Addressing Diversity in the Student Population

MATH Connections was written to be a secondary mathematics curriculum for all learners. Since its creation, it has given students in urban, rural, poor and affluent districts all across the country the opportunities to learn algebra, geometry and higher mathematics in exciting and diverse classrooms. To do this, many features and learning tools were incorporated within the curriculum under one guiding principle: All students can be successful in mathematics. How can this goal be accomplished? MATH Connections accomplishes this using accessible mathematics, real-life / engaging problems, literacy tools, problem solving, and technology.

Mathematics for All, the Origins of MATH Connections

MATH Connections began with a need. The Connecticut Business and Industry Association (CBIA) Education Foundation was concerned that students in Connecticut were graduating from High School without proper skills. Math was a real issue. Many had poor skills, and even those that did well in high school math had difficulties approaching problems that dealt with real-life applications. Specifically, the workers they were receiving were not problem solvers. They also had literacy issues and difficulty working with others. Traditionally, the available mathematic courses were doing very little to address these issues, so the industries were having to spend time and money to retrain their workers.

In a curricular sense, Mathematics was not considered important for all. Some schools would require 1 or 2 years of high school mathematics and many would offer base level skills courses for their lower-track students. In these courses higher-level thinking was never addressed. In the upper level courses, students would memorize steps to help them score high on particular tests, but in general the information was never applied and did not reflect the needs of industry.

The National Science Foundation (NSF) awarded a grant to the CBIA in 1992 to address the above issues and to create a mathematics curriculum for all based on the National Council of Teachers of Mathematics (NCTM) Standards. The authors of MATH Connections then began to create lessons incorporating problem solving using real-life situations. They reviewed the latest research about how students learn best and rediscovered a very old concept that students learn by doing. However, even the best students are not born with problem solving skills and would have a hard time tackling some problems, so the authors incorporated problem solving within clever questioning written in an easy-to-read "conversational" tone.

Accessible Mathematics

Using the NCTM Standards as a guideline, MATH Connections blends the mathematics of algebra, geometry, probability, statistics, trigonometry and discrete mathematics into a meaningful package that is interesting and accessible to all students. The text materials are designed to provide students with mathematical experiences that excite their curiosity, stimulate their imagination and challenge their skills.

Book 1a begins with statistics. Students examine real data, learn ways of displaying it and examine the "stats." The authors chose to do this for many reasons. For one, the mathematics behind finding the mean, calculating standard deviation and finding quartiles involves the simple operations of addition, subtraction, multiplication and division, skills that are readily done by high school and junior high students. For those who have difficulty with these calculations, a calculator can be of assistance. Early success in a mathematics program is important because it shapes a student's self-image and can determine success. Another reason for putting statistics into the first chapter is that many of the real-life applications of mathematics involve data. Students completing this first chapter will not only feel successful, but will have a common language that the book uses as an access point to algebra and the higher mathematics.

MATH Connections is concept driven. It uses common thematic threads that connect and blend many mathematical topics that traditionally have been taught separately and independently. As the series progresses, ideas and techniques build upon others, becoming increasingly more complex to match the sophisticated ideas from the mathematics. Because of the slow buildup, many of these topics are accessible to certain levels of students for the first time. One Vermont teacher tells of a 10^th grade student with a 3^rd grade reading level who could successfully calculate the volume of a two-dimensional shape rotated in space.

Real-Life and Engaging Problems

Problems in MATH Connections use real data and are based on real life experiences and applications. The authors have included examples that would engage and interest high school students. For example, in discussing the Commutative Law, students are asked if it matters whether you first add oil to your car and then drain your crankcase, or whether it matters if you reverse the order. Also in the algebra section, students create a restaurant order that a waiter or waitress might use. Without realizing it, the students preview defining variables, order of operations and evaluating expressions. In Year 2, formulas for finding the areas of sectors are discovered by creating a scale diagram of a Go-Kart track.

Upper-level students find enjoyment in Connections material. Problems are challenging and involve higher-level thinking. Most problems are open-ended and can be extended to more complex problems or general cases. Sometimes these upper-level students are very smart with calculations but aren't able to apply problems to similar situations. MATH Connections helps all to become problem solvers, whether they have been successful in the past or not.

Literacy Tools

MATH Connections Book 1a has an 8^th grade reading level, providing easy access to the content. All books are written in a "conversational" tone that is easy to read even in sections with complex ideas. Most students are not used to reading a math book, so the book introduces literacy skills by asking them to state definitions in their own words and to write down questions about the reading that they still have.

Readings are spaced with questions and activities. In MATH Connections classes, students often work in groups, reading together or on their own. When they get to a question or activity, each group member is required to help the others to understand the question and suggest problem-solving strategies. The "Do this Now," "Discuss This," and "Write This" exercises create interactions with the text. By writing their own questions, discovering the principles, and discussing the material with others, students do much more than read the text. They become active participants.

The team approach ensures that all have access to the reading even when reading levels are low or English is a second language. ESL students improve their English skills with constant practice in reading and writing. In Bronx ESL classes, the books have been used to practice reading aloud but also to practice translating and reading comprehension. There is a Spanish printout of the text in Books 1a and 1b that has been used in several districts to transition their students into an English-speaking classroom.

Writing is an important part of the program. Students are always required to explain themselves and "why" they arrive at certain answers. If a problem is difficult, the book will require the student to explain why they couldn't answer the problems.

In addition to the content reading and questioning, the book provides definitions and explanations in "About Words," "About Symbols," "A Word to Know," "A Phrase to Know," and "A Fact to Know." Problem-solving techniques are shown in "Thinking Tips," as well as in the questions themselves. Learning Outcomes are displayed at the beginning of each section to preview the content and to provide a framework for the reading.

Problem Solving

One of the goals of MATH Connections is to create students who can solve problems on their own. Students are not usually natural problem solvers and therefore need to be introduced to the techniques slowly. Skills like drawing a simpler diagram, rewriting questions, and making a table are part of the lessons. When each skill is first introduced, a "Thinking Tip" appears on the margin of the page. Students apply these skills in other questions, activities and also in the Problem Set at the end. These are "rich" problems, meaning that students can solve them in a number of ways, explore them in depth, and extend their solutions to new problems.

Problem Solving (continued)

Because this technique is taught to all levels of students, some amazing results can occur. Teachers have witnessed upper-level students "taking-off," looking for answers to questions raised by intriguing problems. One 9^th grader discovered a basic idea related to derivatives just by exploring further with his calculator. On the other end, one teacher in Massachusetts, who is only allowed to use MATH Connections with lower-level students, actually had his students outscore the students in traditional classes on the MCAS statewide assessment. This is because his students were learning by reading, writing, and problem-solving every day. On test day, the traditional students doing their skills-based program did not have the tools to read, interpret and solve.

Technology

Aiding students in their discovery of mathematics is the use of graphing calculators. The TI-83 is the preferred calculator for the course, though others can be used. As a tool, the calculator can help lower-level students access some very difficult mathematics and can also extend the thinking of faster paced students. Most Connections teachers allow calculator use for most of the instructional time. In that way, a student who has not mastered fractions or decimal division can still get a correct solution to a difficult problem. For students who have disgraphia or organizational learning disabilities, the calculator can provide a way to organize ideas, create neat graphs, a list, or organized steps for an algebraic solution.

There are also TI-83 centered explorations that can quickly allow all students to derive rules, come up with deeper understandings and explore deeply into a topic. A student using the TABLE can ask "I know what this function does when x = 5, but what happens when x =1,000,000?" Technology can also allow all to answer questions that couldn't be asked before, like "What are the solutions to 2^x = x³ ?"

Conclusion

In short, MATH Connections provides many tools to make mathematics accessible to all. It has the ability to reach students who have not been successful in the past by empowering them with literacy and problem-solving tools. At the same time, upper-level students are engaged by technology, the rich problem-solving environment, and by the opportunity to take the mathematics to the next level. Finally, for ESL students and students with poor English skills, there is practice in reading and writing within a cooperative environment. As a result, districts see not only increased test scores on state math tests, but find that the increased focus on literacy can raise test scores in other areas.