Good day! Welcome as we continue our book study of Math Running Records in Action: A Framework for Assessing Basic Fact Fluency in Grades K-5 by Dr. Nicki Newton. Today we move on to Section III–The Subtraction Running Record.
If you are just arriving today, you’re not too late! 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. If you want to participate, it’s easy–simply read along and comment on posts by sharing what makes you think, what connections you make, what plans are put in motion, etc. I will also be posting some questions to think about as they relate to the reading each time I post, so you may feel free to respond to those as well. It’s wonderful hearing how each of us transacts with the text as we reflect on the reading, our teaching, and our philosophies. Dr. Nicki has also graciously agreed to do a Q & A in conjunction with the study, so make sure to keep a list of your burning questions as we progress.
If you don’t have a copy of the book, portions of the text will be summarized, yet other portions will be mentioned and will require the text for full understanding and benefit. Please feel free to share, even if you don’t have a copy of the text. Of course, I DO recommend you snag yourself a copy. Use Routledge discount code IRK95 to receive 20% off!
In Section III of the text, Dr. Nicki gives readers important details regarding how to administer, analyze, and interpret the Subtraction Running Record (an assessment of basic subtraction facts within 20) as well as the implications the results have for teaching subtraction. The bulk of Section III resembles that of Section II.
Chapter 6: The Subtraction Running Record
As discussed with the Addition Running Record, when used systematically and consistently across grade levels, the Subtraction 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 following is a brief overview of the Subtraction Running Record’s three parts:
Part I: Benchmark Problems – Twelve benchmark subtraction facts (within 20) 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, head bobbing, finger counting, skipping problems, 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 you can ask more specific questions about what the child was doing based on the behaviors noted when given a particular fact.
Part II: Clarifying Questions/Strategy Use – The teacher goes back and asks the students in detail 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…?, That’s interesting: Tell me what you did. 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 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 7 – Analyzing and Interpreting the Subtraction 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. One child may use his/her fingers while another reasons using partial differences and use his/her knowledge of ten. Depending on the fact, the very same student may use highly efficient and less efficient strategies within the same running record. Furthermore, a child can be accurate yet lack efficiency. Each of the above are important to note and will be used in forming 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?
- 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?
Dr. Nicki also gives readers a sample recording sheet for looking at strategy levels as well as a peek into a Subtraction Running Record that shows a teacher’s notations.
Teachers should then go on 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 of subtraction fact fluency. It’s important to remember that groups should 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 8: Implications for Teaching Subtraction
This chapter gives some wonderful suggestions for teaching subtraction basic fact strategies while stressing the importance of allowing students to “play around with the ideas and think about them independently and with each other.” I love the intimacy of small, guided math groups when I give students a problem and ask them to share how they would solve it. It seems so simple, yet it’s so powerful! My students never cease to amaze me as they communicate their thinking, build on previous knowledge, encourage others, and “borrow” strategies.
Instead of explicating teaching a strategy, help for guiding conversations is given. Ask students:
- How could you solve that?
- Is there another way?
- What number fact clue could you use?
- What number fact could you think about to help you with that fact?
- Can you use the (name the strategy) to find the answer?
Dr. Nicki also shares a couple of options for recording what happens in guided groups that make it quick and easy to note how students are progressing.
As with addition, 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 addition strategies. Student practice in the five stages should be differentiated and give students time to practice the use of 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 subtraction facts. Tracking of one’s own progress becomes important as he/she progresses and takes ownership. 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.
If you are interested in some scaffolding flashcards for subtraction, click here to visit my FREE Math Tools page. I think you will find them especially helpful!
Ideas for games/workstations, a list of game websites, and an overview of what parents need to know are also included in Chapter 8.
Now it’s your turn to share your thoughts and reflections of Section III. You may also like to respond to one of the following questions for reflection:
- How do you/plan to guide students in their invention of strategies?
- Do your students currently self-monitor their progress? Explain.
- How do you currently communicate with/involve parents in the process of helping students develop fact fluency? Is there anything you plan to change?
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Please stop back next Thursday, July 28 when we talk about the Multiplication Running Record. You can also click here to view the book study schedule for future weeks.
All the best–