Good day! Today we conclude our book study of Math Running Records in Action: A Framework for Assessing Basic Fact Fluency in Grades K-5 by Dr. Nicki Newton. The Division Running Record is the subject of Section V.
If you are just arriving today, you can view the book study archive to read past posts by clicking on the Book Studies drop down menu of the navigation bar above. It’s been wonderful hearing how each of us has transacted with the text as we’ve reflected on the reading, our teaching, and our philosophies.
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Section V provides important details regarding how to administer, analyze, and interpret the Division Running Record (working with dividends up to 100) as well as the implications the results have for teaching division. This section follows the same format as Section II, III, IV, so much of the summary of this section will be similar, if not identical.
Chapter 12: The Division Running Record
Dr. Nicki begins again by giving readers a glimpse into the Division Running Record of a fourth grade student who thinks multiplication when faced with many facts but at times results to counting up. The information gathered from this running record is invaluable, as the teacher will then able to specifically address the student’s needs. The Division Running Record gives teachers much more information than that which results from a timed test.
As discussed with the previous running records in the book, when used systematically and consistently across grade levels, the Multiplication Running Record yields valuable data that can be used to talk about individual students, classes, and grade levels and can be used at various levels.
As always, the teacher should begin by introducing the assessment to the child. This introduction lets the child know that there are three parts to the assessment and what he/she will be asked to do in each part. A helpful introduction dialogue is provided.
The Division Running Record has three parts:
Part I: Benchmark Problems – Twelve benchmark division facts (dividends to 100) are given to the child to orally answer. The teacher records the child’s responses using a series of codes that relate to his/her accuracy and automaticity. The teacher carefully observes the child’s behaviors and codes them as such on the teacher recording sheet. The teacher also notes behaviors such as self-corrections, thinking time, counting on, etc. Each behavior is recorded with a code and there is room on the recording sheet for comments. A child’s observable behaviors are important to note so that mores specific questions about what the child was doing can be asked in Part II.
Part II: Clarifying Questions/Strategy Use – Next, the teacher asks more detailed questions about each problem. The teacher recording sheet offers a list of possible question prompts for the teacher such as, Can you tell me more about how you…?, How did you solve the problem? What does that mean? What the students says and does is recorded. Part II is essential because the teacher gains important information about a child’s understanding as it relates to strategy use. This information will in turn be used to design small group instruction.
Part III: Mathematical Disposition – How a student feels and thinks about him/herself as a mathematician is at the center in Part III. The child is asked to talk about what was easy and difficult as well as what he/she does when stuck. A child’s answers provide a bit more insight into his/her attitudes.
Chapter 13: Analyzing and Interpreting the Division Running Record
When analyzing the data, a teacher should begin by addressing a child’s automaticity. Ask yourself the following questions:
- Where does the student demonstrate automaticity?
- Which problems does the student not know?
- What happens when the student doesn’t know a problem? How does he/she act? What does he/she do? What are his/her behaviors when stuck?
An analysis of Part II involves taking an up-close look at a child’s strategy use when given each problem. Determining the efficiency of a child’s strategy use is important to note as well. The efficiency of strategy use will be an important consideration when forming small, guided math groups. The last column of the teacher recording sheet is a place to record a child’s level of strategy use from 0 – 4.
The following questions for analysis (with clarifying examples not shown here) are presented for Part II:
- Does the student thoroughly understand the type of fact you are asking about?
- Are there some sets of facts that the student only partially knows?
- What are the main strategies that the student knows?
- Where does the student use inefficient strategies?
- Specifically, what is the student doing when he/she is solving problems?
An analysis of Part II allows teachers to determine which phase of mastery a child falls into:
- Counting all
- Counting on with fingers/head
- Counting on in head/mental strategies
- Using derived strategies
Teachers will find that a child may fall into a different phase of master depending on the type of fact.
Then it’s time to analyze Part III by looking closely at the disposition interview to note a child’s attitude, how the interview compares to his/her performance on Parts I and II of the assessment, what he/she says about struggling, etc.
When analysis has been done, it is then helpful to record individual and class data on larger recording sheets. Dr. Nicki calls this “picturing the data” and shows examples of how this can be done.
Finally, it is time to interpret what has been collected to inform instruction. This involves putting children into groups based on their understanding as it relates to multiplication fact fluency. It’s important to remember that groups must remain flexible, as students will progress from one group/level to another at different rates. It’s also a must to engage students in small guided groups and workstations for independent practice specific to their needs.
Chapter 14: Implications for Teaching Division
Dr. Nicki begins chapter 14 by sharing some guided math division lesson examples and then goes on to give suggestions for teaching division basic fact strategies while stressing the importance of the teacher actively asking questions to help build conceptual understanding. Dr. Nicki also shares a couple of options for recording what happens in guided groups.
A 5-component framework for individual practice is presented. The five stages are research-based (Van de Walle) and give students lots of experience with division strategies. Student practice in the five stages should be differentiated and ample time should given to practice using strategies. The five stages are as follows (more specific information about each is found in the text):
- Model It – A four square is used to practice concrete, pictorial, and abstract representation of facts.
- Flashcard Practice (ongoing every day) – Students should be engaged in flashcard use at three levels (explained in more detail below).
- Strategy Notebooks/Posters – Students make meaning of strategies in the form of writing and models. This can come in the form of strategy explanations, examples of the strategy, explanations of strategy self-talk, etc. This can be done in journal or poster form.
- Word Problem Practice – Students practice using various strategies when given numbers in the context of word problems. Repeated exposure to word problems and the freedom to choose strategies is important in this context.
- Quiz–Just Knew It! – A self-monitoring quick check is taken. This should not be timed or in competition with others. Checks are done so students can reflect on how they are progressing in their understanding of basic multiplication facts. Tracking of one’s own progress becomes important as he/she progresses and takes ownership/values his/her efforts. For this reason, Dr. Nicki offers some different ways students can keep track of their progress.
As noted above, flashcard use is an important part of independent practice. There are three stages of flashcard practice that students should progress through:
- Concrete – Basic fact flashcards are used, but students physically model strategy use with manipulatives/tools.
- Pictorial – Scaffolding flashcards with a fact and visual representation of a strategy are used.
- Abstract – After students have shown mastery using the first two types of flashcards, students use basic fact cards. The goal is NOT to drill but to sort facts by strategy and say from memory.
Several sample flashcard games are shared for students to play together.
Dr. Nicki also provides a sequence for teaching/practicing division facts while stressing the importance of the “think multiplication” strategy. The sequence is as follows:
- Level One – Dividing a number by zero, dividing a number by itself, and dividing a number by one
- Level Two – Dividing a number by five and ten
- Level Three – Dividing a number by two and by its half
- Level Four – Dividing by 3, 4, 6, 7, 8, and 9
In teaching multiplication and division facts, Dr. Nicki has recommended using Cuisenaire Rods (whether purchased or printed). Here are some printable Cuisenaire Rods that can be printed, cut, and put into students’ toolkits as she suggests. For addition resources related to this book study, make sure to visit the Math Running Records in Action book study archive.
Now it’s your turn to share your thoughts and reflections of Section V. You may also like to respond to one of the following questions for reflection:
- Do you use Cuisenaire Rods when teaching division? If so, please share!
- What workstations and/or games for practicing division facts do your kids love? If you can, please share!
- Do your students currently self-monitor their progress? Explain.
- What is your greatest “take-away” from reading this book?
- What are your next steps?
Your time and participation are greatly appreciated! To click in the “Leave a Reply” box at the end of this post to share. If you are used to blogger commenting, it will be new to you when you are asked to enter your email. Your email will not appear for readers to see. Once I read your comment, I will post it for everyone to see. This is a security measure to cut out any spam or advertisements.
Thank you so much for taking the time out of your summer to participate in this book study! BUT, it’s not over yet! Dr. Nicki is doing a Q&A for us! Please send any burning questions you have collected during the book study, and I will get them to her. I will then be posting her responses, so you will want to stop back! Simply email questions to me at firstname.lastname@example.org!
All the best–