Four Steps to Using Skip Counting to Speed up Math Learning

July 15th, 2013

Parents and early childhood educators can use skip counting strategies to speed up math learning in young children. The steps below can also serve as a fun math game! Please note that before using the following strategies, a child must be age and brain ready. This means a child must be able to count to 10 using one-to-one correspondence.

Step 1: Teach verbal counting by 2’s to 8. (In some cases, a child may learn to count by 2’s to 10.) Teachers also call this skip counting because a child is skipping all the numbers that are not counted by 2’s, for example 1, 3, 5, and 7. It is sometimes helpful to have a number line to refer to as a child counts.

For example:

1 2 3 4 5 6 7 8 9 10

One way to learn and remember to count by two’s is to use a simple two –line chant that goes along with number line counting. It might go like this:

“2 – 4 – 6 – 8,

Counting by two’s is really great!’

Or to count to 10:

“2 – 4 – 6 – 8 – 10,

Count by two’s again and again.”

This chant should be repeated several times until a child can recall it perfectly from memory.

Step 2: Collect a total of eight similar objects (e.g. poker chips, quarters, or KENS Math foamies). Begin with a total of four objects keeping the remaining objects out of sight. Place the four objects in two groups.

Explain that one way you could tell how many object you have is by counting each one. Demonstrate this counting strategy by counting each object one at a time. Then ask, “Would you like to learn a faster way to count?” After the child replies, “yes” you say, “we can count faster when we count by two’s. To help us do this, we will use our little song, “2, 4, 6, 8…….” Now watch me as I show how to count by two’s.” This time touch or move each set of two as you count to four saying, “Two, Four! There are four apples. Now let’s see if you can do it the same way I did.” Students may hesitate because this is a different way of counting. With repeated modeling and practice nearly all students can master this approach.

Depending on your child’s interest level and confidence in this method, you may next introduce 6 objects. Proceed the same way by first modeling the strategy and then allowing the child to practice. With time and practice over a couple of days, children may advance to 8 objects.

Step 3: After a child has developed confidence in this strategy, he or she may be ready for a tougher challenge. For step 3, place six objects randomly placed (not in groups of two) in front of you. Say, “We are going to count by two’s again. This time, we will grab 2 objects each time we count.” Then demonstrate by taking first 2 objects and saying, “Two!” and then grabbing two more saying “Four!” Repeat until you reach “Six”. Next ask your child to attempt to do the same thing on his or her own. If needed, you may repeat the little song and repeat modeling. This step will take a little longer to master than step 3. With practice, you may increase the number of objects to eight always keeping an even number of objects.

Step 4: Over time and with practice, a child may be ready to take the final step, which is counting by two’s with an odd number of objects. To be ready for this challenge, a child must be able to either recall what number comes next after 2, 4, 6 and 8. To complete this final step, first present 5 objects. Model counting by two’s and when reaching 4 say aloud, “I have four and one more. I know one more than four is five. So I know that there are five objects!” Repeat with practice after success the numbers 7 and 9 (It is important to note that not all preschool children are ready to master this last step).

You can download the KENS Math Skip & Count Worksheet today and start having fun!

Math Training for Preschoolers

January 9th, 2013

One of the first math skills a child learns is how to count. This is often done out loud by repetition or by song. Later, counting is connected to objects. When a child can count a collection of 5 objects in order, the child is demonstrating several important math principles. One of these

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principals is called “one-to-one correspondence.” It is matching each counted object with a number that is one more than the previously counted object. This gives the number name meaning. For example, when a child counts four objects, he or she learns to associate the number name, “four” with four real objects. This skill develops over time until a child can count fluently (without mistakes) to 10 or more.

With practice, a typical preschooler can also quickly identify very small sets of objects much more quickly without counting. This is called “subitizing.” Subitizing is different from counting because it happens almost instantly. Subitizing involves the brain responding at the speed of thought to visual stimuli. For example, when an adult sees the following objects, the adult would immediately say, “four apples.” Few adults would need to actually sit down and count the apples one by one.

Preschoolers can usually subitize two or three objects instantly without counting. Some preschoolers can also subitize four objects. Very few preschoolers can subitize five. Five is usually the upper limit for both children and adults.

Over the course of my time as an educator, I developed some brand new teaching strategies to advance mathematical thinking and they have recently been incorporated into the Kids’ Education for Number Sense program. These strategies help a child combine small sets of objects more quickly than counting the objects one by one. For example, when older children and adults see the following “apple problem”, they can immediately identify the answer as “four.”

If this were an addition problem, an older child might say this picture represents “2 + 2 = 4.” Researchers also call this “number combination” or the process by which our brains can quickly tell how many by putting small sets together without much thinking.

– Dr. Ken Newbury

Do You Speak Math?

August 14th, 2012

Every teacher has seen it. Students memorize math facts in advance of a timed test only to forget some answers a few days later. In elementary school, it is not uncommon for students to forget simple subtraction or multiplication facts that were “mastered” the year before.

In addition to using brain-based strategies that build subitizing skill, number combinations and number line skill, a teacher’s use of purposeful “math talk” creates the glue that connects “number” to “sense”. To use another metaphor, math talk is the stitching that sews fact to meaning. When teachers discuss with students what they know and how they know it, they gain key insights about student’s math conceptions while student understanding grows beyond following simple algorithms. Consider the following example.

While walking in a park with my niece Lexi, who is in third grade, we encountered an array of solar panels. Never one to miss a mathematical moment, I asked her if she could quickly tell me how many solar panels were in the array. She looked at the array and appeared to be counting, 1, 2, 3, when she blurted out the correct answer – 12!

At first, I thought Lexi knew a method of speed counting to 12. When I engaged in informal math talk, I asked her, “Lexi, how did you know there were 12 panels?” She responded, “I saw there were 6 panels in a row and six times two is twelve.” With the simple, “How do you know?” question, I learned that

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my very bright niece was able to multiply before her school formally taught multiplication.

In the classroom, math talk can also help identify student misconceptions and inefficient strategies. Common observations in kindergarten and first grade classroom often involve language. For example, when told the following story problem, many students incorrectly identify subtraction as the necessary operation when addition is required.The prob lem:

“Cindy gave Myesha 3 piecesof gum from a new pack of gum. After giving Myesha gum, Cindy had 5 pieces of gum left. How many pieces of gum were in the new pack of gum?”

Some students will answer 2 believing that the word “left” always means to subtract. After hearing a student’s explanation, her teacher improved her understanding by using manipulatives, in this case an actual pack of gum.

In another example, two students were asked to solve the problem 2 + 5. Both students gave the correct answer – 7. However, when each student was asked, “How did you figure that out?” they gave very different answers. The first student told her teacher, “I started at 5 because that was the bigger number and counted 2 more to get to 7”. The second student said, “I counted to 2 then counted 5 more.” In the second example, teacher intervention increased the chance that the second student will use a counting on strategy from 5 in the future.

Asking students questions about their problem solving strategy is a good way to gain a snapshot or mental picture of a student’s thinking. As an assessment tool, it is an important way to design instruction and intervention. Simple questions like, “How did you figure that out?” or “How did you find your answer?” are good ways to get this mental snapshot.

Math talk can also be used to challenge students to think about multiple solutions or strategies for a problem. Questions that begin, “How many ways….” provoke student thinking. For example, when learning the number 7, a clever teacher asked her students how many different ways they could represent 7 with dots? Some students made 7 dots in a row. Other students made combinations of dots such as 3 dots and 4 dots, 5 dots and 2 dots. One student showed his array of 7 dots and said his represented 7 dots and “no” dots. Taking a picture of student math thinking is often easy as asking good questions. In KENS Math and for all math curriculum, teachers who want good assessments and great math achievement will ask good questions.

The benefits of Math Talk:

1. As an assessment tool, it is an important way to design instruction and intervention.
2. Create a snapshot or mental picture of a student’s thinking
3. Gain key insights about student’s math conceptions
4. Identify student misconceptions and inefficient strategies.
5. Challenge students to think about multiple solutions or strategies for a problem.

– Dr. Ken Newbury

Putting It On The Line

June 24th, 2012

Sometimes it’s fun to think mathematically through the eyes of a child. Imagine the following scene. A five-year-old asks her mom and dad how much they love her. Her mom reaches her arms out as wide as she can and says, “I love you this much!” The dad, not to be outdone, reaches his long arms out from his six foot six inch frame and says, “And I love you this much!” The little girl giggles and says to her mom, “I guess dad loves me more.”

While this story is made up, a child’s early number sense makes a big developmental leap as he or she begins to connect counting to quantity. Concepts of “How many?” and “How much?” go beyond rote recall to one of understanding as children begin to develop a mental number line. Children’s mental number line develops and changes as they develop and are exposed to more mathematically rich content. Further evidence of a mental number line is provided by scientists who have identified specific areas of the brain that “light up” on brain imaging studies.

A child’s ability to accurately represent numbers on a mental number line is one of the strongest predictors of mathematical achievement and proficiency. Researchers concur that number line accuracy is highly correlated with math grades and achievement test

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scores from kindergarten through sixth grade. Yet, Less than 2.5 % of the school day is spent on teaching young learners math. Underprivileged children are at an even greater disadvantage compared with other children. In one study, 78% more middle class and wealthy students compared with poorer children successfully identified numbers that were larger or smaller on the Kindergarten Number Knowledge Test.

The challenge for teachers and parents is to make a concerted effort to increase the focus on mathematics in the early years of pre-school, kindergarten and First grade. Start by developing a mathematically rich environment that promotes the connection between number and magnitude. This requires going beyond the usual counting and number recall tools adorning most classrooms such as the classroom wall number line. The good news is developing this critical link in the development of a child’s number sense is not difficult. Playing linear board games is an excellent way to begin developing these skills. As a child moves around a board game and observes that moving a pawn 5 spaces is further and longer than 3 spaces, he or she can develop a rudimentary understanding of relative magnitude.

Developing the link between counting and number magnitude in the classroom must be intentional. This is a critical step in the development of young learner’s mental number line. In the KENS Math program, students are provided with both physical and paper number lines to practice their number line skills. Learning supports and the level of challenge increase as students improve their accuracy and proficiency. With practice, students have shown the ability to accurately move a single bead on a wooden dowel rod to its linear value.

A unique tool, called the circle number line, makes it easier for students to equate magnitude and quantity to a number value. As a child develops proficiency with these tools, his or her mental number line skills also improve. The circle number line has also shown value to help students understand and visualize addition and subtraction facts.

With simple tools and a few board games, teachers and parents can improve the mathematical odds that students will develop strong number sense that leads to math achievement. The best part about these strategies is that children have fun as their brains build a stronger mental number line.

– Ken Newbury, Ph.D.