Methods of Math Teaching and Learning

Let’s Talk about Numbers! Embedding Number Talks into Pre-service Teachers Mathematics Methods Course As a classroom teacher, I saw the essential benefits of including mathematical discourse in my mathematics classroom. My elementary students were engaged with solving problems and having discussions about their approaches. As a faculty member, allowing my preservice teachers to have conversations about numbers is even more essential. Preservice teachers come with diverse experience and preconceived feelings about mathematics. They bring their feelings into college and into their teaching practices. These feelings include the following: ·          I can’t stand math! I don’t want to teach it. ·          I love math. It was my favorite subject in school! ·          There is only one way to do math!   My goal is to help develop mathematical thinkers, and, in turn, give them the necessary pedagogy to build mathematically thinkers. Hopefully, my preservice teache

This post is based on the last class session for this semester. We went out with a bang. We tackled NT with fractions. We actually started our talk about fractions the previous class session. Today was more of a review for the final. After much practice order fractions without determining alike denominators and operations with fractions using models, my PST (Pre-service Teachers) engaged in a NT involving fractions. The following is a conversation with adding fractions:   1/4 +1/2 Teacher: How did you get 3/4/ ? PST 1: I know that 1/2   is equal to 1/4 + 1/4which is 2/4.  So I used 1 /4  + 1/4 + 1/4. Therefore   it equals to 3/4.   PST 2: I just found that common denominator which is fourths. Since the first fraction already has fourth, I don’t have to change that fraction. But the second fraction is ½. The second fraction has to be changed to the new fractions that is equivalent. The equivalent fraction is 2/4 . So 1/4 + 2/4   is 3/4  .   Both student used equivalenc

Number Talks with Multiplication Drop the Zero! NOT! April 14, 2016 For Number Talks (NT) this week,  the Pre-Service Teachers (PST) were engage with multiplication using landmark numbers. PST were to mentally solve 6 x 50 and 6 x 300. This type of problem is not a real challenge. However, I wanted to see PST's approach to solving the problems. I wanted to hear thinking as relate to multiplying numbers with the multiples of 10. What approach would they choose? The following conversation took place: Teacher: How did you solve it? PST1: I multiplied 6 x5 first. That is 30. Then I dropped the zero. So the answer is 300. Teacher: What do you mean by dropping the zero at the end? PST1: I mean since the you are multiplying by 50 so I multiply 6x5 and drop the zero at the end. Teacher: So in reality what are you multiplying? Where did you get the 5? PST 1: I got the 5 from 50. 5 x 10 is 50. So I separated the 50 into 5 x 10. Then I multiplied 6 x 5 which is 30 then

This week in math methods class my Pre-service Teachers (PST) were introduced to alternative strategies for multiplication and division. According to Common Core State Standard/ College and Career Readiness Standards(CCSS/CCRS), students learn the standard US algorithm for multi digit multiplication in fifth grade.    Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5]        Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5-NBT6 ]   This mean teachers use inventive strategies and strategies involving place value understanding for multidigit multiplication.   Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers

Number Talks 3/ 15/2016 Every week I make an attempt to conduct a Number Talk (NT) with my Preservice Teacher Candidates (PSC). My goal is to experience math discourse so that they will be capable of implementing NT with their future students. This is a ritual I want my PCS to value not just to talk about math to insure students are getting the answer. I want my PCS to appreciate each other’s thinking and sense making of the mathematics being presented. This week I presented to problems involving addition with strategies. 52 +30 52 + 35 Here is the conversation for 52 +30: Teacher: Who wants to defend 82? (I asked this question after everyone agrees the answer is 82). How did you get 82? PSC 1: I visualized the hundreds chart. Teacher: Wow! You are using your tools. PSC 1: Yes. I knew going down is 10 more. I knew 52 +10 is 62. If I go down 10 more, 62+10 more is 72. So far I added 20. I need to add 10 more. 72 + 10 more is 82. So my answer is 82. Teache

Number Talks with Preservice Teachers Using Landmark Numbers My preservice teachers and I were engaged in a Number Talks (NT) involving Landmark Number to strengthen their mental math capacity. My goal is for this NT is to give my students opportunities calculated basic math problems without relying on paper pencil computation and to gain knowledge on NT strategies.  Since we have been working with place value learning using manipulatives, models, and other tools, I thought it was befitting to have NT with the emphasis on landmark numbers. The Common Core State Standards (CCSS) or College and Career Readiness Standards (CCRS) calls for the formal teaching of US algorithm for addition and subtraction in grade four. Therefore, preservice teacher should be aware of the different instructional strategies that lends itself to development of place value understanding. This include using place value to add and subtract two and three digit numbers. I presented the following sequence

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 subitize quantities. Subitize is the ability t

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.  I displayed dot images for 3 seconds. Then I ask how many did you s