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!

**Let’s continue!**

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?

**Your time and participation are greatly appreciated!** Simply 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.

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–

Liz Conlin says

What I have tried to do more and more is allowing students have some time to “play” with the manipulative with a little direction. I allow them time to talk with their team and learn about the tools they are learning regardless of the concept. Then, I direct them with questions that do not give away what I want them to learn so quickly so that they can continue to investigate patterns and relationships. Many times they learn more through their discussions with team members than a teacher just telling them. It’s more of a reverse of the common practice “I do, we do, you do”… it’s “you do, we do, I do”. It is hard to get used to doing that because that is not how I was taught to teach.

My 5th graders have a data binder to monitor their progress. Depending on the skill, it may be a graph they fill in, or a star for their Math Blaster progress. It is our occasional speed test that we use school wide. If they reach the last level, they get to race against the administration. They also keep their pre/post tests on a skill in their binder to see their progress. They typically bring it to group once a week, for those that are really struggling or less if they have automaticity, so that I can have discussions with them and also let them ask their peers for assistance if necessary.

When I taught 3rd grade and we were really focusing on their facts, I sent games home for homework based on the facts that the student was working on. There was a form for the parents to sign and leave comments if necessary. In 5th grade, I have only done that with students who had a severe deficit in their facts which, until now I thought is rare but I may find out something different using the running records. I also give parents and students links to websites or apps that could help their child but I typically don’t monitor it. Depending on where my students are, that may change.

Adventures in Guided Math says

Thanks so much for sharing, Liz! Sounds like you have some great things already in place to add running records to. Indeed, it is amazing how much comes out through the kids’ discussions–that’s one of my favorite things to take in. There discussions tell us so much more than we can see, and I love when kids’ borrow thinking that is shared and make as strategy their own after exploring it themselves. I hope you have been enjoying the book study!

Ann Elise record says

I have given over a hundred of these subtraction running records now and I have found it to be different than the addition one. For addition, I find the progression linear…one strategy leads directly to the next. For subtraction, though, I find that the strategy used is really dependent on the numbers in the problem. I want the student to have three thoughts of options when they are presented a subtraction problem: count back, count up, and knowing the addition problem that will help solve the subtraction problem. For example, if the problem is 9 – 2, if the student doesn’t know that 7 + 2 = 9 then I would want them to count back the two. If the problem were 9 – 7, though, it is much more efficient to count up from the 7 to the 9. This understanding of subtraction as a distance between the two numbers will be applied all the way through the math journey particularly in middle school when students are finding the distance between two points on a coordinate grid. My favorite tool to use to help model these are cuisenaire rods because they encourage the students to think of numbers as existing as a group rather than a collection of ones. Plus, when the rod for the total amount is on top and the two rods for the addends are beneath it, it looks just like the model for all add/sub problems. So, it is a concrete representation of the model.

The beauty of this is that these very same strategies are applied with larger numbers, fractions, and decimals. I particularly like a beaded numberline to 100 to show concretely what we record in an open numberline. I have asked older students to solve 100 – 98. They are so accustomed to thinking of the take-away method that I have had students take away the 90 and then take away the 8…if they had just thought about finding the distance to add, they would have been at the 2 so quickly! When I see a problem like 52 – 37, I now envision an open numberline and I use 10’s to help me. 3 more makes 40, 10 more to 50, and then 2 more to the 52….so 3 + 10 + 2 =15 which is so much easier than trying to keep track of the regrouping using the algorithm method. This same thought process is applied with fractions… 5 1/4 – 3 3/4….1/4 to 4, 1 whole to get to 5, and 1/4 to get to the 5 1/4. so 1/4 + 1 + 1/4 is 1 2/4.

As a Math Coach, I model number talks based on the book Number Talks by Sherry Parrish as well as Making Number Talks Matter by Kathy Humphries and Ruth Parker which allow the students to explore these strategies and successfully solve problems that they never thought they could!

Liz Conlin says

Hi, we do number talks at our school as well. I was wondering your thoughts on reviewing subtraction strategies for 5th graders starting out the beginning of the year since addition doesn’t seem to be a difficult thing for them for the most part. Thanks

Ann Elise record says

I’m always in favor of meeting the students where they are. The only way you will know is if you see what they can do. You could start off with 98 + 16 and see what they do with it. If they only do the algorithm in their heads, then I think it would be worth the time to talk about breaking apart numbers to make it easier for our brains. Like, take 2 from the 16 to make a 100 with the 98. Or add, the 90 and 10 and then the 8 and 6. That sort of thing. I have a lot of my teachers trying to decide where to begin their year so they can start preparing things, BUT we won’t know where to start until the students are in front of us. If we ignore that and just start where we think we should, we risk pushing on to future topics before the foundation is set on the underlying concepts.

Liz Conlin says

So, do you use the running records to determine where to begin? OR do you use another metric? I understand waiting until the students get there. This year our classes in 5th will be leveled. We have an ALM model, a partial inclusion model and the the other classroom is a majority of our RTI. At least when I left in June, that was the plan. Yes we have only 3 teachers this year and are starting out 32-35 students. It’s just time is a commodity I do not want to squander. In the past we, in 5th, have started with addition and if our entire school is doing it at every level in every class is it the best place to begin?

Sorry for all of the questions…my grade partner tells me my main learning preference is a magnifying glass 🙂 I guess she is right!

Thanks for your input!

Ann Elise record says

Never apologize for asking questions! I don’t pretend to have all the answers…that’s why it is important to share ideas with other people. I will be working full-time in my 3-5 school (I have been in my K-2 and 3-5 building splitting my time these last two years). I created an assessment that took all the priority standards for the previous gradelevel so that we can give it to the students at the beginning of the year to see if there are any gaps we need to fill in before we start the current gradelevel curriculum. I also created a word problem pretest for add/sub and another for mult/div using the South Dakota CGI document and the problem types in the progressions document in the CCSS. That way we can analyze the data and see which problem types the students struggle with. Why waste time on a problem type they all understand? The running records will help us determine which fluency strategy to have them work on during math workshop. I always keep in mind that there are three pillars to our math education – fluency, concepts, and application in word problems. We try to meet all of these in a combination of Guided Math groups and whole group lessons. I wouldn’t think addition would be the best place to start IF your students demonstrate to you that they have mastered it.

Hope this helps!

🙂 Ann Elise

Adventures in Guided Math says

Absolutely! I say addition and subtraction. I always start with problems that are from the previous year because the first number talks of the year provide so much insight into past learning and a great way to start when reviewing procedures and “getting into the swing” again.

Ann Snow says

I teach first and second grade students who struggle with math. I have read chapters 1-8. I’m wondering, maybe I just missed it in the book, if we should be assessing addition and subtraction at the same time? CCSSmath refers to the ‘relationship between addition and subtraction’. Any thoughts on this?