To Doctoral Students

The Visual Modeling and Number Mapping blog on these pages was the site for my dissertation study. I have made most of the content available for other graduate students who are working on designing their own studies. The site was developed because my participants were three and four year olds and I wanted to have a way to update parents. The site contains enough content to inform parents about ongoing research activities without giving away the purpose and hypothesis. The site also provided some useful resources for parents such as apps, websites, and books about math.

I hope you find the materials to be useful in designing your research project!


Thank You

Dear LECC Families, depts_centers_pg

This week we finished all post-study sessions with all of our participating students. Some of the children completed the computer tasks described last week, and some children participated in a hands-on version of the computer task. I noticed the children were more accurate with the manipulative version–  nothing takes the place of good old hands-on play!

I want to thank all of the LECC parents who allowed me and my team of assistants to work and play with your children. After visiting the LECC for ten weeks, I have become quite attached to your children and the program. They are outgoing, fun, and creative little people. They were definitely the highlight of my week, and I was impressed with how quickly they adapted to working with non-symbolic (visual) number problems.

Without people like all of you to support research, we would never be able to learn about the best ways to support children’s intellectual, social, and emotional development. I hope the children 079enjoyed the activities and I hope in some small way we stretched their problem solving skills during our time with them.

I also want to thank program director Nancy Pynchon for her support. The LECC is one of the most engaging, enriched, and happy early childhood programs I have seen, and I was grateful for the opportunity to observe and get ideas.

Finally, I want to thank Janet Auger, Shawna Howard, and Tamra Biedrzycki for their hospitality and flexibility.

If you have any questions about the study, please do not hesitate to contact me at .

Best, Sara
Wordle: Number Study Wordle

Wrapping Up

Dear LECC Families,006

This week we began to close out the number sense study with post-teaching activities. Children repeated two computer tasks they completed at the beginning of the study so we could see whether their number representations had changed over time. The first activity was a quantity comparison task designed by Justin Halberda at Johns Hopkins University. We used a version of the task Dr. Halberda has made available to researchers. We are able to set the parameters so that the activity is child-friendly and accessible to preschoolers. The video below shows a child doing the quantity comparison task and provides a good explanation of number sense.

The children also participated in a Number-to-Position task. On this task, children had to locate visual representations of quantities from 1-10 and 1-20 on an unmarked numberline. This task was presented on the computer. The concept of relative magnitude (the placement of numbers along a numberline) is important to success with mathematics.


If you want to practice this skill with your children at home, there are iPAD apps that you might find helpful such as Numberline Frog, My Numberline and Numberline Tap. I prefer iPAD apps   because of the touch screen feature. It is very important for children to use their motor systems while working with numbers in particular, as motor and number functions are connected in the brain.

Numberline Frog App

Numberline Frog App

Next week, I will be taking a small subset of children (those who are interested) to see if they perform this task differently using our manipulatives.  I will post one more study update next week.

Thank you,


Update Week 6

Dear LECC Families,

Miss Lexi visits Aquarius

Miss Lexi visits Aquarius

We are nearing the end of our number sense work with the Aquarius, Pisces, and Lions classrooms. Dianne and Jamie came in for their final visit today and, judging from the number of hugs all around, they will miss the children a lot! I was lucky to get two such talented and experienced consultants to volunteer their time for this project. They are valued colleagues and friends.

Miss Lexi had her final visit on Friday, and Miss Jackie will visit for the last time on Monday, April 22. It was wonderful to be able to work with two such dedicated graduate students. This was an unusual field experience opportunity and I know they enjoyed working with your children.

We continued exposing the children to specific number models using manipulatives and game boards today. Over the last 8 weeks, we have made 20 visits to the LECC and the children have been exposed to 11 different number sense activities!  We ended this week with a third exposure to our “Number Bugs” games, and we agreed with the children that this was their favorite game.

Numicon version of "Number Bugs" game

Numicon version of “Number Bugs” game

Some of the children started the post-study activities on my laptop computers today. I will report more on that next week.



Giant Number Bugs

Numicon Number Bugs

Giant Number Bugs

Quantiblocks Number Bugs

Study Update Week 5

Dear LECC families,

This week we played two researcher-designed games: “Number Bugs Race” and “Number Bugs Hop”. Children played with quantiblocks or Numicon shapes to move the bugs according to rolls of the giant dice. Some of the bugs jumped, but some crawled all the way to their desired locations. Along the way, children had to follow instructions on game cards if they landed on a “yellow bug space”.  Look out!

These games are quite active. We used big vinyl game boards and rolled them out on the rug to play. Children Leahtossed the giant dice and collected the correct visual representations for numbers, placing the manipulatives on the game board.

Children were also able to see how two rolls of the die added to create a new quantity by placing the manipulatives together and counting (or in many cases recognizing) the total. We are very impressed with the way the children have learned to recognize and name the quantities represented by the manipulatives at this point in the study.

Next week, we will be focusing on making sure all children have had the same number of opportunities to play, and finishing up any activities they may want to try.

As always, we want to thank Mrs. Auger, Ms Howard, and Mrs Biedrzycki for their hospitality. We quite enjoyed “pajama day”.

I look forward to seeing your children next week,



Study Update Week 4

Dear LECC families,012

This week we continued with researcher-designed board games. Some of the games are used to model concepts of relative magnitude, or the relationships between numbers. Other games are designed to model concepts of both relative magnitude and distance traveled along the game board. The basic format of the games is the same for both groups but the manipulatives and number models presented are different.

The children really enjoyed our giant number dice! They rolled them across the floor, chased them, and also used them for their intended purpose– identification of quantities.


Giant dice

We used the characters from Cars to count spaces on a “Number Race” game board. During the race, we modeled successive changes in a car’s position relative to the roll of the dice. Next week, we will introduce a more challenging game I call “Number Bugs”. This game incorporates representation of addends and total quantities on a linear game board. The game is also designed to review all of the concepts and number models that have been presented so far.We look forward to seeing everyone next week,



At the finish line!

Study Update Weeks 2 and 3

Dear LECC Families,

Dianne getting ready for students in Pisces

Dianne getting ready for students in Pisces

Over the last two weeks, we began familiarizing the children with specific number manipulatives and visual models of number representation. We started the process gradually, giving the children the opportunity to play with the manipulatives. Children were able to touch and configure the number shapes, identify quantities, and play simple identification games.

This week, we began playing specially designed board games with the number manipulatives. Children played a train game, racing down the track using number shapes to model the distance traveled. Children then played a car race game, using the number shapes to count specific distances. They also used the game to represent addition problems by using the manipulatives to calculate distance travelled after successive rolls of the dice.

This is a short week due to the Easter holiday, but we will be back on Monday to continue board game play. Monday April 1 will be the half-way point of the study. Over the next three weeks, we will expose the children to progressively more complex number models.

Dianne, Jamie, Lexi, Jackie and I are having a wonderful time getting to know your children. They are fun, energetic, bright, and eager to play new games.

091077We look forward to seeing their smiling faces next week!