1. Beyond the Early Grade Mathematics Assessment:
Informing Practice
Dr. Yasmin Sitabkhan

2. Outline
What we need to know about children’s mathematics
Formal and informal mathematics
Capturing informal mathematics
How informal mathematics can be used

3. What we need to know about children’s mathematics

4. What we need to know about children’s math
Identification of
set of
universal,
foundational
Math concepts
Assessment of student performance on concepts
Informal Math
knowledge
Informing Practice

5. Formal and Informal Mathematics

6. Formal and Informal Mathematics
Historically-developed system taught explicitly through formal education
Abstract
Examples: algorithms, base-10 notation, written equations
Informal Mathematics
Based on everyday activities
Concrete
Often referred to as workplace mathematics, preschool mathematics, out-of-school mathematics, everyday mathematics, street mathematics
Example: math used when shopping

7. Formal and Informal Mathematics
Children develop systems of informal mathematics through experience in the world
Children interpret formal mathematics through their informal mathematics knowledge
Linking concrete with abstract
Everyday understandings give meaning to formal ones, and vice versa (Vygotsky, 1986)

8. Capturing Informal Mathematics- an illustration

9. Capturing Informal-Step 1
Focus on one domain or concept and conduct observations
Example:
Arithmetic
Vending on trains

10. Capturing Informal-Step 1
Infrequent to no formal schooling
Sold small items on trains and railway platforms in Mumbai
Seller:

11. Capturing Informal-Step 1
Seller:
5 rupees
Hairclip
Customer:
x 7
Hairclip
35 rupees
Seller:
Customer:
Seller asks customer to buy one more to make it 40 rupees, because she does not have change
Seller:

12. Capturing Informal-Step 2
Develop Tasks that mirror the observations
Pricing Structure
Example
Single item, single price
Nail polish for 10 rupees
Multiple item, multiple prices
Hair clips for 5 rupees, earrings for 10 rupees
Ratio prices
Hair bands-7 for 10 rupees
All items were either 5, 10, or 20 rupees.
Seller:

13. Capturing Informal-Step 2
Develop Tasks that mirror the observations
Tasks that are routine
Tasks that are not routine
Pencils are 5 rupees each
A customer wants to buy 4.
What is the total price? How do you know?
Pencils are 5 rupees each
A customer wants to buy 56.
What is the total price? How do you know?
Seller:

14. Capturing Informal-Step 3
Interview children on tasks, and look for patterns in the ways they use informal mathematics to solve problems
Pencils are 5 rupees each
A customer wants to buy 56.
What is the total price? How do you know?
12 year-old seller:
He says:
If 5 rupees for 1 pencil, then
50 rupees for 10 pencils
100 rupees for 20 pencils
150 rupees for 30 pencils
200 rupees for 40 pencils
250 rupees for 50 pencils
Then
30 rupees for 6 pencils
250 and 30 is 280 rupees
12 year-old non-seller:
He writes 56 x 5 on paper, then uses a school-based algorithm to solve equation
Seller:

15. Uses of informal math knowledge

16. Everyday Math Stories-Liberia
Under Liberia Teacher Training Project 2
Conducted observations of children engaged in mathematics outside of school

17. Everyday Math Stories-Liberia
Created “everyday math” stories that mirrored the mathematics children used outside of school, based on observations
Lucky Daniel By Yolanda G. Issac-sie
 “We are almost late Daniel,” Mom called as she sat in the car waiting to drop Daniel at school before going to work. Daniel came running, and at last as he sat in the front next to his mother. As his mom was driving, Daniel shouted “Mom, look! That aunty Janet.”
Daniel called out the window. Mom stopped the car and Aunty J came to speak to them. “Here’s 10 dollars for you D. You can add this to your lunch money.” Daniel said thank you. When they reached the school, Daniel’s mom gave him 20 more dollars. Now Daniel had 30 dollars!
During recess, Daniel bought a rice bread, and sour milk. The rice bread was and the milk cost
Daniel paid the lady that was selling the rice bread and milk. It was delicious. Daniel was glad that he had met Aunty Janet on his way to school, because otherwise he would not have been able to buy the rice bread and the milk!

18. Everyday Math Stories-Liberia
Began to integrate stories into curriculum

19. Conclusions and next steps
Informal mathematics is important to capture
Together with an assessment like the EGMA it provides a more complete picture of children’s knowledge of mathematics
Can help curriculum writers bridge formal and informal mathematics to improve teaching and learning
Validates and recognizes the mathematics that occurs in out-of-school settings

20. Thank you!