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### Connected Mathematics Review by Dr. Anne Margaret Wright

Prentice Hallhttp://www.phschool.com/atschool/cmp2/active_math/

"Connected Mathematics takes a critical thinking approach that I think many homeschooling families will find very familiar." -- *The Old Schoolhouse® Magazine*

"Why does your birthday fall on a different day of the week from one year to the next? Why is the same pattern also true for New Year's Day and the Fourth of July?" Not sure? Try this one: "Why is time measured using 60 seconds in a minute (not 50 or 100), 60 minutes in an hour, and 24 hours in a day (not 23 or 25)?" If these questions intrigue you and your kids, Connected Mathematics from Prentice Hall (www.phschool.com/math/cmp/index.html) could be for you. These mindbenders open up the Prime Time unit of Connected Mathematics that takes sixth grade students through the joys of prime numbers and factoring in a creative and in-depth way. The Connected Mathematics Project (CMP) was developed by Prentice Hallwith funding from the National Science Foundation for grades six, seven, and eight. It has been thoroughly studied with very good results on 45,000 students from a diverse range of schools. According to Prentice Hall, "Under the guidance of Project 2061, the American Association for the Advancement of Science (AAAS) critically reviewed all middle school mathematics programs. Connected Mathematics received the highest rating - making it the #1-rated middle school mathematics program in the country." They also reported that the United States Department of Education awarded CMP an Exemplary rating - "the only middle school mathematics program to win a top rating." These are very impressive results!

The idea behind Connected Mathematics is to help kids develop mathematical reasoning skills through critical thinking and understanding the connections between different areas of math and other disciplines, such as science. For example, many traditional math textbooks teach prime numbers, then move on to geometry, then to algebra, etc., without ever exploring the rich connections between these subjects. They also tend to use a purely didactic method of learning, where the teacher explains the formulas or basic process, illustrates how to solve several problems, then sets the kids loose with exercises to solve. Connected Mathematicstakes a critical thinking approach that I think many homeschooling families will find very familiar. Try this game from the Prime Time unit for a great example of how kids use critical thinking, instead of rote memory, to work their way through the exercises. Make a grid on paper with the numbers from 1 to 30. Two players take turns choosing a number that will give them a high score and the other person a low score. The person choosing the number earns that number worth of points, and the other player earns points for all of the factors of the number added together that have not already been used. For example, if the first player chooses 30, he receives 30 points. The other player earns points for all of the factors (1, 2, 3, 5, 6, 10, 15, 30) that have not already been used. The curriculum leads the teacher and student through discussions about the best strategies for winning this game, such as choosing large prime numbers until many numbers are used, then choosing large numbers whose factors are already used, etc. Rather than just presenting a lecture on prime numbers, the students use critical thinking skills to figure out the properties and uses of factors, prime and composite numbers, and how these are interrelated with other subjects. My son, Josiah, and I spent many lunches playing this game and even moved on to the harder version using numbers from 1 to 49.

Here's the lay of the land, so to speak, of Connected Mathematics. First, new concepts are explored as a group using a critical thinking, or investigative approach to learning. For example, the last unit in the eighth grade materials, Clever Counting, deals with counting techniques, permutations and combinations, using mental math to make estimates, using diagrams and tables to organize and interpret data, etc. The unit starts with several questions, such as "A locker at a storage warehouse was robbed. The police suspect that the thief tried possible lock combinations until the lock opened. A lock combination consists of three numbers from 0 to 39, with no repeated numbers. How many combinations are possible?" After discussing the basic principles needed, homework provides opportunities to practice through the ACE method - Applications, Connections, and Extensions - providing progressive levels of understanding and applying information to everyday situations. Then the homework is discussed and summarized, providing students and teachers an opportunity to present their findings and draw conclusions about what they have learned. The Teacher's Guide and Student Edition (workbook) provide direction for analyzing this problem and understanding the issues to be resolved. Each Investigation leads the students further into the concepts and helps them figure out the underlying principles and how to apply these to real situations. There are also Unit Projects, Check-Ups, Quizzes, and Tests that can be used as the teacher finds helpful. The students record their answers and observations, along with definitions and other helpful information, in their notebooks to help organize their work and their thoughts.

This all sounds great, but does it work for homeschooling families? I think the strengths of the program lie in the investigative or critical thinking approach and tying mathematical concepts together across topics, thus making it more like what students experience in everyday situations. Homeschoolers often prefer an investigational approach to rote memorization, so this curriculum seems very natural to how many of us teach. Another excellent feature is the introduction of algebraic concepts throughout the curriculum, rather than teaching algebra as a separate and unrelated unit. Thus students learn about using symbols in math, looking at patterns and relationships, etc., throughout the middle school grades and are well prepared for a more in-depth study of algebra in ninth grade.

Does it have kid appeal? You bet! My precocious fifth-grade son, Josiah, said, "I can't believe I actually want to do math! This [CMP] is the best math program that I've ever seen. I love how kid-friendly it is and I recommend all homeschooling families (except for ones who like to do long pages of practice computation) use this product!" While Josiah is very good at mathematical reasoning, or thinking through complex problems, he hates the "boring" computations. We were at a point where he was ready for more challenging math, but he balked at the thought of doing computations he couldn't figure out easily in his head. However, with Connected Mathematics the problems are interesting, and allow him to focus on using his critical thinking skills while he also gets practice in computing problems.

There are only a few drawbacks that I can see to the CMP curriculum. I don't think it would work well for a student who is very concrete in their thinking or who has no curiosity about why things happen as they do. My son Benjamin, who has Down Syndrome, would probably not do well with the program when he is in middle school, because he tends to be very concrete and to have difficulty with higher-level, abstract reasoning. However, I will use many of the concepts and exercises with him, but adjust the curriculum to his level. If you or your student want pages and pages of practice computations, such as 345 x 123 = ____, this is not the program for you. The student will need to be well grounded in basic mathematical computations before starting Connected Mathematics. While the program was designed for public and private schools and to be used with groups of kids, I think it can be used very successfully with one student or with siblings together. To get the feel of the program, Josiah participated in a CMP group of five kids from several grade-levels working with one homeschool mom. They met for three weeks and completed the Prime Time unit with great success. Josiah and I are now working through the next unit together, also with wonderful results. Again, I think the program could be used well with just the teacher and the student, with a couple of siblings together, or with a small or large homeschooling group.

Sixth grade topics include factors and multiples, statistics, two-dimensional geometry, understanding rational numbers, two-dimensional measurement, probability, using rational numbers, and spatial visualization. Seventh grade topics include introducing algebra, similarity, ratio, proportion and percent, integers, linear relationships, three-dimensional measurement, probability and expected value, and number sense. Eighth grade topics include representing relationships, the Pythagorean theorem, exponential relationships, quadratic relationships, algebraic reasoning, symmetry and transformations, data and statistics, and combinatorics. Now I took math through calculus in high school and several graduate and post-graduate statistics courses in college and these titles left my head spinning a bit. But don't let the titles scare you off - the Teacher's Manuals do a good job of presenting the information in an understandable way. Each unit can be used as a stand-alone unit to fill in certain areas if you don't want to use the whole curriculum. Units are sold separately ($6.47 for Student Editions and $19.97 for the Teacher's Guide) or by the grade with eight units ($159.97 for all eight Student Editions and Teacher's Guides and a Lesson Planner). Manipulatives are also available for each grade, but were not reviewed. The use of manipulatives is encouraged in the curriculum to help make the abstract mathematical concepts more understandable and concrete. The Teacher's Guides are very helpful in providing not only the answers to problems in the Student Editions, but also extra information about how to help the student understand the concepts and apply them effectively. All of the materials are very well written and interesting for both the student and the teacher! Math that is fun for students and teachers, and teaches on a deep level through critical thinking - who knew?