Methods of Math Teaching and Learning

  Teaching Fractions online to Preservice Teachers Late in the semester, I usually teach fractions to my preservice teachers.  For the first week, I teach my students how to recognize fractions with various models and how to model fractions without using conventional methods. For week two, I teach ordering fractions with like and unlike denominators. For the third and fourth week, I teach students how to estimate the operation of fractions and how to operationalize fractions using models and reasoning skills. This year is different. The COVID challenged me to teach fractions online!!!  This year I taught fractions online. The concept of Fractions is very hard to learn even for preservice teachers.  It is hard to teach factions face to face. Well, it is even harder online.  First, the nature of how I teach fraction challenges how they learn the concept in elementary school. They are used to procedural knowledge like converting to common decimals and common denominators.  Another challen

 Number Talks 10.19.2020 The Power of Persuasion    A couple of weeks ago, half of my students attended AMSTI training. I have a very big class this semester and with COVID only half could come. We have been doing NT since the beginning of the semester with my entire class online. However, things did not click until AMSTI training. My PST used to acknowledge my getting too deep in math during class. I use to correct their thinking when it came to regrouping. " THAT IS NOT A ONE!!!! " They did this until AMSTI training.      During training, my PST engaged in different NT with the AMSTI facilitator. She taught them different strategies like compensation, composing and decomposing numbers, adding with place value, and so forth. She also talked to PST about saying the correct value of the digit when regrouping. This was the same concept that my PST voiced their disdain for my in- depths.  When my PST returned from AMSTI training they used those strategies with our NT and the cor

Several times a week I offer study sessions to my pre-service teachers for Praxis Multiple Subject Mathematics, one of five tests elementary teacher candidates have to pass to teach.   My preservice teacher came across the following practice problem from Math Made Easy:   Jan ran 30 blocks in 6 minutes. Assuming that she ran at a constant speed, how long did it take Jan to run one block? My student commenced to solving the problem. She said so I divide 30 by 6 to find out how much time it will take to run 1 block and the answer is 5. After reading the problem again. I ask her to notice the problem. Remember if the speed is constant, should it take her 5 minutes to run 1 block?   She thought about and decided it did not make sense. I am writing this in support of one of the Standards for Mathematical Practices from the Common Core State Standards . Reason abstractly and quantitatively.   Students proficient in mathematics make sense of the relationship of quantities in p

This blog post is a vent post! Please excuse my ranting. I don't understand why some teaching practices in early childhood and elementary mathematics have not evolved. I have had preservice teachers talk to me about witnessing antiquated teachings mathematics practices for younger children and special needs children. The frustration comes from that part of me that wants to advocate for professional development for teachers to learn new pedagogical methods. The other part of me thinks it's just a waste of time. One crucial aspect of being an educator is to become a life long learner. Teaching and learning both go hand in hand. However, if a teacher is used to one method and that methods is not working with students, shouldn't that teacher want to research and learn better practices. The excuse for using old practices should not be "I'm old school and this is how you are going to learn". If students are having a hard time with making tens, teachers should us