Grade Three Mathematics Assessment

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Grade ThreeMathematics Assessment

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• The Atlantic Canada Mathematics Curriculum

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Atlantic Canada Mathematics Curriculum

• The mathematics program is described in
  Department of Education publications called
  Curriculum Documents.
• The program reflects both the content and process
  standards recommended by the NCTM (National
  Council of Teachers of Mathematics).
• We do not use a single text resource or book as
  our program. Teachers are encouraged to
  supplement the curriculum documents with a
  variety of resources.
• Regardless of the texts used, the curriculum
  document is the basis of your childs mathematics
  program.

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Atlantic Canada Mathematics Curriculum Content
Strands

• Our curriculum has seven content strands.
• Each strand has a General Curriculum Outcome
  (GCO).
• These General Curriculum Outcomes are the same
  from grade Primary to Grade Twelve.

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General Curriculum Outcomes

• Number Concepts
• GCO A Students will demonstrate number sense
  and apply number theory concepts.
• GCO B Students will demonstrate operation sense
  and apply operation principles and procedures in
  both numeric and algebraic situations.

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General Curriculum Outcomes

• Patterns and Relations
• GCO C Students will explore, recognize,
  represent and apply patterns and relationships,
  both informally and formally.

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General Curriculum Outcomes

• Space and Shape
• GCO D Students will demonstrate an
  understanding of and apply concepts and skills
  associated with measurement.
• GCO E Students will demonstrate spatial sense
  and apply geometric concepts, properties, and
  relationships.

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General Curriculum Outcomes

• Data Management and Probability
• GCO F Students will solve problems involving
  the collection, display and analysis of data.
• GCO G Students will represent and solve
  problems involving uncertainty.

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Atlantic Canada Mathematics Curriculum

• For each grade level, there is a specific grade
  level document which provides
• specific curriculum outcomes for mathematics for
  that grade level
• a description of the specific outcome
• suggestions for instruction for that outcome
• samples of questions that students should know
  and be able to do at each grade level

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Process Standards

• In addition to the seven content strands, our
  mathematics program has five process standards.
  They are
• Reasoning and Proof
• Problem Solving
• Connections
• Communication
• Representations

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Reasoning and Proof

• Students are expected to
• develop and evaluate mathematical ideas
• select and use various ways to reason and prove
  mathematical ideas
• recognize reasoning and proof as keys to
  mathematical understanding
• create and investigate mathematics ideas

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Problem Solving

• Students are expected to
• learn and do mathematics through problem solving
• solve problems in mathematics
• select, apply and adapt a variety of problem
  solving strategies
• reflect on and evaluate the process of problem
  solving

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Connections Standard

• Students are expected to make connections
  between
• mathematical ideas and strands
• mathematics and real life
• mathematics and to other subjects
• Students are expected to use these connections to
• understand mathematics.

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Communication

• Students are expected to
• read, write, listen and speak mathematically
• organize their mathematical thinking through
  communication
• communicate their understanding of mathematics in
  a variety of ways to others
• use mathematical language/terminology accurately
  as part of the communication process

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Representation Standard

• Students are expected to
• use a variety of representations or ways of
  showing to organize, record and communicate
  mathematical ideas
• translate between representations
• use representations to model mathematics

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Representation Standard

• The five representations are
• Concrete
• Language
• Pictorial
• Contextual
• Symbolic

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Pictures
Manipulative Models
Written Symbols
Real World Situations
Oral Language
Elementary and Middle School Mathematics
Teaching Developmentally by John A. Van de Walle
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Levels of Question

• Our mathematics program also requires that
  students be able to respond to three levels of
  question.

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Level One Questions

• Level One
• These questions include factual knowledge, basic
  fact recall and knowledge of vocabulary and
  formulae.
• Example of a Level One Question
• Draw a hexagon.

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Level Two Questions

• Level Two
• These questions ask students to give explanations
  or to make estimates. Level two questions ask
  students to move between the five different ways
  to show mathematics (concrete manipulative
  materials, pictures, words, symbols and real
  world context).
• Example of a Level Two Question
• Use Base 10 Blocks to solve 23 35.

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Level Three Questions

• Level Three
• These questions ask students to solve problems
  that involve more than one mathematical idea,
  require more than one step and/or use the idea in
  a new way.
• Example of a Level Three Question
• Joey and Beth each had 7 candies. Sam had 5
  fewer candies than Joey. How many candies do the
  three children have altogether?

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Recommended percentages for testing from Dept. of
Education

• Level 1 - 25
• Level 2 - 45
• Level 3 - 30

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Past Mathematics Program

• In past mathematics programs, it may have been
  expected that a student know the answer to
• 3 x 5
• However, more is expected of students in this
• mathematics program.

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Students are expected to be able to answer
questions in pictorial form.

• Which of the pictures below shows 3 groups of 5?
• A. ?????
• ?????
• ?????
• B. ??? ?????
• C. ????????????????
• D. ??? ????? ??? ?????

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Students are expected to apply their knowledge to
a context.

• Which story problem below could be solved using 3
  x 5?
• A. John had three candies. Bill had 5 candies.
  How many
• candies did they have altogether?
• B. John had three candies. Bill had 5 more
  candies than John. How many candies did Bill
  have?
• C. John had 3 bags of candy. There were 5
  candies in each bag. How many candies did John
  have?
• D. Bill had 5 candies. John has 3 fewer candies
  than Bill. How many candies does John have?

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Students are expected to know the meaning and
language associated with concepts and
procedures.

• What does 3 x 5 mean?
• Three and five more
• Three groups of five
• Three is more than five
• Three is less than five

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Students are expected to be able to show their
understanding of mathematics using concrete
materials.

• Use Base 10 Blocks to show 3 x 5.

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Atlantic Canada Mathematics Program

• Our mathematics program is rigorous. It requires
  more of
• students than the simple memorization and
  repetition of rote
• tasks, rules and formulas.
• Our program requires that students be able to use
• mathematics in meaningful ways, apply mathematics
  to real
• life situations, make connections between, among
  and within
• mathematics, understand the meaning of the
  mathematics
• and represent their understanding in a variety of
  ways.
• Our program requires students to know more
  mathematics
• than most of us were required to know.

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• The Grade 3 Mathematics Assessment

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Grade Three MathematicsAssessment

• The mathematics assessment administered by HRSB
  was directly aligned with the mathematics program
  written by the Department of Education. The
  assessment reflected the learning outcomes,
  knowledge and abilities expected of students
  entering grade three.

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Why did we assess?

• To collect data regarding student learning of
  math content and other factors influencing
  mathematics learning
• To provide site specific data to administrators,
  staff and parents regarding student learning,
  strengths and needs
• To identify gaps in learning that impact student
  achievement
• To identify patterns in classes, schools and the
  Board

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What will the data be used for?

• Board
• To focus support and professional development
  opportunities to enhance learning
• To align resources and personnel
• To identify trends in mathematics
• To assess program implementation
• To support school improvement

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What will the data be used for?

• School
• To inform and support school improvement in
  relation to mathematics
• To identify areas requiring Professional
  Development for teachers
• To develop a school action plan

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What will the data be used for?

• Classroom
• To inform and support classroom teaching
  practice
• To identify gaps in student learning
• To identify class patterns

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What did we assess?

• Written Curriculum
• Content Strands
• Levels of Question
• Mental Math
• Paper and Pencil Procedures

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Alignment of the Written and Assessed Curriculum

• Deep alignment between written curriculum and
  assessed curriculum
• Based on the Department of Educations
  Mathematics Curriculum Documents
• Questions were taken from the curriculum
  documents for Grades Primary to Two

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How did we assess?

• 1. Selected response
• 2. Paper and Pencil Task
• 3. Mental Math

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Scope and Sequence of the Assessment

• SELECTED RESPONSE
• Represented curriculum from Grades Primary to Two
• All seven strands of the program A-G
• Two questions per grade level per strand
• Three levels of question
• Five representations

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Scope and Sequence of the Assessment

• PAPER AND PENCIL PROCEDURES
• Six questions focused on Grade One and Two
  number operations
• MENTAL MATH
• 20 questions focused on Grade Primary to Two
  mental math strategies

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Administration of the Assessment Selected
Response

• There was individual testing for selected
  response questions.
• Each question, along with four possible answers,
  was read to the student by the assessor.
• Assessors were not permitted to provide
  definitions, meanings, or hints. They were not
  able to answer students questions about the
  assessment questions.
• Assessors recorded all information on-line.
• Manipulatives were provided and students were
  encouraged to use them.

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Administration of the Assessment Mental Math

• Group setting for mental math
• Each question was read to the students, as it was
  shown on an overhead.
• Five second response time for students to record
  an answer.

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Administration of the Assessment Paper and
Pencil

• Group setting
• 6 questions on various Paper and Pencil
  procedures
• Students were not permitted to use calculators
• Students worked independently
• No time limit

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Summary

• This assessment was one measure of your childs
  development in mathematics.
• It provided a snapshot of your childs
  learning.
• It should be used in partnership with the ongoing
  classroom assessment and evaluation provided by
  your childs teacher.
• Together, they provide a more complete and
  balanced picture of your childs learning.