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Confessions of an Elementary Math Teacher

Embarrassingly traditional. Isn’t admitting your problem the first step to change? I confess: I was an embarrassingly traditional math teacher. And, frankly, I wasn’t enjoying the experience very much.

Actually, I make that confession all the time now. As an elementary mathematics specialist, I introduce myself to elementary school faculties as a born-again math teacher.

The change began in the mid-1990s as I worked on a Master’s in Elementary Education. My whole focus was on how children learn, or brain-based learning. I began to discover that research clearly shows that we know a lot about how children learn math, but rarely do we use that knowledge to inform our teaching.

Decades ago, education revolutionaries John Dewey and George Polya elucidated how bulldozing through a prescribed math program does not give children opportunities to think through concepts. I knew that to be true because of my own self-limiting math background and lack of confidence in my abililties when it came to math.

So, how could I change my teaching so that my students became confident, thinking mathematicians? Well, that journey took me many years – years of growing and becoming a more effective math teacher. It involved a different approach to problem-solving using flexible instructional strategies.

One of those instructional strategies in support of problem-solving was the use of math games – games that help children develop problem-solving behaviors and mathematical thinking habits without realizing they are doing so.

As I began to use games in the classroom, I realized it is not enough to just play a game. When playing math games, it is the teacher’s responsibility to extend math learning by conversing with students about their problem-solving strategies, both before and after they play the games. Such conversations build a laboratory of thought to help students remember new learning by connecting it to already-known concepts and understanding.

Math games support the development of higher-order thinking skills as well as supply test-taking and computational practice. Actually, I began to realize that math games had many benefits.

I was liberated from being a traditional math teacher! But the very best part – I developed a passion for teaching math that I had never had before! Give a math game a try!

Parents Help Their Children with Math!

We live in a world of numbers. In fact, we use numbers constantly as a way of describing our lives. And yet, some will say that learning mathematics is difficult, and some will even say that they are not interested in learning it. However, mathematics is more than just learning about numbers. It is also about learning to think strategically and solve problems.

We want students to view mathematics as an enjoyable experience and to value mathematics. To do so, they must find it in places that they least expect it, such as in real-life situations that are non-threatening and fun. Games provide endless opportunities to experience mathematics, and when children are doing something they enjoy, they tend to spend more time doing it and pay better attention to what they are doing. As a result, they will get more practice with a skill by playing a game than by simply completing a traditional worksheet or using flashcards.

This is where parents can become involved. The parent’s job is to find a game that emphasizes a skill their child needs to master and begin to play. The role of the parent is to be supportive, play along with their child, make sure that the rules are clearly understood, ask questions (not give answers), and share their thinking either while they play or after the game.

As an example, one of the biggest concepts third graders need to master is multiplication. The following is an effective game for helping your second, third, or fourth grader do just that:

Terrific Tens

What you need:
2 players
deck of cards (remove face cards)

Take out one “10” card and lay it face up between the two players. This “10” card becomes the multiplier in each face off. Shuffle the rest of the cards and deal them evenly between both players. Both players put their cards face down in a pile in front of themselves.

Both players turn over the top card of their pile. They say the number, then multiply it by the “10” card and say the product. It is very important that each player say the entire equation out loud. For example: “7 x 10 = 70”
The player with the greatest product wins both cards. If there is a tie (i.e., both players have the same product), players turn over one more card and multiply that card and add it to their previous product. The player with the largest sum, takes all four cards.

When all the cards have been used, players count their cards. The player with the most cards wins.

Variations:
• Nifty Nines – the “9” card becomes the multiplier in each face off.
• Excellent Eights
• Super Sevens
• Sensational Sixes
• Fantastic Fives
• Fun Fours
• ? Threes
• Terrific Twos
• Wonderful Ones

Parents Ask About Playing Games in Math Class

Not too long ago a parent said to me, “My child tells me that he plays games during math class. How will games help my child become better at math?” It was a legitimate question and one that teachers need to be prepared to address.

I’ve been teaching math to children for many years, and I’ve found that math games are, from a teacher’s point of view, wonderfully useful and very effective. Games provide an enjoyable venue for the repeated practice necessary for mastering many basic skills. When carefully selected, games can highlight specific mathematics concepts, activate strategic thinking, and create an opportunity to develop logical reasoning skills. And games can help children learn almost everything they need to master in elementary math. Once I began to use games regularly during math time, I was amazed at the many benefits to be had while having fun!

The value of games should not be underestimated. Depending on the game, the type of learning can vary. Some games allow students to practice skills, such as performing arithmetic operations with efficiency and accuracy. Other games encourage the development of concepts and strategic thinking, requiring students to make predictions, deliberate about possible outcomes, solve problems, and experiment with new strategies. All of them offer the potential of connecting to what is being studied in elementary school mathematics.

The teacher needs to know what essential skills and knowledge are involved in any game. A discussion of the game will help students recognize the skills and knowledge needed, which is essential. In addition, the teacher can assess understanding of concepts and levels of skills by observing and listening to students as they play.

Games can engage and motivate students. The hands-on nature makes the game, and the learning associated with it, more concrete. Students who participate in games often perform more mathematics than when using traditional dittos or worksheets. Participation and practice build confidence.

In addition to improving mathematics abilities and increasing thinking and reasoning skills, games can also help develop social skills. Students must take turns, follow rules, play fairly, pay attention, listen to and learn from others, be persistent, and learn from their mistakes. Can that be said for a worksheet?

Give games a try. You might be surprised at what you discover!

Place Value Activities and Games

Once children have developed a basic number sense for numbers up to ten, a strong “sense of ten” needs to be developed as a foundation for both place value and mental calculations.

Ten is, of course, the building block of our Base Ten numeration system. Young children can usually “read” two-digit numbers long before they understand the effect the placement of each digit has on its numerical value. For example, a five-year-old might be able to correctly read 62 as sixty-two and 26 as twenty-six, and even know which number is larger, without understanding why the numbers are of differing values.

Place value is vitally important to all later mathematics. Without it, keeping track of greater numbers rapidly becomes impossible. (Can you imagine trying to write 999 with only ones?) A thorough mastery of place value is essential to learning the operations with greater numbers. It is the foundation for regrouping in addition, subtraction, multiplication, and division.

Developing students’ understanding of numbers, ways of representing numbers, and the relationships among numbers are focus areas for elementary mathematics. To help children understand these very important concepts and give them the opportunities to explore numbers, the following very effective and engaging game has been developed for First Grade, Second Grade, and Third grade.

Two-Digit War

What you need:
2 players
deck of cards – 10’s removed
Tens and Ones board for each player. Hold an 8 1/2 x 11 piece of paper with long sides on the top and bottom. Fold it in half vertically. At the bottom of the left half write Tens. At the bottom of the right half write Ones.

Shuffle cards and place them face-down in a pile. Player #1 turns over one card and decides whether to put it on the Tens or Ones. Once it has been laid down, it cannot be moved.

Player #2 does the same.

Player #1 turns over one more card and puts it on the remaining space. Again, it cannot be moved once it is laid down.

Player #2 does the same.

Players read their numbers out loud to each other. The player with the biggest two-digit number wins and takes all four cards. When all the cards have been used, players count their cards, and the player with the most cards wins the game.

Variation: The person with the smallest two-digit number wins.
Variation: Play Three-Digit War with Hundreds, Tens, and Ones

There are many really good games that emphasize a thorough understanding of place value

Encouraging Mathematical Reasoning in the Classroom

In this standards-based assessment world in which we educators find ourselves, little thought is given to the development of mathematical reasoning skills. Instead, the focus has become test performance. No longer do we ask students to think. This lack of thinking skills has caused a lessening of enthusiasm in teachers’ and students’ attitudes – about school in general and mathematics specifically.

I think there needs to be a shift in the school culture toward promoting engagement through inquiry-based learning opportunities. I do not think any teacher needs convincing on this point.

One of the best ways to ensure active student engagement in math is the use of games. Good games for the classroom are engaging, fun, and create opportunities for students to explore concepts and develop mathematical reasoning.

Playing a math game is the first step on the road to mathematical reasoning. Teachers need to create opportunities for students to explore mathematical ideas by planning questions that prompt students to reflect on their reasoning during and after the playing of a game. When we carefully consider the questions we ask and plan an appropriate level of competition, students will focus on the mathematics and not just the game.

Questioning
While the students are playing the game, the teacher’s job is to move from group to group listening to their conversations. Ask probing questions, such as:
• What card do you need?
• Which cards would not be helpful?
• Prove to me that a ____ is what you need.
• Why do you think that?
• How did you know to try that strategy?
• How do you know you have an answer?
• Will this work with every number? Every similar situation?
• When will this strategy not work? Can you give a counterexample?
• Who has a different strategy?
• How is your answer like or different from another student’s?
• Can you repeat your classmate’s ideas in your own words?
• Do you agree or disagree with your classmate’s idea? Why?

Too often the other player is willing to give his/her partner the answer, thus making it possible for that player to do no thinking whatsoever. Not good! Your (and the partner’s) questions to that player should be:
• What can you do to help yourself? Use your fingers to count? Count the dots on the dice or cards? Use manipulatives to figure it out? Draw a picture? Start with something you already know?

The power of questioning is in the answering. As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give good answers.

Helping Children Master the Basic Number Combinations

Educators generally agree that it is very important that children master the basic number combinations. In fact, the National Research Council (NRC) concluded that attaining computational fluency is an essential aspect of mathematical proficiency.

Children typically progress through four stages when mastering these basic number combinations.

Stage 1
Elena, a Kindergartener, determines the sum of 6+5 by getting out 6 cubes and then adding 5 more and counting the total.

Stage 2
Kevin, a first grader, determines the sum of 6+5 by saying “six” and then extends five fingers (one at a time), and counts “Seven, eight, nine, ten, eleven”.

Stage 3
Theresa, a second grader, tackles 6+5 by mentally reasoning that if 5+5 is 10, and 6 is 1 more than 5, then 6+5 must be 1 more than 10, or 11.

Stage 4
Sam, a third grader, immediately and reliably answers, “Six plus five is eleven”.

How do we, as teachers and parents, best get our children to stage 4 – mastery (efficient, fast, and accurate production of answers)?

Too often it is thought that memorizing basic facts by rote through extensive, time-tested drill and practice is the most efficient way to help children achieve mastery. This approach makes learning the basic number combinations unduly difficult and anxiety-provoking and undermines interest in mathematics and confidence in mathematical ability. Many children give up on learning all the basic combinations. They may appear inattentive or unmotivated or otherwise fail to learn the combinations.

I believe that one of the best ways to get this kind of practice on the road to mastery is with the use of math games.

I’ve been teaching math to children for many years, and I’ve found that math games are, from a teacher’s point of view, wonderfully useful. Math games put children in exactly the right frame of mind for learning. Children are normally very eager to play games. They relax when they play, and they concentrate. They don’t mind repeating certain facts or procedures over and over.

Children throw themselves into playing games the way they never throw themselves into filling out workbook pages or dittos. And games can, if you select the right ones, help children learn those basic number combinations. Good, child-centered games are designed to take the boredom and frustration out of the repetitive practice necessary for children to master these important math skills and concepts.

Playing math games is even more beneficial than spending the same amount of time drilling basic facts using flash cards. Not only are games a lot more fun, but the potential for learning and reasoning about mathematics is much greater, as well.

The following is a simple game, but one of my favorites, for mastering the basic number combinations:

Turn Over 5

What you need:
2 players
cards 0 – 5, 4 of each

The object of this Concentration-type game is to capture pairs of cards that add up to 5.

Mix up the cards and lay them face down in four rows of six. Players take turns by choosing two cards to turn over, trying to find a combination that adds up to 5. If they find one, they keep (capture) that pair. If they do not, they turn the two cards back over for the next player. When all matches have been made, the player with the most cards wins the game.

Variation: This game can be made more challenging by using higher cards and a different sum, such as 6, 7, 8, 9, 10, 15, 15, etc.

There are many such games that teachers and parents can play with their students/children which will happily put them on the road to mastery.

Why Use a Math Game?

I am a believer in the many benefits of using math games in the classroom. Besides the fact that games can motivate and engage students in thinking about and applying concepts and skills, math games can foster mathematical communication as students explain and justify their moves to one another.

Games afford students an opportunity to communicate their ideas and justify their thinking. In using games, the teacher plays an important role in encouraging students to explain their thinking and in keeping students focused on mathematical ideas. Requiring students to explain and justify their moves during a sample round of the game played as a whole class models the type of thinking and communicating that is important for students to use later when they play the game in pairs.

The ability to pose questions that elicit, extend, and challenge students’ thinking is essential to creating a classroom environment in which intellectual risks, sense making, and deep understanding are expected. In daily lessons, teachers must make on-the-spot decisions about which points of the mathematical conversation to pick up on and which to let go, and when to let students struggle with an issue and when to give direction.

While the students are playing a game, it is the teacher’s responsibility to ask probing questions, such as:
• What card do you need?
• Which cards would not be helpful?
• Prove to me that a ____ is what you need.
• Why do you think that?
• How did you know to try that strategy?
• How do you know you have an answer?
• Will this work with every number? Every similar situation?
• When will this strategy not work? Can you give a counterexample?
• Who has a different strategy?
• How is your answer like or different from another student’s?
• Can you repeat your classmate’s ideas in your own words?
• Do you agree or disagree with your classmate’s idea? Why?
• What can you do to help yourself? Use your fingers to count? Count the dots on the dice or cards? Use manipulatives to figure it out? Draw a picture? Start with something you already know?

The power of questioning is in the answering. As teachers, we not only need to ask good questions to get good answers but need to ask good questions to promote the thinking required to give good answers.

While playing a math game, students’ abilities to learn from, and work with, others should expand. They should become more skilled in speaking to one another and in convincing or questioning their peers. The discourse should focus on making sense of mathematical ideas and on using mathematical ideas effectively in modeling and solving problems. When thinking is discussed regularly in the classroom, students feel comfortable describing their thinking, even if their ideas are different from the ideas of their peers. Discourse is not a goal in itself; rather, the value of mathematical discussions should be judged by whether students are learning important mathematics as they participate in them.

Effective teaching involves observing students, listening carefully to their ideas and explanations, and using the information to make instructional decisions. Through their teaching, teachers can also continue to deepen their understanding of the mathematics they teach, by learning with and from their students and then reflecting on that learning. The ability to reflect on and refine mathematical understanding as well as instructional practice is essential to achieving the vision of an effective mathematics classroom, whatever the grade.

Engage and Motivate Your Students in Math

As a veteran elementary teacher and math specialist, I am absolutely sure that what is important in helping children develop a positive attitude toward math and become confident mathematicians is the power of an effective teacher. Finding those engaging “hooks” to draw children into the math is the challenge.

Many students feel like math is just memorizing facts and processes and then repeating it on a test. Certainly doable, but not very entertaining. Not much real learning is going on.

Overcoming math terror is a job teachers face, and it’s true more often than we would like. How can teachers get students past that terror and into a love of mathematics. What might that “hook” be?

Effective teachers seem to rely on proven approaches, including high expectations, engagement, motivation, and support. All are worthy, but I would like to speak to engagement and motivation.

Research has demonstrated that students learn more if they are actively engaged with the math they are studying. Constance Kamii, a world renowned expert on how children learn math puts it this way, “Children who are mentally active develop faster than those who are passive.”

Active learning is, in short, anything that students do in a classroom other than merely listen to a teacher’s lecture. There are several ways of doing this. Playing math games is a particularly useful one.

Games can provide an atmosphere where children are encouraged and motivated to:
• share their ideas with other children
• be alert and curious
• come up with interesting ideas, problems, and questions
• have confidence in their abilities to figure out things for themselves
• speak their minds with confidence

Games are engaging (maintain interest); dittos or workbook pages rarely are. In the process of playing the game, students may develop initiative, interest, curiosity, resourcefulness, independence, and responsibility. Would that happen with a ditto or workbook page?

Children learn math best when they participate in games that are relevant to them, hold their attention, and require them to “make meaning” for themselves.

Teaching methods that stress rote memorization of basic number facts or algorithmic procedures are usually boring and do not require learners to participate actively in thought and reflection. In other words, they are not engaged or motivated.

Engage and motivate your students in any of the many math games that I have tried and loved.

Learning the Multiplication Facts with Games

Too often, children are asked to memorize the multiplication facts without discovering what they really mean. Teachers need to teach multiplication for understanding. One of the many ways I did that was to ask questions such as:
2 cars – how many mirrors?
7 tricycles – how many wheels?
4 spiders – how many legs?

Once students have grasped the meaning of multiplication, they need to develop speed in the recall of the facts.

For many years, I have been using games instead of worksheets or timed tests after the students developed the logic of multiplication. The results were encouraging. The students began to memorize the facts more easily, and when tested at the end of the school year, had retained the facts. In other words, the multiplication facts had gone into long-term memory!

Motivation to learn the times’ tables must come from within, but the teacher has much to do with this motivation. Students can be motivated to learn the multiplication combinations because games are fun and there are a variety of them. See my 3rd grade multiplication games.

One of my favorites is Salute Multiplication.

Salute Multiplication

What you need:
2 players
deck of cards with face cards removed

Shuffle deck and place face down in a pile.

Player #1 turns over the top card and places it face up on the table for all to see.

Player #2 draws a card and does not look at it. Player 2 holds the card above his or her eyes so that player #1 can see it, but he can’t.

Player #1 multiplies the 2 cards mentally and says the product out loud.

Player #2 listens and decides what his or her card must be and says that number out loud.

Example: Player #1 turns over a 6 for all to see. Without looking at it, player #2 puts a 4 on his forehead. Player #1 mentally
multiplies 6 x 4 and says, “24”. Player #2 must figure out
6 x ? = 24.

Both players decide if the response is correct. If it is, player #1 gets 1 point.

Players reverse roles and play continues until one player has 10 points.

Take some of the frustration out of getting your students to memorize the multiplication tables – give a game a try!

Children Love Math Games

Another elementary school (this one is in Knoxville) has joined the ranks and begun to use math games in the classroom to motivate and engage students in meaningful mathematics.

“Often times, mathematics is viewed by our society as cruel and unusual punishment. That makes it very difficult for teachers to teach math and for students to invest the time and energy it takes to learn math. Through games, you have the motivational factor that helps move learning along.”

Classic games are finding their way into classrooms as educators creatively use the games to reinforce math, language and critical thinking skills.

I have found that games have a multitude of benefits:
• Meets Mathematics Standards
• Easily Linked to Any Mathematics Textbook
• Offers Multiple Assessment Opportunities
• Meets the Needs of Diverse Learners (UA)
• Supports Concept Development in Math
• Encourages Mathematical Reasoning
• Engaging (maintains interest)
• Repeatable (reuse often & sustain involvement
• Open-Ended (allows for multiple approaches & solutions)
• Easy to Prepare
• Easy to Vary for Extended Use & Differentiated Instruction
• Improves Basic Skills
• Enhances Number and Operation Sense
• Encourages Strategic Thinking
• Promotes Mathematical Communication
• Promotes Positive Attitudes Toward Math
• Encourages Parent Involvement

Whichever grade level you teach, there are many games that your students can play which will be effective, useful, and fun!

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