assessmet for Activity 1:

Self-Reflection on what was learned

Assessment for the Culminating Activity:

Develop a lesson plan that incorporates technology to help students explore a new math concept. Use the following rubric to assess the effectiveness and use of technology in your lesson plan.

Guiding Questions	Exceeds Expectation	Meets Expectation	Below Expectation
Does technology SUPPORT instructional activity? Technology should not BE the lesson. Do not teach students how to use Excel for example. Use technology as a tool.	The technology supports the instructional objective in a meaningful way. It enhances it and possibly facilitates additional beneficial outcomes not directly measured.	The technology does support the lesson but may “get in the way” somewhat, e.g., when students need to “learn” to use the software as a separate endeavor.	Technology tends to be the focus of the lesson. Technology intrudes into the lesson or becomes the activity itself, e.g., teaching students how to use a spreadsheet.
Is the use of technology transparent? Students should learn how to use the application without being aware of it. It is a means to an end, not an end in and of itself.	The technology supports the instructional objective in a meaningful way. It enhances it and possibly facilitates additional beneficial outcomes not directly measured.	The technology does support the lesson but may “get in the way” somewhat, e.g., when students need to “learn” to use the software as a separate endeavor.	Technology tends to be the focus of the lesson. Technology intrudes into the lesson or becomes the activity itself, e.g., teaching students how to use a spreadsheet.
Is the lesson/activity intrinsically motivating? If students hate to write, they will hate to write as much using a computer as they do without it. The activity must engage and motivate.	Activity is interesting and engaging for the target population. It is fun; even goofy enough to motivate students to do whatever it takes to accomplish it and would want to do it again.	Activity is reasonably different from students' normal classroom activities. Students are motivated to try the activity.	The activity is dry and boring. Technology cannot make a bad activity good or a boring activity exciting. The activity itself must be imaginative, thoughtful, and creative.
Can the lesson be taught without technology? The answer to this question will often be “yes,” but the lesson should be at least as easy and worthwhile with it as it is without it.	Technology definitely improves the lesson in some fashion.	Technology is appropriate but the lesson could have been carried out without it.	Poor or contrived use of technology -- the activity would be easier and more effective without it.

adapted from Robert D. Hannafin

Evaluation for the Curriculum Web:

Learners will evaluate the effectiveness of this curriculum web using the feedback form. You can access this form by clicking the link at the bottom of any page. The curriculum web will be revised and updated according to feedback responses.
I have spoken with other middle school mathematics teachers while creating this curriculum web and have incorporated some of their suggestions.

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Resources

Ball, L. & Stacey, K. (2005). Teaching strategies for developing judicious technology use. In W.J. Masalski & P.c. Elliott (Eds.), Technology-supported mathematics learning environments (pp. 3-15). Reston, VA: National Council of Teachers of Mathematics.

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