Grade Nine Mathematics Assessment

1. Grade NineMathematics Assessment

2. The Atlantic Canada Mathematics Curriculum

3. 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. • 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 child’s mathematics program.

4. 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.

5. 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.

6. General Curriculum Outcomes Patterns and Relations GCO C: Students will explore, recognize, represent and apply patterns and relationships, both informally and formally.

7. 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.

8. 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.

9. Atlantic Canada Mathematics Curriculum Each grade level document 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

10. 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

11. 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

12. 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

13. 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.

14. 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

15. 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

16. Representation Standard The five representations are: • Concrete • Language • Pictorial • Contextual • Symbolic

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

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

19. 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: • Find the square root of each of the following using patterning and/or prime factorization.

20. 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 pattern blocks to prove that 3 1/3 = 10/3.

21. 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: A certain cube has a surface area of 96 square centimetres. What is the volume of the cube? Justify your answer.

22. Recommended percentages for testing from Dept. of Education: • Level 1 - 25% • Level 2 - 45% • Level 3 - 30%

23. Past Mathematics Programs In past mathematics programs, it may have been expected that a student know how to solve a question such as the one shown below: 2 ¾ + 1 ½ However, more is expected of students in this mathematics program.

24. Now, students are expected to show their understanding with pictures. Draw a picture to show 2 ¾ + 1 ½.

25. Students are expected to apply their knowledge to a context. Write a story problem about pizza that would show 2 ¾ + 1 ½.

26. Students are expected to demonstrate understanding through the use of manipulatives. Use pattern blocks to prove that 2 ¾ + 1 ½ = 4 ¼

27. 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.

28. Grade Nine Mathematics Assessment

29. Grade Nine 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 nine.

30. 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

31. 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

32. 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

33. What will the data be used for? Classroom: • To inform and support classroom teaching practise • To identify gaps in student learning • To identify class patterns

34. What did we assess? Written Curriculum: • Content Strands • Levels of Question • Mental Math • Paper and Pencil Procedures

35. Alignment of the Written and Assessed Curriculum • Deep alignment between written curriculum and assessed curriculum • Based on the Department of Education’s Mathematics Curriculum Documents • Questions were taken from the curriculum documents for Grades Six to Eight

36. How did we assess? 1. Selected Response 2. Paper and Pencil Task 3. Mental Math

37. Scope and Sequence of the Assessment SELECTED RESPONSE • Represented curriculum from Grades Six to Eight • All seven strands of the program A-G • Two questions per grade level per strand • Three levels of question • Five representations

38. Scope and Sequence of the Assessment PAPER AND PENCIL PROCEDURES • Focused on Grade Six to Eight number operations MENTAL MATH • 25 questions focused on Grade Six to Eight mental math strategies

39. 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.

40. 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

41. Administration of the Assessment: Paper and Pencil • Group setting • 10 questions on various Paper and Pencil procedures • Students were not permitted to use calculators • Students worked independently • No time limit

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