Timothy W. Young

I WORKED FOR THIRTY-EIGHT YEARS IN THE PENNSYLVANIA PUBLIC EDUCATION SYSTEM AND RETIRED AFTER SERVING AS A HIGH SCHOOL PRINCIPAL FOR TWO SCHOOLS – CHARTIERS VALLEY HIGH SCHOOL, BRIDGEVILLE, PA AND GLENDALE JUNIOR/SENIOR HIGH SCHOOL, FLINTON, PA. I WAS ALSO A SECONDARY MATHEMATICS TEACHER – TYRONE AREA HIGH SCHOOL, TYRONE, PA AND CHARTIERS VALLEY HIGH SCHOOL, BRIDGEVILLE, PA.

Late in my public education career and after I retired, I became obsessed with mathematics education in the United States and changes which need to be made in order to help all students become successful in arithmetic and mathematics starting in grade school through high school. Some of the methods used to teach arithmetic and mathematics in the United States must change, based on the "TIMSS" and "PISA" test scores for high school students.  The "TIMSS" and "PISA" tests are International Math Tests - and students in the United States frequently (always) score in the lowest quartile for high school students.  (Changes need to occur at both the university/college level when students are preparing to become elementary arithmetic teachers and secondary mathematics teachers and change must also occur with in-service/professional development programs for teachers who are already teaching students.)  If this pattern continues the United States will fall further behind other industrialized countries with respect to technology, unless we import mathematicians and scientist, which is becoming increasingly more difficult because countries whose students score high on these tests are less willing to allow their best math and science students leave their home country.  Therefore, the consequences for the United States in the future could be devastating. 

Shortly after I retired from Public Education, I became friends with Dr. Robert Siegler, who at that time was a Professor at Carnegie Mellon University. Dr. Siegler has devoted over 46 years of his life researching how students learn arithmetic and mathematics throughout the world.  After retiring from CMU he accepted a similar position at the Teachers College, Columbia University. He has continued his research and presently he has authored 9 books, edited 6 others and authored or co-authored over 250 articles and research papers.  For the past 20 plus years, his focus has concentrated on fractions in arithmetic and the long-term effects students experience in advanced mathematics if they do not master concepts and procedures involving fractions.  For six years after I retired, I was an invited guest of Dr. Siegler’s to attend his weekly math research discussion meetings at CMU and other various meetings and speaker presentations at CMU. While attending these meetings and working directly with Dr. Siegler, I realized how much students struggle with all types of fraction, decimal, and percent problems in the United States compared to students in many other countries. I continually ask myself the question, “As an experienced math educator in the United States, "How would I teach fractions and arithmetic concepts starting with third and fourth grade students in arithmetic and then use the same rules and procedures to teach math to students in high school?" The goal for all arithmetic and mathematics teachers must be, "To have all students understand concepts involving all arithmetic and mathematics problems so the concepts discussed and presented help all students determine the correct rules and procedures to solve basic problems." Students must then master the rules and procedures used to solve basic problems, in order to be successful solving all types of problems, simple to the most difficult, in arithmetic and advanced math classes. Understanding arithmetic and mathematics concepts is an important first step, but if the rules and procedures required to solve problems are never "Learned and Remembered" then students are in trouble when they enter a higher level math class.  Dr. Siegler’s research and the research of many other individuals around the world inspired me to write my textbook which will be published by the summer of 2021, titled “THE MOST POWERFUL NUMBER: ONE (1)”.   I suggest you google "Dr. Robert Siegler Teachers College Columbia University" and read some of his research papers and a book or two in order to understand challenges which teachers and students encounter everyday in the classroom as it relates to arithmetic.  

The two main focus groups for my textbook, "THE MOST POWERFUL NUMBER: ONE (1)" are:  1.  Students in college planning to be elementary teachers and 2.  Students in college preparing to be secondary math teachers.  I have asked the following question to many elementary arithmetic teachers and secondary mathematics teachers, "Did you ever take a course in college which focused on preparing you to teach rules and procedures for the arithmetic or mathematics topics which are required in your classes?"  Teachers often respond that they took a course in college with a title similar to the following: "How to teach arithmetic or math", and the college course focused on how to introduce topics by using CONCEPTS not how to teach RULES AND PROCEDURES.  

With this thought in mind, it explains why most young teachers emphasize concepts, which is an extremely important first step when teaching arithmetic and mathematics, but it is not the final step in the teaching process if students are going to be successful in future arithmetic and mathematics classes.

The textbook, "THE MOST POWERFUL NUMBER: NUMBER (1)"  fills the void between teaching concepts and teaching rules and procedures.  The textbook is a "How to teach arithmetic and math topics textbook focused on teaching rules and procedures."  After concepts have been repeatedly illustrated and the students understand why, then it is time to teach the next important step in the learning process which must be learned, if students are going to be successful in future arithmetic and math classes next year and beyond.  Teaching rules and procedures is not as fun as teaching concepts and it requires special teaching skills which are not normally taught or learned in college. 

When you enter the classroom the first time as the arithmetic or math teacher and you illustrate the concepts for the topics required for your class then you must rely on your past experiences to teach the rules and procedures to solve the problems in the book.  Your past experience is usually based on how you learned and how your teachers taught you.  Hopefully, with experience you develop you own approach to teaching rules and procedures for the topics you teach.  One important teaching point to keep in mind when you are teaching rules and procedures in any arithmetic or math class is, "Make sure the rules and procedures you are teaching are the same rules and procedures students will work with when they are in a higher level math class next year or in 6 years."  If you are teaching tricks to solve simple problems in arithmetic or math class,  "Will your students be able to use your tricks to solve more challenging problems?"

My textbook introduces two new theorems and uses these two theorems to help teachers teach the rules and procedures required to solve/simplify all types of fraction problems and conversions problems which students initially encounter as early as 4th grade but usually in 5th grade and then use the same rules and procedures to solve rational expression problems, trigonometry identities, calculus limit and derivative problems, etc.  The rules learned in arithmetic are the basis for the procedures required when students are in higher level math classes. The arithmetic rules never change the problems just become more exciting.

If college professors use my textbook as a template to help future elementary teachers and secondary math teachers to teach rules and procedures before they student teach, the textbook is full of illustrations and written explanations about how to solve problems along with multiply student assignment questions.  

The course would be a semester course and not only would I suggest that the students study the illustrations and solve all the problems in the assignments, but they should also read some of the research papers indicated throughout the textbook.  I learned a great deal about student problems when I read these research papers and only wish I had read more research math articles when I was a classroom teacher. 

This textbook would also be an excellent topic for several in-service days for both elementary arithmetic teachers and secondary math teachers.  Superintendents, Principals, and all other school Administrators need to read and study the textbook so they will have a solid understanding of the problems discussed in the textbook and the problems teachers encounter on a daily basis.  The textbook is written using basic terminology so anyone who  wishes to learn  how to help students learn to work with a wide variety of math problems will acquire some knowledge and teaching strategies which will help them be successful.

WITHOUT CONCEPTS IT IS IMPOSSIBLE TO DEVELOP ARITHMETIC RULES AND PROCEDURES AND WITHOUT ARITHMETIC RULES AND PROCEDURES IT IS IMPOSSIBLE TO DEVELOP RULES IN ALGEBRA AND ADVANCED MATHEMATICS CLASSES.  "WITHOUT ARITHMETIC RULES AND PROCEDURES IT IS IMPOSSIBLE TO SOLVE ADVANCED MATHEMATICS PROBLEMS.  ARITHMETIC RULES AND PROCDURES ARE THE FOUNDATION TO UNDERSTANDING ADVANCED MATHEMATICS RULES AND PROCEDURES."

Based on the last sentence the arithmetic teacher is the most important person in a child's life if they are going to be successful in advanced mathematics classes.