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From Teaching Children Mathematics Mar. 2004

In this article, the author, Lisa Buchholz talks about her interest in helping her second graders improve their fact fluency. After doing some research, she decides to focus on strategies such as doubles and doubles plus one, Each day her class would focus on an aspect of the strategy. On day one, they would use manipulatives to make equations. On day two, they would write about real world situations where they might see the strategy. On the third day, they would write in their math journals. By taking time to make sure the students truly internalized the strategy, not only did all her students improve in fact fluency, but also developed a deeper understanding of  number sense.

Possible classroom application: Carve a few minutes of math instruction each day to focus on specific strategies.

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Gina Kling of WSU recommends to reduce the number of facts a student has to learn, focus on strategies like =0, 1 more, doubles,

near doubles, make a ten, and +10. Stop having students practice facts in isolation.

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Faster Isn't Smarter by Cathy Seely 2009

Cathy Seely discusses the negative aspects of timed fluency tests. In one scenario, a student was unable to complete a timed fluency test, then went on to effortlessly solve a puzzle with the same equations used on the test. He was put into a remediation group and his self-esteem damaged.  It is time for students to stop connecting fluency with speed. Seely states, "Some of the world's greatest thinkers, scientists, and mathematicians have not been fast at arithmetic, even though they were tremendously successful in working with higher level mathematics.'

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Families Ask: Rules or Understanding? by Sherri Martinie

Published in Mathematics Teaching in the Middle School.

This article focuses on how math is learned at the middle school level, but has several key ideas that connect to math fact fluency. Sherri Martinie discusses the difference between procedural and conceptual fluency and the importance of learning beyond rote memory. In this article, she sites a study done by Pesek and Kirschner: " initial rote learning of a concept can create interference to later meaningful learning." For students to best learn, they must actively participate in meaningful and engaging activities. When read with some of the other articles posted, this does apply to my research. The common theme in the articles seem to be moving past memorization and encourage students to discover number patterns of build their foundational knowledge on.

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The Road to Fluency and the License to Think by Lisa Buchholz

Published in Teaching Children Mathematics March 2004

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Fluency with Basic Addition by Gina Kling

Teaching Children Mathematics September 2011

Gina Kling encourages the use of specific strategies that will develop more complex mathematical thinking. Students who memorize facts often forget some and revert back to immature strategies such as counting. Kling believes, " a student who needs a few seconds to work through a meaningful strategy to derive a fact a fact is certainly more efficient (and employing better mathematical thinking) than a student who must resort to counting to figure out the unknown." She also encourages the careful development of number sense with dots, 5 frames, and 10 frames.

Possible classroom application: Use fluency focused games such as tens Go Fish where the students look for pairs of numbers that add to ten.

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"Assessing Basic Fact Fluency" by Gina Kling and Jennifer Bay-Williams

Published in Teaching Children Mathematics April 2014, Vol. 20, No. 8

Gina Kling is a professor at Western Michigan University and a lead researcher in math fact fluency. Her work is referenced by many of the other authors and is considered an expert in this field.

Kling agrees with Arthur Baroody about the inappropriate and negative influence of using timed tests to determine fact fluency. Timed math tests establish test anxiety in students as young as first grade. She also redefines fluency as being separate from speed and more to do with comprehension. Kling advocates for the use of the fluency interview instead of the fluency test. It allows children to explain their thinking and demonstrate the use of strategies.  She also feels teachers should use other formative assessments such as observation and journaling. Like Buchholz, she feels students should focus on specific strategies such as plus one, plus two, and doubles to reduce the number of facts students need to learn. She does not feel memorization is appropriate. Finally, Kling encourages teachers to use meaningful games to reinforce strategies that will foster students success.

Possible classroom application: Use games during fluency practice, stations, and intervention time. Students state not only the answer to an equation, but how they found the answer. This is a great way to encourage math talk.

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"Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them" by Arthur Baroody

Published in Teaching Children Mathematics

August 2006

This article was shared with me last year by Laura Chambliss during a professional development called Math Fluency for All. Laura is our math expert and does professional training through the St. Clair County RESA.

Arthur Baroody is a leading expert in math fact fluency and his name is referenced in several of the articles I found. Baroody talks about the three phases of mastering basic number combinations. To be fluent, a student must work through all three phases or strategies: counting, reasoning, and mastery. To help students move from phase one into two, he recommends students look at the patterns and relationships of numbers instead of rote memorization.

He feels children need to be given the opportunity to develop a "rich grasp of number and arithmetic patterns and relationships." Children should not look explore facts in an isolated manner, but as a collection of "interconnected ideas." He also advocates practice that will encourage children to discover the patterns and relationships mentioned earlier and the abandonment of "drill and kill."

Possible classroom application: Baroody shares the Road Hog Car Race Game which encourages students to compose and decompose numbers which will strengthen their understanding of number relationships.

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From Teaching Children Mathematics Nov. 2014, Vol. 21, No. 4

Gina Kling discusses the 3 phases a student must experience to develop mastery of basic math facts. She discusses the explicit teaching of strategies such as doubles and doubles plus one, but emphasizes the support of student thinking. Kling states that students need meaningful ways to practice the strategies and games are one of the best ways to do it. While playing fluency games, students should be applying strategies and discussing how they figured out an answer. Some aspects of fluency are developmental and can be helped along by playing targeted skill games.

Possible classroom application: Kling talks about a game called Top-It. It is similar to War. The students each flip one card at the same time. The first to find the sum takes the cards. To make this even more meaningful, students should tell the strategy they used.

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From Education Week, published online July 3, 2012

Jo Boaler, a Stanford math professor, writes this commentary to highlight the discrepancy between current research on the damaging aspects of timed fluency testing and how schools continue to use it. More women than men suffer from math anxiety and 50% of the U.S. population suffers from it. The stress of a timed test impedes the function of working memory and impairs student performance. She feels that we equate success in math with working quickly instead of thinking deeply.

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Response to Hes: As I began my reading on the topic,

these reasons were possible barriers I thought my students

may need to overcome to master the basic facts.

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This is a link to fact fluency related videos. This link is from the Developing Fact Fluency presentation.

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When young children first start to add and subtract they have to model every part of the problem. This stage of development is known as Direct Modeling. For a problem like 6+5, a direct modeler would count out 6 objects, count out 5 objects, and then recount them all starting back at 1. This is an important stage of development and allows children lots of practice with counting and one-to-one tagging (tagging each object with only one number name), however we do not want children to stay in this stage for long.

Watch examples of children in the Direct Modeling Stage:

After direct modeling, children progress into the Counting stage. Unfortunately this is the stage that too many children get stuck in and never quite move out of. For the problem 6+5, a counter would hold the "6" in their head and count on from there. We tend to move children straight from counting to just memorizing their facts. However, if a child cannot remember a certain fact they slide back down to the counting stage. Instead of jumping straight to memorizing facts after the counting stage, research shows that if you help children develop flexibility and relationships around facts the memorization will come naturally after this Derived Fact stage. Derived facts are when kids use facts they know to help them with facts they do not know. While kids are in the counting stage we should be providing them with manipulatives like Ten Frames and MathRacks which help children see these derived facts:

Using Doubles
The doubles facts (2+2, 3+3, etc.) tend to be the first facts that kids have memorized. These facts happen in nature and we see them in our daily lives. Helping kids connect the symbolic fact to things they see in everyday life will help these facts become easily recalled. Here are just a few ideas:

1+1 are the front and back wheel of a bicycle
2+2 are the 2 wheels in front and back of a 4-wheeler
3+3 are the legs on insects
4+4 are the legs on a spider
5+5 are their fingers on each hand
6+6 are eggs in a dozen
7+7 are the days in two weeks or football scores
8+8 are crayons in a 16 count box or the number of pawns in a chess game
9+9 are the wheels on an 18-wheeler truck or holes on a golf course
10+10 are your fingers and toes

Watch this video of 3rd, 2nd, and 1st graders using Doubles facts to help them with other facts.

Making 10
Because 10 is such an integral part of our number system, it is essential that children know the numbers that combine together to make 10 (which then helps them as they get to multi-digit numbers and making the next "10", i.e. 43 + 7 makes 50). Using manipulatives like the Ten Frames or MathRacks help children see how many more to make 10 as they are adding numbers. For instance, when solving 7 + 8 using the MathRack, children will move over the 7 beads and then they might see the 3 beads remaining on the top row to make a full row of 10 and then add 5 more on the bottom row:

This strategy hasn't become as popular as Doubles and Make 10 in textbooks, but children invent this strategy on their own when they use manipulatives like Ten Frames and MathRacks. The picture below is using Ten Frames to show 6 + 7:

Kids who use Ten Frames and MathRacks begin to see the groups of 5 within each number. So to solve 6+7, they pull out the two full rows of 5 to make 10 and then add the extra 1 and 2 from the bottom rows.

Watch this video of 2nd & 3rd graders Finding Fives to help them with other facts.

These facts are essentially understanding the teen numbers (10+1, 10+2, 10+3, etc.). When kids see these problems they should instantly know the answer because our teen numbers are just ten plus some more. However, too many kids count on to solve these problems. One of the issues comes from our words for these numbers; eleven, twelve, and thirteen do not help children see the 10 and some more in the number. The words for 11, 12, 13, etc in some other languages are actually their words for 10 and 1, 10 and 2, etc. This starts those kids off from the beginning with the understanding that 11 is 10 and 1. So, we have to do a lot to help children build that connection.

Watch this video of 1st, 2nd, & 3rd graders using, andnot using, the 10 plus Something facts.

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When young children first start to add and subtract they have to model every part of the problem. This stage of development is known as Direct Modeling. For a problem like 6+5, a direct modeler would count out 6 objects, count out 5 objects, and then recount them all starting back at 1.

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From

Teaching Children Mathematics September 2005

At first, I wasn't sure if this article was applicable to my research because the focus was on fourth graders. As I read, I discovered the authors were looking for a way to improve number sense and basic fact fluency that these students should have mastered in first grade. The authors use the same approach of Baroody, Kling, and Buchholz by focusing on specific strategies that develop procedural fluency. hey break down the learning into two categories: repetitive and varied practice. Repetitive practice is the "drill and kill" activities that encourage mindless memorization. Varied practice focuses on developing strategies and engaging in meaningful activities. At the end of the study, the students who engaged in varied practice made large gains in fact fluency and developed math thinking. The authors state that explicit teaching of fact fluency strategies are not common in the United States like in other areas of the world.

Possible classroom application: Focus on strategies such as plus zero, plus one, doubles, near doubles, make a ten, and add ten.

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Developing Fact Fluency is very interesting and I especially liked that it provided you with the three reasons kids don't become fluent. That could help you decide on the intervention you might use.

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From Instructor Mar/Apr 2007

Marilyn Burns talks about the importance of strategies in the use of mental math. Her "hands on the table" math sounds like an interesting idea and would certainly encourage the use of math talk and the develop number sense, but I'm not sure this article has a clear enough connection to my research.

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From Mathematicallyminded.com

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Why are some students able to master addition facts faster than others? Time on task, support/practice at home, memorization, meaningful connection?

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Define fluent: Is it knowing the answer within three seconds without using counting strategies or should it be expanded to accommodate students with learning disabilities?

Read Fluency: Simply Fast and Accurate? I think not! by NCTM President Linda M. Gojack (Nov. 1, 2012)

Linda Gojack is the president of the National Council of Teachers of Mathematics. She stresses the importance of not relating fluency with speed, but with accuracy and flexible thinking. When faced with the stress of timed tests, most students revert to immature strategies such as counting (which they can do accurately and quickly).

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I am interested in finding an intervention that will improve my 1st grade students addition fact fluency.