What does John Van de Walle have to say about...

by Miriam Cortes

This is a virtual professional learning opportunity so to receive credit for this course, please complete the assignments throughout the tackk.  You are welcome to complete this at your own pace.  It is all due by May 1st!  Happy Learning
Miriam Cortes

We will spend the next month reading and learning together about what Van de Walle has to say about ...  Mastering the Basic Facts, Developing Whole Number Place Value Concepts and addition and subtraction strategies.

Together, we will study chapters 10, 11 and 12 of the Elementary and Middle School Mathematics Teaching Developmentally book by John Van de Walle.

Chapter 10
Helping Students Master the Basic Facts

Some effective strategies mentioned by Van de Walle to use in teaching fact mastery:

  1. doubles
  2. near doubles
  3. subtraction as think addition
  4. nifty nines

As a math interventionist, I found this chapter to be especially interesting.  There are several  strategies mentioned in this chapter that I am going to try with some of my students that have yet to master their facts.  On page 186-188, the fact remediation section was an eye opener and great reminder for me as to what approaches I might continue and some that I may discontinue  as I work with my students to maximize their success. 

As you read through this chapter, choose from any of the effective strategies discussed in chapter 10 to respond to the following questions in the stream.

1.  Think about the expectations of your grade levels fact mastery.  What strategies will you try with your students who have not met the level of mastery at this point in the year?  Discuss how might you "map" out the rest of the year for fact mastery with those same students?  (several strategies and games were mentioned, will you choose from those or do you have others that you have tried in years prior that you will try again?)

2.  As you read through chapter 10, did you come across any new strategies or any that you have not tried in years or months?  Please choose one discuss the importance of trying this method  with those that have struggled to learn their basic facts.

Chapter 11
Developing Whole Number Place Value Concepts

How can we, as educators best develop Number concepts in our students?  According to chapter 11, number concepts are usually described and  broken down into the following chunks of both teaching and learning:

  • Count by ones
  • grouping 10's (basic ideas of place value and base ten concepts)
  • Oral and written names/symbols for numbers
  • patterns/ relationships with multi-digit numbers
  • Numbers beyond 1000

Please choose from the above developmental areas to focus on as you respond to the following questions in the stream. 

  1. In your grade level, discuss an activity mentioned in this chapter that you might use with your students at the developmental stage that you consider them to be. 
  2. If this is an activity that you have used, please let us know how it went with them and would you recommend doing this activity again or what changes might you make in order to make it more effective?
  3. How are the strategies and activities described in this chapter similar or different from the way  you learned math as a child?

Chapter 12
Developing Strategies for Addition and Subtraction Computation

Chapter 12 was summed up into the 3 types of computational strategies that were discussed:  Direct modeling, student involved strategies and standard algorithms.  We are reminded that there are developmental stages in what we are asking children to learn as we teach them.  In direct teaching, we are using a variety of manipulatives or drawings to represent our thinking.  Student Invented strategies are often times overlooked.  However, spending time on discussing how other students is proven useful in student learning because not one strategy works for all students.  Finding the one that works for them is key, this will allow for them to find their right "fit".  Standard algorithms for both addition and subtraction are a must.  However, there is so much involved in getting students to this point.  Students must first have a grasp of tens and ones, regrouping. 

Please use the information you  learned from chapter 12 to respond to the following question. (This is a discussion question that came directly from the book.  I am using it here because this is the same question that we are asked as educators in CCISD so often.)

1.  How are standard algorithms different from student invented strategies?  What are the benefits of invented strategies over standard algorithms?

2.  Assessments that we use are critical in gauging student learning so that we can know where we should begin our individual instruction with each child.  Thinking about your grade level's assessments, discuss how you can use this information to drive your  instruction. 

Comment Stream

2 years ago

This is where you will place your responses to questions.

2 years ago

@alyssatoomes glad you are joining us for math leaning! :)

2 years ago

@miriamcortes I need all the help in the world with math!

2 years ago

1. By the end of kindergarten, the students should be able to rote count to 100, recognize to 32, and be exposed to the combinations up to ten. Since we are currently in combinations and will be so until close to the end of the year, I would like focus on my students mastering the combinations up to six. One of the several strategies that I would students to try is one more than with dice. Being able to count on is a prerequisite to understanding the parts of four. For example, a student needs to know 3 and one more is four before they understand that 3 and 1 is a combination of four. I recently tested the students on one more, so I am going to use this strategy with the students who were not successful. Since the students are used to the DNC games, I am going to use some of these new games from the book to keep them engaged. Also, I want to remember that when I am pulling a group in math, it needs to be short. I am going to either play one game, or focus on one problem for that day.
2. The strategy I would like to use is near doubles, it is something I have heard of but not completely understood how to teach. In regards to combinations, several of my students know that 2 and 2 is four, and 3 and 3 is six, but cannot manipulate the numbers. For those specific doubles, just 2 and 3, I am doing to make cards that illustrate the doubles. Then, I will use these and ask my students which card could help them solve the fact. If they are trying to solve 2 and 3 make 5. I will ask them which double will they pick to help. Either the doubles of 2 or 3 can be chosen. This method is important because when students understand doubles, they can be anchors for other facts. Since my students know the doubles of 2 and 3, these can be a help in finding an unknown fact and help their number sense.
1. Since kindergarten in in a pre-place-value stage, I focused on the counting by ones. On page 194 it described the different ways of counting; by ones, by groups, and by tens and ones. One of the suggestions they had were to count by tens and ones on a hundreds chart. We will first count to 53 by ones, then I will ask “What if we counted by tens and then ones”. We counted by tens up to fifty, then counted by ones to 53. Kindergarten is familiar with counting by tens to 100, so this could be a start for them to connect the relationship between counting by ones and by tens.

2. As a child, I remember learning to count by memorization. We were very familiar with counting by rote. I typically counted by ones to reach any answer, instead of counting in groups. These activities and strategies teach you to think about quantities in different ways instead of only a count-by-ones approach.

1. Standard algorithms are necessary, it is important that they are included in student invented strategies. Standard algorithms are a strategy, it is not the only one to be relied one. Like all strategies children use, they need to understand why they work. They tend to be assumed as the correct way, and so students will automatically choose that strategy. Student invented strategies differ from standard algorithms because they are number oriented instead of digit oriented. In the book, they used the example of solving 45+32. Using a standard algorithm, students will focus on the digits 4 and 3 instead of 40 and 30, the place value. Another way algorithms differ from student invented strategies is that they have several different ways to get to the right answer, this helps students develop number sense. If students are working on 17+23, they can take three from 23 and make the 17 a 20. Thus, making 20+20. There are many different methods, which can help students have a stronger basis estimation.

2. One of the assessments that kindergarten uses is the number arrangements. This assessment is key in helping students understand a sense of quantities, and hope they see the relationship from one quantity to other quantities. It measures if the children can accurately count out how many. And also if they can see a number and its parts. Since we are finishing the year learning about the parts of numbers, I can take the results from this assessment and know the working number of each student. If a student is not able to see the parts of 6, it shows me that I need to use the strategies discussed earlier with them in small group instruction.