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Do Not Teach Math Until Sixth Grade?

I just read the most amazing article! When Less is More: The Case for Teaching Less Math in Schools by Peter Gray. Could he be right?

Teaching Elementary Math Can Be Fun!

I firmly believe that the more fun both teacher and child have during a math lesson, the easier the concepts will be to teach, learn, and retain. Believe it or not, there are fun ways to teach math!

Like almost every elementary teacher in the United States, a group in Massachusetts is actively looking for ways to “make teaching math a more comfortable process for early childhood educators”.

Do you feel like you could really use an appealing, effective way to help your students learn basic math concepts and skills? Many elementary schools are impressed with the many benefits of using math games in the classroom.

Games offer a fun and natural link to math concepts. And games can, if you select the right ones, help children learn almost everything they need to master in elementary math. Good, child-centered games are designed to take the boredom and frustration out of the repetitive practice necessary for children to master important math skills and concepts.

The following is one of my favorite games for kindergarteners, first graders, and second graders:

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.

A Few Good How-to-Help-Your-Kids-with-Math Books

As a parent, you are the best person in the world to spark, sustain, or renew your child’s sense of discovery and excitement in math. Whatever your background or experience, you’re the best person to support your child in math – at school and outside of school.

The following are a few good books to help you navigate the educational issues; understand your crucial role in your child’s mathematical success; and put inquiry-based learning into practice with your child. You can light and sustain the flame for learning math in your children.

Beyond Facts and Flashcards: Exploring Math with Your Kids by Jan Mokros
Games and activities that help parents develop their children’s logic and reasoning.

Math: Facing an American Phobia by Marilyn Burns
This book explains how to encourage kids to discover math concepts on their own.

A Family’s Guide: Fostering Your Child’s Success in School Mathematics, edited by Amy J. Mirra
An explanation of today’s math curricula with suggestions for how parents can help their children learn to like math.

Spark Your Child’s Success in Math and Science by Jacqueline Barber, Nicole Parizeau, and Lincoln Bergman
A practical, research-based resource for all parents and adult caregivers of school-aged children.

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.

Taking Time to Understand Time

For years, teachers have observed students’ frustration as they grappled with learning to read an analog clock (as opposed to a digital clock). I remember being frustrated myself and not fully understanding why learning to tell time was so difficult for my students and wondering how to help.

I began to realize that there are two aspects of time that have to be distinguished in teaching time: firstly, one must try to develop a concept of time in a child, and secondly, one must teach the child to “tell the time” (teaching clock time).

Teachers of young children generally concur that their students learn mathematical concepts best when they construct understanding through concrete experiences. When we remember that time can be neither seen nor touched but experienced and measured only indirectly with such tools as clock, we can begin to understand why time-related concepts are difficult for our students to learn.

From the body of research available, as well as from our own firsthand teaching experiences, we know that everything to do with understanding and using time concepts develops rather late. I will go so far as to say that most children do not really fully understand the intricacies of telling time until about the third or fourth grade.

What usually happens in the classroom is that developing the concepts of time is skipped. In keeping with the admonition that children must actively develop concepts of time, I have included a few of the math activities I began to use in my classroom:

Time Intervals

Just How Long Is a Minute?

Have your students close their eyes and you time one minute. Have them keep their eyes closed and put up their hand when they think one minute has passed. Call time at the end of the minute. Now try it again. The more you do it, the better sense of a minute they will have.

Also try some of the following activities:

How many times in one minute do you think (make an estimate) you can:

1. Sing “Happy Birthday”? Estimate ____ Actual _____

2. Touch your toes? Estimate ______ Actual ______

3. Hop on one foot? Estimate ______ Actual ___

4. Do jumping jacks? Estimate ______ Actual ______

5. Write your first name? Estimate ______ Actual ______

6. Run around the basketball court? Estimate ______ Actual ______

7. Draw stars? Estimate ______ Actual _______

8. Recite the alphabet? Estimate ______ Actual _______

9. Snap your fingers? Estimate ______ Actual _______

10. How high do you think you can count in one minute?
Estimate _______ How high did you go? ________

More or Less Than a Minute? Homework

Here are some things you do everyday. For each one, guess whether you think it will take more than one minute or less than a minute to do it. Now try each thing while someone keeps time.

1. Put on your socks and shoes.
Guess ______________ It really took _____________
more or less than 1 minute / more or less than 1 minute

2. Brush your teeth.
Guess ______________ It really took _____________
more or less than 1 minute / more or less than 1 minute

3. Eat a banana.
Guess ______________ It really took _____________
more or less than 1 minute / more or less than 1 minute

4. Read a page from your favorite story.
Guess ______________ It really took _____________
more or less than 1 minute / more or less than 1 minute

5. Pledge Allegiance to the Flag.
Guess ______________ It really took _____________
more or less than 1 minute / more or less than 1 minute

Now make up a short list of things you think will take about one minute, and give them a try.

There are some great games which help children understand time!

Number of the Day

One of my favorite math activities for any age child is Number of the Day.

This is a great activity for anyplace you happen to be! It will give your child lots of computation practice, be a good deal of fun, and everyone (even you) will be forced to “prove” that they are correct!

Let’s say that our “number of the day” is 6. Everyone has to think up one way to make 6. Young children will probably begin with simple addition.

Example: 4 + 2 = 6

Ask your child to “convince you” (prove) that 4 + 2 = 6.

Everyone has to come up with an equation that equals 6, and each one has to be different.

After gaining in confidence, encourage your child to think of 2 different things that equal 6.
Example: 3 + 3 and 5 + 1

Then ask them to find 3 things that equal 6
Example: 1 + 2 + 3 = 6

See how many different ways everyone can find to make the number of the day. Write it all down if pencil and paper are handy.

Depending on your child’s age begin to encourage the use of other operations such as:
• subtraction 9 – 3 = 6
• addition & subtraction 8 – 4 + 2 = 6
• multiplication 3 x 2 = 6
• multiplication & addition 2×2+2 = 6
• division 24 ÷ 4 = 6
• all 4 operations in one equation
(50 ÷ 2) x 3 – 70 + 1 = 6
• coin values – 1 nickel and 1 penny =
6 cents
• fractions 4 ½ + 1 ½ + 6
• decimals 2.4 + 3.6 = 6 or 12 x .5 = 6
• integers – positive 10+negative 4 = 6

Family members can take turns choosing the number of the day. What about the day of the month, someone’s age or weight, number of windows in your home, the sum of your telephone number, etc. Try a variety of numbers, including large ones (such as 555 or 62,437) and small ones (they can be just as challenging as large ones).

Well, you get the idea! Dad might be coming up with 4 x 25 – 80 – 14 = 6!!
Does he have to prove it??!! Absolutely!

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.

Make March Math Awareness Month!

The main goal of Math Awareness Month should be to “demystify” the subject, alleviate the “math anxiety” some students experience, and show students that math can be interesting, challenging, engaging, and fun.

How you, as teachers, encourage and promote your student’s math learning, from preschool to high school, can be pivotal to their attitude toward math and their achievement in this subject area. In an effort to deliver the fundamentals of math in new and interesting ways, teachers should organize a fun-filled month of educational math activities.

Notice math in the world. You can help your students see the usefulness of math by pointing it out wherever you see it. Math is a part of everyday life. Students need to see that math is practical and useful. The more closely you align your teaching with the real-life activities of your students, the more learning will resonate with them. Math is one of the easiest subjects to connect to real-life activities.

Mary Ellen Bafumo in her article Making Math Meaningful suggests trying the following:

“Distribute empty cereal boxes to small groups of students. Practice the four operations via word problems built around preparing a class breakfast. Students use portion info on the side of the box to complete math examples. How many boxes are needed to feed the class? What is the cost per serving? How many gallons of milk are needed? The class votes, via a bar graph with each cereal represented, about which to serve in class. Students measure cereal and milk servings and enjoy!

Distribute flyers from office stores. Pairs of students “shop” for a complete computer station for home. They figure cost, tax and shipping, then respond to word problems. On a $150 monthly budget, how long will it take to pay for the equipment? If you pay off the balance in three, four or five payments, how much is each installment? Students then develop a word problem structured around the task to share with the class.

Distribute travel ads. Small groups of students plan a dream vacation. They calculate transportation, accommodations, meals and incidentals, then multiply by their group members. Ask your class the following questions. If the PTA provides $2,500 for the trip, how much will each group member have to raise? If airfare is donated, how much will the trip cost, etc.?

Create scenarios based on the interests of your students. Use advertisements (movies, video games, cds, bicycles, etc.) that spark their enthusiasm and watch math take on new meaning.”

Another great thing to try is 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. Games incorporate the ways children best learn mathematics: through the use of physical manipulatives within the context of developmentally appropriate practice – games require active involvement.

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 almost everything they need to master in elementary math. Good, child-centered games are designed to take the boredom and frustration out of the repetitive practice necessary for children to master important math skills and concepts.

Games teach or reinforce many of the skills that a formal curriculum teaches, plus a skill that formal learning sometimes, mistakenly, leaves out – the skill of having fun with math, of thinking hard and enjoying it.

Try a math game in March! Need some ideas at your grade level?
Click here to find math games at every elementary grade level.

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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