Math Running Records in Action

A Framework for Assessing Basic Fact Fluency in Grades K-5

Nicki Newton

• Publisher: Taylor & Francis
• Year: 2016
• Print ISBN: 9781138927636
• eBook ISBN: 9781317403005
• Edition: 1
• Topic: Education
• Subtopic: Education General

In this new book from popular consultant and bestselling author Dr. Nicki Newton, you'll discover how to use Math Running Records to assess students' basic fact fluency and increase student achievement. Like a GPS, Math Running Records pinpoint exactly where students are in their understanding of basic math facts and then outline the next steps toward comprehensive fluency. This practical book introduces a research-based framework to assess students' thinking and move them toward becoming confident, proficient, flexible mathematicians with a robust sense of numbers.

Topics include:

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• Learning how often to administer Math Running Records and how to strategically introduce them into your existing curriculum;

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• Analyzing, and interpreting Math Running Records for addition, subtraction, multiplication, and division;

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• Using the data gathered from Math Running Records to implement evidence-based, research-driven instruction.

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• Evaluating students' speed, accuracy, flexibility, and efficiency to help them attain computational fluency;

Each chapter offers a variety of charts and tools that you can use in the classroom immediately, and the strategies can easily be adapted for students at all levels of math fluency across grades K-8. Videos of sample running records are also available for download at https://guidedmath.wordpress.com/math-running-records-videos.

Blackline masters are available on the Running Records Dropbox at https://bit.ly/3gnggIq

1 Math Running Records A Framework for Fluency

DOI: 10.4324/9781315682389-3

Yet a funny thing happens on the way to those final assessments: day-today learning takes place. I am certain that, in education, evaluation needs to pay more attention to the systematic observation of learners who are on their way to those final assessments.

(Clay, 1987, p. 1)

A Math Running Record in Action

Dr. Nicki

What about when you got to 6 times 7?

Josh

I had to practice that one a lot and a lot. I just count by 7s or I go by touchdowns cuz I love football. I figure out the scores easily and it goes in a pattern.

Dr. Nicki

Tell me a little bit more about that I don’t know about football. But if that is going to help me with my 6s …

Josh

If you make a touchdown it’s 6 and then the field goal is 1 and that is 7. And then you just keep counting by 7 and 7 and 7 and that’s how I figured that one out because I had been practicing that one for a long time cuz a lot of games usually at least one team had about that many points …

Dr. Nicki

Oh alright.

Josh

And I keep practicing it and saying it … that over and over and over again and I figure it out ….

Dr. Nicki

If I said what’s 4 × 7 what would you do?

Josh

I’d just go by the touchdowns 7, 14, 21, 28.

Dr. Nicki

Oh wow so football really helps you here.

Josh

Yea, football is a lot of help in math and it is a lot of fun to watch.

Dr. Nicki

Yea, that’s what they tell me.

Josh

I love football.

*

Students use a variety of strategies. When we are trying to figure out what they know and do not yet know, we need to understand their thinking. Math Running Records help us to know what students know about their facts. As we administer them, we notice a variety of things that students are doing and saying while answering questions about the basic math facts. Math Running Records help to make students’ thinking visible. We can see if they have automaticity, if they are accurate, if they take a long time but eventually get the right answer. We can see if they self correct, if they are guessing or if they are using inefficient strategies. We can also see what they do when they get stuck.

Video 1.1.

Just like reading running records, “only when [Math Running] Records are used in standard ways with standard recording and scoring procedures will they provide a reliable and valid assessment of” students’ mathematical proficiency (Clay, 2002). Teachers should use Math Running Records on a consistent basis to record what progress children are making, assess and group children, and determine specific interventions that match individual student fluency levels.

There are different ways for a teacher to look at children’s math understanding, including standardized tests, quizzes, interviews, entrance and exit slips. However, a Math Running Record allows the teacher to get up under all that data, it allows for a 3D view—a layered profile of a mathematical learner. It’s a dynamic view because it allows teachers to interact with the information and design instruction so that it is in tune with the learner. Math Running Records give crucial feedback on how students are responding to instruction. “In every way the information produced by systematic observation reduces our uncertainties and improves our instruction” (Clay, 2005a, p. 3).

What Are Math Running Records?

A Math Basic Fluency Running Record is an assessment of fluency with basic facts. It is a three-part oral assessment. Taken in a systematic way, a Math Running Record provides evidence of a child’s computational thinking. It tells us how automatic a student is when thinking about facts as well as the accuracy level the student has, what the strategic level of competence is and how efficient the student is. Math Running Records also help to look at where students are having difficulty by counting the student’s errors and self-corrections. We must think about the problems that challenged the student, the answers they gave, and what the student did when they got stuck. A Math Fluency Running Record also provides evidence of students’ mathematical behaviors. Math Fluency Running Records help teachers determine the exact level of instruction for students and make sure they are progressing towards fluency in a scaffolded, effective, differentiated manner.

Research Note

The National Math Report notes that “the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts” (National Mathematics Advisory Panel, 2008, p. 11) are all critical aspects of learning math. These elements are all important, no one taking precedence over the other.

Who Should Take Math Running Records and When Should They Do Them?

All students should take Math Running Records at the beginning, middle, and end of the year. It gives an instant snapshot of the fluency levels. Above-level students should take running records every six to eight weeks. On-level students should take running records about once a month. Below-level students should take running records every two to three weeks.

A student named Jeff proves a clear example of why Math Running Records should be given to all students. Jeff was a student in a “gifted” 4th Grade classroom. He told me that he knew all of his facts. I gave him a Multiplication Running Record and he indeed knew most of them. When he got to his 12s, he began to move extremely slowly. When asked what he was doing, he said counting up. We talked about how that was not the most efficient strategy and that given the fact that he knew all of his other facts, he could use some more efficient strategies. We discussed doubling his 6s, or using his 10s and 2s. He decided to think about it and we agreed to meet in a couple of weeks to see how he was coming along. I would have never known about his inefficient thinking had I not given him a running record. I would have gone on believing that he “knew” his facts. And he did, superficially. Once students just learn the facts without understanding, they are often very resistant to building understanding. It has to be planned in a scaffold manner from the start (Hiebert, 1999). The teaching of the facts should be done in a way that focuses on structure of numbers, patterns, place value, properties and the relationship between the operations (NRC, 2001, 2005, 2012).

Research Note

Mastery of basic facts is a sticky proposition in most classrooms. Although most state standards mandate proficiency with addition and sub traction by 2nd Grade and multiplication and division by 4th Grade, students are all over the place. Some are counting up/on, some are using number relationships and mental math strategies while others have automaticity. Research has found that children generally use a variety of strategies for a long time, even after they have learned the more efficient ones (Siegler & Jenkins, 1989).

To add to this, in the upper elementary grades, you still have some students stuck with lower level strategies like finger counting and head bobbing.

Assess students where you think they might be beginning. So for example, you might not test a 5th grader on addition facts—but then again, you might. Depending on the student and the circumstances.

Once you have collected the data, it is a matter of addressing the individual needs of the students through differentiated activities and games.

Know where your students are so you can make meaningful decisions about where they need to go next to achieve full proficiency.

Why Do Math Running Records?

Running records are specifically done to target and improve student achievement. Teachers need evidence-based measures to find, analyze, and implement scaffolded, standards-based, effective basic fact fluency interventions. Math Running Records provide this type of evidence. They allow teachers to get very specific about the areas of need and very intentional about programs of study that address these needs. For example, a teacher might find that Joey needs to learn his 3 times tables, although he self-reported that he was struggling with his 6s, the Math Running Record revealed that he was struggling with his 3s. So the intentional intervention plan would start Joey practicing his 3s before he moves on to practicing his 6s. Math Running Records are taken to find specific basic fluency levels of automaticity, accuracy as well as flexibility and efficiency.

Another example is Maria. When I probed into her use of strategies, I found that she was using a hybrid strategy that consisted of first using a derived fact and then counting up by 1s (Sherin & Fuson, 2005).

Dr. Nicki

What do you do when you see 8 × 7?

Maria

I use my 5s. I know that 8 × 5 is 40. And then I count up from there.

Dr. Nicki

Can you show me exactly what you do? Count out loud so I can see how you count.

Maria

I go 40 … 41, 42, 43, 44, 45, 46, 47, 48 … 49, 50, 51, 52, 53, 54, 55, 56 …

The math coach and I were both astounded. Here was a student who knew how to decompose numbers and use friendly numbers but then resorted to a highly inefficient strategy once getting to the friendly number. She used a count all strategy. Wow! And she wasn’t the only student who did this. This just brings home the usefulness of a Math Running Record. Teachers can see a more complete picture than a timed test gives. A timed test might have left me with th...

Table of contents

• Cover Page
• Half Title Page
• Series Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Running Record Videos
• Meet the Author
• Foreword
• Acknowledgements
• Introduction
• SECTION I Math Running Records: Overview
• 1 Math Running Records: A Framework for Fluency
• 2 Parts of a Math Running Record
• Section II The Addition Running Record
• 3 The Addition Math Running Record
• 4 Analyzing and Interpreting the Addition Running Record: How to Record and Describe What You See and Hear
• 5 Implications for Teaching Addition: Purposeful Practice
• Section III The Subtraction Running Record
• 6 The Subtraction Math Running Record
• 7 Analyzing and Interpreting the Subtraction Running Record: How to Record and Describe What You See and Hear
• 8 Implications for Teaching Subtraction: Purposeful Practice
• Section IV The Multiplication Running Record
• 9 The Multiplication Math Running Record
• 10 Analyzing and Interpreting the Multiplication Running Record: How to Record and Describe What You See and Hear
• 11 Implications for Teaching Multiplication: Purposeful Practice
• Section V The Division Running Record
• 12 The Division Math Running Record
• 13 Analyzing and Interpreting the Division Running Record: How to Record and Describe What You See and Hear
• 14 Implications for Teaching Division: Purposeful Practice
• Section VI Frequently Asked Questions
• 15 FAQs