Getting Ready for Algebra Using Virtual Manipulatives
There is substantial evidence to suggest that a solid foundation in algebra provides a gateway to the higher levels of mathematics necessary for success in higher education, technological or scientific occupations, and business applications. Given this reality, as well as the increased focus on accountability and high academic standards, many schools and districts have instituted policies that require all students to complete algebra as a requirement for high school graduation.
In response to the accountability measures outlined in the No Child Left Behind Act of 2001, the Southern Regional Education Board (SREB) worked with a panel of teachers and experts from the Educational Testing Service (ETS) to develop 17 Algebra I readiness indicators, including the 5 “process” indicators and the 12 “content and skills” indicators. This course is structured around the 12 content and skills readiness indicators and will introduce a collection of virtual manipulatives that will help curriculum planners and classroom teachers meet the demand to prepare students for Algebra I.
This is an introductory workshop for teachers, technology specialists, curriculum specialists, professional development specialists, and other school personnel who integrate technology into mathematics instruction. Participants are expected to have a set of baseline skills in both mathematics and technology. The prerequisite skills and knowledge are as follows:
Participants are expected to have basic technology skills and regular access to computers. Specifically, participants should be proficient with browsing the Internet, using email, and saving and accessing computer files.
This online workshop addresses the mathematics skills and knowledge that are necessary for students to be successful in algebra as described in the SREB report, Getting Students Ready for Algebra I, and the National Council of Teachers of Mathematics’ (NCTM’s) Principles and Standards for School Mathematics (PSSM 2000).
Participants should have a working knowledge of the expectations outlined in the NCTM Algebra Standard, which states:
“Instructional programs from pre-kindergarten through grade 12 should enable all students to:
understand patterns, relations, and functions,
represent and analyze mathematical situations and structures using algebraic symbols,
use mathematical models to represent and understand quantitative relationships, and
analyze change in various contexts” (PSSM p. 37).
Additionally, participants should have specific understanding of the algebra goals and expectations for students in grades 6-8 as outlined in NCTM’s Principles and Standards for School Mathematics (PSSM 2000) on pages 222-231.
This workshop will enable participants to:
identify the essential content and process readiness indicators for student success in Algebra ,I
identify virtual manipulatives and interactive applets that target the essential skills and knowledge aligned with each of the content readiness indicators,
analyze virtual manipulatives and interactive applets according to given criteria including: alignment with mathematics learning goals, instructional strengths and limitations, ease of use, and availability of support materials,
use virtual manipulatives and interactive applets in activities that target the essential skills and knowledge required to meet the essential algebra readiness indicator,s
develop activities that use virtual manipulatives and interactive applets to target the essential skills and knowledge required to meet the essential algebra readiness indicators.
Assessment and Course Requirements
Each session includes readings, an activity, and a discussion assignment, which participants are required to complete.
As a final product, participants will create a lesson plan that incorporates a virtual manipulative or online tool into the curriculum.
Students will be evaluated on the frequency and quality of their discussion board participation. Students are required to post a minimum of three substantial postings each session, including one that begins a new thread and one that responds to an existing thread. Postings that begin new threads will be reviewed based on their relevance, demonstrated understanding of course concepts, examples cited, and overall quality. Postings that respond to other students will be evaluated on relevance, degree to which they extend the discussion, and tone.
Session One: Introduction to Algebra Readiness and Virtual Manipulatives
Read “Getting Students Ready for Algebra I: What Middle Grade Students Need to Know and Be Able to Do
Read “What are Virtual Manipulatives?”
This article defines virtual manipulatives, highlights examples of virtual manipulatives, and discusses their potential classroom uses.
Session Two: Number and Operations Indicators
The activities in this and all other sessions will help you make connections between readiness indicators, instructional strategies, and virtual manipulatives. You will first engage in the activities as learners and then discuss the activities from both the learning and teaching perspectives.
Download the “Visualizing Fractions” activity and complete the assignment.
Session Three: Geometry and Measurement Indicators
Session Four: Data and Probability Indicators
Session Five: Algebra and Functions Indicators
For this activity and the remaining activities in this session, you may want to refer to the attached list called "Notation for Functions," which contains the proper notation for identifying various functions within the online tools.
Session Six: Summary and Final Project
Read “Mathematically Appropriate Uses of Technology.” This reading discusses some of the issues that mathematics educators face in deciding which technology tools can improve student achievement and learning.
Participants will also complete their final project which is a plan, where they are going to select a virtual manipulative and describe a plan for using it to address one of the SREB algebra readiness indicators with middle school students.