“Vision in Elementary Mathematics”
The book, “Vision in Elementary Mathematics”, is about different topics in mathematics that a teacher could use to teach their students in an elementary classroom. It gives several ideas and techniques to teach students so that they can discover mathematics on their own. There are a variety of topics covered in the following chapters: “Even and Odd”, “Divisibility”, “An Unorthodox Point of Entry”, “Tricks, Bags, and Machines”, “Words, Signs, and Pictures”, “Sudden Appearance of a Practical Result”, “A Miniature Problem in Design”, “Investigations”, “The Routines of Algebra I”, “The Routines of Algebra II”, “Graphs”, “Negative Numbers”, and “Fractions”.
While reading this book I gained insight on how to get students to discover different techniques in mathematics rather than just being told. This concept was applied throughout the entire book. I strongly agree that it is important for students to discover concepts on their own rather than just being told a procedure and following it. By discovering a concept on their own, the students tend to remember the idea the problem was trying to convey. A quote from the chapter on divisibility states, “It is necessary for children to understand what is involved in a calculation. If they understand what is happening they can devise methods for themselves and can test by their own thinking correctness of their work.”
There are several methods of teaching discussed in this book. I believe most of the methods in this book are aimed at students who are visual learners. One of the examples that stood out to me was in the chapter “Investigations”. The book was discussing how many students believe (x+y)2 is the same as x2+y2. However, that is not the case. Let’s say x=3 and y=4. In this case (x+y)2 is 72 which equals 49 and x2+y2 is 32+42 which equals 25, and 49 ≠ 25. The way the book illustrated this was by creating a 7x7 table with one square representing 32 and one representing 42 and showing that there are still blank areas that would need to be completed in order to fill the square as shown below.
Overall, I would strongly recommend this book to college students who are going to school to be elementary teachers or an existing elementary teacher who is struggling to connect ideas with students. It shows many techniques that visual learners will be able to relate to and understand. It also does a great job on how to explain these concepts to your students in different ways. I found this book to be very interesting and of such value that I couldn't put it down. The value came from the various techniques and ideas on how to get the students to discover math versus just being told how to do something.