There are numerous instances in mathematics where common errors occur. In my opinion, the most frequent in my career occurred when 0 divided a number. Division by 0 occurs in elementary mathematics, coordinate geometry (finding slope) and calculus (finding limits). Explaining why...
I still remember a comment made to me by an English teacher, Mr. Hook, when I was attending Mission High School. Mr. Hook said, “Leo, you have an innate ability to get people to do what you want, but they believe that they made the decision to act.” Incredibly, this occurre...
During my career, I had to prepare my students for number sense, calculator applications and mathematics. Trying to find time for all three was difficult, but I managed to do it because of the way I organized my lesson content. This became evident several months ago, when I was a...
During my teaching and coaching career, I have been told by the students in my classroom and by those I prepare for competitive mathematics that they learn many more concepts from me than from their other teachers or coaches in the same amount of time. Since I self-analyze, I hav...
Every teacher, academic coach and parent needs to be a good listener. Students and children need to know that what they say is important. They can learn to be good listeners themselves by observing the adults around them. Be willing to answer questions, as each question asked is ...
In recent years, I have learned the value of using YouTube to learn mathematics. There have been times when I am trying to review a concept that I knew in the past, but have trouble with in the present. During these times, it is difficult to reach out to a peer for help. At these...
One of my goals as a teacher and mathematics coach was to inspire excellence. I tried to inspire excellence by modeling. I have been doing that for more than 44 years. I always wanted to show students how much I loved what I did. I demonstrated what I felt by the way that I sough...
Teachers, academic coaches and parents need to emphasize the importance of communication with their students and their children. They should model what effective communication looks like. Communication is not only talking but also listening. When communicating with another indiv...
To promote learning, teachers, academic coaches and parents need to use positive reinforcement. Positive reinforcement is applicable to students or children from early childhood through high school. Students that receive positive reinforcement will develop a good self-image. It i...
Anyone teaching academic concepts needs to organize the concepts and be aware of how it can have a positive impact in student learning. This applies to teachers, academic coaches and parents. Initially you may develop an outline of the major concepts that need to be mastered. To ...
