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 denomi...

 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...

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...

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...

November 4, 2019 Friendly Numbers But Not! The following NT with preservice teachers included the following clusters: 999 +99 998 + 49 199 + 99 + 49 999 + 99 is 1098. Me: How did you get 1098? Explain your thinking? Katherine: I added 1 to 999 to make 1000 and took 1 from 99 to make 98.  1000+ 98 equals to 1098.  All three seemed to have the same idea. 998 + 49 is 1047 Me: How did you get 1047?  Explain your thinking. Chase: I separated  998 to make 990 +8 and 49 to make 40 + 9. Then I added 990 +40 which equals to 1030 and 8+9 equal 17. 1030 +17 equals 1047. Katherine: I just did like I did before but I took 2 from 49 and added it to 998. 998+2 equals 1000. 49-2 equals 47. 1000+47=  1047. 199 +99 + 49 is 347 Katherine: I took 2 from 49 and added it to 199 and 99. 199+1 is 200 and 99+1 is 100. 200 +100 equals to 300+ 47. 347 Erika: 199 +1 is 200             99 +1 is 100  ...

Number Talks October 27, 2019 Friendly Numbers This Number Talks involved expressions with friendly numbers. Friendly numbers are single number used to make a friendly pair. These are numbers that make performing operations easy and flexible. Friendly numbers include multiples of 10's and 100's.  The goal of any NT with preservice teacher to expose them to math strategies that will enhance their teaching and equip them with Mathematics Pedagogical Knowledge. Many school districts in north and central Alabama use NT. Therefore, I want my preservice teachers exposed to various way to solve problems and the ritual of NT.   The following is a cluster of problems: 99 +5 99 + 15 99 + 26 99 + 51 99 + 5 is 104 Me: How did you get 104? Chase: I stack them up 99 on top and 5 on the bottom. Then I just added. Katherine: I added 1 to 99 to make 100 and then I added 4. Me: Where did you get the 1 when you added it to 99? Katherine: I took it from the 5. Tha...

Counting Collections with Preservice Teachers September 30, 2019 This week's blog discusses my PST experience with Counting Collections. Counting Collections is a practice in mathematics where students count objects presented in a bag. The goals is to practice oral counting and to develop more sophisticated methods in counting. Through this practice, students develop oral counting skills, develop efficient counting strategies, group objects strategically, and record their thinking behind their strategies (Schwerdtfeger & Chan, 2007) . Like any open-ended task, students are doing the math instead of passively counting without purpose. Two of my PST were challenged to count Family Counters. These are counters in the form of men, women, and pets of various colors. I wanted to ease them in the counting ritual. I asked PST to count the objects to determine the amount contained in the bag and to record how they counted. At first, they contented by ones and recorded their find...