Methods of Math Teaching and Learning

My pre-service teachers and I had did a Number Talk involving tens frames.  Since we have not had a Number Talk in the couple of weeks, I found it befitting to have one now. The topic for todays class was early number sense and place value. Core part of early number sense is the ability recognize landmark or benchmark numbers, and being able to visualize numbers as one unit or unitize (Boreman & Rucker). The Number Talk session picture is below. Pre-service teachers were shown the image for 3 seconds. They had to remember the number of dots they saw, and how they saw it.  Pre-service teachers immediately saw there were 12 dots. However, how they saw the 12 dots were different. The following is a dialogue of the number talk:  PRT One: I saw groups of threes. Me: How did you see the groups of three? PRT One: 3 at the top left. 3 at the top right. 3 more bottom left. 3 at bottom right. 3, 6, 9, 12. I brought the point that we want to subitiz...

Hello All! I know it has been a while since my last post about my math adventures. I have changed jobs and am no longer worker with young children. I currently teach pre-service teachers. So far it is a joy to prepare future teachers to become effective teachers. My pre-service teachers and I started Number Talks. These teacher candidates include undergraduate and alternative masters program students. Alternative masters students are students who have obtained a bachelors degree in a non teaching field, but are seeking initial certification and will receive a masters degree in education. After giving the back ground history of Number Talks(NT) and assessing to determine if any of my students have knowledge of NT, it was determined this topic is new to them. Therefore, I started from the beginning by teaching the procedures of NT- fist to your chest, thumb up,...... Of course they followed the procedures quite well. ...

It has been a while since my last post. Thanks for your patience. I have been continuosly working with kindergarten class with NT. They are seeing 7 in many different ways. Students are subitizing 3 and 4 dots at a time. KeUndre and Christopher can subitize 5. Some students are exploring couting by two and use couting on as a strategy. These students are making great progress. This blog is about presenting at ACTM. My colleauge LaTesa Sanders and I presented Thursday morning. LaTesa Sanders is the math coach at Hard Elementary. Sanders and I have had several conversations about NT in the past and have wanted to present our findings. So I wrote a proposal and it was accepted.  The participants of our session were teacher with various background such as  elementary schools, middle school, AMSTI reps, and preservice teachers. We discuss the impact NT had on our students' mathematical thinking and the importance of planning. We also allowed teachers to participate. Yes, they had ...

Good evening This will be a brief post. I left my notes at work. I know I will not do the happenings in kindergarten full justice. However, I did want to discuss how one student subitize 5 during the NT this week. Of course, kindergartens know the routine-fist to your chest, thumbs up for the answer, and the agree sign. I love they know this when I walk through the door. AWESOME. The teacher and I are involved with side by side coaching as way to strengthen students counting abilitiy.  I want to focus this post on Christopher. This particular student had trouble with attention during the sessions. So I took him and the four girls to my room to see if having a small group will be beneficial for them with the next NT. Sort of like flip teaching. I used a tens frame again with six dots- two on top and three on the bottom. But the arrange was quite different. This is a conversation between me and the little fellow: Teacher: How many do you see? Christopher: I see 5 and 1. Teacher:...

Number Talks with Five Good evening Please forgive me for not posting a new blog last Sunday.  I will write my continued adventures in kindergarten. Although, I have started a NT with first grade teachers and students. This post will discuss the progress of NT in kindergarten. We continued with tens frames last week. This group remembers procedures very well. As soon as they sat in their places on the carpet, the students immediately place their fist to their chest. We are continuing working with 5 on the tens frame using both bottom and top levels. The questions I ask are "how many do you see?" and "how do you see it?" Quickly students place thumbs up to inform me they know the answer. Students responses for the most part are accurate. Most  students can denote there are 5 dots. A couple of students may say 4 or 3. Therefore, they are making progress. The following link is an example NT problem: https://docs.google.com/document/d/1AOhF0OtPBhByfuMt00IWELRIMoK...

Good evening, In kindergarten this week, we are continuing with the concept of four on our tens frame. This time both levels of the tens frames were use.  The tens frame below is one of the examples from class. Students are beginning to understand that four dots arrange anywhere on the tens frame is four.  Only one student continues to struggle with subitizing four: Teacher: So how many do you see. Student: I see three over here and one more over there to the right. Teacher: Well, lets count the dots. Student: One, two, three, and (with hesitation) four. Teacher: So now how many dots do you see? Student: I see four. After having this student to actually count the dots, she realizes that there are four dots and not three and one more. A couple students manipulated the dots to where they could recognize immediately there were four. This is fine. However, I want them to move from counting to actually readily knowing that there are four dots. Until then, the kin...

Good evening again. I'm sorry this post is late, but I'm in Destin Florida. The internet connection is terrible in this lovely resort. Let me not belabor the point of this blog entitled The Meaning of Four. This week in kindergarten we concentrated on the number four. Not so much of the symbol numeral 4. But what four means and how kindergarten student understand what four truly means. So, the kindergarten teacher and I did a NT involve four dots. The four dots were randomly placed on the upper tier of the tens frame. The students remember the procedures very well. Some continued to raise their hand when posed a question, but for the most part they have it. The challenge was their perception of what four means when looking at four dots. It was quite interesting to see that some students perceive four as three dots and one more. However, they could not make the connection  that there are  four dots. Some of students also quantify four dots as 2 dots and 2 more ...