Author Archives: Beverly Ford
One of my favorite questions to ask a toddler is, “How old are you?” They will often proudly hold up two, three, or four fingers. Most of the time these fingers come up all at once. This is their first experience connecting a number word and their fingers and can be a foundation to building a finger pattern scheme. Children can use these finger patterns to solve additive situations. In this post, I want to talk about how children might use their fingers in additive situations where the sum is less than ten. These situations are the first additive situations children experience and can begin to lay a conceptual foundation for counting-on.
One way children use their fingers is that they lift a finger pattern for each addend and then count all their fingers.
Here are the steps they use to solve the problem:
3 + 5 (Pattern-Pattern-Count)
- Lift a finger pattern for three on one hand
- Lift a finger pattern for five on their other hand
- Count all visible fingers.
Here is a video of Shae solving the problem this way.
Their finger patterns help them to create something that they can count. When students use this method, they struggle to solve problems with the number six because the pattern requires the use of both hands. They will lift up their finger pattern for six and then reuse the one finger on the second hand to create the second pattern. So six plus two is seen as seven. Therefore this method only works when each addend is five or less.
Another way children may use their fingers is that they lift a finger pattern, count the second addend and then they count all of the fingers they see. Here are the steps they may use to solve the problem:
6 + 3 (Pattern-Count-Count)
- Lift six fingers
- Count 1,2,3 while lifting three more fingers
- Count all the fingers visible.
You can see Grace using this method in my blog post on January 18
Some children, like Grace, learn sophisticated finger patterns so they have finger patterns for eleven through nineteen and may not need to count for step three above. They may even recognize a finger pattern of three fingers as 13 in some cases.
These adding schemes are important because they lay a foundation for children to begin to work with figurative material. Finger patterns are used to empower children to add and eventually are used to monitor additive situations like 74 + 7. It amazes me what a powerful learning tool a child’s fingers are. When you can interpret their mental material from their behavior, you can present tasks that will provide opportunities for children to construct a foundation for counting-on. Reading Steffe’s research and using it to inform decisions I make working with children, has convinced me that the mathematics of students is a tool that enhances the ability of a teacher to make decisions that can support children’s conceptual understanding. In my next blog post I will look at a way to create perturbation for children using a pattern-pattern-count method, which could lead to the need for them to construct the pattern-count-count method.
In my first blog about the Mathematics of Grace, I mentioned that by the end of our six week study she was able to answer 98 + 5. This was exciting for me because when we first interviewed her she wasn’t able to combine 19 + 3. She was limited to solving sums within 20.… Continue Reading
In my last blog I wrote about one of the first things I noticed about the mathematics of Grace. She used her fingers to solve addition situations like 7+4 by constructing more advanced finger patterns, where one finger could mean one or eleven and six fingers could mean six or sixteen. This allowed her to… Continue Reading
The mathematics of students is a powerful tool for a teacher. It allows a teacher to hypothesize what is happening in the mind of a child and plan a next step that will allow that child to construct more sophisticated understanding. Today I want to look at the mathematics of a student we call Grace… Continue Reading
Are there any dangers in training your students in the “strategy” of counting-on? After reading Dr. Les Steffe’s work, I would argue it is harmful. He calls counting-on a non-teachable scheme. This means that if you want counting-on to be meaningful for students you can present situations that would promote their construction of counting-on, but… Continue Reading
In my last blog I talked about how the research I have been studying focuses on the “mathematics of children” and I claimed that research that articulates “mathematics of children” can provide powerful tools for a teacher. Many of us experienced elementary school a long time ago and this creates a challenge for our teaching.… Continue Reading
I have had the privilege of being a part of the AIMS Center from its birth. Having been a teacher, coach, and staff developer for the last 15 years, the world of a teacher is something I have experience with. I am now called a Research Associate and my role is to be a bridge… Continue Reading
Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the… Continue Reading
Why do you teach? I remember when I first came into the profession it was because I enjoyed students and wanted to make a difference. I still love watching movies of teachers that have gone into challenging situations and inspired students to think differently. These teachers empowered the students to be all that they were… Continue Reading
Word problems are typically not students’ or teachers’ favorite part of the math lesson. When I talk with teachers, they are frustrated with teaching multiplication word problems. I think one of the things we have been missing is teaching students the structure of what is involved in any multiplication word problem. “Look for and make… Continue Reading