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List of References for my Literature Review Paper

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Minilessons for Addition and Subtraction

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Strategies and Tricks for Learning Basic Math Facts

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Useful addition and subtraction strategies and tricks that will help children memorize addition and subtraction facts. Includes worksheets and flashcards.

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Strategies for Math

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Nine Ways to Catch Kids Up

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November 2007 | Volume 65 | Number 3
Making Math Count Pages 16-21

Marilyn Burns

Paul, a 4th grader, was struggling to learn multiplication. Paul's teacher was concerned that he typically worked very slowly in math and "didn't get much done." I agreed to see whether I could figure out the nature of Paul's difficulty. Here's how our conversation began:

Marilyn: Can you tell me something you know about multiplication?

Paul: [Thinks, then responds] 6 × 8 is 48.

Marilyn: Do you know how much 6 × 9 is?

Paul: I don't know that one. I didn't learn it yet.

Marilyn: Can you figure it out some way?

Paul: [Sits silently for a moment and then shakes his head.]

Marilyn: How did you learn 6 × 8?

Paul: [Brightens and grins] It's easy-goin' fishing, got no bait, 6 × 8 is 48.

As I talked with Paul, I found out that multiplication was a mystery to him. Because of his weak foundation of understanding, he was falling behind his classmates, who were multiplying problems like 683 × 4. Before he could begin to tackle such problems, Paul needed to understand the concept of multiplication and how it connects to addition.

Paul wasn't the only student in this class who was floundering. Through talking with teachers and drawing on my own teaching experience, I've realized that in every class a handful of students are at serious risk of failure in mathematics and aren't being adequately served by the instruction offered. What should we do for such students?

Grappling with Interventions

My exchange with Paul reminded me of three issues that are essential to teaching mathematics:

It's important to help students make connections among mathematical ideas so they do not see these ideas as disconnected facts. (Paul saw each multiplication fact as a separate piece of information to memorize.)

It's important to build students' new understandings on the foundation of their prior learning. (Paul did not make use of what he knew about addition to figure products.)

It's important to remember that students' correct answers, without accompanying explanations of how they reason, are not sufficient for judging mathematical understanding. (Paul's initial correct answer about the product of 6 × 8 masked his lack of deeper understanding.)

For many years, my professional focus has been on finding ways to more effectively teach arithmetic, the cornerstone of elementary mathematics. Along with teaching students basic numerical concepts and skills, instruction in number and operations prepares them for algebra. I've developed lessons that help students make sense of number and operations with attention to three important elements-computation, number sense, and problem solving. My intent has been to avoid the "yours is not to question why, just invert and multiply" approach and to create lessons that are accessible to all students and that teach skills in the context of deeper understanding. Of course, even well-planned lessons will require differentiated instruction, and much of the differentiation needed can happen within regular classroom instruction.

But students like Paul present a greater challenge. Many are already at least a year behind and lack the foundation of mathematical understanding on which to build new learning. They may have multiple misconceptions that hamper progress. They have experienced failure and lack confidence.

Such students not only demand more time and attention, but they also need supplemental instruction that differs from the regular program and is designed specifically for their success. I've recently shifted my professional focus to thinking about the kind of instruction we need to serve students like Paul. My colleagues and I have developed lessons that provide effective interventions for teaching number and operations to those far behind. We've grappled with how to provide instruction that is engaging, offers scaffolded instruction in bite-sized learning experiences, is paced for students' success, provides the practice students need to cement fragile understanding and skills, and bolsters students' mathematical foundations along with their confidence.

In developing intervention instruction, I have reaffirmed my longtime commitment to helping students learn facts and skills-the basics of arithmetic. But I've also reaffirmed that "the basics" of number and operations for all students, including those who struggle, must address all three aspects of numerical proficiency-computation, number sense, and problem solving. Only when the basics include understanding as well as skill proficiency will all students learn what they need for their continued success.

Essential Strategies

I have found the following nine strategies to be essential to successful intervention instruction for struggling math learners. Most of these strategies will need to be applied in a supplementary setting, but teachers can use some of them in large-group instruction.

1. Determine and Scaffold the Essential Mathematics Content

Determining the essential mathematics content is like peeling an onion-we must identify those concepts and skills we want students to learn and discard what is extraneous. Only then can teachers scaffold this content, organizing it into manageable chunks and sequencing these chunks for learning.

For Paul to multiply 683 × 4, for example, he needs a collection of certain skills. He must know the basic multiplication facts. He needs an understanding of place value that allows him to think about 683 as 600 + 80 + 3. He needs to be able to apply the distributive property to figure and then combine partial products. For this particular problem, he needs to be able to multiply 4 by 3 (one of the basic facts); 4 by 80 (or 8 × 10, a multiple of 10); 4 and by 600 (or 6 × 100, a multiple of a power of 10). To master multidigit multiplication, Paul must be able to combine these skills with ease. Thus, lesson planning must ensure that each skill is explicitly taught and practiced.

2. Pace Lessons Carefully

We've all seen the look in students' eyes when they get lost in math class. When it appears, ideally teachers should stop, deal with the confusion, and move on only when all students are ready. Yet curriculum demands keep teachers pressing forward, even when some students lag behind. Students who struggle typically need more time to grapple with new ideas and practice new skills in order to internalize them. Many of these students need to unlearn before they relearn.

3. Build in a Routine of Support

Students are quick to reveal when a lesson hasn't been scaffolded sufficiently or paced slowly enough: As soon as you give an assignment, hands shoot up for help. Avoid this scenario by building in a routine of support to reinforce concepts and skills before students are expected to complete independent work. I have found a four-stage process helpful for supporting students.

In the first stage, the teacher models what students are expected to learn and records the appropriate mathematical representation on the board. For example, to simultaneously give students practice multiplying and experience applying the associative and commutative properties, we present them with problems that involve multiplying three one-digit factors. An appropriate first problem is 2 × 3 × 4. The teacher thinks aloud to demonstrate three ways of working this problem. He or she might say,

I could start by multiplying 2 × 3 to get 6, and then multiply 6 × 4 to get 24. Or I could first multiply 2 × 4, and then multiply 8 × 3, which gives 24 again. Or I could do 3 × 4, and then 12 × 2. All three ways produce the same product of 24.

As the teacher describes these operations, he or she could write on the board:

It's important to point out that solving a problem in more than one way is a good strategy for checking your answer.

In the second stage, the teacher models again with a similar problem-such as 2 × 4 × 5-but this time elicits responses from students. For example, the teacher might ask, "Which two factors might you multiply first? What is the product of those two factors? What should we multiply next? What is another way to start?" Asking such questions allows the teacher to reinforce correct mathematical vocabulary. As students respond, the teacher again records different ways to solve the problem on the board.

During the third stage, the teacher presents a similar problem-for example, 2 × 3 × 5. After taking a moment to think on their own, students work in pairs to solve the problem in three different ways, recording their work. As students report back to the class, the teacher writes on the board and discusses their problem-solving choices with the group.

In the fourth stage, students work independently, referring to the work recorded on the board if needed. This routine both sets an expectation for student involvement and gives learners the direction and support they need to be successful.

4. Foster Student Interaction

We know something best once we've taught it. Teaching entails communicating ideas coherently, which requires the one teaching to formulate, reflect on, and clarify those ideas-all processes that support learning. Giving students opportunities to voice their ideas and explain them to others helps extend and cement their learning.

Thus, to strengthen the math understandings of students who lag behind, make student interaction an integral part of instruction. You might implement the think-pair-share strategy, also called turn and talk. Students are first asked to collect their thoughts on their own, and then talk with a partner; finally, students share their ideas with the whole group. Maximizing students' opportunities to express their math knowledge verbally is particularly valuable for students who are developing English language skills.

5. Make Connections Explicit

Students who need intervention instruction typically fail to look for relationships or make connections among mathematical ideas on their own. They need help building new learning on what they already know. For example, Paul needed explicit instruction to understand how thinking about 6 × 8 could give him access to the solution for 6 × 9. He needed to connect the meaning of multiplication to what he already knew about addition (that 6 × 8 can be thought of as combining 6 groups of 8). He needed time and practice to cement this understanding for all multiplication problems. He would benefit from investigating six groups of other numbers-6 × 2, 6 × 3, and so on-and looking at the numerical pattern of these products. Teachers need to provide many experiences like these, carefully sequenced and paced, to prepare students like Paul to grasp ideas like how 6 × 9 connects to 6 × 8.

6. Encourage Mental Calculations

Calculating mentally builds students' ability to reason and fosters their number sense. Once students have a foundational understanding of multiplication, it's key for them to learn the basic multiplication facts-but their experience with multiplying mentally should expand beyond these basics. For example, students should investigate patterns that help them mentally multiply any number by a power of 10. I am concerned when I see a student multiply 18 × 10, for example, by reaching for a pencil and writing:

Revisiting students' prior work with multiplying three factors can help develop their skills with multiplying mentally. Helping students judge which way is most efficient to multiply three factors, depending on the numbers at hand, deepens their understanding. For example, to multiply 2 × 9 × 5, students have the following options:

Guiding students to check for factors that produce a product of 10 helps build the tools they need to reason mathematically.

When students calculate mentally, they can estimate before they solve problems so that they can judge whether the answer they arrive at makes sense. For example, to estimate the product of 683 × 4, students could figure out the answer to 700 × 4. You can help students multiply 700 × 4 mentally by building on their prior experience changing three-factor problems to two-factor problems: Now they can change a two-factor problem-700 × 4-into a three-factor problem that includes a power of 10-7 × 100 × 4. Encourage students to multiply by the power of 10 last for easiest computing.

7. Help Students Use Written Calculations to Track Thinking

Students should be able to multiply 700 × 4 in their heads, but they'll need pencil and paper to multiply 683 × 4. As students learn and practice procedures for calculating, their calculating with paper and pencil should be clearly rooted in an understanding of math concepts. Help students see paper and pencil as a tool for keeping track of how they think. For example, to multiply 14 × 6 in their heads, students can first multiply 10 × 6 to get 60, then 4 × 6 to get 24, and then combine the two partial products, 60 and 24. To keep track of the partial products, they might write:

14 × 6

10 × 6 = 60

4 × 6 = 24

60 + 24 = 84

They can also reason and calculate this way for problems that involve multiplying by three-digit numbers, like 683 × 4.

8. Provide Practice

Struggling math students typically need a great deal of practice. It's essential that practice be directly connected to students' immediate learning experiences. Choose practice problems that support the elements of your scaffolded instruction, always promoting understanding as well as skills. I recommend giving assignments through the four-stage support routine, allowing for a gradual release to independent work.

Games can be another effective way to stimulate student practice. For example, a game like Pathways (see Figure 1 for a sample game board and instructions) gives students practice with multiplication. Students hone multiplication skills by marking boxes on the board that share a common side and that each contain a product of two designated factors.

Figure 1. Pathways Multiplication Game

9. Build In Vocabulary Instruction

The meanings of words in math-for example, even, odd, product, and factor -often differ from their use in common language. Many students needing math intervention have weak mathematical vocabularies. It's key that students develop a firm understanding of mathematical concepts before learning new vocabulary, so that they can anchor terminology in their understanding. We should explicitly teach vocabulary in the context of a learning activity and then use it consistently. A math vocabulary chart can help keep both teacher and students focused on the importance of accurately using math terms.

When Should We Offer Intervention?

There is no one answer to when teachers should provide intervention instruction on a topic a particular student is struggling with. Three different timing scenarios suggest themselves, each with pluses and caveats.

While the Class Is Studying the Topic

Extra help for struggling learners must be more than additional practice on the topic the class is working on. We must also provide comprehensive instruction geared to repairing the student's shaky foundation of understanding.

The plus: Intervening at this time may give students the support they need to keep up with the class.

The caveat: Students may have a serious lack of background that requires reaching back to mathematical concepts taught in previous years. The focus should be on the underlying math, not on class assignments. For example, while others are learning multidigit multiplication, floundering students may need experiences to help them learn basic underlying concepts, such as that 5 × 9 can be interpreted as five groups of nine.

Before the Class Studies the Topic

Suppose the class is studying multiplication but will begin a unit on fractions within a month, first by cutting out individual fraction kits. It would be extremely effective for at-risk students to have the fraction kit experience before the others, and then to experience it again with the class.

The plus: We prepare students so they can learn with their classmates.

The caveat: With this approach, struggling students are studying two different and unrelated mathematics topics at the same time.

After the Class Has Studied the Topic.

This approach offers learners a repeat experience, such as during summer school, with a math area that initially challenged them.

The plus: Students get a fresh start in a new situation.

The caveat: Waiting until after the rest of the class has studied a topic to intervene can compound a student's confusion and failure during regular class instruction.

How My Teaching Has Changed

Developing intervention lessons for at-risk students has not only been an all-consuming professional focus for me in recent years, but has also reinforced my belief that instruction-for all students and especially for at-risk students-must emphasize understanding, sense making, and skills.

Thinking about how to serve students like Paul has contributed to changing my instructional practice. I am now much more intentional about creating and teaching lessons that help intervention students catch up and keep up, particularly scaffolding the mathematical content to introduce concepts and skills through a routine of support. Such careful scaffolding may not be necessary for students who learn mathematics easily, who know to look for connections, and who have mathematical intuition. But it is crucial for students at risk of failure who can't repair their math foundations on their own.

Marilyn Burns is Founder of Math Solutions Professional Development, Sausalito, California; 800-868-9092; mburns@mathsolutions.com.

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November 2007 | Volume 65 | Number 3 Making Math Count Pages 16-21 Marilyn Burns Paul, a 4th grader, was struggling to learn multiplication. Paul's teacher was concerned that he typically worked very slowly in math and "didn't get much done." I agreed to see whether I could figure out the nature of Paul's difficulty.

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Promoting Meaningful Mastery of Addition and Subtraction

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Fluency with Basic Addition Facts

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Mastering the Basic Number Combinations

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Developing Automatic Recall of Addition and Subtraction Facts

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Developing Automatic Recall of Addition and Subtraction Facts | LD OnLine

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LD OnLine is the leading website on learning disabilities, learning disorders and differences. Parents and teachers of learning disabled children will find authoritative guidance on attention deficit disorder, ADD, ADHD, dyslexia, dysgraphia, dyscalculia, dysnomia, reading difficulties, speech and related disorders.

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Learning Strategies for Addition and Subtraction Facts

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Teacher as Researcher-Literature Review of Action Research Project

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Developing Automatic Recall of Facts

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Technology-Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development

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Technology-Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development | LD Topics | LD OnLine

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LD OnLine is the leading website on learning disabilities, learning disorders and differences. Parents and teachers of learning disabled children will find authoritative guidance on attention deficit disorder, ADD, ADHD, dyslexia, dysgraphia, dyscalculia, dysnomia, reading difficulties, speech and related disorders.

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Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities

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instruction of students with mathematical disabilities

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conceptual basis of automaticity research in mathematics

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Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities | LD Topics | LD OnLine

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This article demonstrates how the number sense concept can offer a useful framework for conceptualizing interventions that will significantly enhance mathematics instruction for students with mathematical disabilities.

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Reinforcing the Basic Facts—while learning new mathematical concepts

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Aha! On-line Math

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Strategies for Learning Math Facts

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Helping Children Learn Their Math Facts

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Helping Children Learn Math Facts | Education.com

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Setting up a math facts program will help your child to develop fluency if they are struggling in math.

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How to Help Struggling Learners with their Math Facts

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Adding and Subtracting-Creative ways to increase fluency

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Teachers have lots of creative ways to increase fluency in these two basic computations.

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Beyond the Drill:
Elementary Math Software That Makes Kids Think

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Spring 2004 | Volume 13 | Number 3
Technology for the Math Classroom

Elementary Math Software That Makes Kids Think

Mary Santilli

Want to get elementary students excited about mathematics and have them acquire technological savvy at the same time? Here are some excellent resources for the classroom computer or for the entire computer lab in your school. Math Arena, Ten Tricky Tiles, and The Logical Journey of the Zoombinis are three software selections that will enrich any math class. These programs, along with calculators and superior Web sites, can help make math class an engaging and exciting place to learn.

Keep Them Coming Back for More

For grades 2-5, Math Arena by Sunburst is a terrific tool for most concepts covered in the upper elementary grades. Math Arena offers a collection of 10 Time Trials and 10 BuZZin activities that will keep students interested and coming back to learn more. Children have the opportunity to compete against a clock or another player. They even have the choice to turn off the timer to explore problems and develop strategies at their own pace. Once students develop confidence and skills, they can modify the level of play to attempt more challenging problems. Players accumulate points as they go through the program, allowing a teacher to easily follow a child's progress.

Favorite Math Arena Time Trials include the following:

Array Reversal requires students to create multiplication arrays within a 100 frame. They must try to cover the grid without any spaces or gaps.

Flipster asks students to use geometric flips, slides, and rotations to match a given tile with the same pattern that is positioned differently within a 3×3 grid of randomly arranged characters.

Percent Crossing challenges students by altering the percent of height increases or decreases necessary for a bug to cross between moving platforms. This is perfect for students exploring decimals and percents.

The Splat Degree challenge uses a flyswatter rotating at 15-degree intervals. The goal is to swat the fly in the fewest moves possible. Students develop meaningful strategies for understanding spatial sense in relation to degree of angle and have a lot of fun in the process.

Whereas Math Arena's Time Trial activities are centered on problem solving, the BuZZin activities focus on predicting, estimating, identifying number relationships, and computation in activities such as Fraction/Match, Equalizer, and Budget Breaker. Other BuZZin activities include

The Predictor. This activity focuses on probability, but with a novel twist. Children buzz in when they think they have enough information to predict how many of the 100 flowers will be blue as the garden blooms one flower at a time. This is a great activity for teaching percentages.

The Price Slasher. This game, everything is on sale. This activity is great for calculating varying percentages off of given amounts.

Finally, Math Arena throws a curve ball at the experienced user with the Tri-Mathlon. Here, students experience a series of three 30-second Time Trials or BuZZins played in succession. A teacher management tool is available to create reports on individual students or teams for any or all of the activities.

A Home Run for Computation

Ten Tricky Tiles, originally developed by Marcy Cook, helps children understand number puzzles and offers gentle assistance when necessary. The activities on this disc include Addition & Subtraction, Balance Tiles, and Crossword Tiles. In the Addition & Subtraction game, students are given five number sentences, both vertically and horizontally oriented, with many missing addends and subtrahends. Operations are identified for students to determine values. Students decide where to place the 10 tiles (0-9) in the equations. Some equations are easy to solve because there is only one missing addend. Other equations are more challenging. If a child needs assistance, there are 10 hints available to help solve the number sentences. This is a great strategy game and one that is very easy for children to master. There is also a built-in calculator to check facts on any of the levels.

The next level of Ten Tricky Tiles is Balance Tiles. In this activity, children use a more algebraic approach to solving addition and subtraction problems. The screen shows three horizontally oriented number sentences with missing addends, and students quickly realize they must make both sides of the equation balance. This is a good introduction to algebraic thinking.

Finally, the most challenging activity in Ten Tricky Tiles is Crossword Tiles. In this interconnected puzzle of vertical and horizontal tiles, children have to carefully place the 0-9 tiles in the correct spaces to solve the problem. Students have to use a very logical approach to correctly solve any of these problems. If any one number is incorrectly placed, it affects the solutions to all of the problems in the crossword.

Challenges at Different Levels

The final software recommendation is The Logical Journey of the Zoombinis from Riverdeep. Designed for grades 2-5, this program caters to a variety of ability levels designated as "Not So Easy," "Very Hard," "Oh So Hard," and, finally, "Very, Very Hard." At each level opportunities for solid student engagement and rich classroom discussion abound as children trek with the imaginary Zoombinis-characters with wild glasses, weird hairdos, and springy shoes-in distant lands and learn such concepts as graphing, data analysis, classifying, patterns, and functions. I recommend the patterns, graphing, and attribute-sorting activities for younger students and the grouping, logical thinking, and algebraic thinking for older students.

Math Arena, Ten Tricky Tiles, and The Logical Journey of the Zoombinis are just some of the resources available to make mathematics meaningful and appropriately challenging for children in elementary school. Add some zest to your mathematics class by introducing one or more of these terrific tools.

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Spring 2004 | Volume 13 | Number 3 Technology for the Math Classroom Elementary Math Software That Makes Kids Think Mary Santilli Want to get elementary students excited about mathematics and have them acquire technological savvy at the same time? Here are some excellent resources for the classroom computer or for the entire computer lab in your school.

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Win-Win Math Games

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Developing Computational Fluency in Addition and Subtraction

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Addition and Subtraction Activities and Strategies

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Tips for learning math facts

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Is Your Child Struggling to Memorize the Math Facts?

Do you want to know how to help a child learn math facts?

Number lines, charts, fingers, and counters will delay memorization of the math facts.

As an educator of children with learning disabilities, I have always stressed mastery of the addition, subtraction, multiplication, and division facts. Unless the facts are automatic, children will have difficulty learning more advanced math skills, and with solving word problems. This is also true for children without learning disabilities.

If you live in an area which follows Common Core State Standards, please view each book to see the complete list of supported standards. The books were not designed to follow Common Core; but do so because they were written to be quality resources.

Need Some Good Strategies to Help Students Memorize Math Facts?

Please view and try out the sample pages from Two Plus Two Is Not Five and Five Times Five Is Not Ten to get an idea of what the workbooks offer. I also offer the first 24 workbook pages from Two Plus Two Is Not Five for free. Just email me and ask for them! Please also try the sample pages from Addition and Subtraction: Beyond Math Facts and Ten Divided by Five Is Not Five.My blog page also has more details on teaching math facts to children and shows some of the tricks and strategies from the books. S earch strategies!

My newest workbook, Ten Divided by Five Is Not Five, helps students remember division facts. It is based on the relationship between multiplication and division. If children can show what multiplication facts such as 4 x 3 means, and be able to draw a picture or explain how to figure out the answer to a word problem such as the following, then they are ready to learn and memorize division facts.
There are 12 children. The teacher wants 4 children to sit at each round table. How many tables are needed?
This new workbook is divided into six sections. Each section first reviews a set of multiplication facts. 8 x 7

The next page has missing factor problems. 7 x ___ = 56

Then the students are given pages of division problems, mixed division and multiplication, and a word math page.

Are you looking for the best way to teach math facts?

Which math facts does your child know?

EMAIL US for a FREE copy of the Baseline Recorders. After you find out which facts your student knows, you can teach the other facts. Read below to learn how you can teach children math facts using a method that works.

My suggestion to anyone teaching math facts is first make sure the child can demonstrate what the calculation means, then teach a way to remember the fact, and give lots of written practice and review.

Both Two Plus Two Is Not Five: Easy Methods to Learn Addition and Subtraction and Five Times Five Is Not Ten: Make Multiplication Easy have strategies to remember the facts, and many reproducible practice and review pages.

Now there is a workbook to give students more advanced practice using their known addition and subtraction facts.

How You Can Teach Math Facts

Many of the after school activities that children are involved in are also suspended during school holidays. Without the pressure of not-enough-time-in-a-day, you can start to help your child focus on learning math facts, or you can set aside some 10-20 minutes for this during school days. Teachers working with small groups of children can also use this method.

Once you get started, you and your child will see that it does not take up a lot of time, and it is easy, and even fun for the children to learn math facts.

1. Use a set of flash cards to determine which math facts are "known," meaning the fact is answered automatically and correctly without counting to get the answer.

2. Record these known facts. If you are using Two Plus Two Is Not Five: Easy Methods to Learn Addition and Subtraction or Five Times Five Is Not Ten: Make Multiplication Easy, the record-keeping pages are provided for you in the books.

3. Use 3″ by 5″ index cards to make a practice card for each known fact, and keep them in a rubber-banded pile. Keep addition and subtraction facts in one pile, and multiplication cards in another.

4. Review these fact cards daily with your child. Remember, your child knows them, so they will be easy to answer, and your child will feel good about knowing the answers quickly!

5. Teach a few new facts each day, and make a 3″ by 5″ card for each one. Add these new facts to the stack of known facts, and continue to practice daily. Remember to teach a way to remember the fact.

6. Repeat the process so that over time, the child masters all of the facts, and will not have to count out answers when working on math assignments. Time will vary depending on the each individual's ability, the number facts known, and the frequency of practice sessions.

A word of advice: Set the pace at the child's ability. Some children will be ready to learn new facts during each practice session; others may not. Keep the child successful, and remember to praise your child.

Request the first 24 practice pages from Two Plus Two Is Not Five: Easy Methods to Learn Addition and Subtraction. Use the Contact Form to request these free pages. Try them out!

What should you do when the stack of practice cards becomes too large to go through every day?

EMAIL US with this question, and we will send you the answer in a copy of our Free Tip on How to Individualize a Math Facts Program. Please let us know if you are a parent or an instructor of a large or small group of students.

Math facts tested in a minute - what are these timed tests really testing?

Adults often assign children arithmetic papers filled with rows of addition or subtraction facts, and perhaps mixed addition and subtraction facts. Sometimes we give the children a set amount of minutes in which to complete these pages, and the children cannot advance to the next stage until they can accurately answer these facts in a specific amount of time. I do not advocate these timed tests before children have memorized answers or have a strategy to use to answer the facts.

I have watched many children take timed tests. There are students who may know the answers automatically, but tend to write slower or are slower by nature to respond. Some of these children could also be the ones that are concerned about neatness; they use time to carefully erase incorrectly formed numerals, and then rewrite answers perfectly. In addition, some children stop to fix their hair when long bangs or hair gets in the way of seeing the page. (I suggest headbands or something to use to tie back hair.)

With this first group, the ability to write fast or stay on task, not math fact knowledge, is tested. Allow another way to test proficiency for these students, who may in fact know the answers without counting, but just cannot seem to complete the page quick enough.

A second group of children tested for speed includes children needing to use fingers, counters, counting in their head, number lines, or charts to get the answers. These children do not know many of the answers, and they are not learning to memorize the facts by taking the timed test. The test measures how quickly and accurately they can count to get answers. I have watched some children in this group get through the first row of facts quickly because they have memorized the sequence of answers. Others, if given the same math fact problem more than once on a page, use a strategy to take the time to search for the answer that is somewhere else on the page. These children ought not to be taking timed tests until we teach them a way to remember the answers.

Just given random written practice, many students will not learn math facts. Timed or not timed, the exercise is frustrating and useless when children do not know answers on the page. Teach them strategies to remember and memorize the math facts. Give children written practice on the math facts they can answer successfully.

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Tips to Help Children Learn and Memorize Math Facts - Longevity Publishing

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Do you want to know how to help a child learn math facts? Number lines, charts, fingers, and counters will delay memorization of the math facts. As an educator of children with learning disabilities, I have always stressed mastery of the addition, subtraction, multiplication, and division facts.

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Fact Family Youtube Video

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List of Interactive Games for Learning Addition and Subtraction Facts

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RTI Math Activities and Ideas

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More Ideas on Pinterest for Building Math Facts Fluency

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Ideas for Learning Math Facts from on Pinterest

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Resources and Tools for Elementary Math

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Developing Fact Fluency | mathlanding.org

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Teachers must determine how best to achieve an appropriate level of fact fluency and how to balance it among the other aspects of a successful mathematics program. Number facts learned purely by rote can be forgotten, or not readily applied effectively in problem solving.

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Strategies and Tips for Building Basic Facts Fluency

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Games for Teaching Basic Facts Fluency

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Every math teacher struggles to find ways to encourage students to master their basic facts. Whether for addition and subtraction facts or for multiplication and division facts, teachers collect many ideas from which they can draw activities to meet the varied needs of learners in their classes. Games and Who Has?

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Numerous Ideas for Teaching Addition and Subtraction Facts

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good ideas for teaching addition and subtraction, shared by teachers

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Tips for Teaching Math Facts

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As teachers of all grade levels know very well, it is extremely difficult to teach students higher order math algorithms when they are not fluent with their basic facts (addition, subtraction, multiplication and division). If students are not automatic in responding to math facts, their attention is necessarily taken away from the multiple steps necessary to solve more complex problems.

Think about long division. Students must be able to come up with the answers to multiplication, subtraction and division facts all in the context of the higher order algorithm. Less than automatic facility with math facts often results in either errors in the algorithm or fact errors. Both kinds of errors appear to be the result of carelessness when in fact it is the result of being distracted by having to figure out the answers to facts. Below are 12 principles necessary to successfully teaching math facts.

There is a big difference between figuring out the answer and memorizing facts. If students have too many facts to learn at one time, they necessarily fall back on figuring out the answer. Instead, we want students to REMEMBER the answers without having to figure them out.

Only add more facts to learn as the previous set has been mastered

Once students have learned a set a set of facts to mastery, it is now possible to add two or three more facts to be learned. Student success is greatest when they have only two or three things to learn in a sea of material they have already mastered.

Practice must be structured in a way that facts which have been previously deemed mastered continue to appear along with the two or three new facts that are being learned.

Students should memorize facts in a way that forms a verbal chain

Students should always practice by saying the whole problem and the answer aloud. In this way, students memorize a verbal chain. As a result of this kind of practice, students hear/see 8x7 and can't stop from saying/writing 56.

Automaticity is the ability to say the answer to a problem immediately after reading the fact. There should be no hesitation.

Students write at different speeds. The speed at which students can write the answer to facts is limited by their writing skill. Automaticity means that students should write answers to math facts exactly as fast they can write.

Practice is most effective when it is distributed throughout the year. Learning math facts is just one part of a math program therefore efficient use of limited time is critical. A standard daily routine is necessary in order to accomplish this goal.

Whenever students hesitate or give an incorrect answer, a corrective procedure should give them the answer, ensure they know it and provide them with a delayed test. It is very important that the delayed test occur before the student has a chance to forget the correct response.

Students cannot maintain focus on drill for more than 2-4 minutes at a time. Practice sessions may occur more than one time during the day, but should remain short.

If students are really learning math facts, the number of facts they can answer within a set time period should gradually increase. Periodically, students should be given a timed test of all the facts in the operations they are learning to see if their fluency is improving.

Because fractions demand instantaneous recognition of multiplication facts, these must be mastered before fractions can be successfully learned. Even those students who need their fingers to add and subtract in Grade 4 and above, should learn multiplication facts to mastery or their continued progress in math is in jeopardy.

Students will be motivated to learn math facts if teachers act like it is important. Finding ways to celebrate students' success is the best way to demonstrate the importance of learning math facts.
Share your tips for teaching math facts in the comments section!

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As teachers of all grade levels know very well, it is extremely difficult to teach students higher order math algorithms when they are not fluent with their basic facts (addition, subtraction , multiplication and division ).

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Ideas for improving fact fluency

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Math Coach / Fact Fluency for Addition and Subtraction

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This is a PowerPoint Presentation with some useful information that I could use for my project.