Bridge to Algebra Review
BevK October 12th, 2006
http://eclectichomeschool….asp?revid=2282
Bridge to Algebra is the pre-algebra portion of Carnegie Learning’s Cognitive Tutor math curriculum. The curriculum is at heart a problem-solving curriculum that divides its instructional time between individualized instruction and group collaboration. Group collaboration is not essential to the curriculum, but it does make it an interesting possibility for the co-op setting. The curriculum covers the basic middle school pre-algebra topics with reviews of number sense, fractions, decimals, ratio and proportion, and percents in the first six units. Units seven and eight cover integers and an introduction to algebraic problem solving followed by four units covering geometry topics and probability and statistics. The last three units finish the preparation for Algebra I with linear functions, number systems, and transformations on a coordinate plane. There are 15 units with 94 lessons. Developed at Carnegie Mellon University and extensively tested, this curriculum strives to bring math into the real world for students by focusing on real world problem solving. Students can easily see that understanding how to compute least common multiples, for example, is useful knowledge. The curriculum requires students to write about their observations in complete sentences, which demands of students that they reason both numerically and verbally about the math. Lessons are presented using a variety of techniques from visual representations such as picture algebra to traditional numerical and algebraic expressions. The curriculum has been used successfully with students who struggle with math and special needs students as well as adept math students. My student had difficulty initially because he is used to math curriculum wanting the answer to the problem. Questions that asked him to describe the context of the problem and to represent the problem with a picture, symbols, or another representation stumped him. He had already worked out the solution in his head and just wanted to know where to write the answer. This curriculum is based on a constructivist approach to learning in which students build their own knowledge of math by forming models to represent the problems posed. Thus, the text begins with picture algebra to expose students to this way of discovering math principles. Since the first topic involves multiplication, addition, and subtraction, the student isn’t faced with both new math concepts and new ways of thinking about math. The software complements this by showing what picture algebra means. It would probably have made it simpler if I’d had my student do the first software unit before attempting the text. This curriculum offers students the why of math concepts by allowing them to see it in terms they understand. The problems in the student text are laid out to guide the student in this process. In some ways, this makes this curriculum ideal for parents who are concerned with their own ability to teach higher math. There are two parts to the homeschool version of Bridge to Algebra, the student text set and the computer software. The student text set comes with three softcover texts: the Student Text, Student Assignments text, and the Homework Helper. These are consumable texts that students will write in daily. Student text sets are available separately, so you can use the curriculum with as many students as needed as long as they all have access to the computer with the curriculum software. The Student Text is softcover with 521 instructional pages with an additional glossary and index. The entire book is three-hole punched and each page can be removed from the book. It would be possible to divide the book into units placed in three ring binders. Doing so would make writing on the pages easier since it is a thick book. Each lesson begins with a brief introduction followed by a problem that is designed to get the student to formulate a method to solve the problem. A variety of problem solving techniques are encouraged. The problem is supposed to be done as a group effort followed by sharing and comparing answers with other groups. This step could be done with the parent if the student has problems answering the questions posed by the text. A second problem is given and in the discussion following introduces the mathematical concepts and terms that fit the problems that have been worked on in that lesson. Thus, the mathematical concepts and terms are only introduced after students have spent time working on real world problems that use those concepts to solve them. Each chapter begins with a looking ahead section that includes a bit of computational and problem solving warm up. Chapters end with a listing of all key terms with page numbers where they were introduced and a summary of concepts that includes an example of the concept. Key terms are also found defined and with examples in the glossary. Since this curriculum is based on the idea that students can construct their own knowledge through a guided inquiry process, the problems found in the Student Text are essential to the learning process. Step-by-step computational procedures are dealt with more extensively in the curriculum software component. The Student Assignment text has an assignment sheet with more problems to solve and a skills practice sheet with review problems and a short set of more traditional computational style problems for each lesson. Although students will be working computationally as they solve problems, problems are initially presented in verbal format. The skills practice sheet computation section offers the more traditional numeric expression of a problem that they will face on standardized tests. The Homework Helper is an additional set of two to three problems. The first problem includes a step-by-step solution. Answers for additional problems are found in the back of the book. Pages in this book cannot be torn out. The publishers suggest that students will spend 40% of their time in the computer lab. The complete homeschool kit of Bridge to Algebra comes with a stand-alone version of the software that allows you to install it on one computer. The Teaching Toolbox provides the teacher tools to administrate multiple classes with multiple teachers and multiple students. You can generate reports about the status of an individual student or entire class. The interface is intuitive and easy to use. Teachers have the ability to pass a student on without finishing requirements in a unit, reset a unit, or reset a problem. The toolbox also gives teachers access to problem solutions and the content of each lesson. The student software is perhaps the most interesting part of this curriculum because it is based on cognitive tutoring that can determine how a student is progressing through the material and provide more or less instruction based on the student’s abilities and mathematical understanding. A set of progress bars monitors a student’s status towards attaining the skills to graduate from a lesson. Students move on to the next lesson only once they have demonstrated that they have attained the necessary skills. I tested this aspect of the curriculum by posing as a student doing well and another doing poorly. I finally allowed the poor student to pass the section when I grew tired of entering wrong answers. A hint button is available that offers suggestions that make solving the problem increasingly easier until eventually it gives the answer. Each problem is broken down into steps and answers must be correctly supplied for each step. The student may answer the step 2 question correctly each time, but if he doesn’t also answer steps 1 and 3 correctly enough times, he won’t be passed on. A student knows immediately that his answer is incorrect because it appears in red with a red exclamation point. This is true when he makes a mistake in creating a graphical representation as well as with entering numeric answers. Each of the units includes a look ahead section that gives the key terms and skills that will be used in the coming lessons. In addition, a look back section concludes each lesson. Students may toggle to either of these sections from the problem-solving page. The look back section includes links to pages with explanations of the skills being practiced. There’s also a link to the software’s glossary, which provides definitions and examples of terms being used. There are 171 lessons in 44 units that do not have one-to-one correspondence with the Student Text lessons. For example, the software has three units with seven lessons that cover topics in the Student Text Unit 1’s seven lessons. The software does not cover the text lessons on prime numbers. You will need to coordinate the software to the text. The software alone is not a complete pre-algebra curriculum. It can be used to supplement another pre-algebra text, but shouldn’t be thought of as a replacement for a complete curriculum. The software comes with 30 days of technical support to assist you in getting up and running. You may also find the Homeschool Quickstart Guide helpful in installing and setting up the program. Additional videos for help in setting up teachers and students in the Teacher Toolbox are available at http://www.carnegielearning.com/homeschool_community/index.cfm?page=forum&forumID=2 Although I was not given a Teacher’s Implementation Guide to review, information at the Carnegie Learning website makes it clear that it is essentially the teacher’s manual for the Student Text. It includes answers for that book and additional teaching suggestions that would help in teaching the course in a group setting. The teacher text set includes a two volume teacher implementation set and a two volume set of resources and assessments. You’ll have to contact the homeschool coordinator at Carnegie Learning to purchase any teacher books. The answers to the Student Assignment text do not come in the homeschool kit. I’m not sure which of the teacher texts, if any, include these answers. If my request for that information is made available, I’ll include it here in the future. Publisher: Carnegie Learning List Price: HS Curriculum Kit: $99.00, Software: $84.99, Student Set: $21.75, Teacher Set: $80 Reviewed By: Beverly Krueger More Information Available From: Carnegie Learning Address: Frick Building, 20th Floor, 437 Grant St., Pittsburgh, PA 15219 Phone: 888.851.7094 Website: http://www.carnegielearning.com/products_homeschool.cfm
