One of the many problems facing some students in learning math is that they have trouble reasoning or thinking logically. The student may have been presented facts previously that they memorized for a tentative period, but they didn’t learn how to use those facts to reason or think logically about problems given to them. Thus, the student tends to forget many of the math facts shortly after the test. One problem with teaching a student to think logically is creating problem samples that are interesting and suitable for applying facts learned to deeper levels. The Critical Thinking Company has long established that they can produce materials designed to teach a student to think mathematically and apply the math facts to useful and interesting problems. Their newest edition to the Mathematical Reasoning series, Mathematical Reasoning: Middle School Supplement continues that tradition beautifully. My high school and middle school-aged students have been using this product recently in order for me to review. Let me tell you about our experience.
First of all, Mathematical Reasoning: Middle School Supplement has fifty problem sets covering topics typical of Middle School level from 2D Geometry to Probability to Per Cents to Statistics to 3D Geometry along with some higher level thinking practice on miscellaneous topics. There are a hundred pages of actual content with fifty-four remaining pages of detailed answers. Each lesson comes with a list for review of any math facts needed to solve the problems for review. In the answers section, strategy tips are also listed for each lesson if the student needs a little help finding the process to solve. Each problem was developed to stimulate mathematical reasoning and provide enrichment and practice for specific skills. The problems are not particularly real-life oriented, though, so if you are looking for that kind of problem set predominantly, you won’t find it here. The author might provide more of that in the future, though, if needed by many. While the answers provided are detailed and comprehensive, many problems do have more than one solution method, so students can be encouraged to be creative in the process. The publisher suggests that the book can be used for enrichment, but also as an overall assessment tool of how well a student learned middle school concepts.
I found Mathematical Reasoning: Middle School Supplement useful with my gifted Sixth graders and for my lower level Ninth graders. The Sixth graders were excited by the idea of doing middle school math problems, and also found them challenging and interesting. The 9th graders needed to revisit the math facts and practice using them and focusing on the thinking process of working the problems designed for a specific skill. Many found the work in their own books too challenging. These problems were just the right fit.
The Critical Thinking Company has its Mathematical Reasoning series in nine levels from Pre-K to 8 all focusing on the strategies need for solving a wide variety of math problems. Other workbooks covering other subjects and topics are also available on their web site. You will find Mathematical Reasoning: Middle School Supplement on their site at for $19.99. The series will be a great step to improved math reasoning preparing students for upper level math courses, as well as improved test scores.
I also recently reviewed The Critical Thinking Company’s Editor In Chief: Beginning 1. Please check it out, too, here.
Though I was provided a product to review for this blog, I have not been compensated in any other way, and the opinion expressed here is entirely my own.