I used to help a single mom homeschool her kindergartner Jacob. Since kindergartners need to understand practical reasons why it’s a good idea to learn math, I tried to include math in our daily routine whenever possible.
So I gave Jacob the job of setting the table for lunch every day. I put unbreakable dishes and plastic glasses in a lower pull-out cabinet that he could reach, and I let him figure out how many people would be there for lunch so he could set the table with the right number of place settings.
The number changed from day to day. My husband Dennis worked from home but he also traveled. My mother-in-law lived in a trailer on our back lot and usually came over for lunch, but not always. Our son Matt lived at home while attending university that year, and a friend of his stayed with us. Sometimes one or both were home, sometimes not.
I quickly discovered that unless Jacob could physically see each person to count them, he could not figure out how many place settings.
At first I tried to help him by showing him how to count people using my fingers: “You (thumb), me (index finger), Dennis (middle finger), Grandma (ring finger) – one-two-three-four – see?”
His face went completely blank. Obviously, to Jacob, a finger could not represent a person.
So I got out some cards.
On each card we drew a picture of one family member and wrote their name underneath (which helped Jacob’s reading readiness, too). After that, we picked out the cards that corresponded to the people who were home for lunch. Then Jacob counted the cards. Then he knew how many place settings.
Although this was a slow way for getting the table set, it was excellent for teaching math at Jacob’s level of readiness.
In order to lay a proper math foundation for children, author Ruth Beechick points out in The Three R’s, parents and teachers need to understand the way a child’s thinking develops.
Adults use three ways of thinking about math: the manipulative mode, the mental mode, and the abstract mode.
They can switch back and forth, using the abstract mode, for example, to figure using only symbols ($50 - $22.48 = $27.52), or the manipulative mode to do the same problem by counting correct change into a customer’s hand.
Young children are unable to switch modes.
They can think only in the manipulative mode. So preschoolers have to see and touch objects in order to understand math concepts like adding and subtracting. Hands-on math is the foundation on which all other kinds of mathematical understanding is built. Lots of hands-on math experiences prepare children to grow into the next two stages of thinking development.
When children are hurried too quickly through this manipulative thinking stage, they feel anxious and uncertain. “Failure (to teach children in the manipulative mode) is probably the greatest single cause of children’s arithmetic difficulties,” Beechick says. “It is why people grow up with Arithmetic Anxiety.”
Children who are ready to move from the manipulative mode to the mental math mode become impatient with counting and handling objects. They prefer to picture objects mentally in their heads because it is quicker.
Pictures help children make the transition from the manipulative mode to the mental image mode.
The child sees a picture of two dogs in a group and four more dogs in another group. If he is still a manipulative thinker, he will need to touch each dog in the picture as he counts out the problem. If he is in transition between the two modes, he can count the dogs in the picture by sight.
According to Jean Piaget’s research on child development, children develop the ability to think abstractly at about age 12 or 13. “In elementary school arithmetic, the abstract mode of thinking does not play a large role,” Beechick says. “You may often think abstractly yourself, but you must guard against trying to push children into this mode before they are ready. Pushing...only leads to anxiety, frustration, (and) dislike of arithmetic.”
Children can “switch back to use a previously learned mode,” Beechick says, “but they cannot jump ahead to use a mode they have not grown into.”
“When we say that a child doesn’t understand something, we usually mean that he is not able to image it in his head,” Beechick says. “The cure for that is to provide more manipulative experience. Try showing something one way and a second way and a third way...Wait awhile and teach it again next month. After sufficient manipulative experience, the child eventually will image the troublesome process in his head. He will understand it.”
“The only route to good abstract thinking in a child’s later years,” Beechick says, “is through lots of manipulative and mental image thinking in early years.”
© 2021 Becky Cerling Powers
Reprint with attribution only (www.beckypowers.com)
You can find more parenting insights from Becky Cerling Powers in Sticky Fingers, Sticky Minds: quick reads for helping kids thrive in the Bookstore
Reflections for Parents in April, Week Two: parenting insights from the Parent Powerline
4/12/2021 4:00:00 AM by: Becky Cerling Powers
Helping Kids with Math: parenting insights from the Parent Powerline
4/5/2021 4:00:00 AM by: Becky Cerling Powers
Reflections for Parents in April, Week One: parenting insights from the Parent Powerline
4/1/2021 4:00:00 AM by: Becky Cerling Powers
Trouble -- the doorway to God's Kingdom: a faith based story from the Story Powerline
3/25/2021 4:00:00 AM by: Becky Cerling Powers
Honey Tree: a faith based story from the Story Powerline
3/23/2021 4:00:00 AM by: Becky Cerling Powers
Watching for the Positives: parenting insights from the Parent Powerline
3/21/2021 4:00:00 AM by: Becky Cerling Powers
Give Your Children Sticky Minds: parenting insights from the Parent Powerline
3/15/2021 4:00:00 AM by: Becky Cerling Powers
The Law of Kindness: a faith based story from the Story Powerline
3/12/2021 4:00:00 AM by: Laura Jane Cerling
Eyes in the Lookout: a faith based story from the Story Powerline
3/10/2021 4:00:00 AM by: Glen A Hinshaw
Focusing on the good stuff: a faith based story from the Story Powerline
3/5/2021 4:00:00 AM by: Joe Herman
The Grumble Family: a faith based story from the Story Powerline
3/3/2021 4:00:00 AM by: Anonymous
Being a Better Parent...One Week at a Time...in March
2/28/2021 4:00:00 AM by: Becky Cerling Powers
Henry O. Flipper: a black history month story from the Story Powerline
2/24/2021 3:33:00 PM by: Randy Limbird
Preparing to Raise Teens: parenting insights from the Parent Powerline
2/18/2021 4:00:00 AM by: Becky Cerling Powers
Neighbor Love: a faith based story from the Story Powerline
2/17/2021 4:00:00 AM by: Becky Cerling Powers
No Matter What, I Love You Every Day: a faith based story from the Story Powerline
2/14/2021 4:00:00 AM by: Becky Cerling Powers and Robert G Cerling
Mental Maps: a faith based story on love from the Story Powerline
2/10/2021 4:00:00 AM by: Becky Cerling Powers
Putting Myself in the Love Chapter: a faith based story from the Story Powerline
2/8/2021 4:00:00 AM by: Erik Powers
Reading to Babies: parenting insights from the Parent Powerline
2/5/2021 4:00:00 AM by: Becky Cerling Powers
Being a Better Parent....One Week at a Time...in February 2021
2/1/2021 4:00:00 AM by: Becky Cerling Powers
Resolving the Past: a faith-based story from the Story Powerline
1/22/2021 4:00:00 AM by: Sharon Withers as told to Becky Cerling Powers
God Sets the Lonely in Families: a faith based story from the Story Powerline
1/21/2021 4:00:00 AM by: Sharon Withers as told to Becky Cerling Powers
Keep Trying: a faith based story from the Story Powerline
1/13/2021 4:00:00 AM by: Laura Jane Cerling
Hooray for Mother Goose! Parenting Insights from the Parent Powerline
1/5/2021 4:00:00 AM by: Becky Cerling Powers
Being a Better Parent....One Week at a Time...in January 2021
1/2/2021 4:00:00 AM by: Becky Cerling Powers
Working With -- Not Against -- Life Seasons: parenting insights from the Parent Powerline
12/28/2020 4:00:00 AM by: Becky Cerling Powers
Why Play With the Kids? parenting insights from the Parent Powerline
12/21/2020 4:00:00 AM by: Becky Cerling Powers
Breaking Barriers with Kindness: a faith based Christmas story from the Story Powerline
12/10/2020 4:00:00 AM by: Laura Jane Cerling
Shoe Shine Boy: a faith based Christmas story from the Story Powerline
12/4/2020 4:00:00 AM by: Ruben Fierro as told to Maria Luisa Navarro
Slow Down for Christmas: a faith based story from the Story Powerline
12/1/2020 4:00:00 AM by: Becky Cerling Powers
Ruth & Boaz, Part 2: a faith based story from the Story Powerline
11/12/2020 4:00:00 AM by: Maria Luisa Navarro
Ruth & Boaz, Part 1: a faith based story from the Story Powerline
11/9/2020 4:00:00 AM by: Maria Luisa Navarro
Enemies No More, Part 2: a faith based Beatitudes story from the Story Powerline
10/30/2020 4:00:00 AM by: Becky Cerling Powers
Enemies No More, Part 1: a faith based Beatitudes story from the Story Powerline
10/28/2020 4:00:00 AM by: Becky Cerling Powers
Double Minded Doggie: a faith based Beatitudes story from the Story Powerline
10/22/2020 4:00:00 AM by: Becky Cerling Powers
The Father's Blessing: a faith based Beatitudes story from the Story Powerline
10/13/2020 4:00:00 AM by: Becky Cerling Powers
Dad's Green Packard: a faith based Beatitudes story from the Story Powerline
10/10/2020 4:00:00 AM by: Paula Kortkamp Combs
Hill of Woman's Fidelity: a faith based Beatitudes story from the Story Powerline
10/1/2020 4:00:00 AM by: Retold by Becky Cerling Powers
In Praise of Naps: tips from the Parent Powerline
9/28/2020 4:00:00 AM by: Becky Cerling Powers
Music Enriches the Family: tips from the Parent Powerline
9/10/2020 4:00:00 AM by: Becky Cerling Powers
Pre-School at Home During Covid-19: tips from the Parent Powerline
8/21/2020 4:00:00 AM by: Becky Cerling Powers
Parenting in the Mess: Tips from the Parent Powerline
8/16/2020 4:00:00 AM by: Becky Cerling Powers
The Way We Homeschooled, Part 1 Balance: from the Parent Powerline
8/4/2020 4:00:00 AM by: Becky Cerling Powers
Grandpa Thure Cerling, Part 1: a faith based story from the Story Powerline
8/4/2020 4:00:00 AM by: Becky Cerling Powers
Grandpa Thure Cerling, Part 2: a faith based story from the Story Powerline
8/4/2020 4:00:00 AM by: Becky Cerling Powers
Temptation: a faith based story from the Story Powerline
7/23/2020 4:00:00 AM by: Glen A. Hinshaw
TALK: A Simple Way to Help Kids with School: tips from the Parent Powerline
7/21/2020 9:00:00 PM by: Becky Cerling Powers
Honest Abe Lincoln: a faith based story from the Story Powerline
7/14/2020 11:00:00 PM by: Randy Limbird
The Most Conscientious Hunter I Ever Met: a faith based story from the Story Powerline
6/24/2020 4:00:00 AM by: Glen A. Hinshaw
Washing Feet: a faith based story from the Story Powerline
6/17/2020 4:00:00 AM by: Becky Cerling Powers and Lee Merrill Byrd
No Parking: a faith based story from the Story Powerline
6/10/2020 4:00:00 AM by: Becky Cerling Powers
Ruby Bridges, part 2: a faith based story from the Story Powerline
6/3/2020 4:00:00 AM by: Becky Cerling Powers
Ruby Bridges, part 1: a faith based story from the Story Powerline
6/2/2020 4:00:00 AM by: Becky Cerling Powers
Raising Fluent Readers: tips from the Parent Powerline
5/29/2020 4:00:00 AM by: Becky Cerling Powers
Unwanted Baby: a faith based story from the Story Powerline
5/26/2020 4:00:00 AM by: Eileen as told to Becky Cerling Powers
Family Funnies: Tips from the Parent Powerline
5/22/2020 4:00:00 AM by: Becky Cerling Powers
Joey's Letters: a faith based story from the Story Powerline
5/21/2020 4:00:00 AM by: Lee Merrill Byrd
Alzheimer Valley: a faith based story from the Story Powerline
5/13/2020 4:00:00 AM by: Paula Kortkamp Combs
New Bride Confusion: a faith based story from the Story Powerline
5/12/2020 4:00:00 AM by: Becky Cerling Powers
Amaris Luz, Light from Darkness: a faith based story from the Story Powerline
4/28/2020 6:00:00 AM by: Lee Merrill Byrd
Losing Poetry: a faith based story from the Story Powerline
4/22/2020 6:00:00 AM by: Becky Cerling Powers
Let Kids Cure Their Own Boredom: Tips from the Parent Powerline
4/15/2020 6:00:00 AM by: Becky Cerling Powers
Naaman, Rich in Money and Presumption: a faith based story from the Story Powerline
4/14/2020 6:00:00 AM by: Paula Kortkamp Combs and Becky Cerling Powers
David, Bathsheba & Psalm 51: a faith based story story from the Story Powerline
4/9/2020 6:00:00 AM by: Paula Kortkamp Combs
The Hundred Chart: math lesson tips from the Parent Powerline
4/8/2020 6:00:00 AM by: Becky Cerling Powers
The Beer Would Call Me: a faith based story from the Story Powerline
4/7/2020 6:00:00 AM by: Beatriz Balcort as told to Becky Cerling Powers
Turned Around: a faith based story from the Story Powerline
4/2/2020 6:00:00 AM by: Brian Bolton with Becky Cerling Powers
Toddlers Helping During COVID-19 and Beyond: tips from the Parent Powerline
4/1/2020 6:00:00 AM by: Becky Cerling Powers
Elijah & the Captain of 50 Men: a faith based story from the Story Powerline
3/31/2020 6:00:00 AM by: Retold by Becky Cerling Powers
Fear in Residence: a faith based story from the Story Powerline
3/24/2020 10:00:00 PM by: Paula Kortkamp Combs
Household Management During COVID-19 Time: tips from the Parent Powerline
3/23/2020 10:00:00 PM by: Becky Cerling Powers
Dreaming of Anita Jo: a faith based story from the Story Powerline
3/12/2020 6:00:00 AM by: Paula Kortkamp Combs
No Complaint Dinners: a faith based story from the Story Powerline
3/10/2020 6:00:00 AM by: Laura Jane Cerling
DIY Plumbing: a faith based story from the Story Powerline
3/5/2020 6:00:00 AM by: Jennifer Cummings
A Brother's Love: a faith based story from the Story Powerline
3/3/2020 7:00:00 AM by: Retold by Becky Cerling Powers
My Two Dads, part three: a faith based story from the Story Powerline
2/27/2020 6:00:00 AM by: Janimarie Rowe as told to Becky Cerling Powers
My Two Dads, part two: a faith based story from the Story Powerline
2/26/2020 6:00:00 AM by: Janimarie Rowe as told to Becky Cerling Powers
My Two Dads, part one: a faith based story from the Story Powerline
2/25/2020 7:00:00 AM by: Janimarie Rowe as told to Becky Cerling Powers
Grandma's Apron: a faith based story from the Story Powerline
2/20/2020 12:45:00 PM by: Jennifer Cummings
Colors of the Beetle: a retold faith based story from the Story Powerline
2/13/2020 12:00:00 PM by: Becky Cerling Powers
Cantaloupe Crop Disaster: a faith based story from the Story Powerline
2/5/2020 6:00:00 AM by: Glen Hinshaw
Afraid to Sleep at Night (Psalm 91): a faith based story from the Story Powerline
1/22/2020 6:00:00 AM by: Paula Kortkamp Combs
How the Camel Got His Hump: a retold faith based story
1/13/2020 10:00:00 PM by: Becky Cerling Powers
Growing Up With Polio: a faith based story from the Story Powerline
1/9/2020 10:01:00 PM by: Laura Jane Cerling
All Things Bright and Beautiful: a faith based story from the Story Powerline
1/7/2020 6:20:00 AM by: Becky Cerling Powers, poem by Cecil Frances Alexander
One Dollar for a Donut: a faith based story from the Story Powerline
1/1/2020 6:00:00 PM by: Becky Cerling Powers
Star of Wonder
12/26/2019 6:00:00 AM by: Paula Kortkamp Combs
The Shepherds
12/24/2019 6:00:00 AM by: Paula Kortkamp Combs
Mary and the Angel
12/18/2019 6:00:00 AM by: Paula Kortkamp Combs
Zechariah
12/17/2019 6:00:00 AM by: Paula Kortkamp Combs
Christmas Cookies: a a faith based story from the Story Powerline
12/10/2019 6:00:00 AM by: Laura Jane Cerling
First Thanksgiving, Part 2: Beginning in Weakness (a faith based story)
11/28/2019 6:00:00 AM by: Rami Scully
First Thanksgiving, Part 3: Gifts & Gratitude (a faith based story from the Story Powerline)
11/28/2019 6:00:00 AM by: Rami Scully
First Thanksgiving, Part 1: Enduring the Sea Voyage (a faith based story)
11/27/2019 6:00:00 AM by: Rami Scully
Rescuing my Family in Wartime, Part 3: a faith based story from the Story Powerline
11/22/2019 6:00:00 AM by: Néaouguen Nodjimbadem as told to Becky Cerling Powers
Rescuing my Family in Wartime, Part 2: a faith based story from the Story Powerline
11/19/2019 6:00:00 AM by: Néaouguen Nodjimbadem
Rescuing my Family in Wartime, Part 1: a faith based story from the Story Powerline
11/12/2019 6:00:00 AM by: Nodji (Néaouguen Nodjimbadem) as told to Becky Cerling Powers
Preventing Parent Burnout: from the Parent Powerline
11/4/2019 5:00:00 AM by: Becky Cerling Powers
Grandma Time: a faith based story from the Story Powerline
11/1/2019 6:00:00 AM by: Jennifer Cummings
Safe Amid Snakes and Semi-Trucks: a faith based story from the Story Powerline
10/30/2019 3:00:00 AM by: Becky Cerling Powers
The Love & Diaper (Nappy) Connection
10/25/2019 6:30:00 PM by: Becky Cerling Powers
Avon Perfume Surprise: a faith based story from the Story Powerline
10/22/2019 7:00:00 AM by: Becky Cerling Powers
Saving Butterscotch: a faith based story from the Story Powerline
10/16/2019 6:00:00 AM by: Karen M. Pickett Ward
The Patient in Room 116: a faith based story from the Story Powerline
10/8/2019 9:10:00 AM by: Paula Kortkamp Combs
Belshazzar: a faith based story from the Story Powerline
10/2/2019 6:45:00 AM by: Retold by Paula Kortkamp Combs
My Mysterious Relative & the Missing Paycheck: a faith based story from the Story Powerline
9/26/2019 3:17:00 PM by: Becky Cerling Powers
Keeping in Touch with Cousins: a faith based story from the Story Powerline
9/24/2019 3:20:00 PM by: Paula Kortkamp Combs
How the Ostrich Got His Long Neck: a faith based retold story from the Story Powerline
9/9/2019 3:49:00 PM by: Retold by Becky Cerling Powers
When Life Goes Up in Smoke: a faith based story from the Story Powerline
8/20/2019 3:28:00 PM by: Glen A. Hinshaw
