Methods of Math Teaching and Learning

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             49-2 is 47             200+100 +47 is 347.  Disc

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. That is w

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

Seek Understanding This video is resurfacing on Facebook again. https://www.facebook.com/conservativecomic/videos/917847655243694/ https://www.facebook.com/conservativecomic/videos/917847655243694/ The video has two settings in a form of a comparison. On the left, a teacher is explaining multi digit multiplication using the open array model. On the right, a person completes the multi digit multiplication problem using the US standard algorithm, makes coffee, and completes  other various activities. In essence, the goal is to compare the time it takes to perform what they call Common Core math (I was doing this method prior to CCSS) to the US traditional algorithm. The purpose of this blog post is not to reject any of these methods. Both methods are essential to understanding the concept of multi digit multiplication. The goal of this post is to open minds to look at both methods as means to achieve a goal and to convey that one method helps to understand and builds the other.

September 9, 2019 It is always fun to do a Number Talk with Preservice Teachers!!!! I want them to get really versed and comfortable with it. I want them to recognized each others strategies and pull out the various domains and properties of mathematics. The NT for this week was a little more challenging from the week before. Again, we are using dot images to build multiplicative strategies and to strengthen algebraic thinking like order of operations and the properties. This first image included 15 dots. This one was pretty simple. You can subitize 5 because of the prior knowledge with dots on dice and playing cards.  PTK said she saw 5+5+5.  PTE skip counted by 2 until 12 then counted on until she arrive at 15.  PTC said he multiplied 3x5 because he saw three groups of 5. The second images was a little difficult. PTC said she saw 5 +4 +5. Then added left to right.  PTK said she saw 5 +3+3+3. Then added left to right.  The third image was a doozy. PTK said

Fall Semester 2019 New Beginnings with New Preservice Teachers!!! This blog post is about the first Number Talks for the new semester. The goal for this Number Talk is to introduce the practice with a new group of Preservice Teachers (PST) in math methods. NT is really taken off in Madison County, and I want to make sure my PST are well versed in the practice. This NT includes dot images. The focus for NT using dot images is to builds accuracy, flexibility, and efficiency strategies in counting (Parrish, 2011). According to Russell (2000), "Accuracy" denotes the ability to produce an accurate answer; "efficiency" denotes the ability to choose an appropriate, expedient strategy for a specific computation problem; and "flexibility" refers to the ability to use number relationships with ease in computation.  Instead of seeing items singularly, students can figure the amount of dots by grouping them. The below  are the dot images for the first NT.  T

The blog is back!!!! I am grateful for another chance to send my thought and research by chronicalling my time with my preervice teachers. The reason for the reboot or deactivation is SOTA. I attended SISTERS OF THE ACADEMY (SOTA) Signature BootCamp, and it was an empowering experience!!! This is the reason why I am deactivating my blog. My senior scholar mentors gave me wonderful advise on how to handle being a scholar in the skin and gender. I plan to be purposeful in all that I do related to publishing and being an intricate part of the academy.  At BootCamp I met wonder ladies like me seeking that needed nudge in the right direction. We exchange ideas. We ate together, receive instruction together, received constructed feedback together, and even exercised together. We listened to sistas who have been in the academy. They were very transparent and their experience. The sistas made me feel I can be successful in the academy.