Welcome! Today 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. Section IV is all about the Multiplication 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!

**On to Multiplication!**

Section IV discusses how to administer, analyze, and interpret the Multiplication Running Record (an assessment of products to 100) as well as the implications the results have for teaching multiplication. This section closely resembles Section II and III as it relates to multiplication.

**Chapter 9: The Multiplication Running Record**

Dr. Nicki begins by giving readers a glimpse into a Multiplication Running Record of a student who has accuracy but needs to develop higher level strategies. The information gathered from this third grader’s running record is invaluable, as the teacher is then able to specifically address the student’s needs by exposing her to a variety of activities and games to move her beyond counting as a main strategy. Such information is impossible to glean from the infamous timed test that students take all at once–a Multiplication Running Record gives the teacher SO much more!

As discussed with the Addition and Subtraction Running Records, 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 Multiplication Running Record has three parts:**

* Part I: Benchmark Problems *– Twelve benchmark multiplication facts (products 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, visible counting in the head, counting on fingers, 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…?, That’s fascinating: Tell me what you were thinking*. 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 10: Analyzing and Interpreting the Multiplication 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?
- What are the main strategies that the student knows?
- Where does the student use inefficient strategies? This includes observing what happens when a student doesn’t know a problem or get stuck.

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
- Mastery/Automaticity

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 11: Implications for Teaching Multiplication**

This chapter gives some wonderful suggestions for teaching multiplication basic fact strategies while stressing that activities need to be engaging, scaffolded, and purposeful. 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.

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 multiplication 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.

**Since jumping into the world of Twitter this summer, I came across an awesome set of scaffolding flashcards created by a math specialist named Cathy Campbell. She has created ten frame and subitizing scaffolding multiplication flashcards. Thanks to Cathy!**

Games and workstation have also been a focus in each section of the book. We all know how much kids enjoy games–and Dr. Nicki always emphasizes the importance of thinking out loud, justifying, defending, and explaining during game play. **I also came across a great multiplication game on Twitter, that was the center of some discussion with Marilyn Burns, called Circles and Stars. I also noticed it pictured as a workstation choice in Figure 11.17. Click here to download directions for playing Circles and Stars!**

Here are a couple more resources you may be interested in:

*Three Steps to Mastering Multiplication Facts*by Kling and Bay-Williams–discusses phases of mastery*Multiplication Tetris: Helping Build a Foundation for Multiplication Fact Fluency**—*a previous blog post about a game shared in the above article

Now it’s your turn to share your thoughts and reflections of Section IV. You may also like to respond to one of the following questions for reflection:

- What is your opinion of the 9s “finger trick” discussed in chapter 11?
- Do you use Cuisenaire Rods when teaching multiplication? If so, please share!
- What workstations and/or games for practicing multiplication facts do your kids love? If you can, please share!
- Do your students currently self-monitor their progress? Explain.

**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, August 4th for a discussion of Section V–The Division Running Record. **You can also click here to view the book study schedule for future weeks and a list of resources for teaching basic facts.**

All the best–

Liz Conlin says

The 9’s finger trick in the book isn’t the one I learned. That seems confusing to me. The trick I had learned as a kid, was a 10-1 pattern, but it was never explained to me what that was. I didn’t learn that until I was an adult. Anyway, I never started out teaching the trick.

This summer during a training, I became enlightened to using Cuisenaire rods. They were foreign to me because honestly, I never learned with manipulatives as a young student. I probably would have been better at math if I had! So if anyone has any good strategies to use them, I am all ears! We are requesting them for our grade level this year.

In the past, as a 5th grade teacher, my workstations were really student choice for them to work on what they were having difficulties with and was left up to them to choose based on our school wide timed tests. They monitored where they were and worked on the facts that they needed to pass the next level. The activities varied. There are puzzles, wrap-ups, flashcards, one minute timed tests and partner games.

After reflecting on this book so far, it seems I just need to be a little more direct in assigning my math fluency center. I will be able to do that after knowing where my students are. That is why I sought out this book in the first place. I just didn’t have anything to use to find out where their gaps were in their basic facts because it is becoming clearer that if there are gaps in the basics, there will most likely be gaps in more difficult concepts like adding, subtracting, multiplying and dividing fractions. They need to see the connection from previous learning to new learning. If they are having trouble modeling fractions, it seems the most logical place is to work backwards and see if they are able to model and understand the concepts with whole numbers. I guess I always knew that but didn’t have a way to find out and now I do. 🙂

Adventures in Guided Math says

It sounds like the book has helped you reflect on your current practices and make some great plans for the future. Thanks so much for participating in the book study, Liz!

Ann Elise record says

I’m really not a fan of any tricks since they are designed to just get students a right answer and math is so much more than that! I would much rather talk the student through thinking of 10 times the number and taking one group away using our knowledge of the numbers that make ten for the ones digit. Inevitably a student will tell me, “My mom showed me this great trick!” I tell them I have no problem with them using it if they can explain to me why it works.

Cuisenaire rods are, in my opinion, one of the most powerful manipulatives we can use! I begin having my K and 1 kiddos exploring the commutative property (we call it the turn around principle) as as well as the decomposition of numbers. For example, my kindergarteners will build a 5 house by putting a 5 rod horizonal, then beneath it will be a 4 and a 1, a 3 and 2 and then a 2 and 3 which is when they say, “It’s the turn around principle” with such glee it is adorable! It also encourages students to think of the number as a group of objects rather than a series of ones that they have to count every time.

We then use them to model and teach the math fact strategies as based in this book. I have created a set of videos on how we can use rekenreks, 10 frames, and Cuisenaire rods to teach the students these strategies. Here’s the link:

https://goo.gl/5IlvoM

For multiplication math facts, Cuisenaire rods are perfect to show why x4 is the same as double double and why x8 is double double double, etc.

We then use them to demonstrate the area model of multiplication and division for problems up to 2 dig by 2dig to show why the algorithm works. I’ve also used them to show why the FOIL method words for algebra in high school. Crazy cool!!

I purchased a book by Sue O”Connell called Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students Beyond Memorization on learning Multiplication/Division Math Facts using Strategies and it came with access to tons of games by each strategy. I then created a series of file folders for my teachers so that there would be games for each strategy. We will be implementing math running records at my 3-5 school this year 3 times a year and I’m hoping to get feedback from the students on the games they like best.

At the moment, there isn’t much self-reflection…but that will be changing this year!!

🙂 Ann Elise

Adventures in Guided Math says

Thanks for commenting! I am with you as far as the 9s trick. Having taught fifth grade, it is so important that kids can derive answers using known facts. Kids can learn the 9s trick with a focus on an understanding of the pattern, but I still don’t feel it’s enough of a benefit to outweigh the reliance kids place on the trick. Thanks for sharing your experience using Cuisenaire Rods with your kids. When I did my undergrad over 25 years ago, they were commonplace. I would be curious to know how many programs today integrate them into their methods classes. Susan O’Connell’s books for addition/subtraction and multiplication/division are phenomenal. I too have a crate (for addition/subtraction)–your kids will love the games! I am excited to share her book and materials with my new teaching partner this year! If you haven’t, and ever get a chance to attend one of her workshops, it’s a MUST! I discovered her MANY years ago when I attended a workshop and always like to get her name out there for those who have not heard of her. She has so many resources and has made such a contribution to the field! Again, thanks for sharing! Your kids and teachers are lucky to have you!

Liz Conlin says

Ann Elise, Thank you for the link and the reference to the book. It has been such a long time I used Cuisenaire Rods I am excited to start incorporating them again. I really appreciate your input.

Just curious, how many benchmark tests does your school give students between math and ELA?

Ann Elise record says

Our students need to take Aimsweb and NWEA since we are a Focus and Priority School..we are required to give nationally normed tests and report out the growth at the end of the year. I’m not a fan of the timing of the Aimsweb, though. We will be giving Running Records at my 3-5 school three times this year which is the first time we have done that. Then, I have created my own benchmark test for each grade that has a question for each priority standard from the previous year so that we can be aware of the gaps we need to fill in before we go on to the current gradelevel content. I also created word problem assessments which have one problem for each problem type in add/sub and mult/div. It seems like a lot of testing, but I really want to help teachers differentiate their teaching for fluency, concepts, and word problems. I don’t know any other way than assessing them, analyzing for deficits, and then getting to work in small group time during Guided Math. I also don’t want to overtest the students, so we’ll see what we do once we get going. The standardized computer-based NWEA and paper 8 minute computation test are absolutes.