mathconnections

Math Connections is an integrated curriculum project for grades 9-12 that “opens the concepts of mathematics to all students and inspires new interest and excitement and in mathematics” (Berlinghoff, 1998). The curriculum develops all topics in mathematics into one program that allows students to make connections between them. The program was developed into eight books spanning all four high school grade levels. The students are given a vision of how all topics in mathematics are interrelated. Each book contains numerous mathematical concepts that tie together real life applications for the students. These real life applications and interrelations allow students to see more importance in mathematics and help them to be more motivated to learn. This addresses the NCTM Connection standards for mathematics.
The program accomplishes this by developing each strand of mathematics across the unit and over the years. For example, the program will introduce a real life scenario in the first section of the unit. This section creates an interest in the unit and begins to develop some basic mathematical skills within the strand. The unit continues by building upon the foundation of the first section. The following sections continue to develop the basic skills taught in previous sections while deepening the mathematical content by introducing new concepts and different scenarios in which the mathematics can be advantageous. After completion of a unit, the program also provides projects that allow students to use and practice their skills in the context of real world problems. Throughout the remainder of each book and over the years, students are also given the opportunity to further develop all mathematical ideas by revisiting each strand. In addition to providing opportunities for review, this allows students to deepen their understanding of ideas and further their mathematical capabilities by discovering more in-depth mathematical concepts.
The mathematical ideas that the students learn throughout the program also allow students to develop important concepts, basic mathematical skills, and problem solving. Each section of any unit begins with opportunities for class discussions and group analysis that allows students to enhance their conceptual understanding. As each section progresses, the students have more opportunities to build their basic skills and problem solving with group problem sets and extension assignments, along with unit projects at the end of each unit. This correlates with the Problem Solving Standard in the NCTM Standards. The students will be able to build new mathematical knowledge and a myriad of appropriate strategies to solve mathematical problems.
The classroom environment is organized in a way that allows students to be at the center of their own learning. The Math Connections program gives the students the freedom to discover new mathematical topics for themselves with the teacher as a guide rather than instructor. The readings and class discussions that each book incorporates into the learning process are ideal for cooperative learning opportunities, student exploration, and self -led learning. The teacher is not given the power to relay information to the students. The students are asked to discover the mathematical ideas for themselves. The gives the students more power and a feeling of greater control.
The class discussions and cooperative learning activities also provide students opportunities to “organize and consolidate their mathematical thinking through communication” (NCTM, 2000). Students are able to develop mathematical skills, cooperative learning skills, and problem solving skills while also acquiring organization and communication abilities. The students are also required to communicate their thinking in various ways. The program allows for students to develop written and verbal communication skills. The program uses specific icons to describe which type of communication is preferred in different situations.
Math Connections provides open-ended questions that require students to think more deeply about the mathematics, express their ideas further, and encourages them to think about new mathematical questions that arise naturally. The program provides open-ended questions in the real-world scenarios, class discussions, group analysis, problem sets, and extending projects. These open-ended problems comprise the core of the curriculum, rather than the supplement of the curriculum as in traditional textbooks. Some of the problems and extending projects allow students to see that mathematics is not solely a set of quickly solved exercises. They provide students chances to analyze real data, which requires extended thinking and longer periods of time. They also provide students opportunities to gather data from their own lives to analyze in class. This makes the investigations more meaningful and motivational.
The open-ended questions included in the program encourages the students to use multiple problem solving strategies while focusing the students to think about the most efficient methods. One of the major strategies that is encouraged by this program is the use of today’s technology. Computers are used for things such as spreadsheets to analyze data and geometry sketchpads to help visualize many geometric concepts. Graphing calculators and integrated into each section. The program has made calculators an important learning tool, concentrating on the TI-82 and TI-83, by suggesting numerous learning activities that focus around their use. However, it is made clear in the program that the graphing calculators are not a replacement for basic understanding of mathematical concepts. One way that they ensure this is by requiring that the students estimate and hypothesize the expected the answers before using the technology.
One major aspect of the Math Connections program is the integration of assessment. Each section allows for a variety of different ways for the students to be assessed. Teachers have the option to assess on such things as group analysis, in class discussions, problem sets, end of the unit projects, and suggested quizzes and tests. All of these types of assessments are different, and will allow the teachers to assess the students on a number of different tasks and ideas and allow the students to be assessed according to different learning styles. This will allow for the teachers to have a more complete understanding of what knowledge the students posses. Similar to the learning opportunities, assessments encourage the students to use different problem solving strategies along with technological tools.
Math Connections is a program that is based on inclusion. This means that every student has the opportunity to learn the intricacies of mathematics. Each student will have the opportunity to learn the curriculum at their own pace and will not be discouraged to further their mathematical knowledge. The program accomplishes this by providing reinforcement chances, extending activities, and activities that incorporated different learning styles. The program connects with more than 50 professions, 20 job fields and all academic disciplines. Because of these things, all students become interested in the topics that are discussed in class, and thus become more motivated to learn the math. The program also addresses student diversity by investigating mathematical topics beginning in general terms and becoming more specific as the unit progresses. This allows students at different levels to engage in and investigate the mathematics.
Math Connections integrates the four process standards of the NCTM into each unit of the curriculum. Mathematics as Problem Solving is accomplished through explorations, projects, simulations, and group problem solving activities. Mathematics as Communication is developed through writing, discussing, and justifying mathematical ideas and opinions. Mathematics as Reasoning is incorporated into the “thematic thread” that spans all four years of the curriculum. Mathematics as Connections is included into each section by relating mathematics to professions, other subject areas, and different mathematical strands. Throughout our analysis, it is obvious that the program meets the NCTM standards of problem solving, reasoning and proof, communication, connections, and representation in many different ways throughout the entire curriculum. We feel very strongly that Math Connections is a program that encompasses the things we feel are most important in mathematics education. It incorporates many ideas of mathematical reform that are crucial to the development of student learning and conceptual understanding. It makes the mathematics meaningful and motivational by making numerous connections to the real world. However, in addition to emphasizing these crucial elements of reform, it is also supplemented with a few aspects of traditional mathematical programs that are important for student learning and understanding.