ELL Regional STEP Session
ELL Initial Mathematics
Assessment
1
Every day, more than one million English language
learners attend Ontario’s publicly funded schools. They
come from every country and every circumstance. They
bring with them a valuable world perspective needed by
all students to operate successfully in a global
community.
Supporting English Language Learners: A practical
guide for Ontario educators, Grades 1 to 8, 2008, p.
17
Agenda
Focused Conversations about the ELL Math
Assessment Tool including:
• Background information and overview
• Materials and organization
• Guidelines for implementation
• Mathematical knowledge/concepts
2
Our Shared Goals
It is important that newly arrived English language
learners receive a warm welcome during their transition
into our Ontario schools. The initial assessment process
has a strong impact on the first impressions of these
students and their families. During this process, it is
critical that educational staff take the opportunity to learn
about the whole child and celebrate the diversity each
student will bring to our classrooms.
Using the Initial Mathematics Assessment Tool for
English Language Learners, Grades K – 8
This tool is not intended to be a replacement for the
ongoing assessment gathered by the classroom teacher.
It is through a variety of assessment strategies and tools
that the programming needs of all students are best
addressed.
Guidelines for Initial
Assessment Development
 Begin with counting and simple computation.
 Give students access to manipulatives and geometric shapes.
 Encourage students to skip over items that seem unfamiliar and
look for others that they understand.
 Assess a student’s knowledge of key concepts and skills in all five
strands of the Ontario mathematics curriculum appropriate for the
grade level (e.g., if an English language learner is placed ageappropriately in Grade 5 in September, then assess knowledge of
the Grade 4 mathematics curriculum. If the student arrives in
January, assess some of the mathematical concepts already
covered in Grade 5 as well.)
 Accept different ways to show calculations, as long as they yield
correct answers.
Supporting English Language Learners: A practical guide for
Ontario educators, Grades 1 to 8, 2008, p. 34-35
Materials
Assessment Flow Chart
Grade level packages which include:
1. One assessment tool for each mathematical strand
2. Teacher Instruction and Observation Page by strand
(including materials) and Student Booklet (for
Number Sense and Numeration grades 1-8 only)
3. List of process expectations relating to the Number
Sense and Numeration problem solving question
included in the grade 1 to grade 8 assessments
4. List of expectations addressed in each strand
assessment tool
Begin with the Flowchart
Initial Mathematics Assessment Tool for English
Language Learners, Grades K – 8
•
•
•
1.
2.
3.
4.
5.
6.
7.
8.
Aligned with Ontario Mathematics curriculum expectations
Grade specific assessment tools are based on previous grade
curriculum expectations
Student assessments do not show specific grade level but are coded
by letter:
A (kindergarten/grade one assessment based on kindergarten
expectations)
B (grade two assessment based on grade one expectations)
C (grade three assessment based on grade two expectations)
D (grade four assessment based on grade three expectations)
E (grade five assessment based on grade four expectations)
F (grade six assessment based on grade five expectations)
G (grade seven assessment based on grade six expectations)
H (grade eight assessment based on grade seven expectations)
Using the Initial Mathematics Assessment Tool for English
Language Learners, Grades K – 8
For each grade level strand assessment, a cluster of
expectations has been selected to provide a starting
point in determining the mathematical knowledge and
skills of the student. It would not be reasonable or
appropriate to assess all curriculum expectations within
this initial assessment.
Taking a Closer Look at the Features of the
Number Sense and Numeration Assessments
Teacher/Assessor Copy
Student Copy
Important Considerations
ELLs arrive in our Ontario schools with varying
background experiences and English language acquisition
skills. The teacher/assessor should always consider the
individual student needs, and use professional judgement
in the use of this assessment tool. At any point, if the
student is experiencing difficulty, the assessor should
allow the student to move ahead to the next question or
stop altogether. There are many factors which may impact
the performance of a student (e.g., acculturation process,
performance anxiety, and subject specific language).
Number Sense and Numeration
Key mathematical number sense and numeration concepts
in the primary assessments include:
• Quantity Relationships (composing and decomposing
numbers - anchors of five and ten, subitizing, comparing
and representing quantities)
• Counting (stable order, one-to-one correspondence,
cardinality, conservation of number, movement is
magnitude)
• Operational sense (addition and subtraction of single
and double digit numbers, multiplication)
Composing and Decomposing Numbers
Anchors of Five and Ten
What is 8 + 7 ?
What is 9 + 6 ?
What is 7 + 6 ?
What is 8 + 3 ?
Subitizing
Identifying a quantity without needing to
count
Subitizing
• What quantity did you see in the first dot
configuration? What strategy did you use
to determine the quantity?
• What quantity did you see in the second
dot configuration? What strategy did you
use to determine the quantity?
Counting Principles
Some of the key counting principles
include:
• stable order
• one-to-one correspondence
• Cardinality
• conservation of number
• movement is magnitude
Principles of Counting
Stable Order Principle
1,2,3,4,5,6…
not
1,2,3,4,6,8,9,10
Principles of Counting
Order Irrelevance Principle
6 in this group
1
6 in this group
2
3
4
5
6
OR
6
1
5
2
4
3
Principles of Counting
Conservation Principle
Principles of Counting
One-to-One Correspondence
Principles of Counting
Cardinality Principle
1
3
2
5
4
7
6
8
Principles of Counting
Movement is Magnitude Principle
1
2
3
4
5
Operational Sense
What strategies
could you use
to find the
sum?
What strategies
could you use
to find the
difference?
83 + 8
55 - 13
Number Sense and Numeration
Key mathematical number sense and numeration concepts in
the junior and intermediate assessments include:
Quantity Relationships
1. read, represent, compare and order whole numbers, fractions,
decimals
Operational Sense
1. single and multi-digit computation involving the four operations
– increasingly focusing on multiplicative thinking
2. Order of Operations (introduced in the grade eight (H)
assessment
3. operations with fractions, decimals, integers (in intermediate
assessments)
Proportional Reasoning
1. Relationships between fractions, decimals and percents
Quantity Relationships
• Form partners and/or trios
• Each group will need a copy of the grade
seven (G) booklet and the accompanying
teacher/assessor instruction booklet
Read and discuss the following questions:
1, 2, 3, 5, 6, 7,10, 12, and 13
Operational Sense
• Continue to work in partners and/or trios
Task One
Read and discuss the following questions:
4, 8, and 11
Task Two
Select one of the expressions in question 4. As a
table group, use chart paper to show how many
different ways you could find the answer. What
manipulatives could help you? What
manipulatives could help the students? Be
prepared to share with our whole group.
Proportional Reasoning
Read and discuss the following question:
9
What are some observations/assessment
information you anticipate could be gathered
from this question?
Using the Initial Mathematics Assessment Tool for
English Language Learners, Grades K – 8
This tool is not intended to be a replacement for the
ongoing assessment gathered by the classroom teacher.
It is through a variety of assessment strategies and tools
that the programming needs of all students are best
addressed.
Our agenda…in review
Focused Conversations about the ELL Math
Assessment Tool including:
• Background information and overview
• Materials and organization
• Guidelines for implementation
• Mathematical knowledge/concepts
Questions??
2